Sahil Sri
Student Name: __________________________
Score:
Sheet 1
Fractions into Decimals
Convert each fraction into decimal:
1)
79
10
=
4)
56
100
=
=
=
=
135
1000
200
10
=
77
1000
=
6394
1000
Copyrighted Material. All rights Reserved.
235
10
=
9
100
=
12)
=
12
100
=
15)
=
17)
=
=
9)
14)
16)
345
100
326
1000
1735
1000
6)
11)
13)
56
10
=
8)
10)
780
1000
90
100
5)
7)
752
100
3)
2)
805
10
=
18)
=
113
100
=
Student Name: __________________________
Score:
Answer key
Sheet 1
Fractions into Decimals
3)
2)
79
10
=
7.9
4)
56
100
=
0.56
=
7.52
=
0.78
=
0.326
135
1000
200
10
=
5.6
77
1000
=
0.135
3.45
6394
1000
Copyrighted Material. All rights Reserved.
1.735
235
10
=
23.5
9
100
=
0.09
=
0.12
=
80.5
=
1.13
12)
=
20
12
100
15)
=
0.077
17)
=
=
9)
14)
16)
345
100
326
1000
1735
1000
6)
11)
13)
56
10
0.9
8)
10)
780
1000
=
5)
7)
752
100
90
100
805
10
18)
=
6.394
113
100
Student Name: __________________________
Score:
Sheet 2
Fractions into Decimals
Convert each fraction into decimal:
1)
239
10
=
4)
6322
100
=
=
=
=
785
10
7521
100
=
699
10
=
774
100
56
1000
=
34
100
=
12)
=
37
10
=
15)
=
64
1000
=
18)
17)
=
=
9)
14)
16)
1007
10
48
10
450
1000
6)
11)
13)
8
100
=
8)
10)
209
1000
7
100
5)
7)
166
100
3)
2)
=
Printable Math Worksheets @ www.mathworksheets4kids.com
211
1000
=
Student Name: __________________________
Score:
Answer key
Sheet 2
Fractions into Decimals
1)
239
10
=
23.9
4)
6322
100
=
63.22
=
1.66
=
0.209
48
10
785
10
7521
100
=
0.08
699
10
=
4.8
100.7
774
100
=
0.45
56
1000
=
0.056
=
0.34
=
3.7
=
0.064
=
0.211
9)
=
78.5
34
100
12)
=
75.21
37
10
15)
=
69.9
17)
=
450
1000
6)
14)
16)
1007
10
0.07
11)
13)
8
100
=
8)
10)
209
1000
7
100
5)
7)
166
100
3)
2)
64
1000
18)
=
7.74
Printable Math Worksheets @ www.mathworksheets4kids.com
211
1000
Student Name: __________________________
Score:
Sheet 1
Fractions into Percent
Convert each fraction into percent:
1)
1
10
2)
=
4)
11
25
=
=
=
18
25
3
4
=
13
50
=
19
20
1
2
=
7
10
=
12)
=
1
50
=
15)
=
17)
=
=
9)
14)
16)
24
25
=
11)
13)
4
5
23
50
2
5
6)
8)
10)
12
25
=
5)
7)
9
20
13
20
3)
3
20
=
18)
=
Printable Math Worksheets @ www.mathworksheets4kids.com
7
50
=
Student Name: __________________________
Score:
Answer key
Sheet 1
Fractions into Percent
1)
1
10
2)
=
10%
4)
11
25
=
44%
=
45%
=
48%
=
46%
18
25
3
4
=
80%
13
50
=
72%
96%
19
20
40%
1
2
=
50%
7
10
=
70%
=
2%
=
15%
=
14%
12)
=
75%
1
50
15)
=
26%
17)
=
=
9)
14)
16)
24
25
23
50
2
5
6)
11)
13)
4
5
65%
8)
10)
12
25
=
5)
7)
9
20
13
20
3)
3
20
18)
=
95%
Printable Math Worksheets @ www.mathworksheets4kids.com
7
50
Student Name: __________________________
Score:
Sheet 2
Fractions into Percent
Convert each fraction into percent:
1)
9
10
2)
=
4)
19
50
=
=
=
21
25
3
10
=
23
25
=
33
50
11
20
=
11
50
=
12)
=
14
25
=
15)
=
17)
=
=
9)
14)
16)
7
25
=
11)
13)
21
50
1
4
13
25
6)
8)
10)
1
20
=
5)
7)
3
5
17
20
3)
7
20
=
18)
=
Printable Math Worksheets @ www.mathworksheets4kids.com
9
25
=
Student Name: __________________________
Score:
Answer key
Sheet 2
Fractions into Percent
1)
9
10
2)
=
90%
4)
19
50
=
38%
=
60%
=
5%
=
25%
21
25
3
10
=
42%
23
25
=
84%
28%
33
50
52%
11
20
=
55%
11
50
=
22%
=
56%
=
35%
=
36%
12)
=
30%
14
25
15)
=
92%
17)
=
=
9)
14)
16)
7
25
1
4
13
25
6)
11)
13)
21
50
85%
8)
10)
1
20
=
5)
7)
3
5
17
20
3)
7
20
18)
=
66%
Printable Math Worksheets @ www.mathworksheets4kids.com
9
25
Student Name: __________________________
Score:
Decimal into Fraction
ES1
Convert each decimal into fraction:
2)
1)
0.6
=
4)
5.2
=
=
=
0.2
3.2
=
0.04
=
2.9
0.3
=
2.3
=
12)
=
3.5
=
15)
=
4.2
=
18)
17)
=
=
9)
14)
16)
0.5
=
11)
13)
1.7
0.1
0.22
6)
8)
10)
2.5
=
5)
7)
1.5
4.3
3)
=
Printable Math Worksheets @ www.mathworksheets4kids.com
1.6
=
Student Name: __________________________
Score:
Answer key
ES1
Decimal into Fraction
1)
0.6
2)
=
3
5
4)
5.2
=
26
5
=
3
2
=
5
2
=
1
10
0.2
3.2
=
17
10
0.04
=
1
5
1
2
2.9
11
50
0.3
=
3
10
2.3
=
23
10
=
7
2
=
21
5
=
8
5
12)
=
16
5
3.5
15)
=
1
25
17)
=
=
9)
14)
16)
0.5
0.1
0.22
6)
11)
13)
1.7
43
10
8)
10)
2.5
=
5)
7)
1.5
4.3
3)
4.2
18)
=
29
10
Printable Math Worksheets @ www.mathworksheets4kids.com
1.6
Student Name: __________________________
Score:
Decimal into Fraction
ES2
Convert each decimal into fraction:
0.8
=
4)
0.12
=
=
=
=
0.09
4.9
=
0.25
=
4.3
0.08
=
5.7
=
12)
=
3.1
=
15)
=
17)
=
=
9)
14)
16)
3.7
7.5
0.7
6)
11)
13)
6.5
=
8)
10)
1.25
1.4
5)
7)
6.4
3)
2)
1)
4.6
=
18)
=
Printable Math Worksheets @ www.mathworksheets4kids.com
2.2
=
Student Name: __________________________
Score:
Answer key
ES2
Decimal into Fraction
1)
0.8
2)
=
4
5
=
3
25
7)
6.4
=
32
5
=
5
4
15
2
0.09
4.9
=
13
2
0.25
=
9
100
37
10
4.3
7
10
0.08
=
2
25
5.7
=
57
10
=
31
10
=
23
5
=
11
5
12)
=
49
10
3.1
15)
=
1
4
17)
=
=
9)
14)
16)
3.7
=
11)
13)
6.5
7.5
0.7
6)
8)
10)
1.25
7
5
=
5)
4)
0.12
1.4
3)
4.6
18)
=
43
10
Printable Math Worksheets @ www.mathworksheets4kids.com
2.2
Student Name: __________________________
Score:
Decimal into Fraction
ES3
Convert each decimal into fraction:
1)
0.15
2)
=
4)
3.3
=
=
=
5.3
3.6
=
1.8
=
0.24
1.3
=
0.02
=
12)
=
5.5
=
15)
=
17)
=
=
9)
14)
16)
0.16
=
11)
13)
4.5
0.4
2.7
6)
8)
10)
1.9
=
5)
7)
0.05
1.2
3)
2.4
=
18)
=
Printable Math Worksheets @ www.mathworksheets4kids.com
1.1
=
Student Name: __________________________
Score:
Answer key
ES3
Decimal into Fraction
1)
0.15
2)
=
3
20
4)
3.3
=
33
10
=
1
20
=
19
10
2
5
=
5.3
3.6
=
9
2
1.8
=
53
10
4
25
0.24
27
10
1.3
=
13
10
0.02
=
1
50
=
11
2
=
12
5
=
11
10
12)
=
18
5
5.5
15)
=
9
5
17)
=
=
9)
14)
16)
0.16
0.4
2.7
6)
11)
13)
4.5
6
5
8)
10)
1.9
=
5)
7)
0.05
1.2
3)
2.4
18)
=
6
25
Printable Math Worksheets @ www.mathworksheets4kids.com
1.1
Student Name: __________________________
Score:
Percent into Fraction
Sheet 1
Convert each percent into fraction:
2)
1)
37%
=
=
7)
2%
=
=
28%
4%
=
44%
=
52%
15%
=
17%
=
12)
=
31%
=
15)
=
33%
=
18)
17)
=
=
9)
14)
16)
46%
=
11)
13)
40%
35%
8%
6)
8)
10)
22%
=
5)
4)
12%
25%
3)
=
Printable Math Worksheets @ www.mathworksheets4kids.com
49%
=
Student Name: __________________________
Score:
Answer key
Percent into Fraction
1)
37%
37
100
4)
12%
=
3
25
=
1
50
=
11
50
35%
28%
4%
=
2
5
44%
=
7
20
23
50
52%
=
2
25
15%
=
3
20
=
17
100
=
31
100
=
33
100
=
49
100
9)
=
7
25
17%
12)
=
1
25
31%
15)
=
11
25
17)
=
8%
6)
14)
16)
46%
1
4
11)
13)
40%
=
8)
10)
22%
25%
5)
7)
2%
3)
2)
=
Sheet 1
33%
18)
=
13
25
Printable Math Worksheets @ www.mathworksheets4kids.com
49%
Student Name: __________________________
Score:
Percent into Fraction
Sheet 2
Convert each percent into fraction:
1)
36%
=
4)
1%
=
=
=
=
32%
9%
=
34%
=
47%
23%
=
18%
=
12)
=
5%
=
15)
=
53%
=
18)
17)
=
=
9)
14)
16)
50%
14%
30%
6)
11)
13)
41%
=
8)
10)
20%
11%
5)
7)
26%
3)
2)
=
Printable Math Worksheets @ www.mathworksheets4kids.com
45%
=
Student Name: __________________________
Score:
Answer key
Percent into Fraction
1)
36%
2)
=
9
25
4)
1%
=
1
100
=
13
50
=
1
5
14%
32%
9%
=
41
100
34%
=
7
50
1
2
47%
=
3
10
23%
=
23
100
=
9
50
=
1
20
=
53
100
=
9
20
9)
=
8
25
18%
12)
=
9
100
5%
15)
=
17
50
53%
18)
17)
=
30%
6)
14)
16)
50%
11
100
11)
13)
41%
=
8)
10)
20%
3)
5)
7)
26%
11%
Sheet 2
=
47
100
Printable Math Worksheets @ www.mathworksheets4kids.com
45%
Student Name: __________________________
Score:
Percent into Fraction
Sheet 3
Convert each percent into fraction:
2)
1)
10%
=
4)
21%
=
=
=
16%
7%
=
19%
=
48%
29%
=
24%
=
12)
=
27%
=
15)
=
17)
=
=
9)
14)
16)
43%
=
11)
13)
42%
54%
6%
6)
8)
10)
38%
=
5)
7)
3%
13%
3)
39%
=
18)
=
Printable Math Worksheets @ www.mathworksheets4kids.com
51%
=
Student Name: __________________________
Score:
Answer key
Percent into Fraction
1)
10%
2)
=
1
10
4)
21%
=
21
100
=
3
100
=
19
50
54%
16%
7%
=
21
50
19%
=
27
50
43
100
48%
=
3
50
29%
=
29
100
=
6
25
=
27
100
=
39
100
=
51
100
9)
=
4
25
24%
12)
=
7
100
27%
15)
=
19
100
39%
18)
17)
=
6%
6)
14)
16)
43%
13
100
11)
13)
42%
=
8)
10)
38%
3)
5)
7)
3%
13%
Sheet 3
=
12
25
Printable Math Worksheets @ www.mathworksheets4kids.com
51%
Student Name: __________________________
Score:
Fractions into Decimal and Percent
Sheet 1
Choose the best option that represents the fraction:
1)
23
100
) 2300%
3)
) 0.023
) 90.0
) 9%
) 0.09%
) 1.1
) 110%
) 0.05
) 50%
) 0.005
22
10
) 0.22
11)
) 22%
) 2%
15
100
) 0.15
13)
) 2.2
) 1.5
) 150%
) 1500%
20
100
) 200%
) 0.02
) 20%
) 0.002
) 500%
) 0.03
) 3%
) 300%
) 0.07
) 7%
) 0.007
) 0.03
) 3.0
) 3%
) 0.33
) 0.03
) 330%
) 0.47
) 470%
) 4700%
47
100
) 0.047
Printable Math Worksheets @ www.mathworksheets4kids.com
) 0.05
33
10
) 33%
14)
) 50%
30
100
) 30%
12)
) 790%
7
10
) 70%
10)
) 0.079
3
10
) 0.3
8)
) 79%
5
100
) 0.5
6)
) 11%
79
100
) 7.9
4)
50
100
) 5%
9)
) 0.23
11
100
) 0.01
7)
) 230%
9
10
) 90%
5)
2)
Student Name: __________________________
Score:
Answer key
Fractions into Decimal and Percent
1)
23
100
) 2300%
3)
) 90.0
) 9%
) 0.09%
) 1.1
) 110%
) 0.05
) %
) 0.005
22
10
) 0.22
11)
) 22%
) 2%
15
100
) . 13)
) . ) 1.5
) 150%
) 1500%
20
100
) 200%
) 0.02
) %
) 0.002
) . ) 500%
) 0.03
) 3%
) 300%
) 0.07
) %
) 0.007
) 0.03
) 3.0
) 3%
) 0.33
) 0.03 ) %
33
10
) 33%
14)
) 50%
30
100
) %
12)
) 790%
7
10
) 7%
10)
) 0.079
3
10
) . 8)
) %
5
100
) 0.5
6)
) %
79
100
) 7.9
4)
50
100
) 5%
9)
) 0.023
11
100
) 0.01
7)
) 230% ) . 9
10
) %
5)
2)
47
100
) 0.047 ) . Printable Math Worksheets @ www.mathworksheets4kids.com
Sheet 1
) 470%
) 4700%
Student Name: __________________________
Score:
Fractions into Decimal and Percent
Sheet 2
Choose the best option that represents the fraction:
1)
2
100
) 20%
3)
) 0.002
) 270%
) 27%
) 0.027
) 39%
) 3.9
) 510%
) 5.1
69
100
) 0.69
11)
) 609%
11
10
)0.11
13)
) 690%
) 11%
) 0.011
35
100
) 0.35
) 350%
) 305%
) 301%
) 430%
) 4.3
) 6000%
) 0.6
) 5.7
) 57%
) 8.7
) 807%
) 870%
) 170%
) 107%
) 0.017%
43
100
60
10
57
10
87
100
) 0.87
14)
) 3.5
) 3.1
31
100
) 507% ) 0.57
12)
) 110%
) 0.12
) 60% ) 6.0
10)
) 6.9
) 102%
) 43% ) 0.043
8)
) 0.051
) 12%
) 310% ) 0.31
6)
) 309%
12
10
) 1.2
4)
51
100
) 51%
9)
) 0.2
39
10
) 0.39
7)
) 2%
27
100
) 2.7
5)
2)
17
10
) 0.17
Printable Math Worksheets @ www.mathworksheets4kids.com
Student Name: __________________________
Score:
Answer key
Fractions into Decimal and Percent
1)
2
100
) 20%
3)
) 0.002
) 270% ) %
) 0.027
) 39%
) . ) 510%
) 5.1
69
100
) . 11)
) 690%
) 609%
11
10
)0.11
13)
) 6.9
) 11%
) 0.011
35
100
) . ) 350%
) 305%
) 301%
) 430%
) 4.3
) 6000%
) 0.6
60
10
57
10
) 8.7
) 807%
) 870%
) %
) 107%
) 0.017%
17
10
) 0.17
Printable Math Worksheets @ www.mathworksheets4kids.com
) 57%
87
100
) . 14)
) 3.5
) 3.1
) 507% ) 0.57 ) . 12)
) %
) 0.12
43
100
) 60% ) . 10)
) 102%
31
100
) % ) 0.043
8)
) 0.051
) 12%
) 310% ) . 6)
) 309%
12
10
) . 4)
51
100
) %
9)
) 0.2
39
10
) 0.39
7)
) %
27
100
) 2.7
5)
2)
Sheet 2
Student Name: __________________________
Score:
Fractions into Decimal and Percent
Sheet 3
Choose the best option that represents the fraction:
1)
4
100
) 4%
3)
) 0.004
) 209%
) 29%
) 2.9
) 410%
) 41%
11)
) 0.061
) 610%
) 6.1
13)
) 7.3
) 703%
) 73%
) 0.037
) 370%
) 3.7
) 409% ) 0.049
) 49%
) 4.9
) 509%
) 0.59
) 9.1
) 91%
) 530%
) 53%
) 5.3
) 6.7
) 607%
) 67%
) 190%
) 19%
) 405%
) 45%
) 0.45
49
10
59
10
) 59%
) 5.9
91
100
) 0.091 ) 901%
67
10
) 0.67
14)
) 1.9
37
100
) 37%
12)
19
100
) 0.019
) 0.013
10)
53
100
) 0.053
) 130%
8)
73
10
) 0.73
) 13%
6)
)4.1
13
10
) 0.13
4)
61
100
) 61%
9)
) 0.4
41
100
) 0.041
7)
) 40%
29
10
) 0.29
5)
2)
45
10
) 4.5
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Student Name: __________________________
Score:
Answer key
Fractions into Decimal and Percent
1)
4
100
) %
3)
) 0.004
) 209%
) 29%
) . ) 410%
) %
11)
) 0.061
) 610%
) 6.1
13)
) . ) 703%
) 73%
) 0.037
) 370%
) 3.7
) 409% ) 0.049
) 49%
) . ) 509%
) 0.59
) 9.1
) %
) 530% ) %
) 5.3
) . ) 607%
) 67%
) 190%
) %
) 405%
) 45%
) 0.45
49
10
59
10
) 59%
) . 91
100
) 0.091 ) 901%
67
10
) 0.67
14)
) 1.9
37
100
) %
12)
19
100
) 0.019
) 0.013
10)
53
100
) 0.053
) %
8)
73
10
) 0.73
) 13%
6)
)4.1
13
10
) 0.13
4)
61
100
) %
9)
) 0.4
41
100
) 0.041
7)
) 40%
29
10
) 0.29
5)
2)
Sheet 3
45
10
) . Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Integers: S1
Square Root - Perfect Square
A) Find the values of the following.
1) √2500
2) √64
3) √729
4) √1156
5) √2401
6) √121
B) Find the square roots of the following numerals.
1849
2) 676
3) 100
4) 256
5) 1681
6) 1369
1)
C) 1) Which of the following is the square root of 484?
i) 28
ii) 24
iii) 22
iv) 27
ii) 8
iii) 5
iv) 4
2) Find the value of √49 .
7
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Answer key
Name :
Integers: S1
Square Root - Perfect Square
A) Find the values of the following.
1) √2500
2) √64
50
3) √729
8
4) √1156
27
5) √2401
34
6) √121
49
11
B) Find the square roots of the following numerals.
1)
1849
2) 676
43
3) 100
26
4) 256
10
5) 1681
16
6) 1369
41
37
C) 1) Which of the following is the square root of 484?
i) 28
ii) 24
iii) 22
iv) 27
ii) 8
iii) 5
iv) 4
2) Find the value of √49 .
i) 7
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Name :
Integers: S2
Square Root - Perfect Square
A) Find the values of the following.
1) √196
2) √1225
3) √81
4) √9
5) √576
6) √2209
B) Find the square roots of the following numerals.
144
2) 400
3) 1936
4) 361
5) 1024
6) 16
1)
C) 1) Find the value of √169.
i) 29
ii) 13
iii) 17
iv) 21
2) Find the number, when multiplied by itself gives 225.
i) 35
ii) 45
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iii) 25
iv) 15
Answer key
Name :
Integers: S2
Square Root - Perfect Square
A) Find the values of the following.
1) √196
2) √1225
14
3) √81
35
4) √9
9
5) √576
3
6) √2209
24
47
B) Find the square roots of the following numerals.
1)
144
2) 400
12
4) 361
3) 1936
20
44
5) 1024
19
6) 16
32
4
C) 1) Find the value of √169.
i) 29
ii) 13
iii) 17
iv) 21
2) Find the number, when multiplied by itself gives 225.
i) 35
ii) 45
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iii) 25
iv) 15
Name :
Integers: S3
Square Root - Perfect Square
A) Find the values of the following.
1) √4
2) √784
3) √2116
4) √289
5) √1089
6) √25
B) Find the square roots of the following numerals.
961
2) 529
3) 2304
4) 1521
5) 900
6) 324
1)
C) 1) Find the number, when multiplied by itself gives 36.
6
ii) 3
iii) 8
iv) 16
2) Which of the following is the square root of 1600?
i) 50
ii) 400
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iii) 40
iv) 80
Answer key
Name :
Integers: S3
Square Root - Perfect Square
A) Find the values of the following.
1) √4
2) √784
2
3) √2116
28
4) √289
46
5) √1089
17
6) √25
33
5
B) Find the square roots of the following numerals.
1)
961
2) 529
31
3) 2304
23
4) 1521
48
5) 900
39
6) 324
30
18
C) 1) Find the number, when multiplied by itself gives 36.
i) 6
ii) 3
iii) 8
iv) 16
2) Which of the following is the square root of 1600?
i) 50
ii) 400
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iii) 40
iv) 80
Name :
Sheet 1
Squaring Numbers
A) Find the values of the following.
1)
(2√3 )2
2)
(4√15 )2
3)
(3√5 )2
4)
(5√31 )2
5)
(√41 )2
6)
(7√11 )2
B) Find the squares of the following numerals.
1)
√43
2)
9√21
3)
2√37
4)
4√23
5)
5√2
6)
10√26
C) 1) Which of the following is the square of √35 ?
i) 70
ii) 35
(
iii) 1,225
iv) 53
iii) 120
iv) 576
)2
2) Which of the following is equal to 5√24 ?
i) 600
ii) 240
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Answer key
Name :
Sheet 1
Squaring Numbers
A) Find the values of the following.
1)
(2√3 )2
2)
(4√15 )2
12
4)
(5√31 )2
3)
(3√5 )2
240
5)
45
(√41 )2
775
6)
(7√11 )2
41
539
B) Find the squares of the following numerals.
1)
√43
2)
9√21
43
4)
4√23
3)
1,701
5)
148
5√2
368
2√37
6)
50
10√26
2,600
C) 1) Which of the following is the square of √35 ?
i) 70
ii) 35
(
iii) 1,225
iv) 53
iii) 120
iv) 576
)2
2) Which of the following is equal to 5√24 ?
i) 600
ii) 240
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Name :
Sheet 2
Squaring Numbers
A) Find the values of the following.
1)
(6√7 )2
2)
(3√22 )2
3)
(5√34 )2
4)
(√10 )2
5)
(2√15 )2
6)
(4√6 )2
B) Find the squares of the following numerals.
1)
3√13
2)
7√26
3)
9√5
4)
6√35
5)
8√29
6)
√46
(
C) 1) Find the value of 2√40
i) 160
)2 ?
ii) 80
iii) 42
iv) 82
iii) 4
iv) 2
2) What do we get when multiply √2 by itself?
i) √2
ii) √4
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Answer key
Name :
Sheet 2
Squaring Numbers
A) Find the values of the following.
1)
(6√7 )2
2)
(3√22 )2
252
4)
3)
(5√34 )2
198
(√10 )2
5)
850
(2√15 )2
10
6)
(4√6 )2
60
96
B) Find the squares of the following numerals.
1)
3√13
2)
117
4)
3)
9√5
1,274
6√35
5)
1,260
405
8√29
6)
1,856
(
C) 1) Find the value of 2√40
i) 160
7√26
√46
46
)2 ?
ii) 80
iii) 42
iv) 82
iii) 4
iv) 2
2) What do we get when multiply √2 by itself?
i) √2
ii) √4
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Name :
Sheet 3
Squaring Numbers
A) Find the values of the following.
1)
(√33 )2
2)
(5√11 )2
3)
(2√10 )2
4)
(3√43 )2
5)
(8√3 )2
6)
(√29 )2
B) Find the squares of the following numerals.
1)
3√16
2)
√47
3)
2√17
4)
7√4
5)
4√22
6)
9√31
(
C) 1) Which of the following is equal to 5√48
i) 101
2) Find the value of
i) 40
)2 ?
ii) √480
iii) 1,200
iv) 240
iii) 76
iv) √38
(√38 )2 .
ii) 38
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Answer key
Name :
Sheet 3
Squaring Numbers
A) Find the values of the following.
1)
(√33 )2
2)
(5√11 )2
33
4)
3)
(2√10 )2
275
(3√43 )2
5)
40
(8√3 )2
387
6)
(√29 )2
192
29
B) Find the squares of the following numerals.
1)
3√16
2)
√47
3)
144
4)
47
7√4
5)
6)
352
(
C) 1) Which of the following is equal to 5√48
2) Find the value of
i) 40
68
4√22
196
i) 101
2√17
9√31
2,511
)2 ?
ii) √480
iii) 1,200
iv) 240
iii) 76
iv) √38
(√38 )2 .
ii) 38
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Name :
Integers: S1
Evaluating Exponents
Evaluate each expression.
(–2)-3
1) 34 . 43
2)
4) (–8)3 – (–4)5
5) 2-2 + (–3)2 – 63
6)
7) 9-2 + 3-3
8) 52 . 3-2 – 6-1
9) (–8)3 . 2-7 + 34
10) (–2)9 + 82 – 3
11) 72 . (–2)-5 + 4-3
12)
13) (–9)2 – 64
14) 44 + 53 – 35
15) 82 . 4-4 + 3-2 – 6-1
62
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3) (–7)-3 . 74 + 2-1
36 . (4)-2
92
62 . (–4)-2
34
Answer key
Name :
Integers: S1
Evaluating Exponents
Evaluate each expression.
1) 34 . 43
2)
(–2)-3
62
–
5,184
4) (–8)3 – (–4)5
512
3) (–7)-3 . 74 + 2-1
5) 2-2 + (–3)2 – 63
–
4
81
10) (–2)9 + 82 – 3
–451
13) (–9)2 – 64
–1,215
6)
36 . (4)-2
92
3
827
or –206
4
4
8) 52 . 3-2 – 6-1
7) 9-2 + 3-3
– 13 or –6 1
2
2
1
288
9
16
9) (–8)3 . 2-7 + 34
11
47
or 2
18
18
11) 72 . (–2)-5 + 4-3
–
33
97
or –1
64
64
14) 44 + 53 – 35
138
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77
12)
62 . (–4)-2
34
1
36
15) 82 . 4-4 + 3-2 – 6-1
7
36
Name :
Integers: S2
Evaluating Exponents
Evaluate each expression.
22 . 35
63
2) 8-3 . (–8)4 + 62
3) (–5)5 – (–9)3
4) 2-9 . 46
5) (–9)-2 + 3-5
6) (–4)3 . 8-2 – 2-7
7) 8-1 – (–2)-8
8)
10) 53 . (–5)2 + 92
11) 44 . 8-4
12) (–2)-2 . 62 + 3-3 – 9-1
13) (–6)2 + 7
14) 33 . 6-3 – 25
15) 72 – 54
1)
34
92
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9) 72 + 6 – 33
Answer key
Name :
Integers: S2
Evaluating Exponents
Evaluate each expression.
1)
22 . 35
63
2) 8-3 . (–8)4 + 62
9 or 4 1
2
2
4) 2-9 . 46
44
–2,396
5) (–9)-2 + 3-5
6) (–4)3 . 8-2 – 2-7
4
243
8
7) 8-1 – (–2)-8
8)
34
43
129
1
or –1
128
128
28
1
11) 44 . 8-4
12) (–2)-2 . 62 + 3-3 – 9-1
1
16
3,206
13) (–6)2 + 7
–
9) 72 + 6 – 33
92
31
256
10) 53 . (–5)2 + 92
3) (–5)5 – (–9)3
14) 33 . 6-3 – 25
–
255
7
or –31
8
8
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241 or 8 25
27
27
15) 72 – 54
–576
Name :
Integers: S3
Evaluating Exponents
Evaluate each expression.
1)
82
44
2) 52 + 7 – (–3)2
42 . 2-6
3) 2-5 . (–2)2 – 8-1
4) (–3)-3 . 62
5)
7) 92 . 3-4 + (–5)4
8) 73 + 2-1
–
9) 25 2-3
82
10) 62 + (–5)3 – 82
11) 35 – 4-1
12) 4-2 . 23 – 6-2
13) 62 . –9)-3
14) 33 . 3-2 + 7-1 – 24
15)
27
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6) 62 – (–4)3
83
26
Answer key
Name :
Integers: S3
Evaluating Exponents
Evaluate each expression.
1)
82
2) 52 + 7 – (–3)2
44
1
4
4) (–3)-3 . 62
23
5)
42 . 2-6
27
1
– 4 or –1
3
3
7) 92 . 3-4 + (–5)4
626
10) 62 + (–5)3 – 82
–153
13) 62 . –9)-3
–
4
81
3) 2-5 . (–2)2 – 8-1
0
6) 62 – (–4)3
1
512
8) 73 + 2-1
100
–
9) 25 2-3
82
687 or 343 1
2
2
11) 35 – 4-1
255
512
12) 4-2 . 23 – 6-2
17
36
971
3
or 242
4
4
14) 33 . 3-2 + 7-1 – 24
–
90
6
or – 12
7
7
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15)
83
26
8
Name :
T1S1
Exponents - Product Rule
A) Use the product rule to rewrite each expression as a single exponent.
1) (–5)-10 . (–5)15
4)
2)
9
3
–7 . –7
6
6
4 -6 . 4 -9
5
5
3) (1.4)-12 . (1.4)5
5) (–13)0 . (–13)-19
6) 8-14 . 8-4
B) Find the value of .
1) 10 . 10-9 = 1011
2)
=
4)
–8
7
-
. –8
7
-15 = – 8 -10
7
=
7 . (5.6)7 = (5.6)14
=
5) (–20)16 . (–20) = (–20)-3
=
3) (–2.9)-13 . (–2.9) = (–2.9)-5
=
6) 11- . 116 = 1116
=
C) 1) Which of the following equals (–19)-12 . (–19)4?
i) (–19)-8
ii) (–19)8
iii) (–19)17
iv) (–19)16
2) Find the value of , if (–4.5) . (–4.5)9 = (–4.5)11.
i) 20
ii) –5
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iii) –3
iv) 2
Answer key
Name :
T1S1
Exponents - Product Rule
A) Use the product rule to rewrite each expression as a single exponent.
1) (–5)-10 . (–5)15
2)
4 -6 . 4 -9
5
5
4 -15
5
(−5)5
4)
9
3
–7 . –7
6
6
−7
6
3) (1.4)-12 . (1.4)5
(1.4)-7
5) (–13)0 . (–13)-19
12
6) 8-14 . 8-4
(−13)-19
8-18
B) Find the value of .
1) 10 . 10-9 = 1011
=
4)
2)
-
. –8
7
=
20
7 . (5.6)7 = (5.6)14
=
–8
7
-15 = – 8 -10
7
–5
5) (–20)16 . (–20) = (–20)-3
=
5.6
–19
3) (–2.9)-13 . (–2.9) = (–2.9)-5
=
8
6) 11- . 116 = 1116
=
–10
C) 1) Which of the following equals (–19)-12 . (–19)4?
i) (–19)-8
ii) (–19)8
iii) (–19)17
iv) (–19)16
2) Find the value of , if (–4.5) . (–4.5)9 = (–4.5)11.
i) 20
ii) –5
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iii) –3
iv) 2
Name :
T1S2
Exponents - Product Rule
A) Use the product rule to rewrite each expression as a single exponent.
1) (2.5)9 . (2.5)10
2) (–12)-8 . (–12)-5
4) 14-16 . 14-4
5)
3) 96 . 9-17
5 19 . 5 -9
9
9
6) (–3.6)3 . (–3.6)5
B) Find the value of .
1)
5
–6 . –6
5
5
-
= –6
5
12
2) (5.4) . (5.4)15 = (5.4)19
=
3)
=
4) (–6.8) . (–6.8)0 = (–6.8)9
=
5) (–7)-10 . (–7) - = (–7)-4
=
5 . 24 = 29
=
6)
1 . 18= 15
2
2
2
=
C) 1) Find the value of , if 4 . 47 = 418.
i) 13
ii) –12
iii) 11
2) Which of the following equals 2
7
i)
27
7
ii)
iv) 8
17 . 2 -10 ?
7
2 -27
7
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iii)
2 27
7
iv)
2 -7
7
Answer key
Name :
T1S2
Exponents - Product Rule
A) Use the product rule to rewrite each expression as a single exponent.
1) (2.5)9 . (2.5)10
2) (–12)-8 . (–12)-5
(2.5)19
(–12)-13
4) 14-16 . 14-4
3) 96 . 9-17
9-11
5 19 . 5 -9
9
9
5)
6) (–3.6)3 . (–3.6)5
5 10
9
14-20
(–3.6)8
B) Find the value of .
1)
5
–6 . –6
5
5
=
-
= –6
5
12
2) (5.4) . (5.4)15 = (5.4)19
=
–7
4) (–6.8) . (–6.8)0 = (–6.8)9
=
=
5 . 24 = 29
=
4
5) (–7)-10 . (–7) - = (–7)-4
9
3)
6)
2
1 . 18= 15
2
2
2
=
–6
–3
C) 1) Find the value of , if 4 . 47 = 418.
i) 13
ii) –12
iii) 11
2) Which of the following equals 2
7
i)
27
7
ii)
iv) 8
17 . 2 -10 ?
7
2 -27
7
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iii)
2 27
7
iv)
2 -7
7
Name :
T1S3
Exponents - Product Rule
A) Use the product rule to rewrite each expression as a single exponent.
1)
–2
9
12 . – 2 6
9
4) 6-7 . 62
2) (–4.1)3 . (–4.1)5
3) (–3)-8 . (–3)-8
5) 17-4 . 17-11
6)
1 9 . 1 -5
8
8
2) 7 . 72 = 7 6
3)
78. 7 = 75
5
5
5
B) Find the value of .
1) (9.2)- . (9.2)7 = (9.2)9
=
=
4) 1610 .
4 = 1614
=
5) (–15)13 . (–15)
=
= (–15)6
=
6) (–8.7)-18 . (–8.7) = (–8.7)-8
=
0
-15
C) 1) Which of the following equals 1 . 1 ?
4
4
i)
1 -15
8
ii)
1 -15
4
iii)
1 15
4
iv)
2 -15
4
-
2) Find the value of , if 12 . 123 = 12-17.
i) 14
ii) –16
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iii) 20
iv) –18
Answer key
Name :
T1S3
Exponents - Product Rule
A) Use the product rule to rewrite each expression as a single exponent.
1)
–2
9
12 . – 2 6
2) (–4.1)3 . (–4.1)5
9
–2
9
18
3) (–3)-8 . (–3)-8
(–4.1)8
4) 6-7 . 62
(–3)-16
5) 17-4 . 17-11
6-5
6)
1 9 . 1 -5
8
8
14
8
17-15
B) Find the value of .
1) (9.2)- . (9.2)7 = (9.2)9
=
2) 7 . 72 = 7 6
=
–2
4) 1610 .
4 = 1614
=
3)
=
4
5) (–15)13 . (–15)
=
16
78. 7 = 75
5
5
5
= (–15)6
–3
6) (–8.7)-18 . (–8.7) = (–8.7)-8
=
7
10
0
-15
C) 1) Which of the following equals 1 . 1 ?
4
4
i)
1 -15
8
ii)
1 -15
4
iii)
1 15
4
iv)
2 -15
4
-
2) Find the value of , if 12 . 123 = 12-17.
i) 14
ii) –16
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iii) 20
iv) –18
Name :
T1S1
Exponents - Quotient Rule
A) Use the quotient rule to rewrite each expression as a single exponent.
1)
(–5)17
(–5)7
2)
(1.4)4
(1.4)-2
3)
2-3
2-5
4)
2 0 ÷ 2 -18
3
3
5)
(–17)2
(–17)8
6)
(–3.8)-5
(–3.8)4
2)
7 ÷ 7 6 = 7 -8
9
9
9
3)
(–14)
= (–14)3
(–14)-8
B) Find the value of .
1)
(2.5)11
-
(2.5)
= (2.5)15
=
4)
-1
(–19)-2
=
= –19
3
= 3-3
37
5)
=
2) Find the value of , if
i) 3
6)
=
C) 1) Which of the following equals
i) (–12)12
=
(–12)10
(–12)2
–4
5
18 ÷ – 4 - = – 4 14
5
=
?
ii) (–12)8
iii) (–12)-8
iv) (–12)-12
iii) –35
iv) 35
(6.1)16
= (6.1)19.
(6.1)ii) –3
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5
Answer key
Name :
T1S1
Exponents - Quotient Rule
A) Use the quotient rule to rewrite each expression as a single exponent.
1)
(–5)17
(–5)7
(1.4)4
(1.4)-2
2)
(−5)10
4)
3)
2-3
2-5
(1.4)6
2 0 ÷ 2 -18
3
3
22
(–17)2
(–17)8
5)
2 18
3
6)
(–3.8)-5
(–3.8)4
(−17)-6
(−3.8)-9
B) Find the value of .
1)
(2.5)11
-
(2.5)
= (2.5)15
=
4)
-1
(–19)-2
=
4
= –19
=
=
−19
i) (–12)12
2) Find the value of , if
(–12)10
(–12)2
3)
−2
3
= 3-3
37
5)
C) 1) Which of the following equals
i) 3
7 ÷ 7 6 = 7 -8
9
9
9
2)
6)
10
(–14)
= (–14)3
(–14)-8
=
−5
–4
5
18 ÷ – 4 - = – 4 14
=
−4
5
?
ii) (–12)8
iii) (–12)-8
iv) (–12)-12
iii) –35
iv) 35
(6.1)16
= (6.1)19.
(6.1)ii) –3
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5
Name :
T1S2
Exponents - Quotient Rule
A) Use the quotient rule to rewrite each expression as a single exponent.
1)
(9.3)8
(9.3)3
2)
5 -9 ÷ 5 4
7
7
3)
(–18)-12
(–18)-6
4)
(–4)-6
(–4)13
5)
1117
1115
6)
–3
4
7 ÷ – 3 -11
4
B) Find the value of .
(–13)-4
1)
= (–13)-20
(–13)
(–8.2)-1
2)
= (–8.2)2
=
4)
1
6
-
5
15
÷ 1 = 1
6
6
=
=
6)
2
(4.7)
= (4.7)-13
(4.7)13
=
(–3.5)-8
(–3.5)-7
?
ii) (–7)-15
2) Find the value of , if – 7
i) 7
=
=
C) 1) Which of the following equals
i) (–3.5)-1
-3
(–2)9
= –2
(–2)
5)
-
9
3)
= 9-19
97
iii) –3.5
iv) (–7)-1
iii) – 7
2
iv) –7
14 ÷ -4 = – 7 18.
2
ii) 7
2
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Answer key
Name :
T1S2
Exponents - Quotient Rule
A) Use the quotient rule to rewrite each expression as a single exponent.
1)
(9.3)8
(9.3)3
5 -9 ÷ 5 4
7
7
2)
(–18)-12
(–18)-6
5 -13
7
(9.3)5
4)
3)
(–4)-6
(–4)13
(−18)-6
1117
1115
5)
6)
(−4)-19
–3
4
7 ÷ – 3 -11
4
−3
4
112
18
B) Find the value of .
(–13)-4
1)
= (–13)-20
(–13)
=
4)
1
6
-
(–8.2)-1
2)
= (–8.2)2
-3
=
16
5
15
÷ 1 = 1
6
6
=
=
−20
C) 1) Which of the following equals
i) (–3.5)-1
2
i) 7
6)
−8
(–3.5)-8
(–3.5)-7
12
(4.7)
= (4.7)-13
(4.7)13
=
0
?
ii) (–7)-15
2) Find the value of , if – 7
=
−8.2
(–2)9
= –2
(–2)
5)
-
9
3)
= 9-19
97
iii) –3.5
iv) (–7)-1
iii) – 7
2
iv) –7
14 ÷ -4 = – 7 18.
2
ii) 7
2
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Name :
T1S3
Exponents - Quotient Rule
A) Use the quotient rule to rewrite each expression as a single exponent.
1)
711
7-4
2)
(–20)-15
(–20)-13
3)
–1
2
11 ÷ – 1 5
4)
(–4.1)6
(–4.1)
5)
3 -7 ÷ 3 2
5
5
6)
16-4
1619
2)
(–8)14
= (–8)7
(–8)
3)
(–5.6)
= (–5.6)-7
(–5.6)11
2
B) Find the value of .
1) (– )13 ÷ 5
4
-3= 5 16
4
=
4)
=
=
-
(–11)
= (–11)-10
(–11)-8
5)
=
(7.9)
= (7.9)-20
7.9
=
6)
158
= 153
15
=
0
15
C) 1) Find the value of , if 6 ÷ 6 = 6 .
7
7
7
i) –15
ii) 0
2) Which of the following equals
i) 13-21
iii) –18
iv) 15
iii) 1311
iv) 1321
13-16
?
13-5
ii) 13-11
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Answer key
Name :
T1S3
Exponents - Quotient Rule
A) Use the quotient rule to rewrite each expression as a single exponent.
1)
711
7-4
2)
(–20)-15
(–20)-13
715
4)
3)
–1
2
11 ÷ – 1 5
2
−1
2
(−20)-2
(–4.1)6
(–4.1)
5)
3 -7 ÷ 3 2
5
5
6)
16-4
1619
3 -9
5
(−4.1)5
6
16-23
B) Find the value of .
1) (– )13 ÷ 5
4
=
4)
-3= 5 16
2)
4
−5
4
=
3)
5)
(7.9)
= (7.9)-20
7.9
=
−18
19
(–5.6)
= (–5.6)-7
(–5.6)11
=
−7
-
(–11)
= (–11)-10
(–11)-8
=
(–8)14
= (–8)7
(–8)
6)
4
158
= 153
15
=
−5
0
15
C) 1) Find the value of , if 6 ÷ 6 = 6 .
7
7
7
i) –15
ii) 0
2) Which of the following equals
i) 13-21
iii) –18
iv) 15
iii) 1311
iv) 1321
13-16
?
13-5
ii) 13-11
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Name :
Exponents - Power of a Power Rule
A) Use the power of a power rule to rewrite each expression as a single exponent.
1)
–1
3
-2 5
4) (512)-3
2) (83)16
3) ((–2.3)-7)2
5) ((–4)-5)-4
6)
5 4 13
4
2) ((–3.2)5) = (–3.2)-20
3)
3 13 = 3 65
2
2
B) Find the value of .
1) (6 )-4 = 6-36
=
=
4) ( 6)7 = (7.9)42
=
6) (168) = 16-16
5) ((–9) )-9 = 1
=
=
=
C) 1) Which of the following equals ((–15)-3)-4?
i) (–15)-28
ii) (–15)-12
2) Find the value of , if 6
7
i) 4
iii) (–15)-7
iv) (–15)12
iii) –6
iv) 15
-8 = 6 32 .
7
ii) –4
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T1S1
Answer key
Name :
T1S1
Exponents - Power of a Power Rule
A) Use the power of a power rule to rewrite each expression as a single exponent.
1)
–1
3
-2 5
2) (83)16
−1
3
3) ((–2.3)-7)2
-10
848
4) (512)-3
(−2.3)-14
5) ((–4)-5)-4
5-36
6)
5 4 13
4
5 52
4
(−4)20
B) Find the value of .
1) (6 )-4 = 6-36
=
2) ((–3.2)5) = (–3.2)-20
=
9
4) ( 6)7 = (7.9)42
=
–4
=
3 13 = 3 65
2
2
=
5
6) (168) = 16-16
5) ((–9) )-9 = 1
7.9
3)
=
0
2
C) 1) Which of the following equals ((–15)-3)-4?
i) (–15)-28
ii) (–15)-12
2) Find the value of , if 6
7
i) 4
iii) (–15)-7
iv) (–15)12
iii) –6
iv) 15
-8 = 6 32 .
7
ii) –4
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Name :
Exponents - Power of a Power Rule
T1S2
A) Use the power of a power rule to rewrite each expression as a single exponent.
1) ((6.1)-7)3
2)
7 10 -4
8
3) ((–3)-6)-1
4) (182)-6
5) (2-11)-3
6) ((–7)-15)5
2) (147) = 14-28
3) ( 5)-3 = (–5)-15
B) Find the value of .
1)
–1
5
9 = – 1 27
5
=
4) (113) = 1121
=
=
5) ((1.5) )-6 = (1.5)-12
=
=
6) ((–6)2) = (–6)-18
=
C) 1) Find the value of , if ((–9.4)2) = (–9.4)24.
i) –26
ii) 22
iii) –12
iv) 12
iii) 195
iv) 19
2) Which of the following equals (190)-5?
i) 1
ii) 19-5
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Answer key
Name :
T1S2
Exponents - Power of a Power Rule
A) Use the power of a power rule to rewrite each expression as a single exponent.
1) ((6.1)-7)3
2)
7 10 -4
8
7 -40
8
(6.1)-21
4) (182)-6
3) ((–3)-6)-1
(−3)6
5) (2-11)-3
18-12
6) ((–7)-15)5
233
(−7)-75
B) Find the value of .
1)
–1
5
9 = – 1 27
=
5
=
3
4) (113) = 1121
=
2) (147) = 14-28
3) ( 5)-3 = (–5)-15
–4
5) ((1.5) )-6 = (1.5)-12
=
–7
=
–5
6) ((–6)2) = (–6)-18
=
2
9
C) 1) Find the value of , if ((–9.4)2) = (–9.4)24.
i) –26
ii) 22
iii) –12
iv) 12
iii) 195
iv) 19
2) Which of the following equals (190)-5?
i) 1
ii) 19-5
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Name :
Exponents - Power of a Power Rule
A) Use the power of a power rule to rewrite each expression as a single exponent.
1) ((–13)11)6
2) ((4.6)-7)-5
4) (3-3)2
5)
–5
6
3) (79)-4
4 -7
6) ((–18)-15)-3
B) Find the value of .
1) ((–5.8)4) = (–5.8)16
2) ((–12) )2 = (–12)20
=
4)
8 -5 = 8 30
7
7
=
=
5) (204) = 20-12
=
3) (96) = 954
6) ( -7)-8 = (–8)56
=
=
2 = – 1 -26 .
C) 1) Find the value of , if – 1
9
9
i) –52
ii) –13
iii) 13
iv) 10
iii) (–4.3)10
iv) (–4.3)16
2) Which of the following equals ((–4.3)8)2?
i) (–4.3)-16
ii) (–4.3)6
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T1S3
Answer key
Name :
T1S3
Exponents - Power of a Power Rule
A) Use the power of a power rule to rewrite each expression as a single exponent.
1) ((–13)11)6
2) ((4.6)-7)-5
(−13)66
4) (3-3)2
3) (79)-4
(4.6)35
5)
–5
6
4 -7
−5
6
3-6
7-36
6) ((–18)-15)-3
-28
(−18)45
B) Find the value of .
1) ((–5.8)4) = (–5.8)16
=
4)
=
–4
8 -5 = 8 30
7
7
=
2) ((–12) )2 = (–12)20
10
5) (204) = 20-12
=
–6
3) (96) = 954
=
–9
6) ( -7)-8 = (–8)56
=
3
–8
2 = – 1 -26 .
C) 1) Find the value of , if – 1
9
9
i) –52
ii) –13
iii) 13
iv) 10
iii) (–4.3)10
iv) (–4.3)16
2) Which of the following equals ((–4.3)8)2?
i) (–4.3)-16
ii) (–4.3)6
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Name :
Sheet 1
Reciprocals
A) Find the reciprocal of the following in exponential form with the positive exponent.
2
1) 1
9
-3
2) 5
8
3) 67
B) Find the reciprocal of the following in exponential form with the negative exponent.
1) 79
2)
. 1 3 = 1, find the value of
8
positive exponent.
C) 1) If
–
25
5
-6
3) 1
4
Express your answer in exponential form with the
2) What is the multiplicative inverse of 34 ? Express your answer in exponential form with
the negative exponent.
5
-5
3) Check whether 6 is the reciprocal of 7 .
7
6
D) 1) Which of the following is the multiplicative inverse of 4 -2?
3
i)
42
3
ii)
2 -2
3
iii)
32
2
iv)
32
4
1 -6
5
iii)
16
5
iv)
6-5
2) What is the reciprocal of 56?
i) 65
ii)
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Answer key
Name :
Sheet 1
Reciprocals
A) Find the reciprocal of the following in exponential form with the positive exponent.
2
1) 1
9
-3
2) 5
8
3) 67
5 3
8
92
1 7
6
B) Find the reciprocal of the following in exponential form with the negative exponent.
1) 79
2)
–
25
5
-6
3) 1
4
–2
7-9
-5
4-6
5
. 1 3 = 1, find the value of
8
positive exponent.
C) 1) If
Express your answer in exponential form with the
83
2) What is the multiplicative inverse of 34 ? Express your answer in exponential form with
the negative exponent.
3-4
5
-5
3) Check whether 6 is the reciprocal of 7 .
7
6
No
D) 1) Which of the following is the multiplicative inverse of 4 -2?
3
i)
42
3
ii)
2 -2
3
iii)
32
2
iv)
32
4
1 -6
5
iii)
16
5
iv)
6-5
2) What is the reciprocal of 56?
i) 65
ii)
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Name :
Sheet 2
Reciprocals
A) Find the reciprocal of the following in exponential form with the positive exponent.
-8
2) 3
7
1) 4-3
4
3) 1
5
B) Find the reciprocal of the following in exponential form with the negative exponent.
-6
2) 9
8
2
1) 5
2
. 4 2 , find the value of
5
negative exponent.
C) 1) If 16 =
3) 85
Express your answer in exponential form with the
-4
2) Check whether 9-4 is the reciprocal of 1 .
9
7
3) What is the multiplicative inverse of 5 ? Express your answer in exponential form with
3
the positive exponent.
D) 1) What is the reciprocal of 7 -5?
2
i)
52
2
ii)
25
7
iii)
–7
2
5
iv)
2 -5
7
iv)
59
8
9
2) Which of the following is the multiplicative inverse of 3 ?
8
i)
39
5
ii)
3 -9
8
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iii)
8 -9
3
Answer key
Name :
Sheet 2
Reciprocals
A) Find the reciprocal of the following in exponential form with the positive exponent.
-8
2) 3
7
1) 4-3
4
3) 1
5
3 8
7
43
54
B) Find the reciprocal of the following in exponential form with the negative exponent.
-6
2) 9
8
2
1) 5
2
5 -2
2
3) 85
8 -6
9
. 4 2 , find the value of
5
negative exponent.
1 -2
5
C) 1) If 16 =
8-5
Express your answer in exponential form with the
-4
2) Check whether 9-4 is the reciprocal of 1 .
9
Yes
7
3) What is the multiplicative inverse of 5 ? Express your answer in exponential form with
3
the positive exponent.
37
5
D) 1) What is the reciprocal of 7 -5?
2
i)
52
2
ii)
25
7
iii)
–7
2
5
iv)
2 -5
7
iv)
59
8
9
2) Which of the following is the multiplicative inverse of 3 ?
8
i)
39
5
ii)
3 -9
8
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iii)
8 -9
3
Name :
Sheet 3
Reciprocals
A) Find the reciprocal of the following in exponential form with the positive exponent.
-3
1) 3
8
6
3) 5
4
2) 92
B) Find the reciprocal of the following in exponential form with the negative exponent.
-4
2) 1
3
1) 27
3) 6-8
5
5
C) 1) Check whether 2 is the reciprocal of 7 .
2
7
. 2 3 = 8, find the value of
3
positive exponent.
2) If
Express your answer in exponential form with the
3) What is the multiplicative inverse of 82 ? Express your answer in exponential form with
the negative exponent.
D) 1) Which of the following is the multiplicative inverse of 5-8 ?
i)
1
5
ii)
18
5
iii)
85
iv)
58
iii)
19
6
iv)
1
9
9
2) What is the reciprocal of – 1 ?
6
i)
– 69
ii)
1 -9
6
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Answer key
Name :
Sheet 3
Reciprocals
A) Find the reciprocal of the following in exponential form with the positive exponent.
-3
1) 3
8
6
3) 5
4
2) 92
4 6
5
1 2
9
3 3
8
B) Find the reciprocal of the following in exponential form with the negative exponent.
-4
2) 1
3
1) 27
3) 6-8
1 -8
6
3-4
2-7
5
5
C) 1) Check whether 2 is the reciprocal of 7 .
2
7
Yes
. 2 3 = 8, find the value of
3
positive exponent.
2) If
Express your answer in exponential form with the
33
3) What is the multiplicative inverse of 82 ? Express your answer in exponential form with
the negative exponent.
8-2
D) 1) Which of the following is the multiplicative inverse of 5-8 ?
i)
1
5
ii)
18
5
iii)
85
iv)
58
iii)
19
6
iv)
1
9
9
2) What is the reciprocal of – 1 ?
6
i)
– 69
ii)
1 -9
6
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Name :
T1L1S1
Exponents
Evaluate.
1)
(–2)6 . (–4)-7
2)
((–2)2)-5
3) (–10)-4 . 3-3 ÷ – 3
5
5)
7)
0 . 104
1 12 . (–7)-11
2
14-11
(–12)4
(–6)2 . (–12)2
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4)
18-18 . 1 -16
3
6-18
9-4 . 152
9-3
-8
6) 16-9 . 1 . 89
4
7
-2
-6
8) ((–3)0)2 . 9 ÷ – 7 . – 9
7
3
7
Answer key
Name :
T1L1S1
Exponents
Evaluate.
1)
(–2)6 . (–4)-7
2)
((–2)2)-5
18-18 . 1 -16
3
6-18
1
9
–4
3) (–10)-4 . 3-3 ÷ – 3
5
0 . 104
4)
9-4 . 152
9-3
1
27
5)
1 12 . (–7)-11
2
14-11
–
7)
1
2
(–12)4
(–6)2 . (–12)2
4
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25
-8
6) 16-9 . 1 . 89
4
128
7
-2
-6
8) ((–3)0)2 . 9 ÷ – 7 . – 9
7
7
3
7
Name :
T1L1S2
Exponents
Evaluate.
1)
3)
5)
7)
((–9)0)3 . (–18)2
(–9)3
154 . (–5)-2
(–3)4 . 5-2
2) 25 . – 7
6
11 ÷ 1 -5 . 6 11
2
7
4) 713 . 14-13 . 84
(–12)7
6-9 . 1 8
3
18-9
6)
(–20)17 . (–2)-15
-12 ÷ (–15)-3 . – 1 -3
8) 5-15 . 1
1017
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(–4)6 . 92
5
2
Answer key
Name :
T1L1S2
Exponents
Evaluate.
1)
((–9)0)3 . (–18)2
3)
6
(–9)3
–
2) 25 . – 7
4
9
154 . (–5)-2
(–3)4 . 5-2
11 ÷ 1 -5 . 6 11
2
–1
4) 713 . 14-13 . 84
1
2
625
5)
6-9 . 1 8
3
18-9
3
7)
(–20)17 . (–2)-15
1017
4
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7
6)
(–12)7
(–4)6 . 92
–108
-12 ÷ (–15)-3 . – 1 -3
8) 5-15 . 1
5
2
216
Name :
T1L1S3
Exponents
Evaluate.
2
-18
1) (–14)3 . 1 ÷ (–7)18 . – 1
7
3)
5)
7
8-2 . 5-3
189
187 . (–3)3
-15 ÷ – 5 -4 . 1 11
4) (–5)-4 . 1
2
(–20)-4
(42)0
6)
45 . 16-3
9
3
7) 67 . 1 ÷ – 1 . 2-3
6
2)
6
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8)
144 . (–3)2
74
(–9)19 . ((–12)0)6
(–9)16
4
2
Answer key
Name :
T1L1S3
Exponents
Evaluate.
2
-18
1) (–14)3 . 1 ÷ (–7)18 . – 1
7
7
2)
189
187 . (–3)3
–56
3)
–12
8-2 . 5-3
-15 ÷ – 5 -4 . 1 11
4) (–5)-4 . 1
2
(–20)-4
1
16
20
5)
(42)0
6)
45 . 16-3
9
3
7) 67 . 1 ÷ – 1 . 2-3
6
–
74
144
4
6
144 . (–3)2
3
4
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8)
(–9)19 . ((–12)0)6
(–9)16
–729
4
2
Name :
Score :
Scientific Notation
Mixed: ES1
Example: 1
Example: 2
Write 6, 224 in scientific notation.
Write 0.0087 in scientific notation.
6 2 2 4.
0.0 0 8 7
We should move the decimal point 3 places to
the left. So, the exponent will be 3.
We should move the decimal point 3 places to
the right. So, the exponent will be -3.
6, 224 = 6.224 × 103
0.0087 = 8.7 × 10-3
Express each number in scientific notation.
1)
0.0259
=
2)
902
=
3)
55, 820 =
4)
0.315
=
5)
0.00973 =
6) 10, 006
=
7)
856
=
8)
0.2058
=
9) 0.00072 =
10)
5, 008
=
11) 0.001216 =
12)
0.00145 =
13)
14)
0.12
75, 919 =
Printable Math Worksheets @ www.mathworksheets4kids.com
=
Name :
Score :
Answer key
Scientific Notation
Mixed: ES1
Example: 1
Example: 2
Write 6, 224 in scientific notation.
Write 0.0087 in scientific notation.
6 2 2 4.
0.0 0 8 7
We should move the decimal point 3 places to
the left. So, the exponent will be 3.
We should move the decimal point 3 places to
the right. So, the exponent will be -3.
6, 224 = 6.224 × 103
0.0087 = 8.7 × 10-3
Express each number in scientific notation.
1)
0.0259
=
2.59 × 10ˉ2
2)
902
=
9.02 × 102
3)
55, 820 =
5.582 × 104
4)
0.315
=
3.15 × 10ˉ1
5)
0.00973 =
9.73 × 10ˉ3
6) 10, 006
=
1.0006 × 104
7)
856
=
8.56 × 102
8)
0.2058
=
2.058 × 10ˉ1
9) 0.00072 =
7.2 × 10ˉ4
10)
5, 008
=
5.008 × 103
11) 0.001216 =
1.216 × 10ˉ3
12)
0.00145 =
1.45 × 10ˉ3
13)
7.5919 × 104
14)
0.12
1.2 × 10ˉ1
75, 919 =
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=
Name :
Score :
Scientific Notation
Mixed: ES2
Example: 1
Example: 2
Write 165 in scientific notation.
Write 0.0641 in scientific notation.
0.0 6 4 1
1 6 5.
We should move the decimal point 2 places to
the left. So, the exponent will be 2.
We should move the decimal point 2 places to
the right. So, the exponent will be -2.
165 = 1.65 × 102
0.0641 = 6.41 × 10-2
Express each number in scientific notation.
1)
360
=
2)
0.00091 =
3)
0.00584 =
4)
44, 268 =
5) 1, 073
=
6) 0.0769
=
7)
0.9861 =
8)
3, 169
=
9)
84, 802 =
10)
0.0058
=
18, 569 =
11) 0.075
=
12)
13)
=
14) 0.000026 =
977
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Answer key
Scientific Notation
Mixed: ES2
Example: 1
Example: 2
Write 165 in scientific notation.
Write 0.0641 in scientific notation.
0.0 6 4 1
1 6 5.
We should move the decimal point 2 places to
the left. So, the exponent will be 2.
We should move the decimal point 2 places to
the right. So, the exponent will be -2.
165 = 1.65 × 102
0.0641 = 6.41 × 10-2
Express each number in scientific notation.
1)
360
=
3.6 × 102
2)
0.00091 =
9.1 × 10ˉ4
3)
0.00584 =
5.84 × 10ˉ3
4)
44, 268 =
4.4268 × 104
=
1.073 × 103
6) 0.0769
=
7.69 × 10ˉ2
7)
0.9861 =
9.861 × 10ˉ1
8)
3, 169
=
3.169 × 103
9)
84, 802 =
8.4802 × 104
10)
0.0058
=
5.8 × 10ˉ3
18, 569 =
5) 1, 073
11) 0.075
=
7.5 × 10ˉ2
12)
13)
=
9.77 × 102
14) 0.000026 =
977
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1.8569 × 104
2.6 × 10ˉ5
Score :
Name :
Scientific Notation
Mixed: ES3
Example: 1
Example: 2
Write 63, 215 in scientific notation.
Write 0.0019 in scientific notation.
0.0 0 1 9
6 3 2 1 5 .
We should move the decimal point 4 places to
the left. So, the exponent will be 4.
We should move the decimal point 3 places to
the right. So, the exponent will be -3.
63, 215 = 6.3215 × 104
0.0019 = 1.9 × 10-3
Express each number in scientific notation.
1)
52
=
2)
0.0733 =
3)
0.0034
=
4)
9, 645
5)
0.8031
=
6) 85, 249 =
7)
746
=
8)
0.00025 =
9)
0.9172
=
10)
3, 564
11)
54, 001 =
12)
0.0585 =
13)
0.00068 =
14)
249
Printable Math Worksheets @ www.mathworksheets4kids.com
=
=
=
Name :
Score :
Answer key
Scientific Notation
Mixed: ES3
Example: 1
Example: 2
Write 63, 215 in scientific notation.
Write 0.0019 in scientific notation.
0.0 0 1 9
6 3 2 1 5 .
We should move the decimal point 4 places to
the left. So, the exponent will be 4.
We should move the decimal point 3 places to
the right. So, the exponent will be -3.
63, 215 = 6.3215 × 104
0.0019 = 1.9 × 10-3
Express each number in scientific notation.
1)
52
=
5.2 × 10
2)
0.0733 =
7.33 × 10ˉ2
3)
0.0034
=
3.4 × 10ˉ3
4)
9, 645
=
9.645 × 103
5)
0.8031
=
8.031 × 10ˉ1
6) 85, 249 =
8.5249 × 104
7)
746
=
7.46 × 102
8)
0.00025 =
2.5 × 10ˉ4
9)
0.9172
=
9.172 × 10ˉ1
10)
3, 564
=
3.564 × 103
11)
54, 001 =
5.4001 × 104
12)
0.0585 =
5.85 × 10ˉ2
13)
0.00068 =
6.8 × 10ˉ4
14)
249
2.49 × 102
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=
Name :
Score :
Scientific Notation
Add/Sub: ES1
Simplify and express in scientific notation:
Example 1
Example 2
(2 × 104) + (3 × 105)
(7 × 108) – (4 × 106)
= (2 × 104) + (3 × 104) × 10
= (7 × 106) × 102 – (4 × 106)
= (2 × 104) + (30 × 104)
= (700 × 106) – (4 × 106)
= 32 × 104
= 696 × 106
= 3.2 × 105
= 6.96 × 108
Simplify each problem and express the answer in scientific notation.
1) (2 × 103) + (5 × 105)
Answer :
3) (8 × 109) – (3 × 107)
Answer :
5) (4 × 102) + (7 × 103)
Answer :
7) (1 × 106) – (8 × 104)
Answer :
2) (4 × 108) – (9 × 107)
Answer :
4) (5 × 107) + (1 × 106)
Answer :
6) (9 × 105) – (6 × 104)
Answer :
8) (5 × 109) + (3 × 108)
Answer :
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Answer key
Scientific Notation
Add/Sub: ES1
Simplify and express in scientific notation:
Example 1
Example 2
(2 × 104) + (3 × 105)
(7 × 108) – (4 × 106)
= (2 × 104) + (3 × 104) × 10
= (7 × 106) × 102 – (4 × 106)
= (2 × 104) + (30 × 104)
= (700 × 106) – (4 × 106)
= 32 × 104
= 696 × 106
= 3.2 × 105
= 6.96 × 108
Simplify each problem and express the answer in scientific notation.
1) (2 × 103) + (5 × 105)
Answer :
5.02 × 105
3) (8 × 109) – (3 × 107)
Answer :
7.97 × 109
5) (4 × 102) + (7 × 103)
Answer :
7.4 × 103
7) (1 × 106) – (8 × 104)
Answer :
9.2 × 105
2) (4 × 108) – (9 × 107)
Answer :
3.1 × 108
4) (5 × 107) + (1 × 106)
Answer :
5.1 × 107
6) (9 × 105) – (6 × 104)
Answer :
8.4 × 105
8) (5 × 109) + (3 × 108)
Answer :
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5.3 × 109
Name :
Score :
Scientific Notation
Add/Sub: ES2
Simplify and express in scientific notation:
Example 1
Example 2
(4 × 103) – (2 × 102)
(9 × 105) + (6 × 107)
= (4 × 102) × 10 – (2 × 102)
= (9 × 105) + (6 × 105) × 102
= (40 × 102) – (2 × 102)
= (9 × 105) + (600 × 105)
= 38 × 102
= 609 × 105
= 3.8 × 103
= 6.09 × 107
Simplify each problem and express the answer in scientific notation.
1) (6 × 106) – (3 × 104)
Answer :
3) (7 × 107) + (4 × 106)
Answer :
5) (5 × 105) – (8 × 104)
Answer :
7) (2 × 108) + (7 × 106)
Answer :
2) (5 × 109) + (10 × 108)
Answer :
4) (3 × 104) – (2 × 102)
Answer :
6) (8 × 106) + (9 × 105)
Answer :
8) (4 × 108) – (3 × 107)
Answer :
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Answer key
Scientific Notation
Add/Sub: ES2
Simplify and express in scientific notation:
Example 1
Example 2
(4 × 103) – (2 × 102)
(9 × 105) + (6 × 107)
= (4 × 102) × 10 – (2 × 102)
= (9 × 105) + (6 × 105) × 102
= (40 × 102) – (2 × 102)
= (9 × 105) + (600 × 105)
= 38 × 102
= 609 × 105
= 3.8 × 103
= 6.09 × 107
Simplify each problem and express the answer in scientific notation.
1) (6 × 106) – (3 × 104)
Answer :
5.97 × 106
3) (7 × 107) + (4 × 106)
Answer :
7.4 × 107
5) (5 × 105) – (8 × 104)
Answer :
4.2 × 105
7) (2 × 108) + (7 × 106)
Answer :
2.07 × 108
2) (5 × 109) + (10 × 108)
Answer :
6 × 109
4) (3 × 104) – (2 × 102)
Answer :
2.98 × 104
6) (8 × 106) + (9 × 105)
Answer :
8.9 × 106
8) (4 × 108) – (3 × 107)
Answer :
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3.7 × 108
Name :
Score :
Scientific Notation
Add/Sub: ES3
Simplify and express in scientific notation:
Example 1
Example 2
(8 × 102) + (4 × 105)
(6 × 107) – (2 × 106)
= (8 × 102) + (4 × 102) × 103
= (6 × 106) × 10 – (2 × 106)
= (8 × 102) + (4000 × 102)
= (60 × 106) – (2 × 106)
= 4008 × 102
= 58 × 106
= 4.008 × 105
= 5.8 × 107
Simplify each problem and express the answer in scientific notation.
1) (3 × 108) + (5 × 107)
Answer :
3) (6 × 106) – (5 × 105)
Answer :
5) (3 × 109) + (7 × 107)
Answer :
7) (4 × 106) – (2 × 105)
Answer :
2) (9 × 104) – (7 × 102)
Answer :
4) (2 × 105) + (8 × 104)
Answer :
6) (5 × 108) – (10 × 106)
Answer :
8) (6 × 109) + (4 × 108)
Answer :
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Answer key
Scientific Notation
Add/Sub: ES3
Simplify and express in scientific notation:
Example 1
Example 2
(8 × 102) + (4 × 105)
(6 × 107) – (2 × 106)
= (8 × 102) + (4 × 102) × 103
= (6 × 106) × 10 – (2 × 106)
= (8 × 102) + (4000 × 102)
= (60 × 106) – (2 × 106)
= 4008 × 102
= 58 × 106
= 4.008 × 105
= 5.8 × 107
Simplify each problem and express the answer in scientific notation.
1) (3 × 108) + (5 × 107)
Answer :
3.5 × 108
3) (6 × 106) – (5 × 105)
Answer :
5.5 × 106
5) (3 × 109) + (7 × 107)
Answer :
3.07 × 109
7) (4 × 106) – (2 × 105)
Answer :
3.8 × 106
2) (9 × 104) – (7 × 102)
Answer :
8.93 × 104
4) (2 × 105) + (8 × 104)
Answer :
2.8 × 105
6) (5 × 108) – (10 × 106)
Answer :
4.9 × 108
8) (6 × 109) + (4 × 108)
Answer :
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6.4 × 109
Name :
Score :
Scientific Notation
Mixed operations: ES1
Simplify each problem and express the answer in scientific notation.
1) (8 × 105) + (5 × 104)
Answer :
3) (3 × 104) – (5 × 102)
Answer :
5) 9 × 103
2 × 10
Answer :
7) (5 × 108) – (3 × 106)
Answer :
9) (4 × 102) + (9 × 104)
Answer :
2)
7 × 106
2 × 103
Answer :
4) (4 × 10) (2 × 103)
Answer :
6) (8 × 103) (3 × 104)
Answer :
8) (7 × 105) + (6 × 107)
Answer :
10) (2 × 103) (5 × 104)
Answer :
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Scientific Notation
Score :
Mixed operations: ES1
Simplify each problem and express the answer in scientific notation.
1) (8 × 105) + (5 × 104)
Answer :
8.5 × 105
3) (3 × 104) – (5 × 102)
Answer :
2.95 × 104
5) 9 × 103
2 × 10
Answer :
4.5 × 102
4.97 × 108
9) (4 × 102) + (9 × 104)
Answer :
7 × 106
2 × 103
Answer :
3.5 × 103
4) (4 × 10) (2 × 103)
Answer :
8 × 104
6) (8 × 103) (3 × 104)
7) (5 × 108) – (3 × 106)
Answer :
2)
9.04 × 104
Answer :
2.4 × 108
8) (7 × 105) + (6 × 107)
Answer :
6.07 × 107
10) (2 × 103) (5 × 104)
Answer :
Printable Math Worksheets @ www.mathworksheets4kids.com
1 × 108
Name :
Score :
Scientific Notation
Mixed operations: ES2
Simplify each problem and express the answer in scientific notation.
1) (5 × 103) + (2 × 105)
Answer :
3) (5 × 106) (7 × 108)
Answer :
5) (8 × 108) – (7 × 105)
Answer :
7) 11 × 105
4 × 102
Answer :
9) (7 × 108) + (5 × 106)
Answer :
2) (3 × 106) – (8 × 104)
Answer :
4) 9 × 105
6 × 102
Answer :
6) (2 × 105) (5 × 109)
Answer :
8) (10 × 102) + (9 × 104)
Answer :
10) (4 × 107) (6 × 106)
Answer :
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Scientific Notation
Score :
Mixed operations: ES2
Simplify each problem and express the answer in scientific notation.
1) (5 × 103) + (2 × 105)
Answer :
2.05 × 105
3) (5 × 106) (7 × 108)
Answer :
3.5 × 1015
5) (8 × 108) – (7 × 105)
Answer :
7.993 × 108
7) 11 × 105
4 × 102
Answer :
Answer :
2.92 × 106
4) 9 × 105
6 × 102
Answer :
1.5 × 103
6) (2 × 105) (5 × 109)
Answer :
1 × 1015
8) (10 × 102) + (9 × 104)
2.75 × 103
9) (7 × 108) + (5 × 106)
Answer :
2) (3 × 106) – (8 × 104)
7.05 × 108
Answer :
9.1 × 104
10) (4 × 107) (6 × 106)
Answer :
Printable Math Worksheets @ www.mathworksheets4kids.com
2.4 × 1014
Name :
Score :
Scientific Notation
Mixed operations: ES3
Simplify each problem and express the answer in scientific notation.
1) (6 × 106) – (8 × 103)
Answer :
3) (4 × 106) (9 × 108)
Answer :
5) (5 × 108) (11 × 107)
Answer :
7) (6 × 106) – (10 × 104)
Answer :
9) (3 × 108) + (13 × 106)
Answer :
2)
2 × 105
5 × 103
Answer :
4) (7 × 105) + (3 × 107)
Answer :
6) (12 × 105) (4 × 108)
Answer :
8) (9 × 102) + (3 × 104)
Answer :
10) 5 × 108
2 × 104
Answer :
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Scientific Notation
Score :
Mixed operations: ES3
Simplify each problem and express the answer in scientific notation.
1) (6 × 106) – (8 × 103)
Answer :
5.992 × 106
3) (4 × 106) (9 × 108)
Answer :
3.6 × 1015
5) (5 × 108) (11 × 107)
Answer :
5.5 × 1016
7) (6 × 106) – (10 × 104)
Answer :
5.9 × 106
9) (3 × 108) + (13 × 106)
Answer :
3.13 × 108
2)
2 × 105
5 × 103
Answer :
4 × 10
4) (7 × 105) + (3 × 107)
Answer :
3.07 × 107
6) (12 × 105) (4 × 108)
Answer :
4.8 × 1014
8) (9 × 102) + (3 × 104)
Answer :
3.09 × 104
10) 5 × 108
2 × 104
Answer :
Printable Math Worksheets @ www.mathworksheets4kids.com
2.5 × 104
Name :
Simplifying Expressions: Exponents
Simplify each expression.
1)
(4x7)(5x5)
2)
2s7
6s2
3)
9p7
p2
4)
8m3
2m5
5)
(3n7)(5n)
6)
(4c2)(6c2)
7)
10z3
2z2
8)
(9k5)(2k3)
9)
(2d7)(5d4)
10)
6t2
12t
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ES1
Name :
Answer key
Simplifying Expressions: Exponents
Simplify each expression.
1)
(4x7)(5x5)
2)
1 s5
3
20x12
3)
9p7
p2
4)
(3n7)(5n)
6)
15n8
7)
10z3
2z2
(2d7)(5d4)
(4c2)(6c2)
24c4
8)
5z
9)
8m3
2m5
4
m2
9p5
5)
2s7
6s2
(9k5)(2k3)
18k8
10)
10d11
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6t2
12t
1t
2
ES1
Name :
Simplifying Expressions: Exponents
Simplify each expression.
1)
12k6
6k3
2)
(4a3)(3a)
3)
(3m3)(2m2)
4)
8z9
6z
5)
21
14p4
6)
(5d10)(7d2)
7)
18r7
9r6
8)
16n9
4n4
9)
(11y2)(2y6)
10)
2s7
8s2
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ES2
Name :
Answer key
Simplifying Expressions: Exponents
Simplify each expression.
1)
12k6
6k3
2)
2k3
3)
(3m3)(2m2)
12a4
4)
21
14p4
6)
3
2p4
7)
18r7
9r6
(11y2)(2y6)
(5d10)(7d2)
35d12
8)
2r
9)
8z9
6z
4 z8
3
6m5
5)
(4a3)(3a)
16n9
4n4
4n5
10)
22y8
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2s7
8s2
1 s5
4
ES2
Name :
Simplifying Expressions: Exponents
Simplify each expression.
1)
(2a7)(3a7)
2)
25x5
5x
3)
4p2
6p
4)
(13c3)(c2)
5)
(7z4)(2z5)
6)
28r
4r2
7)
9s7
21s2
8)
(8b5)(11b9)
9)
(5n3)(2n3)
10)
3y6
24y3
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ES3
Name :
Answer key
Simplifying Expressions: Exponents
Simplify each expression.
1)
(2a7)(3a7)
2)
6a14
3)
4p2
6p
5x4
4)
2p
3
5)
(7z4)(2z5)
9s7
21s2
6)
(5n3)(2n3)
28r
4r2
7
r
8)
3 s5
7
9)
(13c3)(c2)
13c5
14z9
7)
25x5
5x
(8b5)(11b9)
88b14
10)
10n6
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3y6
24y3
1 y3
8
ES3
Name :
Simplifying Expressions: Exponents
Simplify each expression.
1)
(7t3)(9t4)
2)
(11d3)(3d)
3)
15c8
5c9
4)
28a8
49a3
5)
(6x6)(8x2)
6)
20y9
4y2
7)
64b8
16b6
8)
24m9
22m4
9)
(8r2)(5r5)
10)
(7z2)(2z2)
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ES4
Name :
Answer key
Simplifying Expressions: Exponents
Simplify each expression.
1)
(7t3)(9t4)
2)
63t7
3)
15c8
5c9
33d4
4)
(6x6)(8x2)
6)
48x8
7)
64b8
16b6
(8r2)(5r5)
20y9
4y2
5y7
8)
4b2
9)
28a8
49a3
4 a5
7
3
c
5)
(11d3)(3d)
24m9
22m4
12 m5
11
10)
40r7
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(7z2)(2z2)
14z4
ES4
Name :
Simplifying Expressions: Exponents
Simplify each expression.
1)
30n3
6n6
2)
(y4)(8y5)
3)
(4v9)(3v6)
4)
12b4
2b2
5)
7x5
14x
6)
(10a)(a7)
7)
(4r5)(5r5)
8)
6m2
m6
9)
16z7
8z4
10)
(w3)(w8)
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ES5
Name :
Answer key
Simplifying Expressions: Exponents
Simplify each expression.
1)
30n3
6n6
2)
5
n3
3)
(4v9)(3v6)
8y9
4)
12v15
5)
7x5
14x
(4r5)(5r5)
6)
16z7
8z4
(10a)(a7)
10a8
8)
6m2
m6
6
m4
20r10
9)
12b4
2b2
6b2
1 x4
2
7)
(y4)(8y5)
10)
2z3
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(w3)(w8)
w11
ES5
Name :
Evaluate the Expressions: Multi-variables
MS1
Evaluate the algebraic expressions for the given values of each variable.
1)
2c – d at c = 6, d = –3
2)
xz at x = 5, y = 2 , z = 4
y
3)
m2 + n at m = 2, n = 7
4)
p + q + r at p = 3, q = –8, r = 1
5)
xyz at x = –1, y = 4, z = 2
6)
uv2 at u = 3, v = 2
7)
ab + c at a = 2, b = 5, c = 4
8)
r
s – 1 at r = –10, s = 2
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Name :
Answer key
Evaluate the Expressions: Multi-variables
MS1
Evaluate the algebraic expressions for the given values of each variable.
1)
2c – d at c = 6, d = –3
2)
15
3)
m2 + n at m = 2, n = 7
10
4)
11
5)
xyz at x = –1, y = 4, z = 2
ab + c at a = 2, b = 5, c = 4
p + q + r at p = 3, q = –8, r = 1
–4
6)
–8
7)
xz at x = 5, y = 2 , z = 4
y
uv2 at u = 3, v = 2
12
8)
14
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r
s – 1 at r = –10, s = 2
–6
Name :
Evaluate the Expressions: Multi-variables
MS2
Evaluate the algebraic expressions for the given values of each variable.
1)
uvw at u = 3, v = –2, w = 1
2)
pr – s at p = 8, r = 1, s = 4
3)
4a + b at a = –1, b = 5
4)
xyz
at x = 3, y = –1, z = 2
y2
5)
5s – t at s = 3, t = 1
6)
b + c + d at b = 5, c = 3, d = 2
7)
g2 + f at f = –8, g = 2
8)
m–n
at m = 5, n = 9
2
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Name :
Answer key
Evaluate the Expressions: Multi-variables
MS2
Evaluate the algebraic expressions for the given values of each variable.
1)
uvw at u = 3, v = –2, w = 1
2)
–6
3)
4a + b at a = –1, b = 5
4
4)
1
5)
5s – t at s = 3, t = 1
g2 + f at f = –8, g = 2
xyz
at x = 3, y = –1, z = 2
y2
–6
6)
14
7)
pr – s at p = 8, r = 1, s = 4
b + c + d at b = 5, c = 3, d = 2
10
8)
–4
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m–n
at m = 5, n = 9
2
–2
Name :
Evaluate the Expressions: Multi-variables
Evaluate the algebraic expressions for the given values of each variable.
1)
z – xy at x = 3, y = 1, z = –2
2)
a + b at a = 5, b = 1
3b
3)
pq
at p = 4, q = 5
2
4)
3uv at u = –3, v = 2
5)
mn2 at m = –3, n = –2
6)
3s – t at s = 7, t = 5
7)
b + c – d at b = –2, c = 10, d = 1
8)
x – 5y at x = 2, y = 3
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MS3
Name :
Answer key
Evaluate the Expressions: Multi-variables
Evaluate the algebraic expressions for the given values of each variable.
1)
z – xy at x = 3, y = 1, z = –2
2)
–5
3)
pq
at p = 4, q = 5
2
2
4)
10
5)
mn2 at m = –3, n = –2
b + c – d at b = –2, c = 10, d = 1
3uv at u = –3, v = 2
–18
6)
–12
7)
a + b at a = 5, b = 1
3b
3s – t at s = 7, t = 5
16
8)
7
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x – 5y at x = 2, y = 3
–13
MS3
Name :
Evaluate the Expressions: Multi-variables
MS4
Evaluate the algebraic expressions for the given values of each variable.
1)
pq² at p = –4, q = –2
2)
rst
at r = 3, s = 2, t = 8
8
3)
x + y + z at x = 10, y = 3, z = 6
4)
5f – g at f = 5, g = 7
5)
vw
+ w at v = 10, w = 4
v–5
6)
abc at a = 3, b = 4, c = –1
7)
m – 9n at m = 10, n = 1
8)
u – vw at u = –2, v = 3, w = 5
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Name :
Answer key
MS4
Evaluate the algebraic expressions for the given values of each variable.
1)
pq² at p = –4, q = –2
2)
–16
3)
x + y + z at x = 10, y = 3, z = 6
6
4)
vw
+ w at v = 10, w = 4
v–5
6)
12
7)
m – 9n at m = 10, n = 1
5f – g at f = 5, g = 7
18
19
5)
rst
at r = 3, s = 2, t = 8
8
abc at a = 3, b = 4, c = –1
–12
8)
1
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u – vw at u = –2, v = 3, w = 5
–17
Name :
Evaluate the Expressions: Multi-variables
MS5
Evaluate the algebraic expressions for the given values of each variable.
1)
a
– 8 at a = 10, b = 5
b
2)
2m – n at m = 8, n = 4
3)
pq + r at p = –6, q = 1, r = 3
4)
vwx at v = 5, w = 4, x = 1
5)
x – 8y at x = –7, y = 2
6)
f–g
9
7)
9s
– s² + r at r = 9, s = 5
r
8)
t + u + v at t = 3, u = 6, v = –4
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at f = 6, g = –3
Name :
Answer key
MS5
Evaluate the algebraic expressions for the given values of each variable.
1)
a
– 8 at a = 10, b = 5
b
2)
–6
3)
pq + r at p = –6, q = 1, r = 3
12
4)
x – 8y at x = –7, y = 2
6)
–23
7)
9s
– s² + r at r = 9, s = 5
r
vwx at v = 5, w = 4, x = 1
20
–3
5)
2m – n at m = 8, n = 4
f–g
9
at f = 6, g = –3
1
8)
–11
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t + u + v at t = 3, u = 6, v = –4
5
Name :
Multi Variables: S1
Algebra: Measurement
Find the measurement.
g = 2, h = –3
2)
a = 3, b = 6
3)
p = 7, q = –2, r = –8
qr–p
4a–b
h2–1
1)
3g
4)
p–5
Base
=
Radius
=
Radius
=
Height
=
Diameter =
Height
=
x = 2, y = –1, z = 1
5)
u = 1, v = 2, w = 3
6)
c = –2, d = 3
2+3d
w+2
x(y4+2z)
uv+9
Length
=
Radius
=
Diameter =
Width
=
Height
=
f = –6, g = –3
fg–4
8)
p = –1, q = 1, r = 5, s = 2
9)
u = 7, v = 2, w = –1
v3–2
7)
=
s2
Radius
c4–6
uv+w
pq+rs
Radius
=
Diameter =
Base
=
Length
=
Height
=
Width
=
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Name :
Answer key
Multi Variables: S1
Algebra: Measurement
Find the measurement.
g = 2, h = –3
2)
a = 3, b = 6
3)
p = 7, q = –2, r = –8
qr–p
4a–b
h2–1
1)
3g
4)
p–5
Base
=
6 units
Radius
6 units
Radius
=
2 units
Height
=
8 units
Diameter = 12 units
Height
=
9 units
x = 2, y = –1, z = 1
5)
=
u = 1, v = 2, w = 3
6)
c = –2, d = 3
2+3d
w+2
x(y4+2z)
uv+9
7)
=
3 units
Length
= 11 units
Radius
=
Diameter =
6 units
Width
=
Height
= 11 units
f = –6, g = –3
8)
p = –1, q = 1, r = 5, s = 2
9)
u = 7, v = 2, w = –1
s2
fg–4
5 units
uv+w
pq+rs
Radius
=
7 units
Diameter = 14 units
5 units
v3–2
Radius
c4–6
Base
=
9 units
Length
= 13 units
Height
=
4 units
Width
=
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6 units
Name :
Multi Variables: S2
Algebra: Measurement
Find the measurement.
1)
a = 2, b = –3, c = 1, d = 3
2)
s = –1, t = 1
3)
m = 2, n = –1
st+7
c5+6
m3+n2+1
ab+2d2
Length
=
Radius
=
Radius
Width
=
Height
=
Diameter =
5)
g = 1, h = 4
6) w = 1, x = 3, y = –1, z = 2
h–g
v2+u+w
2x2–z2+y
Base
=
Radius
=
Length
=
Height
=
Diameter =
Width
=
8)
f = –2, g = 2, h = 3
9)
p = 5, q = –3
2h+3g
s = 5, t = 3
2s–1
7)
=
w+7
u = 4, v = –2, w = 2
u2–11
4)
s2+t
s+t
p2–q2
f2+1
Diameter =
Base
=
Radius
Height
Height
=
Diameter =
=
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=
Name :
Answer key
Multi Variables: S2
Algebra: Measurement
Find the measurement.
1)
a = 2, b = –3, c = 1, d = 3
2)
s = –1, t = 1
3)
m = 2, n = –1
st+7
c5+6
m3+n2+1
ab+2d2
Length
= 12 units
Radius
=
2 units
Radius
Width
=
Height
=
6 units
Diameter = 10 units
u = 4, v = –2, w = 2
5)
g = 1, h = 4
5 units
6) w = 1, x = 3, y = –1, z = 2
h–g
v2+u+w
2x2–z2+y
Base
= 10 units
Radius
=
3 units
Length
= 13 units
Height
=
Diameter =
6 units
Width
=
5 units
s = 5, t = 3
f = –2, g = 2, h = 3
s+t
8 units
p = 5, q = –3
p2–q2
f2+1
Diameter =
8 units
Base
=
Height
9 units
Height
= 12 units
=
9)
2h+3g
8)
2s–1
7)
=
w+7
7 units
u2–11
4)
s2+t
5 units
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Radius
=
8 units
Diameter = 16 units
Name :
Multi Variables: S3
Algebra: Measurement
Find the measurement.
x = 1, y = 2, z = 3
2)
3)
g = 6, h = 2
t+3
2(yz+x)
s = –2, t = 1, u = –1, v = 2
2g
1)
s3u+v2
(h+1)2
Radius
=
Diameter =
p = 3, q = –5, r = 1
5)
=
Base
=
Height
=
Height
=
u = 9, v = –3
v2
q2–4p
u–6
Length
=
Radius
=
Radius
Width
=
Height
=
Diameter =
8)
m = 3, n = 2
mn–1
9)
=
s = 4, t = 2, u = 3
tu
w = –3, x = 2, y = –2, z = 1
7x–1
7)
6) a = 2, b = –1, c = 1
3a–b2–c3
r–q+1
4)
Base
st+2u
wy+z
Radius
=
Radius
=
Height
=
Diameter =
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Base
=
Height
=
Name :
Answer key
Multi Variables: S3
Algebra: Measurement
Find the measurement.
x = 1, y = 2, z = 3
2)
3)
g = 6, h = 2
t+3
2(yz+x)
s = –2, t = 1, u = –1, v = 2
2g
1)
s3u+v2
(h+1)2
Radius
=
7 units
Diameter = 14 units
p = 3, q = –5, r = 1
5)
= 12 units
Base
=
Height
=
Height
= 12 units
9 units
6) a = 2, b = –1, c = 1
3a–b2–c3
v2
q2–4p
u–6
Length
= 13 units
Radius
=
3 units
Radius
=
4 units
Width
=
Height
=
9 units
Diameter =
8 units
w = –3, x = 2, y = –2, z = 1
8)
m = 3, n = 2
9)
mn–1
s = 4, t = 2, u = 3
tu
7 units
7x–1
7)
4 units
u = 9, v = –3
r–q+1
4)
Base
st+2u
wy+z
Radius
=
Height
= 13 units
7 units
Radius
=
5 units
Diameter = 10 units
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Base
= 14 units
Height
=
6 units
Name :
Multi Variables: S4
Find the measurement.
2) x = 2, y = 3
3) u = 4, v = –3
uv+2v²
4y
2p+5
1) p = 1, q = –2, r = 3, s = 2
q²r+sp²
2x2–y
Base
=
Height
=
Height
=
Diameter =
Radius
Diameter =
5) r = 2, s = 3,t = 5
6) v = –2, w = 1, x = 3
r4–t
ab
v2
4) a = –5, b = –3
=
w(x2–vx+1)
a²–b²–7
8–sr
Height
=
Radius
=
Base
=
Base
=
Height
=
Height
=
8) p = 3, q = 4
9) a = 1, b = 3, c = –5
a2(b2+2b+c)
pq–2
t4+us
7) s = 1, t = –1, u = 3
s2t+9
p2+4
Length
=
Height
=
Radius
Width
=
Radius
=
Diameter =
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=
Name :
Answer key
Algebra: Measurement
Multi Variables: S4
Find the measurement.
2) x = 2, y = 3
3) u = 4, v = –3
uv+2v²
4y
2p+5
1) p = 1, q = –2, r = 3, s = 2
q²r+sp²
2x2–y
Base
= 14 units
Height
Height
=
Diameter =
7 units
= 12 units
5 units
5) r = 2, s = 3,t = 5
=
3 units
Diameter =
6 units
6) v = –2, w = 1, x = 3
r4–t
ab
v2
4) a = –5, b = –3
Radius
w(x2–vx+1)
a²–b²–7
8–sr
Height
= 15 units
Radius
=
Base
=
Height
= 11 units
9 units
2 units
8) p = 3, q = 4
= 16 units
Height
=
4 units
9) a = 1, b = 3, c = –5
a2(b2+2b+c)
pq–2
t4+us
7) s = 1, t = –1, u = 3
Base
s2t+9
p2+4
Length
=
8 units
Height
= 10 units
Radius
Width
=
4 units
Radius
= 13 units
Diameter = 10 units
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=
5 units
Name :
Algebra: Measurement
Multi Variables: S5
Find the measurement.
2) m = –3, n = 2
u3–2s+3
4u+v
3) s = 4, t = 3, u = 2
m2n–1
1) u = 1, v = 5
st–4
(m+1)²
Diameter =
=
Length
=
Base
=
Width
=
5) a = 3, b = 5
f 3–1
4) f = 2, g = –4, h = –2
Height
6) x = –1 y = 4
(x2+1)²
=
ab–5
Radius
b2–a2
2(xy+5)
gh
Height
=
Base
=
Height
=
Radius
=
Height
=
Base
=
8) b = –1, c = 2, d = – 3
9) w = 4, x = 2, y = –1
b4(c2d+26)
x2w– 4
mn–n2
7) m = 7, n =3
mn–8
wx–y
Radius
=
Diameter =
Height
=
Radius
=
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Height
=
Diameter =
Name :
Answer key
Algebra: Measurement
Multi Variables: S5
Find the measurement.
2) m = –3, n = 2
u3–2s+3
4u+v
3) s = 4, t = 3, u = 2
m2n–1
1) u = 1, v = 5
st–4
(m+1)²
9 units
Diameter = 18 units
= 17 units
Length
=
8 units
Base
=
Width
=
3 units
4 units
5) a = 3, b = 5
f 3–1
4) f = 2, g = –4, h = –2
Height
6) x = –1 y = 4
(x2+1)²
=
ab–5
Radius
b2–a2
2(xy+5)
gh
Height
=
7 units
Base
= 16 units
Height
=
4 units
Radius
=
8 units
Height
= 10 units
Base
=
2 units
8) b = –1, c = 2, d = – 3
9) w = 4, x = 2, y = –1
b4(c2d+26)
x2w– 4
mn–n2
7) m = 7, n =3
mn–8
wx–y
Radius
= 13 units
Diameter = 14 units
Height
= 12 units
Radius
=
7 units
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Height
= 12 units
Diameter =
9 units
Name :
Fractions: S1
Evaluating Exponents
Evaluate each expression.
1) 1
3
3
.
6
5
2
2) 2
5
6
÷ 5
4
–3
4) 1
2
–4
1
9
–3
5) – 1
4
7
5
–6
8) 5 + – 1
2
2
–
7
7) 2 ÷ 7
7
4
–3
2
–2
10) 4 . – 1 ÷ 9
8
9
4
. –4 ÷ 1
3
3
2
11) 4
7
5
.
7
8
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2
5
9
. –1
3
3) – 5 + 7
3
3
4
6) – 2
3
.
3
7
4
–8
–3
–2
–4
9) 1 – 1 ÷ 7
6
6
3
4
3
2
12) – 2 + – 1
5
5
Answer key
Name :
Fractions: S1
Evaluating Exponents
Evaluate each expression.
1) 1
3
3
.
2
6
5
2) 2
5
6
÷ 5
4
–4
–
1
9
–3
5) – 1
4
7
7
–6
–3
2
–2
10) 4 . – 1 ÷ 9
8
9
4
144
5
. –4 ÷ 1
3
3
2
3
23
or 5
4
4
11) 4
7
5
.
7
8
4
1
28
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.
3
7
4
4
6) – 2
3
−
9
. –1
3
–8
2
512
or −170
3
3
–3
–2
–4
9) 1 – 1 ÷ 7
6
6
3
8) 5 + – 1
2
2
1
224
5
1
46
or 5
9
9
1
48
−713
7) 2 ÷ 7
7
4
2
3) – 5 + 7
3
3
1
125
4
75
4) 1
2
–3
–213
3
2
12) – 2 + – 1
5
5
−
3
125
Name :
Fractions: S2
Evaluating Exponents
Evaluate each expression.
–2
+ 4
3
3
. 3
4
2) 4
7
1
7
–4
3) 5 ÷ 6
3
5
4) – 4 . – 2
9
9
7
–8
5) 1 – 7
2
2
2
1) – 3
5
4
.
3
3
–2
7) 1 – 3
3
2
–2
5
–5
8) 1 – – 5 . 5
3
5
6
–6
7
6
1
6
2
.
10)
÷
6
7
7
11) 3 ÷ 1
8
8
3
Printable Worksheets @ www.mathworksheets4kids.com
2
6
–6
6) – 1
7
7
. –7 ÷ 1
5
5
9) – 1
2
–5
9
–4
+ 1
4
3
2
1
5
12)
+ –
2
4
8
Answer key
Name :
Fractions: S2
Evaluating Exponents
Evaluate each expression.
1) – 3
5
–2
+ 4
3
3
. 3
4
2) 4
7
4
5
41
or 4
9
9
7
4) – 4 . – 2
9
9
–8
−576
3
–2
7) 1 – 3
3
2
−
224
2
or 74
3
3
1
7
–4
6
3) 5 ÷ 6
3
5
256
3
5) 1 – 7
2
2
−
2
–2
5
–5
8) 1 – – 5 . 5
3
5
6
–6
64
6) – 1
7
1
97
or −12
8
8
11
27
–6
7
6
1
6
2
.
10)
÷
6
7
7
.
7
9
. –7 ÷ 1
5
5
4
49
or 9
5
5
9) – 1
2
–5
–4
+ 1
4
57
224
2
3
2
1
5
12)
+ –
2
4
3
11) 3 ÷ 1
8
8
27
3
or 3
8
8
Printable Worksheets @ www.mathworksheets4kids.com
23
7
or 1
16
16
8
Name :
Fractions: S3
Evaluating Exponents
Evaluate each expression.
3
2
. –5
6
–5
2
–4
5) – 1 + – 7
3
3
2
5
–2
3
7) 2 ÷ 1 . 3
9
3
2
–2
8) 3 .
8
6
7
10) 2 ÷ 1
7
7
4
3
11) 3 + – 1
2
4
1) 2 – 3
5
5
4) – 1 + 3
5
2
2) – 1
6
. 6
5
4
4
–7
. 4
3
–6
3
6) 9 ÷ 2
2
3
5
–5
8 –2
3
2
3
9) 5 – 1
4
4
Printable Worksheets @ www.mathworksheets4kids.com
÷ 1
5
6
3) 1
4
–2
3
2
12) 8 . – 8 – 1
3
5
3
Answer key
Name :
Fractions: S3
Evaluating Exponents
Evaluate each expression.
3
1) 2 – 3
5
5
−
2
2
2) – 1
6
4
. –5
6
37
125
4) – 1 + 3
5
2
–4
. 6
5
4
5
–2
3
7) 2 ÷ 1 . 3
9
3
2
32
5
or 1
27
27
448
÷ 1
5
6
3) 1
4
–7
. 4
3
−30
65
1
or 16
4
4
6
7
10) 2 ÷ 1
7
7
–5
2
5) – 1 + – 7
3
3
−
2,916
3
16
340
or −12
27
27
–2
8) 3 .
8
8 –2
3
1
4
3
11) 3 + – 1
2
4
31
64
Printable Worksheets @ www.mathworksheets4kids.com
–6
5
6) 9 ÷ 2
2
3
–5
243
2
3
9) 5 – 1
4
4
35
99
or 1
64
64
–2
3
2
12) 8 . – 8 – 1
3
5
3
20
74
or 2
27
27
Name :
Example:
Find the slope of a line passing through the points (4, 8) and (3, –2).
Slope = m =
=
y2 – y1
x2 – x1
–2 – 8
= –10 = 10
–1
3–4
Use two-point formula method to find the slope of a line passing through the given
points.
1)
(–4, 2) and (5, 6)
2)
Slope =
Slope =
3)
(2, 1) and (3, –10)
4)
Slope =
5)
(7, 1) and (–2, 3)
(–8, –5) and (–7, –4)
(3, 9) and (1, 8)
Slope =
6)
(0, –2) and (–6, 4)
Slope =
Slope =
7)
(5, –5) and (7, 3)
8)
Slope =
Printable Math Worksheets @ www.mathworksheets4kids.com
(9, 8) and (5, 1)
Slope =
Name :
Answer key
Example:
Find the slope of a line passing through the points (4, 8) and (3, –2).
Slope = m =
=
y2 – y1
x2 – x1
–2 – 8
= –10 = 10
–1
3–4
Use two-point formula method to find the slope of a line passing through the given
points.
1)
(–4, 2) and (5, 6)
Slope =
3)
5)
Slope =
4)
6)
1
Printable Math Worksheets @ www.mathworksheets4kids.com
1
2
(0, –2) and (–6, 4)
Slope =
8)
4
(3, 9) and (1, 8)
Slope =
–2
9
(–8, –5) and (–7, –4)
(5, –5) and (7, 3)
Slope =
–11
(7, 1) and (–2, 3)
Slope =
7)
4
9
(2, 1) and (3, –10)
Slope =
2)
–1
(9, 8) and (5, 1)
Slope =
7
4
Name :
Example:
Find the slope of a line passing through the points (–6, 1) and (–4, –5).
Slope = m =
=
y2 – y1
x2 – x1
–5 – 1
= –6 = –3
2
–4 + 6
Use two-point formula method to find the slope of a line passing through the given
points.
1)
(–9, –6) and (–2, –8)
2)
Slope =
3)
(2, 3) and (–8, 0)
Slope =
4)
Slope =
5)
(5, 1) and (7, –3)
(–9, 2) and (1, 10)
(3, 4) and (5, 6)
Slope =
6)
(2, –3) and (4, 8)
Slope =
Slope =
7)
(–6, 2) and (3, 1)
8)
Slope =
Printable Math Worksheets @ www.mathworksheets4kids.com
(–3, 10) and (0, –2)
Slope =
Name :
Answer key
Example:
Find the slope of a line passing through the points (–6, 1) and (–4, –5).
Slope = m =
=
y2 – y1
x2 – x1
–5 – 1
= –6 = –3
2
–4 + 6
Use two-point formula method to find the slope of a line passing through the given
points.
1)
(–9, –6) and (–2, –8)
Slope =
3)
5)
Slope =
4)
6)
4
5
Printable Math Worksheets @ www.mathworksheets4kids.com
1
(2, –3) and (4, 8)
Slope =
8)
–1
9
(3, 4) and (5, 6)
Slope =
–2
(–9, 2) and (1, 10)
(–6, 2) and (3, 1)
Slope =
3
10
(5, 1) and (7, –3)
Slope =
7)
–2
7
(2, 3) and (–8, 0)
Slope =
2)
11
2
(–3, 10) and (0, –2)
Slope =
–4
Name :
Example:
Find the slope of a line passing through the points (6, 3) and (9, 1).
Slope = m =
=
y2 – y1
x2 – x1
1–3
= –2
3
9–6
Use two-point formula method to find the slope of a line passing through the given
points.
1)
(1, 4) and (3, 2)
2)
Slope =
Slope =
3)
(–5, 3) and (2, 7)
4)
Slope =
5)
(8, 7) and (4, 1)
(6, –7) and (5, 9)
(3, –4) and (–2, 8)
Slope =
6)
(–7, –10) and (–5, –4)
Slope =
Slope =
7)
(2, 5) and (4, –7)
8)
Slope =
Printable Math Worksheets @ www.mathworksheets4kids.com
(1, –8) and (6, –2)
Slope =
Name :
Answer key
Example:
Find the slope of a line passing through the points (6, 3) and (9, 1).
Slope = m =
=
y2 – y1
x2 – x1
1–3
= –2
3
9–6
Use two-point formula method to find the slope of a line passing through the given
points.
1)
(1, 4) and (3, 2)
Slope =
3)
5)
Slope =
7)
6)
–16
Printable Math Worksheets @ www.mathworksheets4kids.com
–
12
5
(–7, –10) and (–5, –4)
Slope =
8)
–6
(3, –4) and (–2, 8)
Slope =
3
2
(6, –7) and (5, 9)
Slope =
4)
4
7
(8, 7) and (4, 1)
(2, 5) and (4, –7)
Slope =
–1
(–5, 3) and (2, 7)
Slope =
2)
3
(1, –8) and (6, –2)
Slope =
6
5
Name :
Example:
Find the slope of a line passing through the points (2, 1) and (6, 4).
Slope = m =
=
y2 – y1
x2 – x1
4–1
= 3
4
6–2
Use two-point formula method to find the slope of a line passing through the given
points.
1)
(5, –2) and (4, –8)
2)
Slope =
Slope =
3)
(–3, 9) and (–2, 5)
4)
Slope =
5)
(6, 8) and (3, 7)
(8, 7) and (–1, 2)
(–6, –8) and (–4, –1)
Slope =
6)
(–1, 2) and (9, –5)
Slope =
Slope =
7)
(9, –3) and (–7, 6)
8)
Slope =
Printable Math Worksheets @ www.mathworksheets4kids.com
(–4, 6) and (5, 7)
Slope =
Name :
Answer key
Example:
Find the slope of a line passing through the points (2, 1) and (6, 4).
Slope = m =
=
y2 – y1
x2 – x1
4–1
= 3
4
6–2
Use two-point formula method to find the slope of a line passing through the given
points.
1)
(5, –2) and (4, –8)
Slope =
3)
5)
Slope =
7)
9
16
–
(–6, –8) and (–4, –1)
7
2
Slope =
6)
1
3
(8, 7) and (–1, 2)
Slope =
4)
–4
(6, 8) and (3, 7)
(9, –3) and (–7, 6)
Slope =
6
(–3, 9) and (–2, 5)
Slope =
2)
(–1, 2) and (9, –5)
Slope =
8)
5
9
Printable Math Worksheets @ www.mathworksheets4kids.com
–
7
10
(–4, 6) and (5, 7)
Slope =
1
9
Name :
Example:
Find the slope of a line passing through the points (–5, 0) and (–1, –2).
Slope = m =
=
y2 – y1
x2 – x1
–2 – 0
= –2 = – 1
4
2
–1 + 5
Use two-point formula method to find the slope of a line passing through the given
points.
1)
(9, 1) and (7, 6)
2)
Slope =
3)
(–4, –6) and (8, –9)
Slope =
4)
Slope =
5)
(2, –5) and (9, 4)
(–7, 3) and (5, 1)
(5, –7) and (–1, 3)
Slope =
6)
(8, 1) and (3, –7)
Slope =
Slope =
7)
(–3, –4) and (–2, –8)
8)
Slope =
Printable Math Worksheets @ www.mathworksheets4kids.com
(–2, –9) and (6, 4)
Slope =
Name :
Answer key
Example:
Find the slope of a line passing through the points (–5, 0) and (–1, –2).
Slope = m =
=
y2 – y1
x2 – x1
–2 – 0
= –2 = – 1
4
2
–1 + 5
Use two-point formula method to find the slope of a line passing through the given
points.
1)
(9, 1) and (7, 6)
Slope =
3)
5)
Slope =
4)
6)
–1
6
Printable Math Worksheets @ www.mathworksheets4kids.com
–5
3
(8, 1) and (3, –7)
Slope =
8)
–4
(5, –7) and (–1, 3)
Slope =
9
7
(–7, 3) and (5, 1)
(–3, –4) and (–2, –8)
Slope =
–1
4
(2, –5) and (9, 4)
Slope =
7)
–5
2
(–4, –6) and (8, –9)
Slope =
2)
8
5
(–2, –9) and (6, 4)
Slope =
13
8
Name :
Score :
Sheet 1
Write each equation in standard form.
1)
8x = –5y + 3
2)
19x = y
3)
y=– 9 x–4
11
4)
15 y – 1 = x
3
5)
x+2=
7 – 3y
6
6)
20x – 28 = 4y
7)
x = 13 y – 1
9
2
8)
2x – y = 1
3 15 3
9)
y
1=–x +
9 7
10)
y – 5 = –(x + 11) + 2
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Answer key
Sheet 1
Write each equation in standard form.
1)
8x = –5y + 3
2)
8x + 5y = 3
3)
y=– 9 x–4
11
19x – y = 0
4)
x+2=
7 – 3y
6
6)
6x + 3y = –5
7)
x = 13 y – 1
9
2
y
1=–x +
9 7
20x – 28 = 4y
5x – y = 7
8)
18x – 26y = –9
9)
15 y – 1 = x
3
x – 15y = –5
9x + 11y = –44
5)
19x = y
2x – y = 1
3 15 3
10x – y = 5
10)
7x – 9y = –63
Printable Math Worksheets @ www.mathworksheets4kids.com
y – 5 = –(x + 11) + 2
x + y = –4
Name :
Score :
Sheet 2
Write each equation in standard form.
2 – 4y
8
1)
y = – 5 (x + 3) + 4
6
2)
2x =
3)
21y = –19x + 5
4)
4 = 11 x – y
2
5)
x = – 3 y – 12
4
6)
6x – 17 = 13y
7)
x + y =1
5 10
8)
7(x – 6) = y
9)
y + 3 = –8x + 7
10)
4x = 9y + 1
3
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Answer key
Sheet 2
Write each equation in standard form.
1)
y = – 5 (x + 3) + 4
6
2)
21y = –19x + 5
4)
x = – 3 y – 12
4
6)
4x + 3y = –48
7)
x + y =1
5 10
y + 3 = –8x + 7
6x – 17 = 13y
6x – 13y = 17
8)
2x + y = 10
9)
4 = 11 x – y
2
11x – 2y = 8
19x + 21y = 5
5)
2 – 4y
8
8x + 2y = 1
5x + 6y = 9
3)
2x =
7(x – 6) = y
7x – y = 42
10)
8x + y = 4
Printable Math Worksheets @ www.mathworksheets4kids.com
4x = 9y + 1
3
12x – 27y = 1
Name :
Score :
Sheet 3
Write each equation in standard form.
1)
5y = –11 x + 1
6
18
2)
16 2y + 1 = x
4
3)
7x – 5 = 2y + 10
4)
3x – 2 = y – 7
5
5)
2y
–1 = – 3x +
3
2
6)
45x = 3y + 30
7)
63x – 9 = 18y
8)
6x = 4 y
3
9)
2x =
4y – 5
6
10)
3y = 7 x + 10
12
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Answer key
Sheet 3
Write each equation in standard form.
1)
5y = –11 x + 1
6
18
2)
33x + 90y = 1
3)
7x – 5 = 2y + 10
x – 32y = 4
4)
7x – 2y = 15
5)
2y
–1 = – 3x +
3
2
63x – 9 = 18y
6)
2x =
4y – 5
6
45x = 3y + 30
15x – y = 10
8)
6x = 4 y
3
18x – 4y = 0
7x – 2y = 1
9)
3x – 2 = y – 7
5
15x – 5y = –33
9x – 4y = 6
7)
16 2y + 1 = x
4
10)
12x – 4y = –5
Printable Math Worksheets @ www.mathworksheets4kids.com
3y = 7 x + 10
12
7x – 36y = –120
Name :
Score :
Sheet 4
Write each equation in standard form.
1)
x = – 2 y – 14
5
2)
8x – 16 = 10y
3)
x + y =2
2 10
4)
9(x – 1) = y
5)
y + 8 = –3x + 19
6)
x = 7y + 1
4
7)
y = – 7 (x + 1) + 4
9
8)
3x =
9)
2y = –25x + 17
10)
4 = 19 x – 5y
3
Printable Math Worksheets @ www.mathworksheets4kids.com
6 – 12y
5
Name :
Score :
Answer key
Sheet 4
Write each equation in standard form.
1)
x = – 2 y – 14
5
2)
5x + 2y = –70
3)
x + y =2
2 10
4x – 5y = 8
4)
5x + y = 20
5)
y + 8 = –3x + 19
y = – 7 (x + 1) + 4
9
6)
2y = –25x + 17
x = 7y + 1
4
4x – 28y = 1
8)
7x + 9y = 29
9)
9(x – 1) = y
9x – y = 9
3x + y = 11
7)
8x – 16 = 10y
3x =
6 – 12y
5
5x + 4y = 2
10)
25x + 2y = 17
Printable Math Worksheets @ www.mathworksheets4kids.com
4 = 19 x – 5y
3
19x – 15y = 12
Name :
Score :
Sheet 5
Write each equation in standard form.
1)
y
4=–x +
8 6
2)
y – 7 = –(x + 11) + 3
3)
5x = –2y + 4
4)
14x = 6y
5)
x = 15 y – 1
2
3
6)
4x – y = 1
5 10 2
7)
x+1=
5 – 4y
12
8)
6x – 16 = 7y
9)
y=– 7 x–7
10
10)
18 y – 2 = x
9
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Answer key
Sheet 5
Write each equation in standard form.
1)
y
4=–x +
8 6
2)
x + y = –1
3x – 4y = –96
3)
5x = –2y + 4
4)
x = 15 y – 1
2
3
6)
6x – 45y = –2
7)
x+1=
5 – 4y
12
y=– 7 x–7
10
4x – y = 1
5 10 2
8x – y = 5
8)
12x + 4y = –7
9)
14x = 6y
7x – 3y = 0
5x + 2y = 4
5)
y – 7 = –(x + 11) + 3
6x – 16 = 7y
6x – 7y = 16
10)
7x + 10y = –70
Printable Math Worksheets @ www.mathworksheets4kids.com
18 y – 2 = x
9
x – 18y = –4
Name :
Score :
Sheet 1
Write each equation in slope-intercept form.
1)
3x + 4y = 8
2)
9x + 35 = –5y
3)
2y – 6 = –6x
4)
–11x – 7y = –56
5)
5 y = –(x – 5)
3
6)
–2(2x + y) = 28
7)
–14x + y = 7
8)
12y = 8x – 48
3
9)
3(x – y)
=9
2
10)
2 x + 4(y – 2) = 0
3
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Answer key
Sheet 1
Write each equation in slope-intercept form.
1)
3x + 4y = 8
2)
y=– 3x+2
4
3)
2y – 6 = –6x
y=–9x–7
5
4)
5 y = –(x – 5)
3
6)
y = – 3x + 3
5
7)
–14x + y = 7
3(x – y)
=9
2
–2(2x + y) = 28
y = –2x – 14
8)
12y = 8x – 48
3
y = 2x – 4
9
3
y = 14x + 7
9)
–11x – 7y = –56
y = – 11x + 8
7
y = –3x + 3
5)
9x + 35 = –5y
10)
y=x–6
Printable Math Worksheets @ www.mathworksheets4kids.com
2 x + 4(y – 2) = 0
3
y=–1x+2
6
Name :
Score :
Sheet 2
Write each equation in slope-intercept form.
1)
–5(x + y) = –20
2)
2 x + 2y = 14
7
3)
6 y – 18 = 6x
5
4)
4(x – 10) = –2y
5)
–2x – 3y = 15
6)
6y – 7x = –36
7)
2y =
8)
–3x – y = 12
9)
x = 2y – 8
10)
4x – 7y
=7
9
10(2 + 4x)
2
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Answer key
Sheet 2
Write each equation in slope-intercept form.
1)
–5(x + y) = –20
2)
y=–1x+7
7
y = –x + 4
3)
6 y – 18 = 6x
5
4)
y = 5x + 15
5)
–2x – 3y = 15
2y =
10(2 + 4x)
2
6)
x = 2y – 8
6y – 7x = –36
y= 7 x–6
6
8)
y = 10x + 5
9)
4(x – 10) = –2y
y = –2x + 20
y=–2x–5
3
7)
2 x + 2y = 14
7
–3x – y = 12
y = –3x – 12
10)
y = 1x + 4
2
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4x – 7y
=7
9
y = 4x – 9
7
Name :
Score :
Sheet 3
Write each equation in slope-intercept form.
1)
8x + 3y
=5
–3
2)
x+y=1
3)
–9(y – 2) = –36x
4)
4 y + x = –4
3
5)
2 x – (y + 10) = 0
5
6)
2(2x – y) = 8
7)
–x = 12 – 4y
8)
14 – 2y
= 4x
4
9)
5y = –10x + 5
10)
x – 7y = –28
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Name :
Score :
Answer key
Sheet 3
Write each equation in slope-intercept form.
1)
8x + 3y
=5
–3
2)
y=–8x–5
3
3)
–9(y – 2) = –36x
y = –x + 1
4)
2 x – (y + 10) = 0
5
6)
y = 2 x – 10
5
7)
–x = 12 – 4y
5y = –10x + 5
2(2x – y) = 8
y = 2x – 4
8)
y = 1x + 3
4
9)
4 y + x = –4
3
y=–3x–3
4
y = 4x + 2
5)
x+y=1
14 – 2y
= 4x
4
y = –8x + 7
10)
y = –2x + 1
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x – 7y = –28
y = 1x + 4
7
Name :
Score :
Sheet 4
Write each equation in slope-intercept form.
4 x + 7(y – 3) = 0
1)
2) –18x + y = 6
3
3)
–2x – 8y = –32
4)
5(x – y)
= 10
3
5)
8y = 4x – 32
2
6)
3y – 9 = –5x
7)
–3(3x + y) = 15
8)
7 y = –(2x – 7)
4
9)
6x + 35 = –7y
10)
4x + 3y = 12
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Name :
Score :
Answer key
Sheet 4
Write each equation in slope-intercept form.
4 x + 7(y – 3) = 0
1)
2) –18x + y = 6
3
y=– 4 x+3
21
3)
–2x – 8y = –32
y = 18x + 6
4)
y = – 1x + 4
4
5)
8y = 4x – 32
2
y=x–6
6)
y = 1x – 2
4
7)
–3(3x + y) = 15
6x + 35 = –7y
3y – 9 = –5x
y = –5 x + 3
3
8)
7 y = –(2x – 7)
4
y = – 8x + 4
7
y = –3x – 5
9)
5(x – y)
= 10
3
10)
y = –6x – 5
7
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4x + 3y = 12
y = –4 x + 4
3
Name :
Score :
Sheet 5
Write each equation in slope-intercept form.
3(12 + 5x)
2
1)
2(x – 15) = –3y
2)
9y =
3)
11x – 9y
=9
7
4)
x = 4y – 16
5)
–6x – 8y = 32
6)
2 y – 20 = 12x
3
7)
5 x + 3y = 24
6
8)
–7(x + y) = –35
9)
4y – x = –20
10)
–13x – 5y = 10
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Score :
Answer key
Sheet 5
Write each equation in slope-intercept form.
1)
2(x – 15) = –3y
2)
y = – 2 x + 10
3
3)
11x – 9y
=9
7
–6x – 8y = 32
4)
5 x + 3y = 24
6
6)
4y – x = –20
2 y – 20 = 12x
3
y = 18x + 30
8)
y=– 5 x+8
18
9)
x = 4y – 16
y = 1x + 4
4
y = – 3x – 4
4
7)
3(12 + 5x)
2
y= 5x+2
6
y = 11 x – 7
9
5)
9y =
–7(x + y) = –35
y = –x + 5
10)
y= 1x–5
4
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–13x – 5y = 10
y = – 13 x – 2
5
Name :
Find the Slope
Sheet 1
Find the slope from the given equation.
1)
2x – 4y + 7 = 0
2)
Slope =
3)
15x – 3y = 2
Slope =
4)
–1 = 4x + 14y
6)
Slope =
7)
–8y = –7x + 20
6x = 8y + 10
Slope =
Slope =
5)
9y = –3x + 5
y = 12x – 17
Slope =
8)
Slope =
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6x + 6y + 11 = 0
Slope =
Name :
Answer key
Find the Slope
Sheet 1
Find the slope from the given equation.
1)
2x – 4y + 7 = 0
1
2
Slope =
3)
15x – 3y = 2
Slope =
7)
6)
–2
7
–8y = –7x + 20
Slope =
7
8
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3
4
y = 12x – 17
Slope =
8)
–1
3
6x = 8y + 10
Slope =
5
–1 = 4x + 14y
9y = –3x + 5
Slope =
4)
Slope =
5)
2)
12
6x + 6y + 11 = 0
Slope =
–1
Name :
Find the Slope
Sheet 2
Find the slope from the given equation.
1)
6x = –3y + 7
2)
Slope =
Slope =
3)
–8y = 9x – 1
4)
5 = –y + 7x
6)
Slope =
7)
1 = 3x – 12y
y = –4x + 19
Slope =
Slope =
5)
3x + 5y + 13 = 0
10x – 4y + 14 = 0
Slope =
8)
Slope =
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–6y = –4x + 16
Slope =
Name :
Answer key
Find the Slope
Sheet 2
Find the slope from the given equation.
1)
6x = –3y + 7
Slope =
3)
–9
8
7
Slope =
1
4
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–4
10x – 4y + 14 = 0
Slope =
8)
–3
5
y = –4x + 19
Slope =
6)
1 = 3x – 12y
3x + 5y + 13 = 0
Slope =
4)
5 = –y + 7x
Slope =
7)
–2
–8y = 9x – 1
Slope =
5)
2)
5
2
–6y = –4x + 16
Slope =
2
3
Name :
Find the Slope
Sheet 3
Find the slope from the given equation.
1)
–2y + 17 = 5x
2)
Slope =
3)
y = 13x + 9
Slope =
4)
7y + 6x = 0
6)
Slope =
7)
–5 = 8x – 6y
4x – 2y + 1 = 0
Slope =
Slope =
5)
3x + 4y = –8
9y = –2x + 7
Slope =
8)
Slope =
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15y – 7 = 3x
Slope =
Name :
Answer key
Find the Slope
Sheet 3
Find the slope from the given equation.
1)
–2y + 17 = 5x
Slope =
3)
6)
–6
7
Slope =
4
3
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2
9y = –2x + 7
Slope =
8)
–3
4
4x – 2y + 1 = 0
Slope =
13
–5 = 8x – 6y
3x + 4y = –8
Slope =
4)
7y + 6x = 0
Slope =
7)
–5
2
y = 13x + 9
Slope =
5)
2)
–2
9
15y – 7 = 3x
Slope =
1
5
Name :
Find the Slope
Sheet 4
Find the slope from the given equation.
1)
21x = –3y + 6
2)
Slope =
Slope =
3)
–4y = 18x – 11
4)
8 = –2y + 36x
6)
Slope =
7)
11 = x – 9y
y = –3x + 12
Slope =
Slope =
5)
35x + 42y + 7 = 0
16x – 6y + 24 = 0
Slope =
8)
Slope =
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–14y = –8x + 13
Slope =
Name :
Answer key
Find the Slope
Sheet 4
Find the slope from the given equation.
1)
21x = –3y + 6
Slope =
3)
Slope =
4)
18
1
9
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–3
16x – 6y + 24 = 0
Slope =
8)
–5
6
y = –3x + 12
Slope =
6)
11 = x – 9y
35x + 42y + 7 = 0
Slope =
–9
2
8 = –2y + 36x
Slope =
7)
–7
–4y = 18x – 11
Slope =
5)
2)
8
3
–14y = –8x + 13
Slope =
4
7
Name :
Find the Slope
Sheet 5
Find the slope from the given equation.
1)
8x – 7y + 5 = 0
2)
Slope =
3)
24x – 4y = 19
Slope =
4)
–17 = 4x + 9y
6)
Slope =
7)
–2y = –7x – 18
x = 3y + 7
Slope =
Slope =
5)
5y = –2x + 3
9y = 72x – 14
Slope =
8)
Slope =
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11x + y = 23
Slope =
Name :
Answer key
Find the Slope
Sheet 5
Find the slope from the given equation.
1)
8x – 7y + 5 = 0
8
7
Slope =
3)
24x – 4y = 19
Slope =
5)
7)
Slope =
–2
5
x = 3y + 7
1
3
Slope =
6
6)
–4
9
–2y = –7x – 18
5y = –2x + 3
Slope =
4)
–17 = 4x + 9y
Slope =
2)
9y = 72x – 14
Slope =
8)
7
2
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8
11x + y = 23
Slope =
–11
Score :
Name :
Equation of a Line
L1S1
Part - A
Find the equation of the line passing through the given points. Express the equation in standard form.
1)
(1, –6) and (–7, 2)
2)
(4, 5) and (–3, –1)
3)
(–7, –9) and (–3, –4)
4)
(2, –8) and (–6, –3)
5)
(–9, 6) and (0, 3)
6)
(3, 0) and (7, 1)
7)
(8, 5) and (6, –7)
8)
(2, 1) and (–4, –2)
Part - B
1)
Find the equation of the line passing through the points (–5, –8) and (6, –4).
2)
A line cuts the y-axis at (0, –6) and passes through the point (9, –3). Find the equation of the line.
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Answer key
Name :
Score :
Equation of a Line
L1S1
Part - A
Find the equation of the line passing through the given points. Express the equation in standard form.
1)
2)
(1, –6) and (–7, 2)
x + y = –5
3)
6x – 7y = –11
(–7, –9) and (–3, –4)
4)
(–9, 6) and (0, 3)
6)
(3, 0) and (7, 1)
x – 4y = 3
x + 3y = 9
7)
(2, –8) and (–6, –3)
5x + 8y = –54
5x – 4y = 1
5)
(4, 5) and (–3, –1)
8)
(8, 5) and (6, –7)
6x – y = 43
(2, 1) and (–4, –2)
x – 2y = 0
Part - B
1)
Find the equation of the line passing through the points (–5, –8) and (6, –4).
4x – 11y = 68
2)
A line cuts the y-axis at (0, –6) and passes through the point (9, –3). Find the equation of the line.
x – 3y = 18
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Score :
Equation of a Line
L1S2
Part - A
Find the equation of the line passing through the given points. Express the equation in standard form.
1)
(8, –1) and (–5, 6)
2)
(4, 2) and (4, 3)
3)
(–1, 0) and (–6, 9)
4)
(–5, –8) and (–9, –6)
5)
(4, 2) and (1, –7)
6)
(–9, –3) and (3, 0)
7)
(–4, 3) and (5, 2)
8)
(8, 0) and (–1, –4)
Part - B
1)
A line cuts the x-axis at x = 6 and passes through the point (–7, 1). Find the equation of the line.
2)
Find the equation of the line passing through the points (–1, –5) and (5, 6).
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Answer key
Name :
Score :
Equation of a Line
L1S2
Part - A
Find the equation of the line passing through the given points. Express the equation in standard form.
1)
2)
(8, –1) and (–5, 6)
7x + 13y = 43
3)
x=4
4)
(–1, 0) and (–6, 9)
6)
(4, 2) and (1, –7)
(–9, –3) and (3, 0)
x – 4y = 3
3x – y = 10
7)
(–5, –8) and (–9, –6)
x + 2y = –21
9x + 5y = –9
5)
(4, 2) and (4, 3)
8)
(–4, 3) and (5, 2)
x + 9y = 23
(8, 0) and (–1, –4)
4x – 9y = 32
Part - B
1)
A line cuts the x-axis at x = 6 and passes through the point (–7, 1). Find the equation of the line.
x + 13y = 6
2)
Find the equation of the line passing through the points (–1, –5) and (5, 6).
11x – 6y = 19
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Score :
Equation of a Line
L1S3
Part - A
Find the equation of the line passing through the given points. Express the equation in standard form.
1)
(–1, 1) and (–3, –7)
2)
(9, 4) and (–7, 0)
3)
(–8, 2) and (–2, –5)
4)
(–5, 3) and (–4, 6)
5)
(3, 1) and (1, 8)
6)
(–7, 9) and (0, 9)
7)
(–4, 8) and (–8, 2)
8)
(–6, –2) and (–5, –9)
Part - B
1)
A line cuts the y-axis at (0, 1) and passes through the point (3, –2). Find the equation of the line.
2)
Find the equation of the line passing through the points (–7, 3) and (9, –6).
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Answer key
Name :
Score :
Equation of a Line
L1S3
Part - A
Find the equation of the line passing through the given points. Express the equation in standard form.
1)
2)
(–1, 1) and (–3, –7)
4x – y = –5
3)
x – 4y = –7
4)
(–8, 2) and (–2, –5)
6)
(3, 1) and (1, 8)
(–7, 9) and (0, 9)
y=9
7x + 2y =23
7)
(–5, 3) and (–4, 6)
3x – y = –18
7x + 6y = –44
5)
(9, 4) and (–7, 0)
8)
(–4, 8) and (–8, 2)
3x – 2y = –28
(–6, –2) and (–5, –9)
7x + y = –44
Part - B
1)
A line cuts the y-axis at (0, 1) and passes through the point (3, –2). Find the equation of the line.
x+y=1
2)
Find the equation of the line passing through the points (–7, 3) and (9, –6).
9x + 16y = –15
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Score :
Equation of a Line
L1S4
Part - A
Find the equation of the line passing through the given points. Express the equation in standard form.
1)
(–9, 2) and (4, 5)
2)
(3, 8) and (–6, –6)
3)
(7, 6) and (1, –9)
4)
(–2, –5) and (0, 8)
5)
(4, –8) and (–6, 0)
6)
(1, –7) and (8, –9)
7)
(–6, –4) and (–1, –3)
8)
(–5, 9) and (–3, 2)
Part - B
1)
Find the equation of the line passing through the points (–2, 4) and (–9, 5).
2)
A line cuts the x-axis at x = –2 and passes through the point (1, 7). Find the equation of the line.
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Answer key
Name :
Score :
Equation of a Line
L1S4
Part - A
Find the equation of the line passing through the given points. Express the equation in standard form.
1)
2)
(–9, 2) and (4, 5)
3x – 13y = –53
3)
14x – 9y = –30
4)
(7, 6) and (1, –9)
6)
(4, –8) and (–6, 0)
(1, –7) and (8, –9)
2x + 7y = –47
4x + 5y = –24
7)
(–2, –5) and (0, 8)
13x – 2y = –16
5x – 2y = 23
5)
(3, 8) and (–6, –6)
8)
(–6, –4) and (–1, –3)
(–5, 9) and (–3, 2)
7x + 2y = –17
x – 5y = 14
Part - B
1)
Find the equation of the line passing through the points (–2, 4) and (–9, 5).
x + 7y = 26
2)
A line cuts the x-axis at x = –2 and passes through the point (1, 7). Find the equation of the line.
7x – 3y = –14
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Score :
Equation of a Line
L1S5
Part - A
Find the equation of the line passing through the given points. Express the equation in standard form.
1)
(5, 1) and (–4, 0)
2)
(–5, –2) and (–5, –1)
3)
(0, 1) and (4, 4)
4)
(–7, 6) and (3, 6)
5)
(2, –3) and (7, –9)
6)
(–6, 5) and (–1, –8)
7)
(–9, 6) and (–8, 7)
8)
(–2, 7) and (–3, –9)
Part - B
1)
A line cuts the y-axis at (0, 3) and passes through the point (–6, –5). Find the equation of the line.
2)
Find the equation of the line passing through the points (2, 8) and (–1, –1).
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Answer key
Name :
Score :
Equation of a Line
L1S5
Part - A
Find the equation of the line passing through the given points. Express the equation in standard form.
1)
2)
(5, 1) and (–4, 0)
x – 9y = –4
3)
x = –5
4)
(0, 1) and (4, 4)
3x – 4y = –4
5)
(–7, 6) and (3, 6)
y=6
6)
(2, –3) and (7, –9)
6x + 5y = –3
7)
(–5, –2) and (–5, –1)
(–6, 5) and (–1, –8)
13x + 5y = –53
8)
(–9, 6) and (–8, 7)
(–2, 7) and (–3, –9)
16x – y = –39
x – y = –15
Part - B
1)
A line cuts the y-axis at (0, 3) and passes through the point (–6, –5). Find the equation of the line.
4x – 3y = –9
2)
Find the equation of the line passing through the points (2, 8) and (–1, –1).
3x – y = –2
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Name :
Score :
Sheet 1
Graphing: Two Points
Graph the line using the given points.
1)
(–2, 1) and (0, –1)
5
4
3
2
1
-5 -4 -3 -2 -1
4)
-1
-2
-1
1 2 3 4 5
-5 -4 -3 -2 -1
-1
(6, –2) and (8, 2)
5
4
3
2
1
-1
1 2 3 4 5
-1
-2
-2
-3
-3
-3
-4
-4
-4
-5
-5
-5
5)
(–3, –3) and (2, –3)
6)
5
4
3
2
1
-5 -4 -3 -2 -1
1 2 3 4 5 6 7 8 9
-1
1 2 3 4 5 6 7 8 9
(–2, 6) and (–1, 4)
9
8
7
6
5
4
1 2 3 4 5
3
-2
-2
2
-3
-3
1
-4
-4
-5
-5
8)
(3, 6) and (5, 3)
8
5
4
3
2
1
6
5
4
3
-5 -4 -3 -2 -1
2
1
-1
-2
-9 -8 -7 -6 -5 -4 -3 -2 -1
1 2 3 4 5 6 7 8 9
9)
(–2, –3) and (0, 4)
7
-1
3)
5
4
3
2
1
(4, 3) and (7, 0)
-1
(1, 3) and (2, 1)
5
4
3
2
1
7)
2)
-1
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-2
-3
-3
-4
-4
-5
-5
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1
(–3, 3) and (5, –4)
1 2 3 4 5
-1
1 2 3 4 5
Name :
Score :
Answer key
Sheet 1
Graphing: Two Points
Graph the line using the given points.
1)
(–2, 1) and (0, –1)
5
4
3
2
1
-5 -4 -3 -2 -1
4)
-1
-2
-1
1 2 3 4 5
-5 -4 -3 -2 -1
-1
(6, –2) and (8, 2)
5
4
3
2
1
-1
1 2 3 4 5
-1
-2
-2
-3
-3
-3
-4
-4
-4
-5
-5
-5
5)
(–3, –3) and (2, –3)
6)
5
4
3
2
1
-5 -4 -3 -2 -1
1 2 3 4 5 6 7 8 9
-1
1 2 3 4 5 6 7 8 9
(–2, 6) and (–1, 4)
9
8
7
6
5
4
1 2 3 4 5
3
-2
-2
2
-3
-3
1
-4
-4
-5
-5
8)
(3, 6) and (5, 3)
8
5
4
3
2
1
6
5
4
3
-5 -4 -3 -2 -1
2
1
-1
-2
-9 -8 -7 -6 -5 -4 -3 -2 -1
1 2 3 4 5 6 7 8 9
9)
(–2, –3) and (0, 4)
7
-1
3)
5
4
3
2
1
(4, 3) and (7, 0)
-1
(1, 3) and (2, 1)
5
4
3
2
1
7)
2)
-1
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-2
-3
-3
-4
-4
-5
-5
Printable Math Worksheets @ www.mathworksheets4kids.com
1
(–3, 3) and (5, –4)
1 2 3 4 5
-1
1 2 3 4 5
Name :
Score :
Sheet 2
Graphing: Two Points
Graph the line using the given points.
1)
(–5, 2) and (5, –4)
2)
(7, 6) and (8, 7)
7
6
5
4
3
1 2 3 4 5
-1
1
-1
-4
-5
(0, 3) and (4, –1)
5)
1 2 3 4 5
-5
(1, –5) and (6, 3)
-1
-2
-3
-4
1 2 3 4 5 6 7 8 9
-1
-2
6)
(–6, 4) and (–3, 5)
5
4
3
2
1
5
4
3
2
1
7)
-5 -4 -3 -2 -1
2
-3
-5 -4 -3 -2 -1
5
4
3
2
1
8
-2
4)
(–2, 2) and (0, 0)
5
4
3
2
1
-5 -4 -3 -2 -1
3)
1 2 3 4 5
-1
-1
-1
9
8
7
6
5
4
1 2 3 4 5 6 7 8 9
3
-2
-2
2
-3
-3
1
-4
-4
-5
-5
(3, 1) and (4, –3)
8)
-9 -8 -7 -6 -5 -4 -3 -2 -1
(–3, –4) and (–1, –2)
-1
5
5
4
3
2
1
1 2 3 4 5
-5 -4 -3 -2 -1
-1
1
(8, 2) and (8, –2)
5
4
3
2
1
-5 -4 -3 -2 -1
9)
-1
4
3
2
1
1 2 3 4 5
-1
-1
-2
-2
-2
-3
-3
-3
-4
-5
-4
-4
-5
-5
Printable Math Worksheets @ www.mathworksheets4kids.com
1 2 3 4 5 6 7 8 9
Name :
Score :
Answer key
Sheet 2
Graphing: Two Points
Graph the line using the given points.
1)
(–5, 2) and (5, –4)
2)
(7, 6) and (8, 7)
7
6
5
4
3
1 2 3 4 5
-1
1
-1
-4
-5
(0, 3) and (4, –1)
5)
1 2 3 4 5
-5
(1, –5) and (6, 3)
-1
-2
-3
-4
1 2 3 4 5 6 7 8 9
-1
-2
6)
(–6, 4) and (–3, 5)
5
4
3
2
1
5
4
3
2
1
7)
-5 -4 -3 -2 -1
2
-3
-5 -4 -3 -2 -1
5
4
3
2
1
8
-2
4)
(–2, 2) and (0, 0)
5
4
3
2
1
-5 -4 -3 -2 -1
3)
1 2 3 4 5
-1
-1
-1
9
8
7
6
5
4
1 2 3 4 5 6 7 8 9
3
-2
-2
2
-3
-3
1
-4
-4
-5
-5
(3, 1) and (4, –3)
8)
-9 -8 -7 -6 -5 -4 -3 -2 -1
(–3, –4) and (–1, –2)
-1
5
5
4
3
2
1
1 2 3 4 5
-5 -4 -3 -2 -1
-1
1
(8, 2) and (8, –2)
5
4
3
2
1
-5 -4 -3 -2 -1
9)
-1
4
3
2
1
1 2 3 4 5
-1
-1
-2
-2
-2
-3
-3
-3
-4
-5
-4
-4
-5
-5
Printable Math Worksheets @ www.mathworksheets4kids.com
1 2 3 4 5 6 7 8 9
Name :
Score :
Sheet 3
Graphing: Two Points
Graph the line using the given points.
1)
(2, 1) and (5, –2)
2)
(–4, –4) and (1, 1)
4)
-5 -4 -3 -2 -1
1 2 3 4 5 6 7 8 9
-1
8
7
6
5
4
1 2 3 4 5
-1
3
-2
2
-3
-3
1
-4
-4
-5
-5
5)
6)
6
5
4
3
-5 -4 -3 -2 -1
2
1
1 2 3 4 5 6 7 8 9
-2
(–4, 3) and (–1, –3)
8)
-1
1
(5, 1) and (7, 3)
5
5
4
3
2
1
7
-1
-9 -8 -7 -6 -5 -4 -3 -2 -1
(–3, 1) and (1, 3)
8
7)
9
-2
(2, 6) and (7, 2)
-1
(–4, 2) and (–6, 4)
5
4
3
2
1
5
4
3
2
1
-1
3)
4
3
2
1
-1
1 2 3 4 5
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
(–5, –1) and (0, –2)
9)
1 2 3 4 5 6 7 8 9
(–2, –4) and (4, 3)
-5 -4 -3 -2 -1
-1
5
4
3
2
1
5
4
3
2
1
5
4
3
2
1
1 2 3 4 5
-5 -4 -3 -2 -1
-1
1 2 3 4 5
-5 -4 -3 -2 -1
-1
-2
-2
-2
-3
-3
-4
-4
-3
-4
-5
-5
-5
Printable Math Worksheets @ www.mathworksheets4kids.com
1 2 3 4 5
Name :
Score :
Answer key
Sheet 3
Graphing: Two Points
Graph the line using the given points.
1)
(2, 1) and (5, –2)
2)
(–4, –4) and (1, 1)
4)
-5 -4 -3 -2 -1
1 2 3 4 5 6 7 8 9
-1
8
7
6
5
4
1 2 3 4 5
-1
3
-2
2
-3
-3
1
-4
-4
-5
-5
5)
6)
6
5
4
3
-5 -4 -3 -2 -1
2
1
1 2 3 4 5 6 7 8 9
-2
(–4, 3) and (–1, –3)
8)
-1
1
(5, 1) and (7, 3)
5
5
4
3
2
1
7
-1
-9 -8 -7 -6 -5 -4 -3 -2 -1
(–3, 1) and (1, 3)
8
7)
9
-2
(2, 6) and (7, 2)
-1
(–4, 2) and (–6, 4)
5
4
3
2
1
5
4
3
2
1
-1
3)
4
3
2
1
-1
1 2 3 4 5
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
(–5, –1) and (0, –2)
9)
1 2 3 4 5 6 7 8 9
(–2, –4) and (4, 3)
-5 -4 -3 -2 -1
-1
5
4
3
2
1
5
4
3
2
1
5
4
3
2
1
1 2 3 4 5
-5 -4 -3 -2 -1
-1
1 2 3 4 5
-5 -4 -3 -2 -1
-1
-2
-2
-2
-3
-3
-4
-4
-3
-4
-5
-5
-5
Printable Math Worksheets @ www.mathworksheets4kids.com
1 2 3 4 5
Name :
Score :
Sheet 4
Graphing: Two Points
Graph the line using the given points.
1)
(3, –2) and (–4, 4)
2)
(7, 4) and (1, –3)
4)
5
4
3
2
1
4
3
2
1
-1
1 2 3 4 5
-1
-2
1 2 3 4 5 6 7 8 9
-1
-1
-2
-2
-3
-3
-4
-4
-4
-5
-5
-5
(–5, –3) and (–4, 2)
5)
(–8, 6) and (–1, 8)
6)
-6 -5 -4 -3 -2 -1
-1
7
6
5
4
2
-2
1
-3
-9 -8 -7 -6 -5 -4 -3 -2 -1
8)
-4
-5
1
(6, 7) and (–1, 4)
9)
(7, 7) and (7, 1)
5
4
3
2
1
1 2 3 4 5
-2
-5
-1
-2 -1
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
-1
1 2 3 4 5 6 7 8 9
-1
-3
-4
-1
3
-2
(–2, 0) and (4, –3)
-3
5
4
3
2
1
8
-5
-1
1 2 3 4
1 2 3 4 5
(8, 0) and (2, 2)
9
-4
-5 -4 -3 -2 -1
-5 -4 -3 -2 -1
-3
5
4
3
2
1
7)
(4, 3) and (–1, –2)
5
5
4
3
2
1
-5 -4 -3 -2 -1
3)
1 2 3 4 5 6 7 8
-2
Printable Math Worksheets @ www.mathworksheets4kids.com
-1
-1
-2
1 2 3 4 5 6 7 8 9
Name :
Score :
Answer key
Sheet 4
Graphing: Two Points
Graph the line using the given points.
1)
(3, –2) and (–4, 4)
2)
(7, 4) and (1, –3)
4)
5
4
3
2
1
4
3
2
1
-1
1 2 3 4 5
-1
-2
1 2 3 4 5 6 7 8 9
-1
-1
-2
-2
-3
-3
-4
-4
-4
-5
-5
-5
(–5, –3) and (–4, 2)
5)
(–8, 6) and (–1, 8)
6)
-6 -5 -4 -3 -2 -1
-1
7
6
5
4
2
-2
1
-3
-9 -8 -7 -6 -5 -4 -3 -2 -1
8)
-4
-5
1
(6, 7) and (–1, 4)
9)
(7, 7) and (7, 1)
5
4
3
2
1
1 2 3 4 5
-2
-5
-1
-2 -1
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
-1
1 2 3 4 5 6 7 8 9
-1
-3
-4
-1
3
-2
(–2, 0) and (4, –3)
-3
5
4
3
2
1
8
-5
-1
1 2 3 4
1 2 3 4 5
(8, 0) and (2, 2)
9
-4
-5 -4 -3 -2 -1
-5 -4 -3 -2 -1
-3
5
4
3
2
1
7)
(4, 3) and (–1, –2)
5
5
4
3
2
1
-5 -4 -3 -2 -1
3)
1 2 3 4 5 6 7 8
-2
Printable Math Worksheets @ www.mathworksheets4kids.com
-1
-1
-2
1 2 3 4 5 6 7 8 9
Name :
Score :
Sheet 5
Graphing: Two Points
Graph the line using the given points.
1)
(4, 3) and (–3, –4)
2)
(2, 5) and (2, –1)
-1
5
7
4
6
3
5
2
4
1
-5 -4 -3 -2 -1
2
-1
-4
-5
(–7, 8) and (–1, 2)
5)
7)
-1
-3
1 2 3 4 5 6 7 8 9
-1
-2
-4
-5
(4, 5) and (7, 2)
6)
(2, –2) and (4, 1)
9
8
7
6
5
4
3
2
1
5
4
3
2
1
-1
1
(1, 4) and (6, –2)
8)
1 2 3 4 5
-1
-2
1
-3
-9 -8 -7 -6 -5 -4 -3 -2 -1
8
3
1 2 3 4 5
-2
4)
(–4, –3) and (2, 3)
5
4
3
2
1
-5 -4 -3 -2 -1
3)
5
4
3
2
1
1 2 3 4 5 6 7 8 9
-1
-2
-3
-4
-5
(6, –8) and (9, –4)
-5 -4 -3 -2 -1
9)
1 2 3 4 5
-1
-2
-3
-4
-5
(–3, –3) and (–1, –2)
1
5
4
3
2
1
-1
-1
-2
-3
-4
-5
-1
1 2 3 4 5 6 7 8 9
-1
-2
-3
-4
-5
-6
-7
-8
-9
5
4
3
2
1
1 2 3 4 5 6 7 8 9
Printable Math Worksheets @ www.mathworksheets4kids.com
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
1 2 3 4 5
Name :
Score :
Answer key
Sheet 5
Graphing: Two Points
Graph the line using the given points.
1)
(4, 3) and (–3, –4)
2)
(2, 5) and (2, –1)
-1
5
7
4
6
3
5
2
4
1
-5 -4 -3 -2 -1
2
-1
-4
-5
(–7, 8) and (–1, 2)
5)
7)
-1
-3
1 2 3 4 5 6 7 8 9
-1
-2
-4
-5
(4, 5) and (7, 2)
6)
(2, –2) and (4, 1)
9
8
7
6
5
4
3
2
1
5
4
3
2
1
-1
1
(1, 4) and (6, –2)
8)
1 2 3 4 5
-1
-2
1
-3
-9 -8 -7 -6 -5 -4 -3 -2 -1
8
3
1 2 3 4 5
-2
4)
(–4, –3) and (2, 3)
5
4
3
2
1
-5 -4 -3 -2 -1
3)
5
4
3
2
1
1 2 3 4 5 6 7 8 9
-1
-2
-3
-4
-5
(6, –8) and (9, –4)
-5 -4 -3 -2 -1
9)
1 2 3 4 5
-1
-2
-3
-4
-5
(–3, –3) and (–1, –2)
1
5
4
3
2
1
-1
-1
-2
-3
-4
-5
-1
1 2 3 4 5 6 7 8 9
-1
-2
-3
-4
-5
-6
-7
-8
-9
5
4
3
2
1
1 2 3 4 5 6 7 8 9
Printable Math Worksheets @ www.mathworksheets4kids.com
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
1 2 3 4 5
Name :
Score :
L1S1
Graphing a Line
Graph the line using the given slope and the y-intercept.
1)
Slope = – 7 ; y-intercept = –1
6
2)
Slope = –4 ; y-intercept = 7
-1
1 2 3 4 5 6 7
-3
-4
-5
-6
-7
-5 -4 -3 -2 -1
-8
Slope = 8 ; y-intercept = –4
5)
1 2 3 4 5 6 7 8 9
-3
-4
-5
-6
-7
1 2 3 4 5
-8
-9
6)
Slope = –1 ; y-intercept = –3
7
6
5
4
3
2
1
1 2 3 4 5
-1
-1
-2
-1
-2
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-5 -4 -3 -2 -1
-1
-4
-2
-4
-5
-3
-5
8)
-3
9)
Slope = – 3 ; y-intercept = 4
5
9
8
7
6
5
4
3
2
5
4
3
2
1
5
4
3
2
1
-5 -4 -3 -2 -1
1
-1
1 2 3 4 5
Slope = –2 ; y-intercept = –2
1 2 3 4 5
-1
1 2 3 4 5
-2
-3
Slope = 5 ; y-intercept = 3
-5 -4 -3 -2 -1
-1
Slope = 3 ; y-intercept = 2
4
5
4
3
2
1
7)
1
-2
-9
-5 -4 -3 -2 -1
8
7
6
5
4
3
2
1
-2
4)
Slope = 5 ; y-intercept = –6
7
1
-3 -2 -1
3)
1 2 3 4 5
-2 -1
-1
-2
-2
-3
-3
-4
-4
-5
-5
Printable Math Worksheets @ www.mathworksheets4kids.com
1 2 3 4 5 6 7 8
Name :
Score :
Answer key
L1S1
Graphing a Line
Graph the line using the given slope and the y-intercept.
1)
Slope = – 7 ; y-intercept = –1
6
2)
Slope = –4 ; y-intercept = 7
-1
6 units
-3
7 units
-4
-5
-6
-7
-5 -4 -3 -2 -1
-8
Slope = 8 ; y-intercept = –4
5)
-3
1 2 3 4 5
-5
-6
7 units
-7
-8
6)
Slope = –1 ; y-intercept = –3
1 unit
Slope = 5 ; y-intercept = 3
8)
5
4
3
2
1
3 units
4 units
-5 -4 -3 -2 -1
-1
-5
-5 -4 -3 -2 -1
-2
1 2 3 4 5
-3
-4
-3
-5
Slope = –2 ; y-intercept = –2
9)
1
5
4
3
2
1
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
1 2 3 4 5
1 unit
-3
1 2 3 4 5
1 unit
1 unit
Slope = – 3 ; y-intercept = 4
5
9
8
7
6
5 units
5
4
3
1 unit
2
1 2 3 4 5
-1
-2
-1
5 units
-4
-3
-4
1 2 3 4 5 6 7 8 9
-2
Slope = 3 ; y-intercept = 2
4
8 units
-1
-1
-9
7
6
5
4
3
2
1
-2
-5 -4 -3 -2 -1
-1
1 2 3 4 5
-1
5
4
3
2
1
7)
1
-2
-9
-5 -4 -3 -2 -1
8
1 unit
7
6
4 units
5
4
3
2
1
1 2 3 4 5 6 7
-2
4)
Slope = 5 ; y-intercept = –6
7
1
-3 -2 -1
3)
2 units
-2 -1
-1
-2
-3
-4
-4
-5
-5
Printable Math Worksheets @ www.mathworksheets4kids.com
5 units
3 units
1 2 3 4 5 6 7 8
Name :
Score :
L1S2
Graphing a Line
Graph the line using the given slope and the y-intercept.
1)
Slope = 3 ; y-intercept = 1
5
2)
Slope = 7 ; y-intercept = –3
Slope = –4 ; y-intercept = –2
5
4
3
2
1
-2 -1
-1
3)
5
4
3
2
1
1 2 3 4 5 6 7 8
2
1
-5 -4 -3 -2 -1
1 2 3 4 5
-1
-2
-5 -4 -3 -2 -1
-1
-3
1 2 3 4 5
-4
-2
-2
-5
-3
-3
-6
-4
-4
-7
-5
-5
-8
-4
4)
Slope = –5 ; y-intercept = 4
5)
Slope = – 6 ; y-intercept = –1
5
7)
-4 -3 -2 -1
-1
2
1
-2
-3
-3
-4
-4
-2
-5
-5
-3
-6
-6
-4
-7
-7
-5
-8
-8
-1
1 2 3 4 5
8)
Slope = – 8 ; y-intercept = 2
3
9)
3
2
1
1 2 3 4 5 6 7 8 9
-5 -4 -3 -2 -1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
1 2 3 4 5
Slope = 2 ; y-intercept = 5
3
2
1
-1
-5 -4 -3 -2 -1
-1
1 2 3 4 5 6
-2
Slope = 7 ; y-intercept = –6
8
-1
Slope = 3 ; y-intercept = –7
2
1
5
4
3
2
1
-5 -4 -3 -2 -1
6)
8
7
6
5
4
3
2
1
1 2 3 4 5
Printable Math Worksheets @ www.mathworksheets4kids.com
-5 -4 -3 -2 -1
-1
-2
1 2 3 4 5
Name :
Score :
Answer key
L1S2
Graphing a Line
Graph the line using the given slope and the y-intercept.
1)
Slope = 3 ; y-intercept = 1
5
2)
Slope = 7 ; y-intercept = –3
5
4
3
2
1
-2 -1
-1
3)
Slope = –4 ; y-intercept = –2
5
4
3
2
1
3 units
5 units
1 2 3 4 5 6 7 8
2
1
-5 -4 -3 -2 -1
-2
7 units
-5 -4 -3 -2 -1
-1
1 2 3 4 5
-1
1 unit
-3
1 2 3 4 5
-4
-2
-2
-3
-3
-4
-4
-7
-5
-5
-8
4 units
-5
-6
1 unit
-4
4)
Slope = –5 ; y-intercept = 4
5)
Slope = – 6 ; y-intercept = –1
5
7)
-1
-4 -3 -2 -1
-1
2
1
5 units
-3
6 units
-4
-5
-5
-3
-6
-6
-4
-7
-7
-5
-8
-8
Slope = – 8 ; y-intercept = 2
3
3
2
1
1 2 3 4 5 6 7 8 9
-2
7 units
-3
-5 -4 -3 -2 -1
-1
-4
-5
8 units
1 unit
Slope = 2 ; y-intercept = 5
8
7
2 units
6
5
1 unit
4
3
2
1
3 units
1 2 3 4 5
8 units
-3
-5
3 units
-2
-4
-7
9)
3
2
1
-6
-4
-2
8)
1 2 3 4 5
-2
-3
-1
-5 -4 -3 -2 -1
-1
1 2 3 4 5 6
-2
1 2 3 4 5
Slope = 7 ; y-intercept = –6
8
-1
Slope = 3 ; y-intercept = –7
2
1
5
1 unit
4
3
2
5 units
1
-5 -4 -3 -2 -1
6)
-6
-7
Printable Math Worksheets @ www.mathworksheets4kids.com
-5 -4 -3 -2 -1
-1
-2
1 2 3 4 5
Name :
Score :
Answer key
L1S3
Graphing a Line
Graph the line using the given slope and the y-intercept.
1)
Slope = –2 ; y-intercept = 6
2)
Slope = – 5 ; y-intercept = –1
7
4)
5
4
3
2
1
2
1
-2 -1
-1
1 2 3 4 5 6 7 8
-2
-3
-5 -4 -3 -2 -1
-4
-2
-6
-3
-2
-7
-4
-3
-8
-5
Slope = 4 ; y-intercept = 3
3
5)
Slope = 8 ; y-intercept = –7
7
-5 -4 -3 -2 -1
6
5
4
3
2
1
-5 -4 -3 -2 -1
-1
Slope = – 7 ; y-intercept = 4
5
2
1
8
1 2 3 4 5
Slope = –1 ; y-intercept = –1
8)
-1
-2
-3
-4
-5
-6
-7
-8
5
4
3
2
1
1 2 3 4 5
Slope = 5 ; y-intercept = –8
6
-4 -3 -2 -1
-1
1 2 3 4 5 6
-2
-3
-4
-5
9)
Slope = 1 ; y-intercept = 2
5
4
3
2
1
-5 -4 -3 -2 -1
-1
6)
5
4
3
2
1
1
-1
-1
1 2 3 4 5 6 7 8 9
-2
-3
1 2 3 4 5
1 2 3 4 5
-1
-5
1 2 3 4 5
-1
9
7)
Slope = 3 ; y-intercept = 1
7
6
5
4
3
2
1
-5 -4 -3 -2 -1
3)
-4
-5
-5 -4 -3 -2 -1
-1
-2
-6
-2
-3
-7
-3
-4
-8
-4
-5
-9
-5
Printable Math Worksheets @ www.mathworksheets4kids.com
1 2 3 4 5
Name :
Score :
Answer key
L1S3
Graphing a Line
Graph the line using the given slope and the y-intercept.
1)
Slope = –2 ; y-intercept = 6
2)
Slope = – 5 ; y-intercept = –1
7
4)
5
4
3
2
1
2
1
-2 -1
-1
1 2 3 4 5 6 7 8
7 units
-2
-3
-5 -4 -3 -2 -1
5 units
-4
-2
-6
-3
-2
-7
-4
-3
-8
-5
Slope = 4 ; y-intercept = 3
3
5)
Slope = 8 ; y-intercept = –7
7
-5 -4 -3 -2 -1
6
4 units
5
4
3
3 units
2
1
-5 -4 -3 -2 -1
-1
1 2 3 4 5
Slope = –1 ; y-intercept = –1
8)
5
4
3
2
1
1 2 3 4 5
-1
-2
-3
8 units
-4
-5
-6
-7
1 unit
-8
-4 -3 -2 -1
-1
5 units
7 units
1 2 3 4 5 6
-2
-3
-4
-5
9)
Slope = 1 ; y-intercept = 2
5
4
3
2
1
5
4
3
1 unit
2 1 unit
1
1
-1
-1
1 2 3 4 5 6 7 8 9
-2
-3
-5 -4 -3 -2 -1 1 unit
1 2 3 4 5
-1
1 unit
-4
-5 -4 -3 -2 -1
-5
5 units
-6
-3
-7
-4
-8
-5
-9
1 2 3 4 5
Slope = 5 ; y-intercept = –8
6
1 unit
Slope = – 7 ; y-intercept = 4
5
2
1
8
-2
6)
3 units
-1
-5
1 2 3 4 5
-1
9
7)
Slope = 3 ; y-intercept = 1
7
1 unit
6
5
2 units
4
3
2
1
-5 -4 -3 -2 -1
3)
-1
-2
-3
6 units
Printable Math Worksheets @ www.mathworksheets4kids.com
-4
-5
1 2 3 4 5
Name :
Score :
L1S4
Graphing a Line
Graph the line using the given slope and the y-intercept.
1)
Slope = 3 ; y-intercept = 3
2)
Slope = – 5 ; y-intercept = 2
2
-5 -4 -3 -2 -1
1 2 3 4 5
-2
4)
Slope = – 8 ; y-intercept = –1
5
5)
-5 -4 -3 -2 -1
1 2 3 4 5
-1
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
-8
6)
Slope = –4 ; y-intercept = 4
1 2 3 4 5 6
-1
-3
-1
5
4
3
2
1 2 3 4 5 6 7 8 9
1
-4
-2
-5
-3
-6
-4
-2
-7
-5
-3
-8
-9
-6
-4
-7
-5
Slope = 8 ; y-intercept = –3
8)
-5 -4 -3 -2 -1
Slope = –6 ; y-intercept = –1
-5 -4 -3 -2 -1
-1
9)
-1
1 2 3 4 5
-2
1 2 3 4 5
1 2 3 4 5
2
1
-5 -4 -3 -2 -1
-1
Slope = 2 ; y-intercept = 2
7
5
4
3
2
1
1 2 3 4 5
-1
-2
3
2
1
-2
7)
2
1
Slope = 6 ; y-intercept = –4
7
1
-4 -3 -2 -1
-1
3
2
1
-1
Slope = 5 ; y-intercept = –6
8
7
6
5
4
3
2
1
-5 -4 -3 -2 -1
3)
-3
5
4
3
2
1
-4
-2 -1
-1
-2
-5
-2
-3
-6
-3
-4
-7
-4
-5
-8
-5
Printable Math Worksheets @ www.mathworksheets4kids.com
1 2 3 4 5 6 7 8
Name :
Score :
Answer key
L1S4
Graphing a Line
Graph the line using the given slope and the y-intercept.
1)
Slope = 3 ; y-intercept = 3
2)
Slope = – 5 ; y-intercept = 2
2
-5 -4 -3 -2 -1
-2
4)
Slope = – 8 ; y-intercept = –1
5
5)
-5 -4 -3 -2 -1
1 2 3 4 5
-1
-2
5 units
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
-8
6)
5 units
-1
-3
-1
8 units
-5
4
2
1 2 3 4 5 6 7 8 9
6 units
-5 -4 -3 -2 -1
-1
-5
-3
-8
-9
-6
-4
-7
-5
7 units
Slope = –6 ; y-intercept = –1
-5 -4 -3 -2 -1
-1
9)
Slope = 2 ; y-intercept = 2
7
2
1
-5 -4 -3 -2 -1
8 units
1 2 3 4 5
1 2 3 4 5
-1 1 unit
-2
-3
-4
6 units
5
4
3
2
1
-2 -1
-1
-2
-5
-2
-3
-6
-3
-7
-4
-8
-5
-4
-5
1 unit
Printable Math Worksheets @ www.mathworksheets4kids.com
1 2 3 4 5
-2
-4
-7
5
4
3
2
1
4 units
1
-3
8)
1 unit
3
-6
Slope = 8 ; y-intercept = –3
1 unit
5
-2
-4
5 units
Slope = –4 ; y-intercept = 4
3
2
1
1 2 3 4 5 6
1 2 3 4 5
-1
-2
7)
2
1
Slope = 6 ; y-intercept = –4
7
1
-4 -3 -2 -1
-1
3
2 units
2
1
1 2 3 4 5
-1
Slope = 5 ; y-intercept = –6
8
7
6
5
3 units
4
3
1 unit
2
1
-5 -4 -3 -2 -1
3)
2 units
7 units
1 2 3 4 5 6 7 8
Score :
Name :
L1S5
Graphing a Line
Graph the line using the given slope and the y-intercept.
1)
Slope = 5 ; y-intercept = 3
4
2)
Slope = 6 ; y-intercept = –4
7
6
5
4
-5 -4 -3 -2 -1
3
2
1
1 2 3 4 5
-1
Slope = –5 ; y-intercept = –3
5)
-1
-3
-1
1 2 3 4 5 6
-2
-3
6)
Slope = 3 ; y-intercept = 2
-1
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9
-4
-2
-5
-3
-6
-4
-7
-5
-2
-8
-9
-6
-3
-7
-4
Slope = –4 ; y-intercept = 2
8)
-5 -4 -3 -2 -1
Slope = – 7 ; y-intercept = 0
3
9)
Slope = 8 ; y-intercept = 1
7
2
9
6
1
8
-2 -1
4
-1
7
1 2 3 4 5 6 7 8
6
3
-2
5
2
-3
4
1
-4
3
-1
1 2 3 4 5
-5
2
-6
1
-2
-7
-3
-8
1 2 3 4 5
-1
5
-5 -4 -3 -2 -1
-4 -3 -2 -1
-2
7)
1 2 3 4 5
3
2
1
1 2 3 4 5
-1
-1
-2
-3
-4
-5
Slope = 6 ; y-intercept = –5
7
1
-5 -4 -3 -2 -1
7
6
5
4
3
2
1
5
4
3
2
1
8
4)
Slope = – 2 ; y-intercept = 6
5
9
-5 -4 -3 -2 -1
3)
Printable Math Worksheets @ www.mathworksheets4kids.com
-5 -4 -3 -2 -1
-1
1 2 3 4 5
Score :
Name :
Answer key
L1S5
Graphing a Line
Graph the line using the given slope and the y-intercept.
1)
Slope = 5 ; y-intercept = 3
4
2)
Slope = 6 ; y-intercept = –4
7
6
5 units
5
4
-5 -4 -3 -2 -1
4 units
1
-5 -4 -3 -2 -1
4)
1 2 3 4 5
-1
Slope = –5 ; y-intercept = –3
5)
-2
-3
-1
-1
-4
-7
-5
-8
-9
-6
Slope = 3 ; y-intercept = 2
6
5
4
3 units
3
2
1 unit
1
6 units
-5 -4 -3 -2 -1
8)
-3
-4
Slope = – 7 ; y-intercept = 0
3
9)
Slope = 8 ; y-intercept = 1
2
6
1
5
-2 -1
4
1 unit
-1
4 units
1 2 3 4 5
9
8
3 units
7
1 2 3 4 5 6 7 8
6
-2
-3
-4
1
1 2 3 4 5
-1
-2
7 units
7
-1
6)
1 2 3 4 5 6 7 8 9
-5 -4 -3 -2 -1
-3
-7
Slope = –4 ; y-intercept = 2
2
1 2 3 4 5 6
-2
-3
5 units
-6
3
2 units
-2
-4
7)
-1
5 units
1 unit
-5
-4 -3 -2 -1
3
2
1
1 2 3 4 5
-1
1 2 3 4 5
-1
6 units
-2
-3
-4
1 unit
-5
Slope = 6 ; y-intercept = –5
7
1
-5 -4 -3 -2 -1
7
6
5
4
3
2
1
5
4
3
2
1
8
2
Slope = – 2 ; y-intercept = 6
5
9
3
3)
5
3
-5
2
-6
1
-2
-7
-3
-8
Printable Math Worksheets @ www.mathworksheets4kids.com
8 units
4
7 units
-5 -4 -3 -2 -1
-1
1 unit
1 2 3 4 5
Name :
L2S1
Constant of Proportionality - Table
The values of and are proportional. Determine the constant of proportionality(k)
and find the missing values.
1)
9
36
3)
16
12
30
7
11
5
14
25
24
30
6
8)
12
Printable Math Worksheets @ www.mathworksheets4kids.com
9
4
6)
4
15
2
4)
8
32
7)
48
6
4
8
3
5)
2)
5
40
20
60
15
3
14
21
6
3
4
18
7
54
Name :
Answer key
L2S1
Constant of Proportionality - Table
The values of and are proportional. Determine the constant of proportionality(k)
and find the missing values.
1)
9
4
5
2
36
16
20
8
2)
12
6
15
9
4
2
5
3
k= 1
3
k=4
3)
12
18
30
48
2
3
5
8
4)
5
8
4
12
25
40
20
60
k= 1
6
5)
k=5
7
11
4
3
56
88
32
24
6)
49
14
35
7
21
6
15
3
k= 3
7
k=8
7)
35
5
15
30
14
2
6
12
8)
k= 2
5
Printable Math Worksheets @ www.mathworksheets4kids.com
3
4
9
7
18
24
54
42
k=6
Name :
L2S2
Constant of Proportionality - Table
The values of and are proportional. Determine the constant of proportionality(k)
and find the missing values.
1)
18
20
15
3)
5)
7)
10
11
63
42
4
5
4)
35
16
9
12
13
15
39
2)
6
36
15
14
26
30
62
78
16
31
6)
23
5
6
81
10
8)
42
Printable Math Worksheets @ www.mathworksheets4kids.com
28
9
21
18
10
90
7
36
Name :
Answer key
L2S2
Constant of Proportionality - Table
The values of and are proportional. Determine the constant of proportionality(k)
and find the missing values.
1)
24
18
6
12
20
15
5
10
2)
7
13
15
9
14
26
30
18
k= 5
6
3)
k=2
9
6
11
5
63
42
77
35
4)
62
78
16
46
31
39
8
23
k= 1
2
k=7
5)
12
4
16
36
9
3
12
27
6)
5
9
6
10
45
81
54
90
k= 3
4
7)
k=9
13
14
15
10
39
42
45
30
8)
k=3
Printable Math Worksheets @ www.mathworksheets4kids.com
28
21
7
42
24
18
6
36
k= 6
7
Name :
L2S3
Constant of Proportionality - Table
The values of and are proportional. Determine the constant of proportionality(k)
and find the missing values.
1)
4
20
3)
5)
7)
8
32
28
9
6
20
2)
2
15
30
60
3
13
18
8
12
25
50
40
24
4)
6)
5
12
21
8
3
14
12
21
14
28
10
13
91
8)
20
Printable Math Worksheets @ www.mathworksheets4kids.com
21
18
57
54
72
Name :
Answer key
L2S3
Constant of Proportionality - Table
The values of and are proportional. Determine the constant of proportionality(k)
and find the missing values.
1)
4
2
3
6
40
20
30
60
2)
40
20
5
35
24
12
3
21
k= 3
5
k = 10
3)
8
7
3
13
32
28
12
52
4)
56
21
14
28
8
3
2
4
k= 1
7
k=4
5)
9
6
12
18
6
4
8
12
6)
14
12
10
13
98
84
70
91
k= 2
3
7)
k=7
20
15
25
50
16
12
20
40
8)
k= 4
5
Printable Math Worksheets @ www.mathworksheets4kids.com
21
19
18
24
63
57
54
72
k=3
Name :
L2S4
Constant of Proportionality - Table
The values of and are proportional. Determine the constant of proportionality(k)
and find the missing values.
1)
40
15
3)
18
98
40
5)
25
7)
65
90
60
5
7
30
5
16
6)
39
8
4
48
4)
2
10
3
6
35
5
91
2)
24
8)
36
Printable Math Worksheets @ www.mathworksheets4kids.com
48
18
15
5
81
36
64
40
30
12
27
6
3
Name :
Answer key
L2S4
Constant of Proportionality - Table
The values of and are proportional. Determine the constant of proportionality(k)
and find the missing values.
1)
20
40
24
8
15
30
18
6
2)
3
5
7
4
36
60
84
48
k= 3
4
3)
k = 12
56
98
35
42
40
70
25
30
4)
2
6
8
5
16
48
64
40
k= 5
7
5)
k=8
7
5
3
2
91
65
39
26
6)
18
6
30
12
15
5
25
10
k= 5
6
k = 13
7)
15
10
6
8
90
60
36
48
8)
k=6
Printable Math Worksheets @ www.mathworksheets4kids.com
81
36
54
27
9
4
6
3
k= 1
9
Name :
L2S5
Constant of Proportionality - Table
The values of and are proportional. Determine the constant of proportionality(k)
and find the missing values.
1)
6
4
3
75
3)
50
5)
7)
2
45
27
8
22
50
11
17
45
25
5
2
35
10
6)
16
8
16
24
90
6
9
20
65
33
4)
30
18
2)
8)
85
Printable Math Worksheets @ www.mathworksheets4kids.com
10
7
2
90
54
50
24
15
Name :
Answer key
L2S5
Constant of Proportionality - Table
The values of and are proportional. Determine the constant of proportionality(k)
and find the missing values.
1)
6
4
5
3
90
60
75
45
2)
33
3
24
45
22
2
16
30
k= 2
3
k = 15
3)
50
30
45
10
30
18
27
6
4)
45
35
25
5
90
70
50
10
k= 3
5
5)
k=2
2
8
5
9
20
80
50
90
6)
64
56
16
24
8
7
2
3
k= 1
8
k = 10
7)
11
13
17
16
55
65
85
80
8)
k=5
Printable Math Worksheets @ www.mathworksheets4kids.com
18
90
54
27
10
50
30
15
k= 5
9
Name :
Solving Proportions - Decimals
Solve each proportion.
1)
12.8
m
=
0.8
1.8
2)
1.2
r
=
73.2
91.5
3)
22.8
18.4
=
11.4
f
4)
6.4
28.8
=
1.8
z
5)
32.3
7.6
=
1.7
d
6)
s
33.6
=
5.6
1.4
7)
43.7
71.3
=
v
3.1
8)
50.4
w
=
7.2
4.6
Printable Math Worksheets @ www.mathworksheets4kids.com
Sheet 1
Name :
Answer key
Solving Proportions - Decimals
Solve each proportion.
1)
12.8
m
=
0.8
1.8
2)
1.2
r
=
73.2
91.5
m = 28.8
3)
22.8
18.4
=
11.4
f
r = 1.5
4)
f = 9.2
5)
32.3
7.6
=
1.7
d
z = 0.4
6)
d = 0.4
7)
43.7
71.3
=
v
3.1
6.4
28.8
=
1.8
z
s
33.6
=
5.6
1.4
s = 8.4
8)
v = 1.9
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50.4
w
=
7.2
4.6
w = 32.2
Sheet 1
Name :
Solving Proportions - Decimals
Solve each proportion.
1)
3.6
6.9
=
y
7.2
2)
c
1.8
=
23.2
34.8
3)
73.6
k
=
4.6
5.4
4)
3.2
8.6
=
r
17.2
5)
30.4
79.8
= p
0.8
6)
g
52.2
=
0.3
1.8
7)
2.1
d
=
25.2
69.6
8)
q
28.2
=
84.6
43.8
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Sheet 2
Name :
Answer key
Solving Proportions - Decimals
Solve each proportion.
1)
3.6
6.9
=
y
7.2
2)
y = 13.8
3)
73.6
k
=
4.6
5.4
c = 1.2
4)
k = 86.4
5)
30.4
79.8
= p
0.8
2.1
d
=
25.2
69.6
3.2
8.6
=
r
17.2
r = 6.4
6)
p = 2.1
7)
c
1.8
=
23.2
34.8
g
52.2
=
0.3
1.8
g = 8.7
8)
d = 5.8
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q
28.2
=
84.6
43.8
q = 14.6
Name :
Solving Proportions - Decimals
Solve each proportion.
1)
1.8
0.9
=
b
41.4
2)
64.8
w
=
5.4
6.3
3)
8.4
9.1
=
v
54.6
4)
y
77.5
=
2.5
1.2
5)
h
46.5
=
3.7
9.3
6)
1.3
0.8
=
48.8
m
7)
94.6
u
=
8.6
7.7
8)
8.3
7.2
=
d
14.4
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Sheet 3
Name :
Answer key
Solving Proportions - Decimals
Solve each proportion.
1)
1.8
0.9
=
b
41.4
2)
b = 82.8
3)
8.4
9.1
=
v
54.6
w = 75.6
4)
v = 50.4
5)
h
46.5
=
3.7
9.3
94.6
u
=
8.6
7.7
y
77.5
=
2.5
1.2
y = 37.2
6)
h = 18.5
7)
64.8
w
=
5.4
6.3
1.3
0.8
=
48.8
m
m = 79.3
8)
u = 84.7
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8.3
7.2
=
d
14.4
d = 16.6
Name :
Solving Proportions - Decimals
Solve each proportion.
1)
8.9
k
=
44.5
33.5
2)
4.5
13.5
=
t
1.5
3)
3.7
a
=
48.1
67.6
4)
16.8
31.5
=
n
2.4
5)
73.6
94.3
=
x
4.1
6)
p
8.3
=
74.7
51.3
7)
3.8
0.8
=
91.2
b
8)
y
9.5
=
36.5
47.5
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Sheet 4
Name :
Answer key
Solving Proportions - Decimals
Solve each proportion.
1)
8.9
k
=
44.5
33.5
2)
k = 6.7
3)
3.7
a
=
48.1
67.6
t = 0.5
4)
a = 5.2
5)
73.6
94.3
=
x
4.1
3.8
0.8
=
91.2
b
16.8
31.5
=
n
2.4
n = 4.5
6)
p
8.3
=
74.7
51.3
p = 5.7
x = 3.2
7)
4.5
13.5
=
t
1.5
8)
b = 19.2
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y
9.5
=
36.5
47.5
y = 7.3
Name :
Solving Proportions - Decimals
Solve each proportion.
1)
7.3
n
=
43.8
33.6
2)
4.7
9.8
=
32.9
b
3)
78.3
z
=
0.9
0.8
4)
q
12.8
=
3.2
5.4
5)
83.7
60.3
=
s
6.7
6)
d
1.8
=
14.4
20.8
7)
6.9
0.5
=
48.3
h
8)
7.3
9.9
=
c
49.5
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Sheet 5
Name :
Answer key
Solving Proportions - Decimals
Solve each proportion.
1)
7.3
n
=
43.8
33.6
2)
n = 5.6
3)
78.3
z
=
0.9
0.8
b = 68.6
4)
83.7
60.3
=
s
6.7
6)
s = 9.3
7)
6.9
0.5
=
48.3
h
q
12.8
=
3.2
5.4
q = 21.6
z = 69.6
5)
4.7
9.8
=
32.9
b
d
1.8
=
14.4
20.8
d = 2.6
8)
h = 3.5
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7.3
9.9
=
c
49.5
c = 36.5
Name :
Sheet 1
1) Jack’s and Mo’s orchards had a harvest of 450 lb and 1,215 lb of oranges respectively. If
Jack had 6 orange trees and Mo had 15 orange trees, whose orchard acquired the higher
yield per tree?
2) Zoe visits a departmental store to pick a pack of salted mixed nuts. A pack of 15.25 oz
of mixed nuts is priced at S 7.93, and the offer on a pack containing 25 oz of nuts is
S 11.75. Assist Zoe pick up the better deal.
3) Kathleen, a florist, designs 5 bridesmaid bouquets with 95 rose stems. She also creates
3 bouquets with 63 tulips for the flowergirls. Which type of bouquet was designed with
lesser number of flowers?
4) Andre, Rick, and Ty were practicing for a track cycling race. Andre covered a distance of
750 m in 3 minutes. Rick clocked 4 minutes for a distance of 800 m. Ty raced 950 m in
5 minutes. Who covered the least distance per minute?
5) Sam visits 3 stores to find the best deal for a pair of jeans. Store A offers a discounted
price of S120 for 4 pairs of jeans. Two pairs of jeans sell for S100 at Store B. Store C offers
3 pairs of jeans at S 99. Which store offers the best deal?
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Name :
Answer key
Sheet 1
1) Jack’s and Mo’s orchards had a harvest of 450 lb and 1,215 lb of oranges respectively. If
Jack had 6 orange trees and Mo had 15 orange trees, whose orchard acquired the higher
yield per tree?
Jack’s orchard: 75 lb of oranges/tree ; Mo’s orchard: 81 lb of oranges/tree
Mo’s orchard acquired the higher yield of oranges per tree.
2) Zoe visits a departmental store to pick a pack of salted mixed nuts. A pack of 15.25 oz
of mixed nuts is priced at S 7.93, and the offer on a pack containing 25 oz of nuts is
S 11.75. Assist Zoe pick up the better deal.
15.25 oz pack: S 0.52/oz ; 25 oz pack: S 0.47/oz
The 25 oz pack of salted mixed nuts makes a better deal.
3) Kathleen, a florist, designs 5 bridesmaid bouquets with 95 rose stems. She also creates
3 bouquets with 63 tulips for the flowergirls. Which type of bouquet was designed with
lesser number of flowers?
Bridesmaid bouquets: 19 rose stems/bouquet ; Flowergirl bouquets: 21 tulips/bouquet
The bridesmaid bouquets contained lesser flowers.
4) Andre, Rick, and Ty were practicing for a track cycling race. Andre covered a distance of
750 m in 3 minutes. Rick clocked 4 minutes for a distance of 800 m. Ty raced 950 m in
5 minutes. Who covered the least distance per minute?
Andre: 250 m/minute ; Rick: 200 m/minute ; Ty: 190 m/minute
Ty clocked the least distance per minute.
5) Sam visits 3 stores to find the best deal for a pair of jeans. Store A offers a discounted
price of S120 for 4 pairs of jeans. Two pairs of jeans sell for S100 at Store B. Store C offers
3 pairs of jeans at S 99. Which store offers the best deal?
Store A: S30/pair of jeans ; Store B: S 50/pair of jeans ; Store C: S 33/pair of jeans
Store A offers the best deal.
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Name :
Sheet 2
1) A contact center provides incentives based on the number of sales achieved by its
representatives. Ross made 27 sales in 3 days. His colleague, Mona secured 49 sales in
one week. Who achieved a higher sales target per day?
2) Kris’s bike used up 4.5 gallons of gas to cover a distance of 297 miles. Jake travels 366
miles on a full tank capacity of 6 gallons. Ben’s bike consumed 5.2 gallons of gas for a
265.2 miles long drive. Whose bike gave the best mileage?
3) It was a busy evening at the restaurant. Ron waited on 48 tables for 3 hours. Joe served
45 customers in 5 hours. Sue waited on 34 tables for 2 hours. Who had the busiest day
serving the most number of customers per hour?
4) Store A offers a pack of 4 LED bulbs for S 14.96. Six LED bulbs are sold for S18.42 at
Store B. The offer price for a pack of 5 LED bulbs was S17.95 at store C. Find the store
that offers the best deal.
5) Angela baked 5 batches of lemon sugar cookies with 17.5 cups of flour. She also made
3 batches of vanilla cookies using 11.25 cups of flour. Which type of cookies required
more flour?
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Name :
Answer key
1) A contact center provides incentives based on the number of sales achieved by its
representatives. Ross made 27 sales in 3 days. His colleague, Mona secured 49 sales in
one week. Who achieved a higher sales target per day?
Ross: 9 sales/day ; Mona: 7 sales/day
Ross achieved a higher sales target per day.
2) Kris’s bike used up 4.5 gallons of gas to cover a distance of 297 miles. Jake travels 366
miles on a full tank capacity of 6 gallons. Ben’s bike consumed 5.2 gallons of gas for a
265.2 miles long drive. Whose bike gave the best mileage?
Kris: 66 miles/gallon ; Jake: 61 miles/gallon ; Ben: 51 miles/gallon
Kris’s bike gave the best mileage.
3) It was a busy evening at the restaurant. Ron waited on 48 tables for 3 hours. Joe served
45 customers in 5 hours. Sue waited on 34 tables for 2 hours. Who had the busiest day
serving the most number of customers per hour?
Ron: 16 tables/hour ; Joe: 9 tables/hour ; Sue: 17 tables/hour
Sue served more customers per hour.
4) Store A offers a pack of 4 LED bulbs for S 14.96. Six LED bulbs are sold for S18.42 at
Store B. The offer price for a pack of 5 LED bulbs was S17.95 at store C. Find the store
that offers the best deal.
Store A: S3.74/LED bulb ; Store B: S3.07/LED bulb ; Store C: S3.59/LED bulb
Store B offers the best deal.
5) Angela baked 5 batches of lemon sugar cookies with 17.5 cups of flour. She also made
3 batches of vanilla cookies using 11.25 cups of flour. Which type of cookies required
more flour?
Lemon sugar cookies: 3.5 cups of flour/batch ; Vanilla cookies: 3.75 cups of flour/batch
Vanilla cookies required more flour.
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Name :
1) Sam and John planted green beans in their respective gardens. Sam’s garden harvested
19.5 lb of green beans in 3 weeks. John’s garden produced a yield of 14.7 lb in 2 weeks.
Whose garden yielded a higher harvest of beans per week?
2) Peter and Matt went on separate kayaks to catch fish in Onondaga lake, NY during the
wee hours of Sunday morning. Peter caught 96 lb of fish in 4 hours. Matt netted120 lb
of fish in 5 hours. Who caught more fish per hour?
3) Serena and Stacey are professional hairdressers who work at two different beauty salons
in the city. Serena works for 8 hours and earns S 112. Stacey is paid S 75 for 5 hours of
work. Which of the two hairdressers earns more per hour?
4) Twin brothers, Zac and Preston took up a math online test. Zac answered 30 questions in
5 minutes. Preston took 7 minutes to answer 35 questions. Which of the two siblings
solved the problems at a faster rate per minute?
5) Derek was surfing through the internet for a good deal on t-shirts. Help Derek find the
best buy among the following deals: Three t-shirts for S 28.95, four t-shirts priced at
S 39, and an offer of five t-shirts for S 49.95.
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
1) Sam and John planted green beans in their respective gardens. Sam’s garden harvested
19.5 lb of green beans in 3 weeks. John’s garden produced a yield of 14.7 lb in 2 weeks.
Whose garden yielded a higher harvest of beans per week?
Sam’s garden: 6.5 lb of green beans/week ; John’s garden: 7.35 lb of green beans/week
John’s garden yielded a higher harvest of green beans per week.
2) Peter and Matt went on separate kayaks to catch fish in Onondaga lake, NY during the
wee hours of Sunday morning. Peter caught 96 lb of fish in 4 hours. Matt netted120 lb
of fish in 5 hours. Who caught more fish per hour?
Peter’s catch: 24 lb of fish/hour ; Matt’s catch: 24 lb of fish/hour
Peter and Matt caught the same amount of fish per hour!
3) Serena and Stacey are professional hairdressers who work at two different beauty salons
in the city. Serena works for 8 hours and earns S 112. Stacey is paid S 75 for 5 hours of
work. Which of the two hairdressers earns more per hour?
Serena’s earnings: S14/hour ; Stacey’s earnings: S 15/hour
Stacey earns more per hour than Serena.
4) Twin brothers, Zac and Preston took up a math online test. Zac answered 30 questions in
5 minutes. Preston took 7 minutes to answer 35 questions. Which of the two siblings
solved the problems at a faster rate per minute?
Zac solved: 6 questions/minute ; Preston solved: 5 questions/minute
Zac solved the problems at a faster rate per minute.
5) Derek was surfing through the internet for a good deal on t-shirts. Help Derek find the
best buy among the following deals: Three t-shirts for S 28.95, four t-shirts priced at
S 39, and an offer of five t-shirts for S 49.95.
Three t-shirts offer: S 9.65/t-shirt ; Four t-shirts offer: S 9.75/t-shirt ; Five t-shirts offer: S 9.99/t-shirt
The best deal is three t-shirts for S 28.95.
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Name :
Sheet 4
1) Henry bought 118 oz of dried figs for S36.58 from a wholesale store. Karen picked a
7 oz pack of dried figs for S2.73. Who clinched the better buy?
2) Flight A traveled a distance of 980 miles in 95 minutes. Flight B reached its destination in
82 minutes and covered a distance of 854 miles. Which of the two flights traveled at a
faster speed?
3) Nancy types 388 words in 4 minutes. Her friend, Jenna types 294 words in 3 minutes.
Who types at a faster rate, Nancy or Jenna?
4) A supermarket has the following offers on storage containers during an X-mas sale: A set
of 5 storage containers for S3.05, 4 containers priced at S 3.12 and an offer of S2.73 on
3 storage containers. Determine the best deal available.
5) A total of 348 people attended a health screening on day one of a medical camp over a
6 hour period. The team of doctors attended to 228 people in 4 hours on day two.
Determine the day which recorded lesser number of people per hour.
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Name :
Answer key
Sheet 4
1) Henry bought 118 oz of dried figs for S36.58 from a wholesale store. Karen picked a
7 oz pack of dried figs for S2.73. Who clinched the better buy?
Henry’s pick: S 0.31/oz ; Karen’s pick: S0.39/oz
Henry picked the better deal.
2) Flight A traveled a distance of 980 miles in 95 minutes. Flight B reached its destination in
82 minutes and covered a distance of 854 miles. Which of the two flights traveled at a
faster speed?
Flight A travelled: 10.32 miles/minute ; Flight B travelled: 10.41 miles/minute
Flight B travelled at a faster speed.
3) Nancy types 388 words in 4 minutes. Her friend, Jenna types 294 words in 3 minutes.
Who types at a faster rate, Nancy or Jenna?
Nancy’s typing speed: 97 words/minute ; Jenna’s typing speed: 98 words/minute
Jenna types at a faster rate.
4) A supermarket has the following offers on storage containers during an X-mas sale: A set
of 5 storage containers for S3.05, 4 containers priced at S 3.12 and an offer of S2.73 on
3 storage containers. Determine the best deal available.
Set of 5: S0.61/container ; Set of 4: S0.78/container ; Set of 3: S0.91/container
The best deal is the offer on 5 storage containers.
5) A total of 348 people attended a health screening on day one of a medical camp over a
6 hour period. The team of doctors attended to 228 people in 4 hours on day two.
Determine the day which recorded lesser number of people per hour.
Day 1 screening: 58 people/hour ; Day 2 screening: 57 people/hour
Day two recorded lesser number of people per hour.
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Name :
Sheet 5
1) Frank and Victor are having a high school reunion at Keywest. Frank drove 184.5 miles in
3 hours and Victor took 2 hours to cover a distance of 131.6 miles to reach their
destination. Which of the two friends has covered more miles per hour?
2) Steve creates a flyer for a Christmas yard sale. Printer A took 48 seconds to make 8 copies.
Printer B reproduced 7 copies in 49 seconds. Which printer took lesser time to print
a card?
3) Ally visited the theme park with her family. She paid S 160 for 5 entry tickets. The
following weekend, she booked 15 tickets for S 450 to visit the same location along
with her friends. For which of the two outings did Ally spend more per ticket?
4) The electricity consumption of the Ryan household for the first month was 451 kWh that
had a billing cycle of 29 days. The following month recorded a consumption of 440 kWh
in 28 days. Which month recorded a lesser consumption of electricity?
5) A pet rescue and adoption center provides new homes for abandoned dogs. Forty-two
labradors were given away for adoption in 6 days and 56 beagles were given new homes
in 8 days. Which breed of dog found more homes per day?
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Name :
Answer key
1) Frank and Victor are having a high school reunion at Keywest. Frank drove 184.5 miles in
3 hours and Victor took 2 hours to cover a distance of 131.6 miles to reach their
destination. Which of the two friends has covered more miles per hour?
Frank drove: 61.5 miles/hour ; Victor drove: 65.8 miles/hour
Victor drove more miles per hour.
2) Steve creates a flyer for a Christmas yard sale. Printer A took 48 seconds to make 8 copies.
Printer B reproduced 7 copies in 49 seconds. Which printer took lesser time to print
a card?
Printer A speed: 6 seconds/copy ; Printer B speed: 7 seconds/copy
Printer A took lesser time to print a card.
3) Ally visited the theme park with her family. She paid S 160 for 5 entry tickets. The
following weekend, she booked 15 tickets for S 450 to visit the same location along
with her friends. For which of the two outings did Ally spend more per ticket?
Family outing: S32/ticket ; Outing with friends: S 30/ticket
Ally spent more per ticket on the family outing.
4) The electricity consumption of the Ryan household for the first month was 451 kWh that
had a billing cycle of 29 days. The following month recorded a consumption of 440 kWh
in 28 days. Which month recorded a lesser consumption of electricity?
First month consumption: 15.55 kWh/day ; Second month consumption: 15.71 kWh/day
The first month recorded a lesser consumption of electricity.
5) A pet rescue and adoption center provides new homes for abandoned dogs. Forty-two
labradors were given away for adoption in 6 days and 56 beagles were given new homes
in 8 days. Which breed of dog found more homes per day?
Adoption of Labradors: 7/day ; Adoption of Beagles: 7/day
Both breeds of dogs found the same number of homes per day.
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Name :
Score :
Sheet 1
Part - A
Find the equation of the line with the given x and y intercepts.
1)
x-intercept =
5
; y-intercept = 6
4
2)
x-intercept = –6 ; y-intercept = –6
3)
x-intercept = –8 ; y-intercept = 8
4)
x-intercept = 5 ; y-intercept =
5)
x-intercept = 9 ; y-intercept = –
3
4
6)
x-intercept = –2 ; y-intercept = 4
7)
x-intercept = –1 ; y-intercept = –7
8)
x-intercept = 3 ; y-intercept = – 5
2
6
2
3
Part - B
1)
Find the equation of the line which cuts the x-axis at (10, 0) and the y-axis at (0, 1).
2)
A line has the x and y intercepts –2 and –8 respectively. Find the equation of the line .
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Name :
Score :
Answer key
Sheet 1
Part - A
Find the equation of the line with the given x and y intercepts.
1)
x-intercept =
5
; y-intercept = 6
4
2)
24x + 5y = 30
3)
x + y = –6
4)
x-intercept = –8 ; y-intercept = 8
x – y = –8
5)
x-intercept = 9 ; y-intercept = –
x-intercept = 5 ; y-intercept =
2
3
2x + 15y = 10
3
4
6)
x-intercept = –2 ; y-intercept = 4
2x – y = –4
x – 12y = 9
7)
x-intercept = –6 ; y-intercept = –6
8)
x-intercept = –1 ; y-intercept = –7
7x + y = –7
x-intercept = 3 ; y-intercept = – 5
2
6
10x – 18y = 15
Part - B
1)
Find the equation of the line which cuts the x-axis at (10, 0) and the y-axis at (0, 1).
x + 10y = 10
2)
A line has the x and y intercepts –2 and –8 respectively. Find the equation of the line .
4x + y = –8
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Score :
Name :
Sheet 2
Part - A
Find the equation of the line with the given x and y intercepts.
4
3
1)
x-intercept = –1 ; y-intercept = 3
2)
x-intercept = 2 ; y-intercept =
3)
x-intercept = 5 ; y-intercept = 5
6
3
4)
x-intercept = –3 ; y-intercept = 7
5)
x-intercept = – 6 ; y-intercept = –9
5
6)
x-intercept = – 2 ; y-intercept = – 5
7
2
7)
x-intercept = –8 ; y-intercept = 4
8)
x-intercept = –6 ; y-intercept = 1
Part - B
1)
Find the equation of the tangent whose x-intercept is –7 and touches the circle at the point (0, 6).
2)
Find the equation of the line which cuts the x-axis at (1, 0) and the y-axis at (0, –2).
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Name :
Score :
Answer key
Sheet 2
Part - A
Find the equation of the line with the given x and y intercepts.
1)
2)
x-intercept = –1 ; y-intercept = 3
3x – y = –3
3)
x-intercept = 5 ; y-intercept = 5
6
3
4)
x-intercept = –3 ; y-intercept = 7
7x – 3y = –21
x-intercept = – 6 ; y-intercept = –9
5
6)
x-intercept = – 2 ; y-intercept = – 5
7
2
35x + 4y = –10
15x + 2y = –18
7)
4
3
2x + 3y = 4
6x + 3y = 5
5)
x-intercept = 2 ; y-intercept =
8)
x-intercept = –8 ; y-intercept = 4
x – 2y = –8
x-intercept = –6 ; y-intercept = 1
x – 6y = –6
Part - B
1)
Find the equation of the tangent whose x-intercept is –7 and touches the circle at the point (0, 6).
6x – 7y = –42
2)
Find the equation of the line which cuts the x-axis at (1, 0) and the y-axis at (0, –2).
2x – y = 2
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Score :
Name :
Sheet 3
Part - A
Find the equation of the line with the given x and y intercepts.
1)
x-intercept = –2 ; y-intercept = –8
2)
x-intercept = –1 ; y-intercept = – 1
2
3)
x-intercept = 9 ; y-intercept = – 1
5
4
4)
x-intercept = 1 ; y-intercept = – 1
7
3
5)
x-intercept =
5
; y-intercept = 6
3
6)
x-intercept = 7 ; y-intercept = 3
7)
x-intercept = –4 ; y-intercept = 9
8)
x-intercept = –2 ; y-intercept = 2
Part - B
1)
Find the equation of the line which cuts the x-axis at (–4, 0) and the y-axis at (0, –2).
2)
A line
has the x and y intercepts 3 and –7 respectively. Find the equation of the line .
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Answer key
Sheet 3
Part - A
Find the equation of the line with the given x and y intercepts.
1)
2)
x-intercept = –2 ; y-intercept = –8
4x + y = –8
3)
x + 2y = –1
x-intercept = 9 ; y-intercept = – 1
5
4
4)
5x – 36y = 9
5)
x-intercept =
x-intercept = 1 ; y-intercept = – 1
7
3
7x – 3y = 1
5
; y-intercept = 6
3
6)
x-intercept = 7 ; y-intercept = 3
3x + 7y = 21
18x + 5y = 30
7)
x-intercept = –1 ; y-intercept = – 1
2
8)
x-intercept = –4 ; y-intercept = 9
9x – 4y = –36
x-intercept = –2 ; y-intercept = 2
x – y = –2
Part - B
1)
Find the equation of the line which cuts the x-axis at (–4, 0) and the y-axis at (0, –2).
x + 2y = –4
2)
A line
has the x and y intercepts 3 and –7 respectively. Find the equation of the line .
7x – 3y = 21
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Sheet 4
Part - A
Find the equation of the line with the given x and y intercepts.
1)
x-intercept = 3 ; y-intercept =
3)
6
7
2)
x-intercept = –4 ; y-intercept = 2
x-intercept = –2 ; y-intercept = –5
4)
x-intercept = – 3 ; y-intercept = 8
2
5)
x-intercept = –9 ; y-intercept = – 1
2
6)
x-intercept = 5 ; y-intercept = –4
8
7)
x-intercept = – 1 ; y-intercept = 2
5
3
8)
x-intercept = –6 ; y-intercept =
9
5
Part - B
1)
A line has the x and y intercepts 5 and 6 respectively. Find the equation of the line .
2)
Find the equation of the tangent whose x-intercept is –9 and touches the circle at the point (0, 3).
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Answer key
Sheet 4
Part - A
Find the equation of the line with the given x and y intercepts.
1)
x-intercept = 3 ; y-intercept =
6
7
2)
2x + 7y = 6
3)
x – 2y = –4
4)
x-intercept = –2 ; y-intercept = –5
5x + 2y = –10
5)
x-intercept = – 3 ; y-intercept = 8
2
16x – 3y = –24
x-intercept = –9 ; y-intercept = – 1
2
6)
x-intercept = 5 ; y-intercept = –4
8
32x – 5y = 20
x + 18y = –9
7)
x-intercept = –4 ; y-intercept = 2
x-intercept = – 1 ; y-intercept = 2
5
3
8)
10x – 3y = –2
x-intercept = –6 ; y-intercept =
9
5
3x – 10y = –18
Part - B
1)
A line has the x and y intercepts 5 and 6 respectively. Find the equation of the line .
6x + 5y = 30
2)
Find the equation of the tangent whose x-intercept is –9 and touches the circle at the point (0, 3).
x – 3y = –9
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Sheet 5
Part - A
Find the equation of the line with the given x and y intercepts.
1)
x-intercept = – 4 ; y-intercept = –3
5
2)
x-intercept = – 5 ; y-intercept = 7
2
4
3)
x-intercept = –1 ; y-intercept =
9
4
4)
x-intercept = –8 ; y-intercept = –6
5)
x-intercept = 2 ; y-intercept = 8
3
5
6)
x-intercept = –4 ; y-intercept = – 3
7
7)
x-intercept = – 6 ; y-intercept = –5
7
8)
x-intercept = 7 ; y-intercept =
1
9
Part - B
1)
Find the equation of the line which cuts the x-axis at (–3, 0) and the y-axis at (0, 7).
2)
A line has the x and y intercepts –8 and 5 respectively. Find the equation of the line .
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Answer key
Sheet 5
Part - A
Find the equation of the line with the given x and y intercepts.
1)
x-intercept = – 4 ; y-intercept = –3
5
2)
15x + 4y = –12
3)
x-intercept = –1 ; y-intercept =
14x – 20y = –35
9
4
4)
9x – 4y = –9
5)
x-intercept = –8 ; y-intercept = –6
3x + 4y = –24
x-intercept = 2 ; y-intercept = 8
3
5
6)
x-intercept = –4 ; y-intercept = – 3
7
3x + 28y = –12
12x + 5y = 8
7)
x-intercept = – 5 ; y-intercept = 7
2
4
x-intercept = – 6 ; y-intercept = –5
7
8)
35x + 6y = –30
x-intercept = 7 ; y-intercept =
1
9
x + 63y = 7
Part - B
1)
Find the equation of the line which cuts the x-axis at (–3, 0) and the y-axis at (0, 7).
7x – 3y = –21
2)
A line has the x and y intercepts –8 and 5 respectively. Find the equation of the line .
5x – 8y = –40
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L1S1
Part - A
Write the equation of the line whose slope and the point through which it passes are given. Express
the equation in standard form.
1)
(–5, –8) and slope m = 5
2)
(1, 5) and slope m = –7
3)
(6, 7) and slope m = 2
4)
(–4, 3) and slope m = 0
5)
(2, –9) and slope m = 1
6)
(–8, –1) and slope m =
7)
(–7, 2) and slope m = – 7
5
8)
(6, –4) and slope m = –3
2
7
Part - B
1)
Find the equation of the line that cuts the x-axis at x = –1 and whose slope is 9.
2)
Find the equation of the line that passes through the point (3, 6) and whose slope is –1.
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Answer key
L1S1
Part - A
Write the equation of the line whose slope and the point through which it passes are given. Express
the equation in standard form.
1)
(–5, –8) and slope m = 5
2)
5x – y = –17
3)
7x + y = 12
4)
(6, 7) and slope m = 2
2x – y = 5
5)
(–4, 3) and slope m = 0
y=3
6)
(2, –9) and slope m = 1
x – y = 11
7)
(1, 5) and slope m = –7
(–8, –1) and slope m =
2
7
2x – 7y = –9
(–7, 2) and slope m = – 7
5
8)
(6, –4) and slope m = –3
3x + y = 14
7x + 5y = –39
Part - B
1)
Find the equation of the line that cuts the x-axis at x = –1 and whose slope is 9.
9x – y = –9
2)
Find the equation of the line that passes through the point (3, 6) and whose slope is –1.
x+y=9
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L1S2
Part - A
Write the equation of the line whose slope and the point through which it passes are given. Express
the equation in standard form.
1)
(4, –3) and slope m = –1
2)
(5, 6) and slope m = –9
3)
(–8, –5) and slope m = –3
4)
(–7, 3) and slope m = 6
7
5)
(2, 1) and slope m =
6)
(4, –1) and slope m = 6
7)
(–5, 1) and slope m = – 4
3
8)
(–9, –7) and slope m = –4
5
4
Part - B
1)
Find the equation of the tangent whose slope is –7 and touches the circle at the point (–5, –7).
2)
Find the equation of the line that cuts the y-axis at (0, 1) and the slope 8.
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Answer key
L1S2
Part - A
Write the equation of the line whose slope and the point through which it passes are given. Express
the equation in standard form.
1)
(4, –3) and slope m = –1
2)
x+y=1
3)
9x + y = 51
4)
(–8, –5) and slope m = –3
3x + y = –29
5)
(2, 1) and slope m =
(–7, 3) and slope m = 6
7
6x – 7y = –63
5
4
6)
5x – 4y = 6
7)
(5, 6) and slope m = –9
(4, –1) and slope m = 6
6x – y = 25
(–5, 1) and slope m = – 4
3
8)
4x + 3y = –17
(–9, –7) and slope m = –4
4x + y = –43
Part - B
1)
Find the equation of the tangent whose slope is –7 and touches the circle at the point (–5, –7).
7x + y = –42
2)
Find the equation of the line that cuts the y-axis at (0, 1) and the slope 8.
8x – y = –1
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L1S3
Part - A
Write the equation of the line whose slope and the point through which it passes are given. Express
the equation in standard form.
1)
(5, 1) and slope m = 8
2)
(–2, –6) and slope m = 0
3)
(–9, 4) and slope m = 7
4)
(–3, 7) and slope m = –5
5)
(3, –8) and slope m = 5
6)
(–1, –5) and slope m = 3
7)
(4, 1) and slope m = – 1
3
8)
(6, –9) and slope m =
2
5
Part - B
1)
Find the equation of the line that cuts the y-axis at y = –6 and whose slope is 2 .
7
2)
If a line passes through the point (–4, 5) with the slope 2, then find the equation of the line.
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L1S3
Part - A
Write the equation of the line whose slope and the point through which it passes are given. Express
the equation in standard form.
1)
(5, 1) and slope m = 8
2)
8x – y = 39
3)
y = –6
4)
(–9, 4) and slope m = 7
7x – y = –67
5)
(–3, 7) and slope m = –5
5x + y= –8
6)
(3, –8) and slope m = 5
5x – y = 23
7)
(–2, –6) and slope m = 0
(–1, –5) and slope m = 3
3x – y = 2
(4, 1) and slope m = – 1
3
8)
x + 3y = 7
(6, –9) and slope m =
2
5
2x – 5y = 57
Part - B
1)
Find the equation of the line that cuts the y-axis at y = –6 and whose slope is 2 .
7
2x – 7y = 42
2)
If a line passes through the point (–4, 5) with the slope 2, then find the equation of the line.
2x – y = –13
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L1S4
Part - A
Write the equation of the line whose slope and the point through which it passes are given. Express
the equation in standard form.
1
1) (–7, –4) and slope m = –5
2) (–8, 8) and slope m =
6
3)
(9, 0) and slope m =
5)
7)
3
4
4)
(1, –2) and slope m = 2
(–3, 1) and slope m = – 7
2
6)
(–4, –6) and slope m = –1
(2, –5) and slope m = –8
8)
(6, 3) and slope m = –4
Part - B
1)
Find the equation of the tangent whose slope is 3 and touches the circle at the point (6, –9).
2)
Find the equation of the line that cuts the y-axis at (0, 7) and the slope –6.
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Answer key
L1S4
Part - A
Write the equation of the line whose slope and the point through which it passes are given. Express
the equation in standard form.
1
1) (–7, –4) and slope m = –5
2) (–8, 8) and slope m =
6
5x + y = –39
3)
(9, 0) and slope m =
x – 6y = –56
3
4
4)
3x – 4y = 27
5)
2x – y = 4
(–3, 1) and slope m = – 7
2
6)
7x + 2y = –19
7)
(1, –2) and slope m = 2
(–4, –6) and slope m = –1
x + y = –10
8)
(2, –5) and slope m = –8
(6, 3) and slope m = –4
4x + y = 27
8x + y = 11
Part - B
1)
Find the equation of the tangent whose slope is 3 and touches the circle at the point (6, –9).
3x – y = 27
2)
Find the equation of the line that cuts the y-axis at (0, 7) and the slope –6.
6x + y = 7
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L1S5
Part - A
Write the equation of the line whose slope and the point through which it passes are given. Express
the equation in standard form.
1)
(3, 8) and slope m = 0
2)
(–6, 0) and slope m = 9
3)
(4, –5) and slope m = 7
4)
(–7, –9) and slope m = –6
5)
(–1, 2) and slope m = – 8
5
6)
(5, –3) and slope m = –2
7)
(–9, –1) and slope m = 3
8)
(2, 7) and slope m = – 5
6
Part - B
1)
Find the equation of the line that cuts the x-axis at x = –4 and whose slope is 4.
2)
Find the equation of the line that passes through the point (0, –8) and whose slope is 7.
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Answer key
L1S5
Part - A
Write the equation of the line whose slope and the point through which it passes are given. Express
the equation in standard form.
1)
(3, 8) and slope m = 0
2)
y=8
3)
9x – y = –54
4)
(4, –5) and slope m = 7
7x – y = 33
5)
(–7, –9) and slope m = –6
6x + y = –51
(–1, 2) and slope m = – 8
5
6)
8x + 5y = 2
7)
(–6, 0) and slope m = 9
(5, –3) and slope m = –2
2x + y = 7
8)
(–9, –1) and slope m = 3
(2, 7) and slope m = – 5
6
5x + 6y = 52
3x – y = –26
Part - B
1)
Find the equation of the line that cuts the x-axis at x = –4 and whose slope is 4.
4x – y = –16
2)
Find the equation of the line that passes through the point (0, –8) and whose slope is 7.
7x – y = 8
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Multi-Step Equations: Integers
Level 1: S1
Solve each equation.
1)
3(x – 4) = 2(–2x + 1)
2)
8q + 6 = 4q – 14
3)
9= v+4
v + 12
4)
7 – (5t – 13) = –25
5)
–3(7p + 5) = 27
6)
14 + 13y = 20y – 21
7)
–8 – 3k = 11
2
8)
–15b + 21 + 5b = –19
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Answer Key
Multi-Step Equations: Integers
Level 1: S1
Solve each equation.
1)
3(x – 4) = 2(–2x + 1)
2)
q = –5
x=2
3)
9= v+4
v + 12
4)
–3(7p + 5) = 27
6)
–8 – 3k = 11
2
k = –10
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14 + 13y = 20y – 21
y=5
p = –2
7)
7 – (5t – 13) = –25
t=9
v = –13
5)
8q + 6 = 4q – 14
8)
–15b + 21 + 5b = –19
b=4
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Multi-Step Equations: Integers
Level 1: S2
Solve each equation.
1)
7h – 5 = 11
4
2)
4(–2k – 8) = 6(k + 18)
3)
–24 = 12(–s – 8)
4)
6 = –3
x+9
5)
15f – 23 = 2(4f + 20)
6)
32 = 6v – (2v + 8)
7)
5c + 17 = 9(–c + 12 + 3c)
8)
13g = –(9 – 12g) – 5
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Answer Key
Multi-Step Equations: Integers
Level 1: S2
Solve each equation.
1)
7h – 5 = 11
4
2)
k = –10
h=7
3)
–24 = 12(–s – 8)
4)
s = –6
5)
15f – 23 = 2(4f + 20)
5c + 17 = 9(–c + 12 + 3c)
c = –7
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6 = –3
x+9
x = –11
6)
f=9
7)
4(–2k – 8) = 6(k + 18)
32 = 6v – (2v + 8)
v = 10
8)
13g = –(9 – 12g) – 5
g = –14
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Multi-Step Equations: Integers
Level 1: S3
Solve each equation.
5(4n – 1)
3
1)
42 = 3(–4a) + 6
2)
5=
3)
14 + 7r + 15 = 10r – 4
4)
–2(–d – 9) = 3d + 14
5)
6(2 + 3z) = –24
6)
9 – 2(7 – 8w) = 11w
7)
–19 – m = 8(1 + m)
8)
7 + u = u + 12
4
8
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Answer Key
Multi-Step Equations: Integers
Level 1: S3
Solve each equation.
1)
42 = 3(–4a) + 6
2)
14 + 7r + 15 = 10r – 4
4)
r = 11
5)
6(2 + 3z) = –24
–19 – m = 8(1 + m)
m = –3
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–2(–d – 9) = 3d + 14
d=4
6)
9 – 2(7 – 8w) = 11w
w=1
z = –2
7)
5(4n – 1)
3
n=1
a = –3
3)
5=
8)
7 + u = u + 12
4
8
u = –17
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Multi-Step Equations: Integers
Level 1: S4
Solve each equation.
1)
–8(r + 9) – 7 = 9
2)
–34 = 19 – 15z + 7
3)
2 – (13 – m) = –(m – 19) – 6
4)
10 = 7
h+5 2+h
5)
18 =
9(6 – 2b)
7
6)
2(–4k + 1)
= –6
9
7)
6g + 21 = 3(4g + 21)
8)
–2(2q – 4) = 10q – 20
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Answer Key
Multi-Step Equations: Integers
Level 1: S4
Solve each equation.
1)
–8(r + 9) – 7 = 9
2)
z=4
r = –11
3)
2 – (13 – m) = –(m – 19) – 6
4)
m = 12
5)
18 =
9(6 – 2b)
7
6g + 21 = 3(4g + 21)
g = –7
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10 = 7
h+5 2+h
h=5
6)
2(–4k + 1)
= –6
9
k=7
b = –4
7)
–34 = 19 – 15z + 7
8)
–2(2q – 4) = 10q – 20
q=2
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Multi-Step Equations: Integers
Level 1: S5
Solve each equation.
1)
1=
2(t + 13)
10 + t
2)
–5(3d + 8) = 35
3)
p – 16
=p+4
5
4)
8(2y –1) = 3(16 + 3y)
5)
13n – 28 = 9n + 32
6)
21 – 9f = –20(f – 6)
7)
47 = 2(w – 1) + 5w
8)
3=
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–3(11 – s)
7
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Answer Key
Multi-Step Equations: Integers
Level 1: S5
Solve each equation.
1)
1=
2(t + 13)
10 + t
2)
d = –5
t = –16
3)
p – 16
=p+4
5
4)
p = –9
5)
13n – 28 = 9n + 32
47 = 2(w – 1) + 5w
w=7
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8(2y –1) = 3(16 + 3y)
y=8
6)
21 – 9f = –20(f – 6)
f=9
n = 15
7)
–5(3d + 8) = 35
8)
3=
–3(11 – s)
7
s = 18
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Multi-Step Equations: Integers
Level 1: S6
Solve each equation.
–4g +12
3–g
1)
10(–2q – 16) = 40
2)
14 =
3)
6(–6u + 4 + 7u) = –12
4)
32(2a + 17) = 8(5 + a)
5)
9v + 15 = 4v + 10
6)
2(–5r + 7) = –11r
7)
9(7 – z) + z = –33
8)
4
=1
2(m – 13)
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Answer Key
Multi-Step Equations: Integers
Level 1: S6
Solve each equation.
1)
10(–2q – 16) = 40
2)
6(–6u + 4 + 7u) = –12
4)
u = –6
5)
9v + 15 = 4v + 10
9(7 – z) + z = –33
z = 12
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32(2a + 17) = 8(5 + a)
a = –9
6)
2(–5r + 7) = –11r
r = –14
v = –1
7)
–4g +12
3–g
g=3
q = –10
3)
14 =
8)
4
=1
2(m – 13)
m = 15
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Score :
Multi-Step Equations - Integers
Sheet 1
1) Aiden borrows a book from a public library. He read a few pages on day one. On day
two, he reads twice the number of pages than he read on day one. On the third day,
he reads six pages less than what he read on the first day. If he read the entire book
that contains 458 pages in three days, how many pages did he read on day three?
2) ‘The Godfather’ sold one million more than twice the number of tickets that were
sold for ‘The Santa Clause’. ‘E.T.’ sold 15 million more than twice the tickets sold for
‘The Godfather’. If 270 million tickets were sold in all, how many tickets were sold out
for ‘The Godfather’ ?
3) Linda is twice as old as Vera. Tanya is four less than four times the age of Linda. Their
total age is two more than nine times the age of Vera. How old is Tanya?
4) The lifespan of a guinea pig is 6 years less than that of a giraffe. The lifespan of a tiger
is 4 times that of the guinea pig. If the total lifespan of the animals is 30 years,
calculate the longevity for the giraffe.
5) A website received 9,347 visits during the first month of its launch. The third
month witnessed three times the number of visits than the second month. If
the website received 13,455 visits over the three month period, how many
visits did it witness during the second month?
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Answer key
Multi-Step Equations - Integers
Sheet 1
1) Aiden borrows a book from a public library. He read a few pages on day one. On day
two, he reads twice the number of pages than he read on day one. On the third day,
he reads six pages less than what he read on the first day. If he read the entire book
that contains 458 pages in three days, how many pages did he read on day three?
x + 2x + x – 6 = 458 ; 110 pages
2) ‘The Godfather’ sold one million more than twice the number of tickets that were
sold for ‘The Santa Clause’. ‘E.T.’ sold 15 million more than twice the tickets sold for
‘The Godfather’. If 270 million tickets were sold in all, how many tickets were sold out
for ‘The Godfather’ ?
x + 2x + 1 + 15 +2(2x + 1) = 270 ; 73 million tickets
3) Linda is twice as old as Vera. Tanya is four less than four times the age of Linda. Their
total age is two more than nine times the age of Vera. How old is Tanya?
x + 2x + 4(2x) - 4 = 9x + 2 ; 20 years
4) The lifespan of a guinea pig is 6 years less than that of a giraffe. The lifespan of a tiger
is 4 times that of the guinea pig. If the total lifespan of the animals is 30 years,
calculate the longevity for the giraffe.
x + x – 6 + 4(x – 6) = 30 ; 10 years
5) A website received 9,347 visits during the first month of its launch. The third
month witnessed three times the number of visits than the second month. If
the website received 13,455 visits over the three month period, how many
visits did it witness during the second month?
9347 + x + 3x = 13455 ; 1,027 visits
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Name :
Score :
Multi-Step Equations - Integers
Sheet 2
1) In the 2006 Winter Olympics, Sweden won 3 medals more than China. Germany
secured one more than twice the number of medals bagged by sweden. If 54
medals were won in all, how many medals did Germany secure?
2) A ship departs from Port Miami with 5,678 tons of cargo. The ship docks at the
Bahamas and unloads some cargo. The crew also loads three times the quantity of
cargo that was unloaded. If the ship holds 8,588 tons now, how many tons of cargo
did the ship unload at the Bahamas?
3) In 2013, a State Library received a three-year grant to add 69,678 books to their
collection. During a used book sale, the library sold 430 books. If the collection
now is five times more than the original number of books, how many books did
the library hold before it received the grant?
4) Harriet gifts each of her friends a pack of markers that costs $7 and 6 retractable
pens. If she has 5 friends and has spent a total of $95 on the gifts, calculate the
price of each pen.
5) Darren has $579 in his checking account. He swipes the card to buy three equally
priced sweaters. He pays five times the amount that he paid for the sweaters to pay
his credit card bill. If he has $165 in his account now, how much did his credit card
dues amount to?
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Answer key
Multi-Step Equations - Integers
Sheet 2
1) In the 2006 Winter Olympics, Sweden won 3 medals more than China. Germany
secured one more than twice the number of medals bagged by sweden. If 54
medals were won in all, how many medals did Germany secure?
x + x + 3 + 2(x + 3) + 1 = 54 ; 29 medals
2) A ship departs from Port Miami with 5,678 tons of cargo. The ship docks at the
Bahamas and unloads some cargo. The crew also loads three times the quantity of
cargo that was unloaded. If the ship holds 8,588 tons now, how many tons of cargo
did the ship unload at the Bahamas?
5678 – x + 3x = 8588 ; 1,455 tons
3) In 2013, a State Library received a three-year grant to add 69,678 books to their
collection. During a used book sale, the library sold 430 books. If the collection
now is five times more than the original number of books, how many books did
the library hold before it received the grant?
69678 + x – 430 = 5x ; 17,312 books
4) Harriet gifts each of her friends a pack of markers that costs $7 and 6 retractable
pens. If she has 5 friends and has spent a total of $95 on the gifts, calculate the
price of each pen.
5(7 + 6x) = 95 ; $2
5) Darren has $579 in his checking account. He swipes the card to buy three equally
priced sweaters. He pays five times the amount that he paid for the sweaters to pay
his credit card bill. If he has $165 in his account now, how much did his credit card
dues amount to?
579 – 3x – 5(3x) = 165 ; $345
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Name :
Score :
Multi-Step Equations - Integers
Sheet 3
1) A gardener plants three different saplings at East Green, Central Park . The number
of magnolia saplings he planted was 3 less than crab apple saplings. The Kwanzan
cherry saplings planted amounted to twice the number of magnolias. If 35 saplings
were planted in all, how many Kwanzan cherry saplings he planted?
2) Mrs. Wilson’s class was asked to paint clay figurines. There were 24 pots of paint in
all, of which 6 pots contained yellow paint and a few pots had green paint. Besides,
there were 2 more pots of brown paint than green paint. How many pots contained
green paint?
3) Gina’s mom filled a pinata with 45 lollypops, a few milk chocolates and peanut
butter cups. The number of peanut butter cups in the pinata was twice the number
of milk chocolates and lollypops. If there were 150 candies in all, how many milk
chocolates were in the pinata?
4) Emma, Noah and Mindy volunteer for a Read Out program at a local preschool
every day. Emma reads 2 hours less than Noah. Mindy reads for twice as many
hours as Emma. Together, they volunteer for a total of 78 hours in a week. How
many hours did Mindy read in a week?
5) The sum of three consecutive numbers is 141. Find the least and the greatest
numbers in the series.
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Name :
Score :
Answer key
Multi-Step Equations - Integers
Sheet 3
1) A gardener plants three different saplings at East Green, Central Park . The number
of magnolia saplings he planted was 3 less than crab apple saplings. The Kwanzan
cherry saplings planted amounted to twice the number of magnolias. If 35 saplings
were planted in all, how many Kwanzan cherry saplings he planted?
x + x – 3 + 2(x – 3) = 35 ; 16 Kwanzan cherry saplings
2) Mrs. Wilson’s class was asked to paint clay figurines. There were 24 pots of paint in
all, of which 6 pots contained yellow paint and a few pots had green paint. Besides,
there were 2 more pots of brown paint than green paint. How many pots contained
green paint?
6 + x + x + 2 = 24 ; 8 pots of green paint
3) Gina’s mom filled a pinata with 45 lollypops, a few milk chocolates and peanut
butter cups. The number of peanut butter cups in the pinata was twice the number
of milk chocolates and lollypops. If there were 150 candies in all, how many milk
chocolates were in the pinata?
45 + x + 2(45 + x) = 150 ; 5 milk chocolates
4) Emma, Noah and Mindy volunteer for a Read Out program at a local preschool
every day. Emma reads 2 hours less than Noah. Mindy reads for twice as many
hours as Emma. Together, they volunteer for a total of 78 hours in a week. How
many hours did Mindy read in a week?
x + x – 2 + 2(x – 2) = 78 ; 38 hours
5) The sum of three consecutive numbers is 141. Find the least and the greatest
numbers in the series.
x + x + 1 + x + 2 = 141 ; 46 and 48
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Name :
Sheet 1
Parallelogram
A) Find the indicated side length of each parallelogram.
1)
2)
3)
33
)y
d
Q
(10 – ) in
Y
X
R
P
(–5
(1 +
+6
3 )
) ft
ft
(
B
+
C
D
A
Z
(–3 ) in
W
S
=
=
=
AB =
XY =
PS =
2
(–
+
6
d
)y
B) Find the indicated side lengths of each parallelogram.
5)
6)
V
2
ft
0
+1
d
)y
d
)y
(2 – 2) ft
(9
(13
(3 + 14) yd
E
K
(
H
=
=
– 8) f t
W
=
=
=
=
MN =
GH =
TU =
KN =
FG =
UV =
Printable Worksheets @ www.mathworksheets4kids.com
in
N
+ 2)
U
( + 2) ft
G
F
(3 + 23) in
M (–18 + 7 ) yd L
(–3
(–13 + 7 ) in
4)
(56 +
6 )i
n T
Name :
Answer key
Sheet 1
Parallelogram
A) Find the indicated side length of each parallelogram.
1)
2)
3)
33
)y
d
Q
(10 – ) in
Y
X
R
P
(–5
(1 +
+6
3 )
) ft
ft
(
B
+
C
D
A
Z
(–3 ) in
W
S
2
(–
+
6
d
)y
=
2
=
–5
=
7
AB =
7 ft
XY =
15 in
PS =
40 yd
B) Find the indicated side lengths of each parallelogram.
5)
6)
V
2
ft
(9
0
+1
(13
d
)y
d
)y
(2 – 2) ft
in
N
(3 + 14) yd
E
K
(
H
+ 2)
U
( + 2) ft
G
F
(3 + 23) in
M (–18 + 7 ) yd L
(–3
(–13 + 7 ) in
4)
=
8
=
3
– 8) f t
=
16
=
4
W
(56 +
6 )i
n T
=
9
=
–6
MN =
39 yd
GH =
6 ft
TU =
50 in
KN =
38 yd
FG =
8 ft
UV =
20 in
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 2
Parallelogram
A) Find the indicated side length of each parallelogram.
1)
2)
3)
U
yd
n
)i
G
3
M
F
(–
24
L
(2
+
7
)i
n
(2
–5
T
)f
t
t
(6
6+
H
( – 6) yd
N
E
K
W
=
=
=
TW =
EH =
KL =
B) Find the indicated side lengths of each parallelogram.
5)
(7
Q
X
(7 + 46) in
W
R
=
=
(6
+
3)
in
yd
) ft
0 )
+5
S
+1
(5 ) ft
( 28
=
=
=
YZ =
PS =
AB =
ZW =
SR =
BC =
Printable Worksheets @ www.mathworksheets4kids.com
A
=
B
D
(–6
Z
) yd
ft
(–9 + 29) yd
0)
) in
–6
(26 – 10 ) yd
+2
+1
(6 – 5) ft
(9
C
P
(9
Y
6)
(3 + 62) in
4)
–
3
V
)f
4
Name :
Answer key
Sheet 2
Parallelogram
A) Find the indicated side length of each parallelogram.
1)
2)
3)
U
yd
n
)i
G
3
M
F
(–
24
L
(2
+
7
)i
n
(2
–5
T
)f
t
t
(6
6+
H
( – 6) yd
N
E
K
W
=
–8
=
9
=
6
TW =
42 in
EH =
3 yd
KL =
18 ft
B) Find the indicated side lengths of each parallelogram.
5)
(7
Q
X
=
5
=
2
YZ =
ZW =
(7 + 46) in
W
R
(6
+
3)
in
A
=
9
=
4
25 ft
PS =
38 ft
SR =
Printable Worksheets @ www.mathworksheets4kids.com
yd
) ft
0 )
+5
S
+1
(5 ) ft
( 28
B
D
(–6
Z
) yd
ft
(–9 + 29) yd
0)
) in
–6
(26 – 10 ) yd
+2
+1
(6 – 5) ft
(9
C
P
(9
Y
6)
(3 + 62) in
4)
–
3
V
)f
4
=
–3
=
7
74 in
AB =
56 yd
57 in
BC =
64 yd
Name :
Sheet 3
Parallelogram
A) Find the indicated side length of each parallelogram.
1)
2)
3)
(13 + 2 ) yd
Y
+
(4
G
t Q
(–7 ) in
R
(3 + 4) yd
X
Z
10
)f
P
1
(1
S
W
+
ft
1)
H (–9 – 8) in E
=
=
=
YZ =
PS =
GF =
B) Find the indicated side lengths of each parallelogram.
5)
6)
7)
yd
+1
(3
=
t
T
M
=
A
(4
W (4
in
– 3)
(7 – 10 ) yd
N
)f
D
2
L
–1
(5
B
(–8 + 17) yd
+1
)y
d
(7 + 24) in
(11 ) in
C
+
3
)f
t
K
(1
V
(18
in U
+ )
(3 – 45) ft
4)
=
=
=
=
TU =
AB =
LM =
UV =
DA =
KL =
Printable Worksheets @ www.mathworksheets4kids.com
ft
F
Name :
Answer key
Sheet 3
Parallelogram
A) Find the indicated side length of each parallelogram.
1)
2)
3)
(13 + 2 ) yd
Y
+
(4
G
t Q
(–7 ) in
R
(3 + 4) yd
X
Z
10
)f
P
W
+
1
(1
S
ft
1)
H (–9 – 8) in E
=
9
=
3
=
–4
YZ =
31 yd
PS =
34 ft
GF =
28 in
B) Find the indicated side lengths of each parallelogram.
5)
6)
7)
yd
+1
(3
=
6
=
7
TU =
UV =
T
t
(4
W (4
in
– 3)
A
(7 – 10 ) yd
N
)f
D
2
L
–1
(5
B
(–8 + 17) yd
+1
)y
d
(7 + 24) in
(11 ) in
C
+
3
)f
t
K
(1
V
(18
in U
+ )
(3 – 45) ft
4)
M
=
8
=
–5
66 in
AB =
25 in
DA =
Printable Worksheets @ www.mathworksheets4kids.com
=
2
=
18
41 yd
LM =
9 ft
57 yd
KL =
7 ft
ft
F
Name :
Type 1: S1
Multi-Step Equations: Shapes
Find the unknown value given in each shape.
13
2)
6 cm
3)
m
22
8+
4 cm
+
2s
m+
2
5+m
m
)+
10 70 m
5r
(
–6
+
3(6
s+
1)
s)
s =
m =
t–
cm
6m
2(9
m
8 mm
6)
13
+3
5)
1)
4)
r =
9x – 2
2
5(4q – 3) – (7q – 8)
t =
10 cm
2p
–7 +
p =
)
+8
14 cm
v =
Printable Worksheets @ www.mathworksheets4kids.com
6)
)–9
+ 2p
19 m
9)
a–
–2(
2(–9
2
(5 – 2v)
3
( 4a
8)
15 m
3) –
7)
x =
(a +
q =
36 m
a =
Name :
Answer Key
Type 1: S1
Multi-Step Equations: Shapes
Find the unknown value given in each shape.
13
2)
6 cm
3)
m
22
8+
4 cm
+
2s
m+
2
5+m
m
)+
10 70 m
5r
(
–6
+
3(6
s+
1)
s)
m =
s =
–6
r =
8 mm
13
t–
cm
6m
2(9
m
–2
6)
+3
5)
1)
4)
–1
9x – 2
2
5(4q – 3) – (7q – 8)
10 cm
2p
–7 +
p =
10
14 cm
v =
Printable Worksheets @ www.mathworksheets4kids.com
6)
)–9
+ 2p
19 m
9)
a–
–2(
2(–9
2
(5 – 2v)
3
)
8)
15 m
2
+8
7)
x =
( 4a
t =
3) –
1
(a +
q =
2
3
–8
36 m
a =
–17
Name :
Type 1: S2
Multi-Step Equations: Shapes
Find the unknown value given in each shape.
1)
2)
3)
2(g – 3) + 1
m
c
30
18
54
9(–
6u
–18
)
mm
cm
6(2y –3)
9m
g =
4h
24 +
– 1)
5w
cm
w=
8)
6
12
2k +
9)
9 mm
10)
21 cm
3n +
3(5 –
30 cm
7)
h=
5 mm
5(b
8
0
)–3
w–
+ 15
30
28 mm
b =
3m
14 m
3(w
–1
6)
12 –
5)
+2
)
4)
u=
–8(h
y =
2f + 6
2
3k
n =
k =
Printable Worksheets @ www.mathworksheets4kids.com
f =
Name :
Answer Key
Type 1: S2
Multi-Step Equations: Shapes
Find the unknown value given in each shape.
1)
2)
3)
2(g – 3) + 1
m
c
30
18
54
9(–
6u
–18
)
mm
cm
6(2y –3)
14 m
4h
– 1)
12 –
5w
30
cm
28 mm
8)
3n +
6
3m
12
3(5 –
2k +
30 cm
7)
h=
13
9)
–1
9 mm
10)
5 mm
w=
–18
21 cm
b =
–4
0
)–3
w–
+ 15
24 +
8
5(b
6)
3(w
–1
u=
7
5)
+2
)
4)
g =
3
–8(h
y =
9m
2f + 6
2
3k
n =
2
k =
Printable Worksheets @ www.mathworksheets4kids.com
5
f =
6
Name :
Type 1: S3
Multi-Step Equations: Shapes
Find the unknown value given in each shape.
2)
3)
)
34 m
5–8
h)
–y
2(h –
2
7(1
1
6(2
cm
27
–t
)+
9
1)
63 mm
y =
t =
6)
z+
12
18
–6
2(–s + 6) + 4
10 cm
5)
10 mm
4)
h=
5m
5(d – 1)
10(6 – d) + 5d
9(4 – 2s) – 4
d =
z =
8)
9)
7
w=
Printable Worksheets @ www.mathworksheets4kids.com
p)
+2
7 cm
p=
4
–1
3(7
65 m
13p
2(3
m
+ 4)
56 m
8c
8(6k
–w
)
m
m
75 m
k =
30
7)
s =
Name :
Answer Key
Type 1: S3
Multi-Step Equations: Shapes
Find the unknown value given in each shape.
2)
3)
)
34 m
5–8
h)
–y
2(h –
2
7(1
1
6(2
cm
27
–t
)+
9
1)
63 mm
y =
–1
6)
z+
12
18
–6
2(–s + 6) + 4
5m
5(d – 1)
10(6 – d) + 5d
9(4 – 2s) – 4
11
z =
s =
8)
9)
7
2(3
m
3(7
+2
7 cm
p)
13p
+ 4)
56 m
8c
8(6k
–w
)
m
m
75 m
–25
p=
5
65 m
k =
1
2
1
30
7)
–4
4
d =
–6
10 cm
5)
10 mm
4)
h=
2
w=
Printable Worksheets @ www.mathworksheets4kids.com
–1
t =
Name :
Score :
Solving Multi-Step Inequalities
Solve each inequality.
1)
3(6x + 2) < 9
2)
2x + 1 ≥ 5
3
3)
3x + 2x > 2
4
4)
25 + 2x ≤ 35 – x
3
5)
4x + 11 ≥ 6
2
6)
8(1 + 2x) < 32
7)
3x + x ≤ 30
7
8)
7x – 4 > 4
6
Printable Math Worksheets @ www.mathworksheets4kids.com
ES1
Name :
Answer key
Score :
Solving Multi-Step Inequalities
Solve each inequality.
1)
3(6x + 2) < 9
2)
x< 1
6
3)
3x + 2x > 2
4
x≥7
4)
x> 8
11
5)
4x + 11 ≥ 6
2
3x + x ≤ 30
7
25 + 2x ≤ 35 – x
3
x≤6
6)
8(1 + 2x) < 32
x< 3
2
x≥ 1
4
7)
2x + 1 ≥ 5
3
8)
x ≤ 21
Printable Math Worksheets @ www.mathworksheets4kids.com
7x – 4 > 4
6
x>4
ES1
Name :
Score :
Solving Multi-Step Inequalities
Solve each inequality.
1)
x + 2x ≤ 10
3
2)
6x – x > 5
5
3)
2(3x + 4) < 12
4)
4x + 3 ≥ 8
2
5)
5x – 7 ≤ 15 – x
6
6)
7(2 + 6x) < 21
7)
2x – 5 > 3
7
8)
8x + 14 ≥ 7
3
Printable Math Worksheets @ www.mathworksheets4kids.com
ES2
Name :
Score :
Answer key
Solving Multi-Step Inequalities
Solve each inequality.
1)
x + 2x ≤ 10
3
2)
x≤6
3)
2(3x + 4) < 12
x > 25
4)
x< 2
3
5)
5x – 7 ≤ 15 – x
6
2x – 5 > 3
7
4x + 3 ≥ 8
2
x ≥ 13
4
6)
7(2 + 6x) < 21
x< 1
6
x ≤ 12
7)
6x – x > 5
5
8)
x > 13
Printable Math Worksheets @ www.mathworksheets4kids.com
8x + 14 ≥ 7
3
x≥ 7
8
ES2
Name :
Score :
Solving Multi-Step Inequalities
Solve each inequality.
1)
4x – 6 > 2
5
2)
3(6x – 8) < 9
3)
9x – x > 3
3
4)
5x + 4 ≥ 6
4
5)
3(2 + 11x) < 18
6)
2x + 26 ≤ 56 – x
3
7)
6x + 13 ≥ 2
10
8)
x + 7x ≤ 4
2
Printable Math Worksheets @ www.mathworksheets4kids.com
ES3
Name :
Answer key
Score :
Solving Multi-Step Inequalities
Solve each inequality.
1)
4x – 6 > 2
5
2)
x < 11
6
x>4
3)
9x – x > 3
3
4)
x> 3
2
5)
3(2 + 11x) < 18
6x + 13 ≥ 2
10
5x + 4 ≥ 6
4
x≥4
6)
x< 4
11
7)
3(6x – 8) < 9
2x + 26 ≤ 56 – x
3
x ≤ 18
8)
x≥ 7
6
Printable Math Worksheets @ www.mathworksheets4kids.com
x + 7x ≤ 4
2
x≤ 8
9
ES3
Name :
Score :
Solving & Graphing Inequalities
ES1
Solve each inequality and graph the solution.
1) 2(6x – 5) < 14
-6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
3) 7x + 1 ≥ 5
3
-12 -10 -8 -6
-4 -2
0
5
10 15 20 25 30
0
2
4
6
8
10 12
-4
-3 -2 -1
0
1
2
3
4
5
6
7
8
6) 4x + 8 ≤ 12
2
-42 -35 -28 -21 -14 -7
0
7
14 21 28 35 42
0
-4
-2
0
2
4
6
8
8) 3 + 2x ≥ 17 – x
5
7) 5(x – 2) > 6
10
-14
-30 -25 -20 -15 -10 -5
4) 4(5x + 2) ≤ 28
5) 9x – x < 2
7
-28
3x – 8 > 1
7
2)
14
28
42
56
-20 -15 -10 -5
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0
5
10 15 20 25 30 35 40
Name :
Score :
Answer key
Solving & Graphing Inequalities
ES1
Solve each inequality and graph the solution.
1) 2(6x – 5) < 14
3x – 8 > 1
7
2)
x<2
-6 -5 -4
x>5
-3 -2 -1
0
1
2
3
4
5
6
3) 7x + 1 ≥ 5
3
-30 -25 -20 -15 -10 -5
-4 -2
0
2
4
6
8
10 12
-4
-3 -2 -1
0
6) 4x + 8 ≤ 12
2
x<7
x≤4
-42 -35 -28 -21 -14 -7
0
7
14 21 28 35 42
-4
-2
1
2
3
4
0
2
4
5
6
6
7
8
8
8) 3 + 2x ≥ 17 – x
5
7) 5(x – 2) > 6
10
x > 14
-14
10 15 20 25 30
x≤1
5) 9x – x < 2
7
-28
5
4) 4(5x + 2) ≤ 28
x≥2
-12 -10 -8 -6
0
x ≥ 10
0
14
28
42
56
-20 -15 -10 -5
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0
5
10 15 20 25 30 35 40
Name :
Score :
Solving & Graphing Inequalities
ES2
Solve each inequality and graph the solution.
1) 5x – 3 ≤ 11
2
-30 -25 -20 -15 -10 -5
2) 4(2x – 8) > 16
0
5
10 15 20 25 30
-3 -2 -1
0
1
2
3
4
5
6
0
4
8 12 16 20 24
7) x – 3x < 8
5
-4
0
4
0
2
4
6
8
10 12
-42 -35 -28 -21 -14 -7
0
7
14 21 28 35 42
6) 6x + 8 ≥ 10 + x
5
5) 8x + 14 > 10
11
-24 -20 -16 -12 -8 -4
-4 -2
4) 7x + 5 < 9
6
3) 3(4x + 1) ≥ 27
-6 -5 -4
-12 -10 -8 -6
8 12 16 20 24 28 32 36 40 44
-20
8)
-16
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-10
0
10
20
30
40
8
16
24
32
9(x – 4) ≤ 3
12
-8
0
Name :
Score :
Answer key
Solving & Graphing Inequalities
ES2
Solve each inequality and graph the solution.
1) 5x – 3 ≤ 11
2
2) 4(2x – 8) > 16
x≤5
x>6
-30 -25 -20 -15 -10 -5
0
5
10 15 20 25 30
-12 -10 -8 -6
-4 -2
0
2
4
-42 -35 -28 -21 -14 -7
0
7
14 21 28 35 42
x≥2
-3 -2 -1
0
1
2
3
4
5
6
6) 6x + 8 ≥ 10 + x
5
x > 12
x ≥ 10
-24 -20 -16 -12 -8 -4
0
4
8 12 16 20 24
7) x – 3x < 8
5
-20
8)
x < 20
0
4
10 12
x<7
5) 8x + 14 > 10
11
-4
8
4) 7x + 5 < 9
6
3) 3(4x + 1) ≥ 27
-6 -5 -4
6
-10
0
10
20
30
40
8
16
24
32
9(x – 4) ≤ 3
12
x≤8
8 12 16 20 24 28 32 36 40 44
-16
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-8
0
Name :
Score :
Solving & Graphing Inequalities
ES3
Solve each inequality and graph the solution.
2) 3(x – 10) < 6
9
1) x + 5x > 33
6
-18
-9
0
9
18
27
36
-42 -35 -28 -21 -14 -7
0
7 14 21 28 35 42
5) 7x – 5 ≤ 18
4
0 11 22 33 44 55 66
3
14
28
42
56
-20 -15 -10 -5
0
5
10 15 20 25 30 35 40
6
-6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
0
2
4
6
8
10 12
8) 6x + 4 > 8
5
7) 2(4x + 8) ≥ 40
0
0
6) 6(9x – 2) < 42
-66 -55 -44 -33 -22 -11
-6 -3
-14
4) 3x – 16 ≥ 24 – x
5
3) 2x + 14 ≤ 7
8
-9
-28
9 12 15 18 21 24 27
-12 -10 -8 -6
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-4 -2
Name :
Score :
Answer key
Solving & Graphing Inequalities
ES3
Solve each inequality and graph the solution.
1) x + 5x > 33
6
2) 3(x – 10) < 6
9
x > 18
x < 28
-18
-9
0
9
18
27
36
-28
x ≤ 21
14
28
42
56
x ≥ 25
-42 -35 -28 -21 -14 -7
0
7 14 21 28 35 42
5) 7x – 5 ≤ 18
4
-20 -15 -10 -5
0
5
10 15 20 25 30 35 40
6) 6(9x – 2) < 42
x ≤ 11
x<1
-66 -55 -44 -33 -22 -11
0 11 22 33 44 55 66
-6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
0
2
4
6
8
10 12
8) 6x + 4 > 8
5
7) 2(4x + 8) ≥ 40
x≥3
-6 -3
0
4) 3x – 16 ≥ 24 – x
5
3) 2x + 14 ≤ 7
8
-9
-14
x>6
0
3
6
9 12 15 18 21 24 27
-12 -10 -8 -6
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-4 -2
Name :
Score :
Solving Compound Inequalities
Multi-step: S1
Solve each inequality.
4x – 8
> –16
5
1)
x + 2x ≤ –5 and 6(9 + 3x) < 18
3
2)
12 >
3)
–x + 23
–x − 5
> 4 or
≤ –9
7
2
4)
–21 < x + x and –38 > 19(6x − 8)
6
5)
–13 ≤
9x + 2
<5
4
6)
6(2x + 13) < –18 or 5x – 7 ≥ 3
6
7)
–45 ≥ 15(7x + 18) or –10 ≥
8)
14 > –x + 35 and –x − 46 ≤ –5
3
11
x
+x
9
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Name :
Score :
Answer key
Solving Compound Inequalities
Multi-step: S1
Solve each inequality.
1)
x + 2x ≤ –5 and 6(9 + 3x) < 18
3
2)
x ≤ −3
3)
–x + 23
–x − 5
> 4 or
≤ –9
7
2
–13 ≤
4)
9x + 2
<5
4
6)
–45 ≥ 15(7x + 18) or –10 ≥
–21 < x + x and –38 > 19(6x − 8)
6
−18 < x < 1
−6 ≤ x < 2
7)
4x – 8
> –16
5
–18 < x < 17
x < −5 or x ≥ 13
5)
12 >
6(2x + 13) < –18 or 5x – 7 ≥ 3
6
x < −8 or x ≥ 5
x
+x
9
8)
x ≤ –3
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14 > –x + 35 and –x − 46 ≤ –5
3
11
x≥9
Name :
Score :
Solving Compound Inequalities
Multi-step: S2
Solve each inequality.
1)
–52 ≥ 13(4x + 36) or –6 ≥ x + x
2
3)
–9 ≤
5)
7)
2)
3 ≥ x + 19 and x − 15 < –4
8
10
4)
6(9x + 14) < –24 or 7x – 2 ≥ 8
5
–x + 35
–x − 6
> 11 or
≤ –1
4
7
6)
–18 < x + x and –27 > 3(2x − 5)
8
x + 6x ≤ –22 and 13(7 + 5x) < 26
5
8)
6>
8x + 5
< 15
3
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3x – 9
> –12
2
Name :
Score :
Answer key
Solving Compound Inequalities
Multi-step: S2
Solve each inequality.
1)
–52 ≥ 13(4x + 36) or –6 ≥ x + x
2
2)
3 ≥ x + 19 and x − 15 < –4
8
10
x ≤ −4
3)
–9 ≤
8x + 5
< 15
3
x < −25
4)
6(9x + 14) < –24 or 7x – 2 ≥ 8
5
−4 ≤ x < 5
5)
–x + 35
–x − 6
> 11 or
≤ –1
4
7
x < −2 or x ≥ 6
6)
–18 < x + x and –27 > 3(2x − 5)
8
x < −9 or x ≥ 1
7)
x + 6x ≤ –22 and 13(7 + 5x) < 26
5
−16 < x < –2
8)
x ≤ –10
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6>
3x – 9
> –12
2
−5 < x < 7
Name :
Score :
Solving Compound Inequalities
Multi-step: S3
Solve each inequality.
3x + 2
< –1
10
2)
2(6x + 8) < –32 or 5x – 9 ≥ 3
7
x + 8x ≥ –11 and 5(13 + 2x) > 45
3
4)
7>
5)
–36 ≥ 9(6x + 14) or 10 ≥ x + x
4
6)
–12 < –x − 6 and –x + 19 ≤ 2
2
13
7)
–x + 15 > 2 or –x − 7 ≤ –3
9
6
8)
–4 < x + x and –26 > 2(11x + 9)
3
1)
–4 ≤
3)
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4x – 1
> –9
5
Name :
Score :
Answer key
Solving Compound Inequalities
Multi-step: S3
Solve each inequality.
1)
–4 ≤
3x + 2
< –1
10
2)
2(6x + 8) < –32 or 5x – 9 ≥ 3
7
−14 ≤ x < −4
3)
x + 8x ≥ –11 and 5(13 + 2x) > 45
3
x < −4 or x ≥ 6
4)
x > –2
5)
–36 ≥ 9(6x + 14) or 10 ≥ x + x
4
–x + 15 > 2 or –x − 7 ≤ –3
9
6
4x – 1
> –9
5
−11 < x < 9
6)
x≤8
7)
7>
–12 < –x − 6 and –x + 19 ≤ 2
2
13
−7 ≤ x < 18
8)
x < −3 or x ≥ 11
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–4 < x + x and –26 > 2(11x + 9)
3
−3 < x < −2
Name :
Systems of Equations
Sheet 1
A) Determine whether the ordered pair is a solution to the given system of
equations.
1)
(1, 5) ;
3)
(7, –4) ;
B)
5)
–5
+ 6 = 25
–7
+ 8 = 33
9 + 4 = –8
6 + 5 – 42 = 0
2)
(–2, 0) ;
4)
(–3,– 2) ;
8 – 3 = –16
50 = –9 – 2
–7 – 4 = 29
3 = –7 +
Check whether (6, 9) is a solution of the systems of linear equations.
+ 7 = 69
6)
6 + 4 = 78
–2 + 5 = 34
–7 = –61 – 8
C) Write a system of linear equations that has the solution (4, 3).
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Name :
Answer key
Systems of Equations
Sheet 1
A) Determine whether the ordered pair is a solution to the given system of
equations.
1)
(1, 5) ;
–5
+ 6 = 25
–7
+ 8 = 33
2)
(–2, 0) ;
Yes
3)
(7, –4) ;
9 + 4 = –8
6 + 5 – 42 = 0
5)
50 = –9 – 2
No
4)
No
B)
8 – 3 = –16
(–3,– 2) ;
–7 – 4 = 29
3 = –7 +
Yes
Check whether (6, 9) is a solution of the systems of linear equations.
6)
+ 7 = 69
6 + 4 = 78
Yes
–2 + 5 = 34
–7 = –61 – 8
No
C) Write a system of linear equations that has the solution (4, 3).
(Answer may vary)
3 + = 15 ; –5 + 4 = –8
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Name :
Systems of Equations
Sheet 2
A) Determine whether the ordered pair is a solution to the given system of
equations.
1)
(2, 6) ;
3)
(–3, 9) ;
B)
5)
39 = 2 + 5
–3 – 7 = –50
+ 3 =0
–2 + 9 = 87
2)
(–1, –4) ;
4)
(11, –7) ;
–7 + 4 = –9
6 = –10 –
–3 – 9 = 7
8 + 4 = 23
Check whether (–5, 7) is a solution of the systems of linear equations.
–5 + 7 = 74
6)
– 5 = –40
26 = 6 + 8
2 – 4 = –38
C) Write a system of linear equations that has the solution (0, –9).
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Name :
Answer key
Systems of Equations
Sheet 2
A) Determine whether the ordered pair is a solution to the given system of
equations.
1)
(2, 6) ;
39 = 2 + 5
2)
–3 – 7 = –50
(–1, –4) ;
No
3)
(–3, 9) ;
5)
6 = –10 –
Yes
+ 3 =0
4)
–2 + 9 = 87
Yes
B)
–7 + 4 = –9
(11, –7) ;
–3 – 9 = 7
8 + 4 = 23
No
Check whether (–5, 7) is a solution of the systems of linear equations.
6)
–5 + 7 = 74
– 5 = –40
26 = 6 + 8
2 – 4 = –38
Yes
Yes
C) Write a system of linear equations that has the solution (0, –9).
(Answer may vary)
4
+ 6 = –54 ; 7
– 3 = 27
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Name :
Systems of Equations
Sheet 3
A) Determine whether the ordered pair is a solution to the given system of
equations.
1)
(–7, 8) ;
3)
(5, 12) ;
B)
5)
–7 = –77 – 3
5 + 2 + 19 = 0
–8 + 5 = 20
4 – 7 = 13
2)
(3, –1) ;
4)
(0, 6) ;
9 – 8 = –33
6 – 3 = 21
–9 = + 2
9 – 8 = 54
Check whether (2, –4) is a solution of the systems of linear equations.
7 – 6 = 38
6)
16 = –4 +
3 = –22 + 5
–2
– 9 = 47
C) Write a system of linear equations that has the solution (–9, –10).
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Name :
Answer key
Systems of Equations
Sheet 3
A) Determine whether the ordered pair is a solution to the given system of
equations.
1)
(–7, 8) ;
–7 = –77 – 3
5 + 2 + 19 = 0
2)
(3, –1) ;
Yes
3)
(5, 12) ;
–8 + 5 = 20
4 – 7 = 13
5)
6 – 3 = 21
Yes
4)
(0, 6) ;
Yes
B)
9 – 8 = –33
–9 = + 2
9 – 8 = 54
No
Check whether (2, –4) is a solution of the systems of linear equations.
7 – 6 = 38
6)
16 = –4 +
3 = –22 + 5
–2
No
– 9 = 47
No
C) Write a system of linear equations that has the solution (–9, –10).
(Answer may vary)
2 – = –8 ; –3 – 6 = 87
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Name :
Sheet 1
Systems of Equations - Graphing
Graph each system of equations and find the solution.
1)
=6–2 ;
= –4 + 16
2)
=
1
4
+8 ;
16
14
12
10
8
6
4
2
10
8
6
4
2
-3 -2 -1
-2
1 2 3 4 5 6 7
-4
-6
3)
-8
-12 -8 -4
-2
-10
-4
= +7 ;
=8
= –35 – 5
4)
=–
1
3
4 8 12 16 20 24 28
7
6
5
4
3
2
1
1 2
-2
5)
=–
2
– 18 ;
7
-3
-21 -18 -15 -12 -9 -6 -3
-1
-4
-2
-5
-3
= 4 – 48
6)
=2 ;
3 6 9
=2+3
8
4
-35 -28 -21 -14 -7
-4
-8
5
4
3
2
1
-8 -7 -6 -5 -4 -3 -2 -1
-1
2
3
=–
+3 ;
7 14 21 28 35
-12
-16
8
6
4
2
-10 -8 -6 -4 -2
-2
-4
-20
-6
-24
-28
-8
-32
Printable Worksheets @ www.mathworksheets4kids.com
-10
-12
2 4 6 8 10
Name :
Answer key
Sheet 1
Systems of Equations - Graphing
Graph each system of equations and find the solution.
=6–2 ;
= –4 + 16
2)
=
1
4
+8 ;
16
14
12
10
8
6
4
2
10
8
6
=–
=
4
6–
4
2
6
+1
2
-3 -2 -1
-2
1 2 3 4 5 6 7
-4
-6
-8
-12 -8 -4
-2
-10
-4
(5, –4)
3)
=8
= +7 ;
4 8 12 16 20 24 28
(8, 10)
= –35 – 5
4)
=–
1
3
+
=
7
6
5
4
5
= –35 –
-4
-2
-5
-3
(–7, 0)
=–
2
– 18 ;
7
6)
=2 ;
=2+3
8
4
7 14 21 28 35
-10 -8 -6 -4 -2
-2
3
-24
-28
(7, –20)
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2 4 6 8 10
-6
-20
-32
-4
=2+
8
6
4
2
= 4 – 48
-35 -28 -21 -14 -7
-4
-8
=– 2
7 – 1 -12
8
-16
3 6 9
(–9, 6)
= 4 – 48
=2
5)
3
-21 -18 -15 -12 -9 -6 -3
-1
+
-3
1
– 3
-2
=
2
=– 3
1 2
3
2
1
-8 -7 -6 -5 -4 -3 -2 -1
-1
5
4
3
2
1
7
2
3
=–
+3 ;
8
1 +
= 4
=8
1)
-8
-10
-12
(–2, –4)
Name :
Sheet 2
Systems of Equations - Graphing
Graph each system of equations and find the solution.
1)
1
3
=
–3 ;
= –6 +
1
6
2)
= –4 ;
= 2 – 12
12
9
6
3
-36 -30 -24 -18 -12 -6
-3
3)
2
3
=
16
12
8
4
6 12 18 24
-5 -4 -3 -2 -1
-4
-6
-8
-9
-12
-12
-16
-15
-20
-18
-24
+ 22 ;
=
1
3
+ 17
4)
=8 +3 ;
5
4
3
2
1
-3 -2 -1
-1
1 2 3 4 5 6 7
-3
3 6 9
-4
-5
=6
-2
-12
= + 10 ;
6)
=
3
4
+2 ;
=6–
1
4
8
6
4
2
-10 -8 -6 -4 -2
-2
48
42
36
30
24
18
12
6
5)
1 2 3 4 5
=3+
-21 -18 -15 -12 -9 -6 -3
-6
2 4 6 8 10
-4
-6
7
6
5
4
3
2
1
-8
-20 -16 -12 -8 -4
-1
-10
-2
-12
-3
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4 8 12 16 20
Name :
Answer key
Sheet 2
Systems of Equations - Graphing
Graph each system of equations and find the solution.
1)
1
3
=
–3 ;
= –6 +
1
6
2)
= –4 ;
= 2 – 12
12
9
6
3
16
12
8
4
=
–4
-36 -30 -24 -18 -12 -6
3 -3
1 –
-6
= 3
6 12 18 24
-5 -4 -3 -2 -1
-4
1
+
= –6 6
-12
-12
2-16
–1
-20
=2
-15
-18
-24
(–18, –9)
3)
2
3
=
+ 22 ;
1 2 3 4 5
-8
-9
(2, –8)
1
3
=
+ 17
4)
=8 +3 ;
=3+
48
42
36
30
24
2
2 +2
= 3
18
1 + 17 12
=3
6
5
4
3
=
3
+
2
1
-4
-5
(–15, 12)
= + 10 ;
(0, 3)
=6
-2
-3
3 6 9
-12
5)
1 2 3 4 5 6 7
=8 +3
-21 -18 -15 -12 -9 -6 -3
-6
-3 -2 -1
-1
6)
=
3
4
+2 ;
=6–
=6
2 4 6 8 10
-4
-6
7
6
5
4
3
2
1
-8
-20 -16 -12 -8 -4
-1
-10
-2
-12
-3
(–4, 6)
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= 3
4 +2
1
– 4
-10 -8 -6 -4 -2
-2
6
8
6
4
2
=
=
+
10
1
4
4 8 12 16 20
(4, 5)
Name :
Sheet 3
Systems of Equations - Graphing
Graph each system of equations and find the solution.
1)
= 3 + 28 ;
= 2 + 22
2)
=
2
3
–2 ;
12
10
8
4
;
1 2 3 4 5 6 7
-4
1 2 3
-5
-6
-4
-3 -2 -1
-1
-2
-3
6
= –4 +
=2 –7
4)
=–
1
2
–5 ;
= –2 +
;
3 6 9 12 15
-6 -5 -4 -3 -2 -1
-1
1 2 3 4
-2
-3
-4
-5
-6
=2 –6
6)
= –5 + 3 ;
= +5
20
15
10
5
12
10
8
6
4
2
-2 -1
-2
4
3
2
1
-15 -12 -9 -6 -3
-1
-2
-3
-4
-5
-6
-7
-8
=1+
1
4
2
1
5)
–2
4
3
2
1
14
3)
16
2
-7 -6 -5 -4 -3 -2 -1
-2
4
3
=
1 2 3 4 5 6 7 8
-25 -20 -15 -10 -5
-5
-10
-15
-4
-20
-6
-25
-8
-30
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5 10 15 20 25
Name :
Answer key
Sheet 3
Systems of Equations - Graphing
Graph each system of equations and find the solution.
= 3 + 28 ;
= 2 + 22
2)
=
2
3
–2 ;
8
22
+2
12
2
+
=3
10
8
2
2 –
= 3
1 2 3 4 5 6 7
-3 -2 -1
-1
-2
-3
6
4
2
-7 -6 -5 -4 -3 -2 -1
-2
-5
-6
(–6, 10)
= –4 +
;
(0, –2)
=2 –7
4)
=–
1
2
–5 ;
= –2 +
3 6 9 12 15
=2 –7
+
=– 1
-4
2 –5
-5
-6
(–4, –3)
=2 –6
6)
= –5 + 3 ;
= +5
8
6
=1
+
2
=
2
–
6
1 2 3 4 5 6 7 8
-25 -20 -15 -10 -5
-5
5
+
-10
=
-15
-4
-20
-6
-25
-8
-30
(7, 8)
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= –5
10
+3
20
15
10
5
12
-2 -1
-2
-3
4
1
= –2 + 4
= –4
;
1 2 3 4
-2
(3, –1)
=1+
-6 -5 -4 -3 -2 -1
-1
5)
4
3
2
1
1
4
2
1
-15 -12 -9 -6 -3
-1
-2
-3
-4
-5
-6
-7
-8
-4
1 2 3
-4
3)
–2
2
4
3
2
1
14
=
16
4
3
=
= 4
3 –
1)
5 10 15 20 25
(5, 10)
Name :
Systems of Equations - Elimination Method
Solve each system of equations using elimination method.
1)
2 + 5 = 20
2)
6 – 5 = 12
3)
–7 + 3 = 15
– + 4 = –15
4)
7 – 6 = –3
5)
5 +8 =3
– 4 = 13
+ = 11
– + =9
6)
4 + 8 = –4
7)
3 + 4 = –3
–9 – 2 = 8
–9 – = 6
8)
– 6 = 12
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3 + 7 = 18
3 – 4 = –48
L1S1
Name :
Answer key
Systems of Equations - Elimination Method
Solve each system of equations using elimination method.
1)
3)
2 + 5 = 20
2)
6 – 5 = 12
– + 4 = –15
4, 12
5
(3, –3)
–7 + 3 = 15
4)
7 – 6 = –3
5 +8 =3
(1, 10)
6)
4 + 8 = –4
– 4 = 13
–9 – 2 = 8
–9 – = 6
– 4 , –2
9
(7, –4)
7)
+ = 11
– + =9
– 27, –4
7
5)
3 + 4 = –3
8)
3 + 7 = 18
– 6 = 12
3 – 4 = –48
15, 1
2
(–8, 6)
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L1S1
Name :
Systems of Equations - Elimination Method
Solve each system of equations using elimination method.
1)
4 + 7 = 37
2)
4 – 5 = –23
3)
+ =9
6 – 3 = –3
4)
– = 21
5)
–6 – 3 = 15
3 – 8 = –33
5 +4 =8
–5 + 2 = 1
6)
–6 – 2 = 18
7)
2 + 3 = 19
8 – 4 = –4
– 4 = –25
8)
9 + 8 = 29
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7 + 3 = –48
7 – 5 = –32
L1S2
Name :
Answer key
Systems of Equations - Elimination Method
Solve each system of equations using elimination method.
1)
4 + 7 = 37
2)
4 – 5 = –23
6 – 3 = –3
1,5
2
3)
+ =9
(2, 5)
4)
– = 21
7)
–6 – 3 = 15
5 +4 =8
–5 + 2 = 1
2, 3
5 2
(15, –6)
5)
2 + 3 = 19
6)
8 – 4 = –4
–6 – 2 = 18
– 4 = –25
(–4, 3)
(3, 7)
3 – 8 = –33
8)
7 + 3 = –48
9 + 8 = 29
7 – 5 = –32
–1 ,4
3
(–6, –2)
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L1S2
Name :
Systems of Equations - Elimination Method
Solve each system of equations using elimination method.
1)
+ = 13
2)
– =3
3)
–8 + 3 = –12
4)
–8 – = 36
5)
4 – 4 = 22
5 – 2 = 47
+ 9 = –7
5
–3 =1
–4 + 7 = 24
3 + 7 = –18
6)
–2 – 4 = 19
7)
5
6 – = 52
6 + 9 = 12
8)
– 2 = 11
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9 +3 =7
–9 – 6 = –8
L1S3
Name :
Answer key
Systems of Equations - Elimination Method
Solve each system of equations using elimination method.
1)
+ = 13
2)
– =3
–8 + 3 = –12
4)
–8 – = 36
7)
4 – 4 = 22
5
–3 =1
–4 + 7 = 24
3 + 7 = –18
(–3, –12)
5)
+ 9 = –7
–1, –2
5
3
(8, 5)
3)
5
(–6, 0)
6)
6 – = 52
–2 – 4 = 19
6 + 9 = 12
1 , –5
2
(8, –4)
5 – 2 = 47
8)
– 2 = 11
(9, –1)
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9 +3 =7
–9 – 6 = –8
2, 1
3 3
L1S3
Name :
Sheet 1
Systems of Equations
Use the best method to solve each system of equations.
4
1)
2
3)
–
3
1
+
8
1
1
–
1
=2 +
2)
2=
2
= 10
1
–
= 17
+
–
5)
5
+
5
4)
4
= 1
= –10
6)
10
1
+
3
+
+
5
6
7)
1
+
3
14 =
7
+
8
= 16
= 20
5 +6 =
=0
3 +4 =
1
+
=8
+
2
8)
= 26
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–
2
9
+
–
6
2
–6=0
= –5
Name :
Answer key
Sheet 1
Systems of Equations
Use the best method to solve each system of equations.
4
1)
5
+
2
= 17
3
+
2)
2=
2
= 10
10
1
+
2, 1
3
3)
1
–
1
–
1
=2 +
+
1
=0
(4, –2)
5
4)
4
= 1
3
+
+
5
= 16
= 20
– 2 , –2
3
5)
–
8
1
–
= –10
5, 1
4 4
6)
3 +4 =
6
1
+
3
14 =
7
+
8
=8
1, 1
2
7)
5 +6 =
1
+
+
2
(1, –1) or (0, 0)
8)
= 26
1, –1
6 2
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–
2
9
+
–
6
2
–6=0
= –5
–3, – 2
3
Name :
Sheet 2
Systems of Equations
Use the best method to solve each system of equations.
1)
2
3
3)
–
1
5)
3
+
2
+
5
– 2=0
3
+
7 +4 =
4)
1
–
5
6)
8
10 =
2
7
+
+
1
4
+
10
=5
= 21
+
3
3
+
7)
–5=0
+
–3 =
5
=
1
+
–
= –2
3 +5 =
1
=4
7
15 –
=4
1
–
2)
3
8)
=5
Printable Worksheets @ www.mathworksheets4kids.com
–
4
6
= –2
9
–
+ 25 = 0
6
+
5
= 26
Name :
Answer key
Sheet 2
Systems of Equations
Use the best method to solve each system of equations.
1)
2
3
+
3
– 2=0
2
+
2)
7
15 –
1
=4
1
+
5, –5
8 2
3)
–
1
5
1
–
3
+
=4
–5=0
–1, 1
5 10
4)
1
–
5
–
= –2
1
+
4
+
3 +5 =
7 +4 =
6)
10
–3 =
3
+
6
1 , –1 or (0, 0)
2
8
10 =
2
7
+
+
= 21
+
3
7)
=5
–1, 1
4
(–1, 1)
5)
5
=
3
= –2
(–4, –6)
8)
=5
–1, 1
6
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–
4
9
–
+ 25 = 0
6
+
5
= 26
1, 1
4
Name :
Sheet 3
Systems of Equations
Use the best method to solve each system of equations.
1)
7
3)
12 = –
1
1
+
2
5)
2
+
2+
+
4
–
7)
5
4=–
1
4
2)
3
= –6
1
1
+
4)
2
2
+ =
6)
=1
7
= 10
–
6
–
–
=0
8)
3 + =–
2
+
5
–
=2
1
+
1
–3=0
3
+
6
– 10 = 0
=3
1
+
9
–
–5=
Printable Worksheets @ www.mathworksheets4kids.com
5
+
3
8
+ 24 = 0
= –51
–
4
=–9
Name :
Answer key
Sheet 3
Systems of Equations
Use the best method to solve each system of equations.
1)
5
4=–
7
+
4
–
4
2)
6
3
= –6
5
+
2
+
1
12 = –
1
1
+
1
+
4)
7
2
= 10
3
+
2
2
+
2+
1
+
1
–
2
=3
–1, 1
7 17
6)
=1
=2
–1 , 1
11
5)
–3=0
8 , –4
15
(–1, –4)
3)
– 10 = 0
–
–
=0
6
1
1
+
9
–
–3 , 6
5
7)
+ =
+ 24 = 0
= –51
1, 1
5 6
8)
3 + =–
–5=
5
–1, 1 or (0, 0)
2
Printable Worksheets @ www.mathworksheets4kids.com
–
3
8
–
4
=–9
(–1, 2)
Name :
Sheet 1
Rhombus
A) Find the value of in each rhombus.
1)
2)
C
O
D
Y
X
O
B
A
Z
OA = ( + 20) in ; OC = (6 ) in
XZ =
=
W
ft ; OZ = 21 ft
2
=
R
3)
4)
G
F
S
O
O
Q
H
E
P
OQ = (8 – 49) yd ; OS = (94 – 5 ) yd
GO = (2 + 9) in ; GE = (38 + 3 ) in
=
=
B) Solve for and
1)
in each rhombus and find the indicated measure.
L
K
U
2)
O
O
V
M
T
J
S
MK = (4 ) ft ; OK = 30 ft
VO = (9 – 20) yd ; TO = (5 ) yd
OL = (5 – 2 ) ft ; LJ = (– + 13) ft
OU = (27 + 7 ) yd ; OS = 41 yd
=
;
=
; LJ =
Printable Worksheets @ www.mathworksheets4kids.com
=
;
=
; VT =
Name :
Answer key
Sheet 1
Rhombus
A) Find the value of in each rhombus.
1)
2)
C
O
D
Y
X
O
B
A
Z
OA = ( + 20) in ; OC = (6 ) in
XZ =
4
=
ft ; OZ = 21 ft
2
84
=
R
3)
W
4)
G
F
S
O
O
Q
H
E
P
OQ = (8 – 49) yd ; OS = (94 – 5 ) yd
11
=
B) Solve for and
1)
GO = (2 + 9) in ; GE = (38 + 3 ) in
20
=
in each rhombus and find the indicated measure.
L
K
U
2)
O
O
V
M
T
J
S
MK = (4 ) ft ; OK = 30 ft
VO = (9 – 20) yd ; TO = (5 ) yd
OL = (5 – 2 ) ft ; LJ = (– + 13) ft
OU = (27 + 7 ) yd ; OS = 41 yd
=
15
;
=
–1
; LJ = 14 ft
Printable Worksheets @ www.mathworksheets4kids.com
=
2
;
=
5
; VT = 50 yd
Name :
Sheet 2
Rhombus
A) Find the value of in each rhombus.
1)
2)
V
L
M
O
O
W
N
U
K
T
NL =
2
ft ; NO = 23 ft
VO = (20 – ) yd ; OT = (95 – 6 ) yd
=
=
3)
4)
E
O
F
S
R
O
D
T
C
FD = (7 + 92) in ; OD = (66 + 6 ) in
Q
SO = (8 ) yd ; SQ = 80 yd
=
=
B) Solve for and
1)
in each rhombus and find the indicated measure.
H
V
2)
G
W
O
O
U
E
F
X
EG = (65 + 9 ) ft ; EO = 19 ft
XO = (–65 + 7 ) in ; VX = (4 ) in
OH = (14 + ) ft ; OF = (3 – 4) ft
UW = (2 + 50) in ; WO = (–5 + 7) in
=
;
=
; HF =
Printable Worksheets @ www.mathworksheets4kids.com
=
;
=
; VX =
Name :
Answer key
Sheet 2
Rhombus
A) Find the value of in each rhombus.
1)
2)
V
L
M
O
O
W
N
U
K
T
NL =
2
ft ; NO = 23 ft
VO = (20 – ) yd ; OT = (95 – 6 ) yd
92
=
3)
4)
E
O
F
S
R
O
D
T
C
FD = (7 + 92) in ; OD = (66 + 6 ) in
Q
SO = (8 ) yd ; SQ = 80 yd
–8
=
B) Solve for and
1)
15
=
5
=
in each rhombus and find the indicated measure.
H
V
2)
G
W
O
O
U
E
F
X
EG = (65 + 9 ) ft ; EO = 19 ft
XO = (–65 + 7 ) in ; VX = (4 ) in
OH = (14 + ) ft ; OF = (3 – 4) ft
UW = (2 + 50) in ; WO = (–5 + 7) in
=
9
;
=
–3
; HF = 46 ft
Printable Worksheets @ www.mathworksheets4kids.com
=
–3
;
=
13
; VX = 52 in
Name :
Sheet 3
Rhombus
A) Find the value of in each rhombus.
1)
2)
U
G
T
O
O
H
V
E
S
OU = 13 yd ; SU =
3
F
yd
HO = (6 ) ft ; OF = 48 ft
=
=
3)
K
4)
Y
L
O
O
Z
X
J
W
M
MK = (10 – 54) in ; OK = (–51 + 7 ) in
OW = (2 – 9 ) ft ; OY = 47 ft
=
=
B) Solve for and
1)
in each rhombus and find the indicated measure.
2)
R
D
C
Q
O
O
S
A
B
P
OR = (7 + 26) in ; PR = (2 + 28) in
AC = (4 ) yd ; OA = (17 + ) yd
SO = (1 – 8 ) in ; QO = (67 + 3 ) in
BD = 82 yd ; OB = (95 – 6 ) yd
=
;
=
; PR =
Printable Worksheets @ www.mathworksheets4kids.com
=
;
=
; AC =
Name :
Answer key
Sheet 3
Rhombus
A) Find the value of in each rhombus.
1)
2)
U
G
T
O
O
H
V
E
S
OU = 13 yd ; SU =
3
yd
HO = (6 ) ft ; OF = 48 ft
78
=
3)
F
8
=
K
4)
Y
L
O
O
Z
X
J
W
M
MK = (10 – 54) in ; OK = (–51 + 7 ) in
OW = (2 – 9 ) ft ; OY = 47 ft
–5
=
B) Solve for and
1)
12
=
in each rhombus and find the indicated measure.
2)
R
D
C
Q
O
O
S
A
B
P
OR = (7 + 26) in ; PR = (2 + 28) in
AC = (4 ) yd ; OA = (17 + ) yd
SO = (1 – 8 ) in ; QO = (67 + 3 ) in
BD = 82 yd ; OB = (95 – 6 ) yd
=
–2
;
=
–6
; PR = 24 in
Printable Worksheets @ www.mathworksheets4kids.com
=
17
;
=
9
; AC = 68 yd
Name :
Sheet 4
Rhombus
A) Find the value of in each rhombus.
1)
2)
F
G
N
M
O
O
L
K
E
D
OD = (4 + 5) yd ; OF = (–3 + 40) yd
LN = (3 – 10) in ; NO = 16 in
=
=
3)
4)
Y
T
S
O
O
V
U
R
W
OS = (2 ) in ; SU = 80 in
OW = (12 + 22) ft ; OY = ( + 55) ft
=
=
B) Solve for and
in each rhombus and find the indicated measure.
D
1)
2)
O
E
S
R
O
C
EO = (24 + 4 ) yd ; EC = (7 + 46) yd
OS = (6 + 57) ft ; OQ = 9 ft
DB = (8 ) yd ; OB = (5 – 10) yd
OT =
;
=
Q
T
B
=
X
; EC =
Printable Worksheets @ www.mathworksheets4kids.com
=
6
;
ft ; OR = (42 – ) ft
=
; QS =
Name :
Answer key
Sheet 4
Rhombus
A) Find the value of in each rhombus.
1)
2)
F
G
N
M
O
O
L
K
E
D
OD = (4 + 5) yd ; OF = (–3 + 40) yd
LN = (3 – 10) in ; NO = 16 in
5
=
14
=
4)
3)
Y
T
S
O
O
V
U
R
W
OS = (2 ) in ; SU = 80 in
OW = (12 + 22) ft ; OY = ( + 55) ft
20
=
B) Solve for and
in each rhombus and find the indicated measure.
2)
O
E
S
R
O
C
EO = (24 + 4 ) yd ; EC = (7 + 46) yd
OS = (6 + 57) ft ; OQ = 9 ft
DB = (8 ) yd ; OB = (5 – 10) yd
–2
OT =
;
=
10
Q
T
B
=
3
=
D
1)
X
; EC = 32 yd
Printable Worksheets @ www.mathworksheets4kids.com
=
36
6
;
ft ; OR = (42 – ) ft
=
–8
; QS = 18 ft
Name :
Sheet 5
Rhombus
A) Find the value of in each rhombus.
1)
2)
Y
S
O
Z
R
O
X
Q
P
W
YW = (62 – 3 ) ft ; WO = 7 ft
OP = (7 – ) in ; OR = (19 + 2 ) in
=
3)
=
4)
L
C
K
O
M
J
BO = (6 + 83) ft ; DB = 34 ft
=
=
B) Solve for and
in each rhombus and find the indicated measure.
2)
U
G
T
H
O
O
F
V
S
E
OT = (5 ) in ; VT = (7 + 9 ) in
UO =
=
B
A
LO = ( + 15) yd ; OJ = (78 – 2 ) yd
1)
O
D
;
4
=
in ; SO = 18 in
; VT =
Printable Worksheets @ www.mathworksheets4kids.com
GE = (–10 + 6 ) yd ; OG = (9 – 59) yd
OH = (4 + 25) yd ; OF = (33 + 8 ) yd
=
;
=
; GE =
Name :
Answer key
Sheet 5
Rhombus
A) Find the value of in each rhombus.
1)
2)
Y
S
O
Z
R
O
X
Q
P
W
YW = (62 – 3 ) ft ; WO = 7 ft
16
=
3)
OP = (7 – ) in ; OR = (19 + 2 ) in
–4
=
4)
L
C
K
O
M
J
BO = (6 + 83) ft ; DB = 34 ft
21
=
B) Solve for and
B
A
LO = ( + 15) yd ; OJ = (78 – 2 ) yd
1)
O
D
–11
=
in each rhombus and find the indicated measure.
2)
U
G
T
H
O
O
F
V
S
E
OT = (5 ) in ; VT = (7 + 9 ) in
UO =
=
72
;
4
=
in ; SO = 18 in
7
; VT = 70 in
Printable Worksheets @ www.mathworksheets4kids.com
GE = (–10 + 6 ) yd ; OG = (9 – 59) yd
OH = (4 + 25) yd ; OF = (33 + 8 ) yd
=
9
;
=
–2
; GE = 44 yd
Name :
Score :
Identifying Inequalities
ES1
Choose the correct inequality that best describes each graph.
1)
2)
-15
-10
-5
0
5
10
a) x ≤ 1 +
6x
5
b)
1+
c) 1 + 6x < x
5
d)
x≥1+
15
-5 -4 -3 -2
-1
0
1
2
3
4
5
6
7
6x
>x
5
a)
15 < 3(4x – 7)
b)
3(4x – 7) ≤ 15
6x
5
c)
3(4x – 7) ≥ 15
d)
15 > 3(4x – 7)
3)
4)
-7
0
7
14
21
28
35
-5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
a)
3x – x ≤ 7
2
b)
7 < 3x –x
2
a)
9x – 14 < 2
11
b)
2 ≤ 9x – 14
11
c)
7 > 3x –x
2
d)
3x – x ≥ 7
2
c)
2 ≥ 9x – 14
11
d)
9x – 14 > 2
11
5)
6)
-8 -7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
-24 -20 -16 -12 -8 -4
0
4
8
12 16 20 24
a)
25 ≥ 5(2x + 3)
b) 5(2x + 3) < 25
a)
5x
+ x ≥ 22
6
b)
22 < x +
c)
5(2x + 3) > 25
d) 25 ≤ 5(2x + 3)
c)
22 > x +
5x
6
d)
5x
+ x ≤ 22
6
-7
0
7
7)
5x
6
8)
3
6
9
14
21
28
35
-3
0
a)
7x + 9
>6
5
b)
6≥
7x + 9
5
a)
9>x–
10x
7
b)
10x
–x≥9
7
c)
6≤
7x + 9
5
d)
7x + 9
<6
5
c)
10x
–x≤9
7
d)
9<x–
Printable Math Worksheets @ www.mathworksheets4kids.com
10x
7
Name :
Score :
Answer key
Identifying Inequalities
ES1
Choose the correct inequality that best describes each graph.
1)
2)
-15
-10
-5
0
5
10
a) x ≤ 1 +
6x
5
b)
1+
c) 1 + 6x < x
5
d)
x≥1+
15
-5 -4 -3 -2
-1
0
1
2
3
4
5
6
7
6x
>x
5
a)
15 < 3(4x – 7)
b)
3(4x – 7) ≤ 15
6x
5
c)
3(4x – 7) ≥ 15
d)
15 > 3(4x – 7)
3)
4)
-7
0
7
14
21
28
35
-5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
a)
3x – x ≤ 7
2
b)
7 < 3x –x
2
a)
9x – 14 < 2
11
b)
2 ≤ 9x – 14
11
c)
7 > 3x –x
2
d)
3x – x ≥ 7
2
c)
2 ≥ 9x – 14
11
d)
9x – 14 > 2
11
5)
6)
-8 -7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
-24 -20 -16 -12 -8 -4
0
4
8
12 16 20 24
a)
25 ≥ 5(2x + 3)
b) 5(2x + 3) < 25
a)
5x
+ x ≥ 22
6
b)
22 < x +
c)
5(2x + 3) > 25
d) 25 ≤ 5(2x + 3)
c)
22 > x +
5x
6
d)
5x
+ x ≤ 22
6
-7
0
7
7)
5x
6
8)
3
6
9
14
21
28
35
-3
0
a)
7x + 9
>6
5
b)
6≥
7x + 9
5
a)
9>x–
10x
7
b)
10x
–x≥9
7
c)
6≤
7x + 9
5
d)
7x + 9
<6
5
c)
10x
–x≤9
7
d)
9<x–
Printable Math Worksheets @ www.mathworksheets4kids.com
10x
7
Name :
Score :
Identifying Inequalities
ES2
Choose the correct inequality that best describes each graph.
1)
2)
-5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
-3
0
6
9
8x
3
b)
x+
8x
< 22
3
d)
22 ≥ x +
a)
18 < 2(5x – 1)
b)
2(5x – 1) ≤ 18
a)
22 ≤ x +
c)
2(5x – 1) ≥ 18
d)
18 > 2(5x – 1)
c)
x+
-2
0
3)
3
8x
> 22
3
8x
3
4)
-66
-44
-22
0
22
44
66
2
4
6
8 10 12 14 16 18 20 22
a)
2x – 17 > 3
9
b)
3 ≤ 2x – 17
9
a) 3(2x + 6) ≤ 66
b)
66 < 3(2x + 6)
c)
3 ≥ 2x – 17
9
d)
2x – 17 < 3
9
c)
d)
3(2x + 6) ≥ 66
5)
66 > 3(2x + 6)
6)
-21
-14
-7
a)
3x
+ x ≥ 10
7
c) 10 > x +
0
7
3x
7
14
21
-5 -4 -3 -2
-1
0
1
2
3
4
5
6
7
b) 10 < x + 3x
7
a)
28 ≥ 2(9x + 5)
b)
2(9x + 5) < 28
3x
+ x ≤ 10
7
c)
2(9x + 5) > 28
d)
28 ≤ 2(9x + 5)
d)
7)
8)
-18 -15 -12 -9 -6 -3
0
3
6
9
12 15 18
-8 -7 -6 -5 -4 -3 -2 -1
0
1
2
3
6x + 4
8
a)
5>x–
14x
9
b)
14x
–x≤5
9
a)
6x + 4 > 2
8
b)
2≥
c)
14x
–x≥5
9
d)
5<x–
14x
9
c)
2≤
6x + 4
8
d)
6x + 4
<2
8
Printable Math Worksheets @ www.mathworksheets4kids.com
4
Name :
Score :
Answer key
Identifying Inequalities
ES2
Choose the correct inequality that best describes each graph.
1)
2)
-5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
-3
0
6
9
8x
3
b)
x+
8x
< 22
3
d)
22 ≥ x +
a)
18 < 2(5x – 1)
b)
2(5x – 1) ≤ 18
a)
22 ≤ x +
c)
2(5x – 1) ≥ 18
d)
18 > 2(5x – 1)
c)
x+
-2
0
3)
3
8x
> 22
3
8x
3
4)
-66
-44
-22
0
22
44
66
2
4
6
8 10 12 14 16 18 20 22
a)
2x – 17 > 3
9
b)
3 ≤ 2x – 17
9
a) 3(2x + 6) ≤ 66
b)
66 < 3(2x + 6)
c)
3 ≥ 2x – 17
9
d)
2x – 17 < 3
9
c)
d)
3(2x + 6) ≥ 66
5)
66 > 3(2x + 6)
6)
-21
-14
-7
a)
3x
+ x ≥ 10
7
c) 10 > x +
0
7
3x
7
14
21
-5 -4 -3 -2
-1
0
1
2
3
4
5
6
7
b) 10 < x + 3x
7
a)
28 ≥ 2(9x + 5)
b)
2(9x + 5) < 28
3x
+ x ≤ 10
7
c)
2(9x + 5) > 28
d)
28 ≤ 2(9x + 5)
d)
7)
8)
-18 -15 -12 -9 -6 -3
0
3
6
9
12 15 18
-8 -7 -6 -5 -4 -3 -2 -1
0
1
2
3
6x + 4
8
a)
5>x–
14x
9
b)
14x
–x≤5
9
a)
6x + 4 > 2
8
b)
2≥
c)
14x
–x≥5
9
d)
5<x–
14x
9
c)
2≤
6x + 4
8
d)
6x + 4
<2
8
Printable Math Worksheets @ www.mathworksheets4kids.com
4
Name :
Score :
Identifying Inequalities
ES3
Choose the correct inequality that best describes each graph.
1)
2)
-12
-8
-4
a)
9x – 8 > 14
2
0
c) 14 ≥ 9x – 8
2
4
8
12
-28 -21 -14 -7
0
7
14 21 28 35 42 49 56
b) 14 ≤ 9x – 8
2
a)
49 ≤ 7(3x – 14)
b)
7(3x – 14) > 49
9x – 8 < 14
2
c)
7(3x – 14 ) < 49
d)
49 ≥ 7(3x – 14)
d)
3)
4)
-18 -15 -12 -9 -6 -3
0
3
6
9
12 15 18
-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60
3x
5
b)
x–
3x
≥ 12
5
d)
12 > x –
a)
4(6x – 12) ≤ 24
b)
24 > 4(6x – 12)
a)
12 < x –
c)
24 < 4(6x – 12)
d)
4(6x – 12) ≥ 24
c)
x–
5)
3x
≤ 12
5
3x
5
6)
-8 -7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
-36 -27 -18 -9
0
9
18 27 36 45 54 63 72
a)
63 ≥ 7(8x + 1)
b)
7(8x + 1) < 63
a)
5x
+ x ≥ 28
9
b)
28 < x +
c)
7(8x + 1) > 63
d)
63 ≤ 7(8x + 1)
c)
28 > x +
5x
9
d)
5x
+ x ≤ 28
9
7)
5x
9
8)
-39
-26
-13
0
13
26
39
-2
0
2
a)
2x + 4
>3
10
b)
3≥
2x + 4
10
a)
13 > x –
c)
3≤
2x + 4
10
d)
2x + 4
<3
10
c)
15x
– x ≥ 13
2
Printable Math Worksheets @ www.mathworksheets4kids.com
15x
2
4
6
b)
8
10
15x
– x ≤ 13
2
d) 13 < x –
15x
2
Name :
Score :
Answer key
Identifying Inequalities
ES3
Choose the correct inequality that best describes each graph.
1)
2)
-12
-8
-4
a)
9x – 8 > 14
2
0
c) 14 ≥ 9x – 8
2
4
8
12
-28 -21 -14 -7
0
7
14 21 28 35 42 49 56
b) 14 ≤ 9x – 8
2
a)
49 ≤ 7(3x – 14)
b)
7(3x – 14) > 49
9x – 8 < 14
2
c)
7(3x – 14 ) < 49
d)
49 ≥ 7(3x – 14)
d)
3)
4)
-18 -15 -12 -9 -6 -3
0
3
6
9
12 15 18
-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60
3x
5
b)
x–
3x
≥ 12
5
d)
12 > x –
a)
4(6x – 12) ≤ 24
b)
24 > 4(6x – 12)
a)
12 < x –
c)
24 < 4(6x – 12)
d)
4(6x – 12) ≥ 24
c)
x–
5)
3x
≤ 12
5
3x
5
6)
-8 -7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
-36 -27 -18 -9
0
9
18 27 36 45 54 63 72
a)
63 ≥ 7(8x + 1)
b)
7(8x + 1) < 63
a)
5x
+ x ≥ 28
9
b)
28 < x +
c)
7(8x + 1) > 63
d)
63 ≤ 7(8x + 1)
c)
28 > x +
5x
9
d)
5x
+ x ≤ 28
9
7)
5x
9
8)
-39
-26
-13
0
13
26
39
-2
0
2
a)
2x + 4
>3
10
b)
3≥
2x + 4
10
a)
13 > x –
c)
3≤
2x + 4
10
d)
2x + 4
<3
10
c)
15x
– x ≥ 13
2
Printable Math Worksheets @ www.mathworksheets4kids.com
15x
2
4
6
b)
8
10
15x
– x ≤ 13
2
d) 13 < x –
15x
2
Name :
Sheet 1
Kite
A) Solve for and find the indicated side length of each kite.
1)
2)
D
3)
R
M
( 90
(3 +
+ )
in
Q
in
5
2 )
yd
L
N
) ft
–
C
(15 –
A
(4 ) ft
S
B
d
7) y
(6
P
K
=
=
=
CD =
SP =
KL =
38
+
5)
8
G
(3 + 7) yd
6)
F
(85 – 2 )
) ft
–
D
–2
+
) yd
(20
2)
ft
V
(60
X
V
4+
(3
) ft
(–2
5 )
yd
W
(4 + 1) in
E
U
=
=
=
=
=
=
XW =
GF =
WT =
UV =
DE =
TU =
Printable Worksheets @ www.mathworksheets4kids.com
U
in
in
3
W (–
( 31 + )
(
–
61
) ft
and find the indicated side lengths of each kite.
(– + 56) in
4)
and
(6 – 8) yd
B) Solve for
–3
T
Name :
Answer key
Sheet 1
Kite
A) Solve for and find the indicated side length of each kite.
1)
2)
D
3)
R
M
( 90
(3 +
+ )
in
Q
in
5
2 )
yd
L
N
) ft
–
C
(15 –
A
(4 ) ft
S
d
7) y
–3
(6
P
K
=
B
–75
=
3
=
10
CD =
15 in
SP =
12 ft
KL =
23 yd
38
+
5)
8
G
(3 + 7) yd
6)
F
(85 – 2 )
) ft
–
D
–2
+
) yd
(20
2)
ft
V
(60
X
V
4+
(3
) ft
(–2
5 )
yd
W
(4 + 1) in
E
=
U
9
=
14
=
11
=
21
=
5
=
18
XW =
34 ft
GF =
22 yd
WT =
45 in
UV =
41 ft
DE =
46 yd
TU =
49 in
Printable Worksheets @ www.mathworksheets4kids.com
U
in
in
3
W (–
( 31 + )
(
–
61
) ft
and find the indicated side lengths of each kite.
(– + 56) in
4)
and
(6 – 8) yd
B) Solve for
T
Name :
Sheet 2
Kite
A) Solve for and find the indicated side length of each kite.
1)
2)
3)
B
W
M
5
L
–
)f
(8
0
X
C
2
) in
–1
(6
8
7+
A
(15
J
yd
(–
(
6
) in
7)
yd
t
+7
26
)f
+
t
K
U
D
=
JK =
and find the indicated side lengths of each kite.
5 )
yd
=
=
P
( +
8) ft
U
yd
F
ft
S ( – 23) yd
6) G
3 )
) yd
–9
2
(7 )
(3
Q
V
(92 –
in
7+
(43 – ) in
W
ft
5)
R
(–4
VW =
(–21 + 2 )
and
=
BC =
B) Solve for
4)
=
(6 – 62) in
V
) in
– 18
(9
D
T
=
=
=
=
PQ =
UV =
EF =
QR =
WT =
GD =
Printable Worksheets @ www.mathworksheets4kids.com
t
( – 3) f
E
Name :
Answer key
Sheet 2
Kite
A) Solve for and find the indicated side length of each kite.
1)
2)
3)
B
W
M
5
L
–
)f
(8
0
X
C
2
) in
–1
(6
8
7+
A
(15
J
yd
(–
(
6
) in
7)
yd
t
+7
26
)f
+
t
K
U
D
=
13
JK =
39 ft
BC =
11 yd
5)
5 )
(43 – ) in
W
yd
=
46
=
19
PQ =
QR =
P
6) G
( +
8) ft
U
yd
F
ft
55 in
3 )
) yd
–9
S ( – 23) yd
V
(7 )
(3
Q
2
VW =
(92 –
in
7+
–4
and find the indicated side lengths of each kite.
R
(–4
=
ft
4)
and
66
(–21 + 2 )
B) Solve for
=
(6 – 62) in
V
) in
– 18
(9
D
T
=
9
=
15
23 yd
UV =
48 yd
WT =
Printable Worksheets @ www.mathworksheets4kids.com
t
( – 3) f
=
18
=
21
28 in
EF =
15 ft
63 in
GD =
29 ft
E
Name :
Sheet 3
Kite
A) Solve for and find the indicated side length of each kite.
1)
2)
F
3)
C
) yd
X
) yd
(5 – 44) in
(–40
+ 14
+ 10
(4
W
G
E
D
B
(–4
0+
U
(28 – ) in
ft
3
) ft
V
A
D
=
=
=
EF =
WV =
CD =
) in
5)
V
6)
(4 ) ft
d
M
L
S
+
4)
in
N
(5 – 48) ft
K
P
=
=
=
=
=
ST =
NK =
RS =
VU =
LM =
PQ =
Printable Worksheets @ www.mathworksheets4kids.com
)y
Q
U
=
(2
d
) yd
(7
(
R
(1 +
) in
( + 51) ft
(84 –
T
(–4 + 3 ) ft
27
–7
)y
) yd
(–9 – 19) in
S ( 11 – 4
+4
4)
and find the indicated side lengths of each kite.
(–41
and
B) Solve for
Name :
Answer key
Sheet 3
Kite
A) Solve for and find the indicated side length of each kite.
1)
2)
F
3)
C
) yd
X
) yd
(5 – 44) in
(–40
+ 14
+ 10
(4
W
G
E
D
B
(–4
0+
U
(28 – ) in
ft
3
) ft
V
A
D
=
9
EF =
50 yd
60
WV =
16 in
CD =
20 ft
and find the indicated side lengths of each kite.
5)
) in
V
6)
(4 ) ft
d
M
L
S
+
4)
in
N
(5 – 48) ft
–6
=
10
ST =
VU =
)y
Q
K
P
U
=
(2
d
) yd
(7
(
R
(1 +
) in
( + 51) ft
(84 –
T
(–4 + 3 ) ft
27
–7
)y
) yd
(–9 – 19) in
S ( 11 – 4
=
+4
4)
12
(–41
and
B) Solve for
=
=
17
=
22
35 in
NK =
74 in
LM =
Printable Worksheets @ www.mathworksheets4kids.com
=
3
=
14
62 ft
RS =
6 yd
68 ft
PQ =
15 yd
Name :
Multi-Step Equations
Mixed Review: S1
Solve each equation.
1)
3 = 4 + 2s –5
2 3 3
2)
–4(–2q + 8) = –6(q – 18) + 12q
3)
–1.7(–2r + 6.6 – 4r) = 15.3
4)
5 (2 + x) = 4 x + 1
3
5
2
5)
6–t
= –2
2t + 9
6)
1.8u + 10.2 = 2.7u + 12.9
7)
5.3(v – 5) = 3(1 + 3.5v) – 2.98
8)
10w + 6 = –3w – 21 + 10w
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer Key
Multi-Step Equations
Mixed Review: S1
Solve each equation.
1)
3 = 4 + 2s –5
2 3 3
2)
s = 31 or 7 3
4
4
3)
–1.7(–2r + 6.6 – 4r) = 15.3
q = 70
4)
6–t
= –2
2t + 9
6)
5.3(v – 5) = 3(1 + 3.5v) – 2.98
v = –5.1
Printable Worksheets @ www.mathworksheets4kids.com
1.8u + 10.2 = 2.7u + 12.9
u = –3
t = –8
7)
5 (2 + x) = 4 x + 1
3
5
2
x = – 44 or –3 5
13
13
r = 2.6
5)
–4(–2q + 8) = –6(q – 18) + 12q
8)
10w + 6 = –3w – 21 + 10w
w = –9
Name :
Multi-Step Equations
Mixed Review: S2
Solve each equation.
1)
3.9(z + 5.7) = 8.19 + 7.8z
2)
y + 8 = – 1 + 3y – 2 3
4
4
3
3)
7(2 + x) + 15 = 10x – 4
4)
3(4p – 5.5) + 11.1 = 8.1 + 3p
5)
q+ 2 =
3
5q + 2
4
6)
–15r + 21 – (5r – 3) = 44
7)
13s + 4 = –3(3 – 4s) – 1
8)
5 t + 1 = 2 1t + 2
3
4
8
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Name :
Answer Key
Multi-Step Equations
Mixed Review: S2
Solve each equation.
1)
3.9(z + 5.7) = 8.19 + 7.8z
2)
y = 17 or 2 5
6
6
z = 3.6
3)
7(2 + x) + 15 = 10x – 4
4)
q+ 2 =
3
5q + 2
4
6)
q= 2
3
7)
3(4p – 5.5) + 11.1 = 8.1 + 3p
p = 1.5
x = 11
5)
y + 8 = – 1 + 3y – 2 3
4
3
4
13s + 4 = –3(3 – 4s) – 1
s = –14
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–15r + 21 – (5r – 3) = 44
r = –1
8)
5 t + 1 = 2 1t + 2
3
4
8
t= 1
3
Name :
Multi-Step Equations
Mixed Review: S3
Solve each equation.
1)
19k = 2(k + 13) + 3(8k + 3)
2)
1.4(6.5 – 6m) = 3.22
3)
2 4n + 1 = 5 n + 7
5
3
3
4)
5+
5)
4.2(1.2b) – (–0.9b) = 5.94
2
6)
7 (c + 3) = 1 – c
3
3
7)
15 g + 4 1 – 2 1 – 4 = 0
6
2
3
8)
9.1 = 2.8(4h – 1)
4
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35 = –2
2a + 9
Name :
Answer Key
Mixed Review: S3
Multi-Step Equations
Solve each equation.
1)
19k = 2(k + 13) + 3(8k + 3)
2)
m = 0.7
k = –5
3)
2 4n + 1 = 5 n + 7
5
3
3
4)
n = 29
95
5)
4.2(1.2b) – (–0.9b) = 5.94
2
15 g + 4 1 – 2 1 – 4 = 0
6
2
3
g=1
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5+
35 = –2
2a + 9
a = –7
6)
7 (c + 3) = 1 – c
3
3
c = –2
b=2
7)
1.4(6.5 – 6m) = 3.22
8)
9.1 = 2.8(4h – 1)
4
h = 3.5
Name :
Multi-Step Equations
Mixed Review: S4
Solve each equation.
1)
4w+6= 3 + 1 w–3
5
4 4
2)
–7(8 + t) = 5(–t + 20) − 18
3)
2.4(7u + 3.1 – 5u) = 19.44
4)
9 (1 + s) = 1 s + 1
7
7
2
5)
8–r
= –4
11 − 3r
6)
1.5v + 8 = 2v + 15
7)
6.7(q – 9) = 8.2q – 1.5
8)
−13m + 3 = –14m – 30 + 4m
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Name :
Answer Key
Multi-Step Equations
Mixed Review: S4
Solve each equation.
1)
4w+6= 3 + 1 w–3
5
4 4
2)
t = –69
w = –15
3)
2.4(7u + 3.1 – 5u) = 19.44
4)
8–r
= –4
11 − 3r
6)
6.7(q – 9) = 8.2q – 1.5
q = –39.2
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1.5v + 8 = 2v + 15
v = –14
r=4
7)
9 (1 + s) = 1 s + 1
7
7
2
s = – 17 or –1 1
16
16
u = 2.5
5)
–7(8 + t) = 5(–t + 20) − 18
8)
−13m + 3 = –14m – 30 + 4m
m = 11
Name :
Mixed Review: S5
Multi-Step Equations
Solve each equation.
1)
3(–h + 7) + 4(–6h + 3) = 6h
2)
8.8 = 2.2(6.4 – 2k)
3)
5 2b + 1 = 9b + 7
8
2 8
4)
7+
5)
3.1(1.4c) + 0.5c = 9.24 + 2c
2
6)
7 (n + 6) = 10 – n
9
9
7)
3a + 8 = 1 (2 + a)
3
4
8)
9.2 =
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22 = –4
m+7
2(6g – 1)
5
Name :
Answer Key
Mixed Review: S5
Multi-Step Equations
Solve each equation.
1)
3(–h + 7) + 4(–6h + 3) = 6h
2)
k = 1.2
h=1
3)
5 2b + 1 = 9b + 7
8
2 8
4)
b= 1
22
5)
3.1(1.4c) + 0.5c = 9.24 + 2c
2
3a + 8 = 1 (2 + a)
3
4
a = – 26 or –2 8
9
9
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7+
22 = –4
m+7
m = –9
6)
7 (n + 6) = 10 – n
9
9
n = –2
c = 22
7)
8.8 = 2.2(6.4 – 2k)
8)
9.2 =
g=4
2(6g – 1)
5
Name :
Type 2: S1
Multi-Step Equations: Shapes
Find the unknown value given in each shape.
2)
Perimeter = 21 cm
3)
2q
20
n+2
Area = 2(5a + 3)
8m
Area = 40 mm²
–3
1)
3n + 1
4a – 24
n=
Perimeter = 25 m
7+
5)
a=
Area = 3 (5k – 1)
2
6)
Perimeter = 2(9y – 7)
t
t–1
10 – t
9 mm
4)
q=
14 cm
4t – 11
t =
Area = b – 1
8)
y=
Perimeter = 37u –2 + 29u
2
Area = 55 mm²
s+5
b–4
b=
9)
5 mm
5 cm
7)
k =
13 m
u=
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s =
2s – 13
Name :
Answer Key
Type 2: S1
Multi-Step Equations: Shapes
Find the unknown value given in each shape.
2)
Perimeter = 21 cm
3)
2q
20
n+2
Area = 2(5a + 3)
8m
Area = 40 mm²
–3
1)
3n + 1
n=
q=
3
Perimeter = 25 m
7+
5)
a=
5
Area = 3 (5k – 1)
2
6)
Perimeter = 2(9y – 7)
t
t–1
10 – t
14 cm
4t – 11
t =
k =
4
Area = b – 1
8)
Perimeter = 37u –2 + 29u
2
9)
7
Area = 55 mm²
5 mm
s+5
b–4
b=
y=
11
5 cm
7)
9
9 mm
4)
4a – 24
2s – 13
13 m
6
u=
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2
s =
10
Name :
Type 2: S2
Multi-Step Equations: Shapes
Find the unknown value given in each shape.
1)
Perimeter = 5d – 7
2)
Area = 21v + 32
2
3)
Perimeter = 2(3s + 4)
19 mm
27 – d
cm
d=
v=
5)
s=
Perimeter = 28 cm
6)
Area = 54 m²
10 – r
Area = 1 (11p – 5)
5
(4p – 18)
s–1
5 mm
4)
24
r+1
2g – 20
Perimeter = 42 m
8)
r=
Area = 26 mm²
17 – 2a
Perimeter = 31 cm
2u
–
5a
u–6
15 – k
k=
a=
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u=
8 cm
2 mm
2k – 1
9)
10
g=
p=
7)
6
10 m
d+1
2+s
20
s+
Name :
Answer Key
Type 2: S2
Multi-Step Equations: Shapes
Find the unknown value given in each shape.
1)
Perimeter = 5d – 7
2)
Area = 21v + 32
2
3)
Perimeter = 2(3s + 4)
19 mm
27 – d
cm
s–1
v=
11
5)
Perimeter = 28 cm
6)
(4p – 18)
Area = 54 m²
24
r+1
2g – 20
p=
7)
g=
5
Perimeter = 42 m
8)
r=
12
Area = 26 mm²
9)
1
Perimeter = 31 cm
2u
–
8 cm
2 mm
10
17 – 2a
2k – 1
6
10 – r
Area = 1 (11p – 5)
5
s=
8
5 mm
4)
6
10 m
d+1
d=
2+s
20
s+
5a
u–6
15 – k
k=
7
a=
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3
u=
13
Name :
Type 2: S3
Multi-Step Equations: Shapes
Find the unknown value given in each shape.
1)
Area = 1 (29k – 12)
2
2)
Area = 1 (47s + 15)
2
3)
Perimeter = 36 cm
12 + y
y
s+3
11
cm
9m
19 mm
k=
4)
s=
Perimeter = 3(2v – 6)
5)
y=
Perimeter = a + 7
6)
6m
u+1
8 mm
a–1
2
5 cm
v=
7)
a=
Perimeter = 30 mm
Area = 2(5u – 1)
8)
u=
Area = 44 cm²
9)
Area = 2(9t + 7)
t+5
10 m
1
(3n – 2)
5
11 cm
3t – 5
3r + 1
r=
n=
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t=
Name :
Answer Key
Type 2: S3
Multi-Step Equations: Shapes
Find the unknown value given in each shape.
1)
Area = 1 (29k – 12)
2
2)
Area = 1 (47s + 15)
2
3)
Perimeter = 36 cm
12 + y
y
s+3
11
cm
9m
19 mm
k=
4)
s=
6
Perimeter = 3(2v – 6)
5)
y=
11
Perimeter = a + 7
6)
6m
v=
7)
Area = 2(5u – 1)
u+1
8 mm
a–1
2
5 cm
a=
8
Perimeter = 30 mm
8)
2
u=
9
Area = 44 cm²
9)
5
Area = 2(9t + 7)
t+5
10 m
1
(3n – 2)
5
11 cm
3t – 5
3r + 1
r=
3
n=
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14
t=
7
Score :
Name :
Multi-Step Equations - Fractions and Decimals
Sheet 1
1)
Danielle baked macaroni for her children for which she used up 1 th of a jug of milk. She also poured
9
20.5 ounces of milk into a bowl of cornflakes. If 25.5 ounces of milk remain in the jug, how much milk
did the jug originally contain?
2)
Nancy has a freshwater aquarium at home. She buys goldfish four more than twice the number of
platies she bought last Sunday. She also buys 2 black mollies and a few guppies that amounted to
one quarter of the total number of goldfish she bought. If there are 35 fish in all, how many goldfish
did she buy?
3)
A total of 119 golden tickets were sold for an NBA match. A hundred general tickets and 6 platinum
tickets were also sold. The price of a general ticket was three-fourth the cost of the golden ticket.
The price of a platinum ticket was twice that of the golden ticket. How much was a golden ticket
priced at, if the total collection from ticket sales was $6,592?
4)
David bought a variety pack of delicious donuts from the famous Donut house for his daughters,
Amy and Anna. Amy ate two-third of the pack and Anna devoured one-fourth of them. Finally David
ate the remaining one donut. Find out the total number of donuts in the pack.
5)
Robert earns $512.75 less than the salary earned by Noel. John earns three times Robert’s salary. If the
total salary earned by them is $47,645.25, how much salary do Robert earn?
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Answer key
Multi-Step Equations - Fractions and Decimals
1)
Sheet 1
Danielle baked macaroni for her children for which she used up 1 th of a jug of milk. She also poured
9
20.5 ounces of milk into a bowl of cornflakes. If 25.5 ounces of milk remain in the jug, how much milk
did the jug originally contain?
x – 1 x – 20.5 = 25.5 ; 51.75 ounces
9
2)
Nancy has a freshwater aquarium at home. She buys goldfish four more than twice the number of
platies she bought last Sunday. She also buys 2 black mollies and a few guppies that amounted to
one quarter of the total number of goldfish she bought. If there are 35 fish in all, how many goldfish
did she buy?
x + 2x + 4 + 2 + 1 (2x + 4) = 35 ; 20 goldfish
4
3)
A total of 119 golden tickets were sold for an NBA match. A hundred general tickets and 6 platinum
tickets were also sold. The price of a general ticket was three-fourth the cost of the golden ticket.
The price of a platinum ticket was twice that of the golden ticket. How much was a golden ticket
priced at, if the total collection from ticket sales was $6,592?
119x + 100 3 x + 6(2x) = 6592 ; $32
4
4)
David bought a variety pack of delicious donuts from the famous Donut house for his daughters,
Amy and Anna. Amy ate two-third of the pack and Anna devoured one-fourth of them. Finally David
ate the remaining one donut. Find out the total number of donuts in the pack.
2 x + 1 x + 1 = x ; 12 donuts
3
4
5)
Robert earns $512.75 less than the salary earned by Noel. John earns three times Robert’s salary. If the
total salary earned by them is $47,645.25, how much salary do Robert earn?
x + x – 512.75 + 3(x – 512.75) = 47645.25 ; $9426.50
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Multi-Step Equations - Fractions and Decimals
Sheet 2
1)
In a local park, a few children were on the monkey bars. The number of children occupying the slides
was one-eighth of the number of children playing on the monkey bars. 8 children were playing in the
sandbox. If there are 35 children in all, how many children occupied the slides?
2)
Ivan had 120 baseball cards. He gave some baseball cards to Nathan. Ivan gave Jack two-thirds of the
cards he gave Nathan. If Ivan is left with 55 cards, how many cards did he give Nathan?
3)
Mrs. Telles bakes a turkey for Thanksgiving. She gives one-seventh of the turkey to her neighbors. If
her family consumed two-thirds of the turkey and 3.6 pounds of meat remains, how much did the
turkey originally weigh?
4)
There are two pear trees in Charles’s backyard. The height of the first tree is two more than three
times taller than the other. If the difference in height between the two trees is 14.5 feet, calculate the
height of the shorter pear tree.
5)
A bake sale was held at Juvena High to raise funds for an NGO. The sale of maple pecan pies
amounted to 15 more than half the lemon tarts that were sold. The number of brownie pops sold
amounted to two-thirds of the sale of maple pecan pies. If 223 pieces were sold in all, how many
lemon tarts were sold?
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Answer key
Multi-Step Equations - Fractions and Decimals
1)
Sheet 2
In a local park, a few children were on the monkey bars. The number of children occupying the slides
was one-eighth of the number of children playing on the monkey bars. 8 children were playing in the
sandbox. If there are 35 children in all, how many children occupied the slides?
x + 1 x + 8 = 35 ; 3 children
8
2)
Ivan had 120 baseball cards. He gave some baseball cards to Nathan. Ivan gave Jack two-thirds of the
cards he gave Nathan. If Ivan is left with 55 cards, how many cards did he give Nathan?
120 – x – 2 x = 55 ; 39 cards
3
3)
Mrs. Telles bakes a turkey for Thanksgiving. She gives one-seventh of the turkey to her neighbors. If
her family consumed two-thirds of the turkey and 3.6 pounds of meat remains, how much did the
turkey originally weigh?
x – 1 x – 2 x = 3.6 ; 18.9 pounds
7
3
4)
There are two pear trees in Charles’s backyard. The height of the first tree is two more than three
times taller than the other. If the difference in height between the two trees is 14.5 feet, calculate the
height of the shorter pear tree.
2 + 3x – x = 14.5 ; 6.25 feet
5)
A bake sale was held at Juvena High to raise funds for an NGO. The sale of maple pecan pies
amounted to 15 more than half the lemon tarts that were sold. The number of brownie pops sold
amounted to two-thirds of the sale of maple pecan pies. If 223 pieces were sold in all, how many
lemon tarts were sold?
x + 15 + 1 x + 2 15 + 1 x = 223 ; 108 lemon tarts
2
3
2
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Multi-Step Equations - Fractions and Decimals
Sheet 3
1)
Susan visits a grocery store. She places a few pounds of cucumber in her shopping cart. The carrots
she picked weighed 2.3 pounds more than cucumber. She also bought cuts of flank steak that was
four times the weight of carrots. If the total weight of all items was 35.5 pounds, how much did the
cuts of flank steak weigh?
2)
A recipe calls for two and a half cups of water, some lemon extract and orange juice which is eight
times that of the lemon extract to make orangeade. Kylie uses five times the amount mentioned in
the recipe to make 35 cups of orangeade. How much lemon extract was required to prepare the
orangeade?
3)
Michelle uses up 40.15 yards of wall fabric panels to do up her home. For the portico, she uses 7.5
yards less than the amount of fabric panel that was used to decorate the kid’s room. For the hall, she
uses three times the amount than what she used to do up the portico. How many yards of wall fabric
panel did Michelle use to decorate the kid’s room?
4)
Leslie has a voucher worth $5 coupon from Wal-Mart. She visits the store and purchases a wallet that
amounted to double the price she paid for the groceries she bought. If Leslie was billed for a total of
$34.45 after the voucher was redeemed, what was the cost of the wallet?
5)
The perimeter of a pool table is 368.4 inches. The length of the table is twice of three more than its
width. Find the length of the table.
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Answer key
Multi-Step Equations - Fractions and Decimals
1)
Sheet 3
Susan visits a grocery store. She places a few pounds of cucumber in her shopping cart. The carrots
she picked weighed 2.3 pounds more than cucumber. She also bought cuts of flank steak that was
four times the weight of carrots. If the total weight of all items was 35.5 pounds, how much did the
cuts of flank steak weigh?
x + 2.3 + x + 4(2.3 + x) = 35.5 ; 25.2 pounds
2)
A recipe calls for two and a half cups of water, some lemon extract and orange juice which is eight
times that of the lemon extract to make orangeade. Kylie uses five times the amount mentioned in
the recipe to make 35 cups of orangeade. How much lemon extract was required to prepare the
orangeade?
5 2 1 + x + 8x = 35 ; 1 cup
2
2
3)
Michelle uses up 40.15 yards of wall fabric panels to do up her home. For the portico, she uses 7.5
yards less than the amount of fabric panel that was used to decorate the kid’s room. For the hall, she
uses three times the amount than what she used to do up the portico. How many yards of wall fabric
panel did Michelle use to decorate the kid’s room?
x + x – 7.5 + 3(x – 7.5) = 40.15 ; 14.03 yards
4)
Leslie has a voucher worth $5 coupon from Wal-Mart. She visits the store and purchases a wallet that
amounted to double the price she paid for the groceries she bought. If Leslie was billed for a total of
$34.45 after the voucher was redeemed, what was the cost of the wallet?
x + 2x – 5 = 34.45 ; $26.30
5)
The perimeter of a pool table is 368.4 inches. The length of the table is twice of three more than its
width. Find the length of the table.
2(2(x + 3) + x) = 368.4 ; 124.8 inches
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Identifying Solutions
ES1
Choose the correct solution that best describes each inequality.
1)
8x – 2x > 12
3
a)
(–∞ –18)
b)
c)
(–∞ 18]
d)
3)
4(2 + 5x) < 48
a)
(–∞ 2)
b)
c)
(–∞ 2]
d)
5)
3x + 5 ≥ 7
2
a)
(–∞ –3)
b)
c)
(–∞ 3]
d)
7)
3x + 5x ≤ 26
2
a)
(–∞ –4)
b)
c)
(–∞ 4]
d)
2)
7x + 1 ≥ 4
2
(18 ∞)
a)
(1 ∞)
b)
(–∞ 1)
[18 ∞)
c)
[1 ∞)
d)
(–∞ 1]
4)
3x + 5x ≤ 34
4
(2 ∞)
a)
(–∞ –8)
b)
(–∞ 8)
[2 ∞)
c)
(–∞ 8]
d)
[8 ∞)
6)
9 (3x – 13) < 45
(3 ∞)
a)
(–∞ –6)
b)
(–∞ 6)
[3 ∞)
c)
(–∞ 6]
d)
[6 ∞)
8)
4x – 8 > 2
6
(4 ∞)
a)
(–∞ –5)
b)
[5 ∞)
[4 ∞)
c)
(–∞ 5]
d)
(5 ∞)
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Answer key
Identifying Solutions
ES1
Choose the correct solution that best describes each inequality.
1)
8x – 2x > 12
3
a)
(–∞ –18)
b)
c)
(–∞ 18]
d)
3)
4(2 + 5x) < 48
a)
(–∞ 2)
b)
c)
(–∞ 2]
d)
5)
3x + 5 ≥ 7
2
a)
(–∞ –3)
b)
c)
(–∞ 3]
d)
7)
3x + 5x ≤ 26
2
a)
(–∞ –4)
b)
c)
(–∞ 4]
d)
2)
7x + 1 ≥ 4
2
(18 ∞)
a)
(1 ∞)
b)
(–∞ 1)
[18 ∞)
c)
[1 ∞)
d)
(–∞ 1]
4)
3x + 5x ≤ 34
4
(2 ∞)
a)
(–∞ –8)
b)
(–∞ 8)
[2 ∞)
c)
(–∞ 8]
d)
[8 ∞)
6)
9 (3x – 13) < 45
(3 ∞)
a)
(–∞ –6)
b)
(–∞ 6)
[3 ∞)
c)
(–∞ 6]
d)
[6 ∞)
8)
4x – 8 > 2
6
(4 ∞)
a)
(–∞ –5)
b)
[5 ∞)
[4 ∞)
c)
(–∞ 5]
d)
(5 ∞)
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Identifying Solutions
ES2
Choose the correct solution that best describes each inequality.
1)
7x – x ≤ 25
2
a)
(–∞ –10)
b)
c)
(–∞ 10]
d)
3)
3 (8 + 2x) < 30
a)
(–∞ 1)
b)
c)
(–∞ 1]
d)
5)
2x + 3 >11
3
a)
(–∞ 15)
b)
c)
(–∞ 15]
d)
7)
5x + 4 ≥ 4
6
a)
(–∞ –4)
b)
c)
(–∞ 4]
d)
2)
4 (2x – 5) < 28
(10 ∞)
a)
(6 ∞)
b)
(–∞ 6)
[10 ∞)
c)
[6 ∞)
d)
(–∞ 6]
4)
9x – 3x ≥ 12
2
(1 ∞)
a)
(–∞ –8)
b)
(–∞ 8)
[1 ∞)
c)
(–∞ 8]
d)
[8 ∞)
6)
3x – x ≤ 20
4
(15, ∞)
a)
(–∞ 80)
b)
(80 ∞)
[15 ∞)
c)
[–80 ∞)
d)
(–∞ –80]
8)
6x – 11 > 5
5
(4 ∞)
a)
(–∞ –6)
b)
(6 ∞)
[4 ∞)
c)
(–∞ 6]
d)
[6 ∞)
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Name :
Score :
Answer key
Identifying Solutions
ES2
Choose the correct solution that best describes each inequality.
1)
7x – x ≤ 25
2
a)
(–∞ –10)
b)
c)
(–∞ 10]
d)
3)
3 (8 + 2x) < 30
a)
(–∞ 1)
b)
c)
(–∞ 1]
d)
5)
2x + 3 >11
3
a)
(–∞ 15)
b)
c)
(–∞ 15]
d)
7)
5x + 4 ≥ 4
6
a)
(–∞ –4)
b)
c)
(–∞ 4]
d)
2)
4 (2x – 5) < 28
(10 ∞)
a)
(6 ∞)
b)
(–∞ 6)
[10 ∞)
c)
[6 ∞)
d)
(–∞ 6]
4)
9x – 3x ≥ 12
2
(1 ∞)
a)
(–∞ –8)
b)
(–∞ 8)
[1 ∞)
c)
(–∞ 8]
d)
[8 ∞)
6)
3x – x ≤ 20
4
(15, ∞)
a)
(–∞ 80)
b)
(80 ∞)
[15 ∞)
c)
[–80 ∞)
d)
(–∞ –80]
8)
6x – 11 > 5
5
(4 ∞)
a)
(–∞ –6)
b)
(6 ∞)
[4 ∞)
c)
(–∞ 6]
d)
[6 ∞)
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Identifying Solutions
ES3
Choose the correct solution that best describes each inequality.
1)
7 (6 + 2x) < 56
a)
(–∞ 1)
b)
c)
(–∞ 1]
d)
3)
2x + x ≤ 10
3
a)
(–∞ 6)
b)
c)
(–∞ 6]
d)
5)
8 (2x – 5) < 72
a)
(–∞ 7)
b)
c)
(–∞ 7]
d)
7)
3x – 2 > 5
8
a)
(–∞ –14)
b)
c)
(–∞ 14]
d)
2)
4x + 2 >15
2
(1 ∞)
a)
(–∞ 7]
b)
(–∞ 7)
[1 ∞)
c)
[7 ∞)
d)
(7 ∞)
4)
9x – 4x ≥ 13
2
(6 ∞)
a)
[–26 ∞)
b)
(–∞ 26)
[6 ∞)
c)
(–∞ 26]
d)
[26 ∞)
6)
9x + 5 ≥ 7
11
(7, ∞)
a)
(–∞ 8)
b)
(8 ∞)
[7 ∞)
c)
(–∞ 8]
d)
[8 ∞)
8)
x – x ≤ 12
5
[14 ∞)
a)
(–∞ 15]
b)
[–15 ∞)
(14 ∞)
c)
(–∞ 15)
d)
(–15 ∞)
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Score :
Answer key
Identifying Solutions
ES3
Choose the correct solution that best describes each inequality.
1)
7 (6 + 2x) < 56
a)
(–∞ 1)
b)
c)
(–∞ 1]
d)
3)
2x + x ≤ 10
3
a)
(–∞ 6)
b)
c)
(–∞ 6]
d)
5)
8 (2x – 5) < 72
a)
(–∞ 7)
b)
c)
(–∞ 7]
d)
7)
3x – 2 > 5
8
a)
(–∞ –14)
b)
c)
(–∞ 14]
d)
2)
4x + 2 >15
2
(1 ∞)
a)
(–∞ 7]
b)
(–∞ 7)
[1 ∞)
c)
[7 ∞)
d)
(7 ∞)
4)
9x – 4x ≥ 13
2
(6 ∞)
a)
[–26 ∞)
b)
(–∞ 26)
[6 ∞)
c)
(–∞ 26]
d)
[26 ∞)
6)
9x + 5 ≥ 7
11
(7, ∞)
a)
(–∞ 8)
b)
(8 ∞)
[7 ∞)
c)
(–∞ 8]
d)
[8 ∞)
8)
x – x ≤ 12
5
[14 ∞)
a)
(–∞ 15]
b)
[–15 ∞)
(14 ∞)
c)
(–∞ 15)
d)
(–15 ∞)
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 1
Functions - Ordered Pairs
A) State whether each set of ordered pairs represents a function.
1) {(10, 9), (–2, –16), (–6, 7), (5, 8), (8, –16), (–11, 9)}
2) {(–7, 4), (–8, 3), (–7, 7), (–20, 8), (5, 9), (3, 1), (2, 6)}
3) {(–13, 4), (7, –15), (–13, 9), (6, –12), (–18, 0)}
4) {(15, –3), (–6, 9), (–3, 0), (–1, 16)}
5) {(–4, 3), (5, –9), (11, 4), (9, 6), (5, –3), (8, –9), (1, 4)}
6) {(12, –18), (15, 1), (12, 5), (0, 9), (–5, –17)}
7) {(6, 0), (–12, –16), (–6, 10), (20, –7)}
8) {(–2, –4), (–8, 3), (–7, –4), (–2, –8), (11, 8), (9, –4)}
B) State whether each set of ordered pairs on the graph represents a function.
1)
20
2)
y
15
3)
y
14
16
12
12
12
9
10
8
6
8
4
3
6
-20 -16 -12 -8 -4
-4
x
4 8 12 16 20
-2
-3
x
2 4 6 8 10 12 14 16 18
4
2
-8
-6
-12
-9
-2 -1
-2
-16
-12
-4
-20
-15
-6
Printable Worksheets @ www.mathworksheets4kids.com
y
x
1 2 3 4 5 6 7 8
Answer key
Name :
Sheet 1
Functions - Ordered Pairs
A) State whether each set of ordered pairs represents a function.
1) {(10, 9), (–2, –16), (–6, 7), (5, 8), (8, –16), (–11, 9)}
2) {(–7, 4), (–8, 3), (–7, 7), (–20, 8), (5, 9), (3, 1), (2, 6)}
Yes
No
3) {(–13, 4), (7, –15), (–13, 9), (6, –12), (–18, 0)}
4) {(15, –3), (–6, 9), (–3, 0), (–1, 16)}
No
Yes
5) {(–4, 3), (5, –9), (11, 4), (9, 6), (5, –3), (8, –9), (1, 4)}
6) {(12, –18), (15, 1), (12, 5), (0, 9), (–5, –17)}
No
No
7) {(6, 0), (–12, –16), (–6, 10), (20, –7)}
8) {(–2, –4), (–8, 3), (–7, –4), (–2, –8), (11, 8), (9, –4)}
Yes
No
B) State whether each set of ordered pairs on the graph represents a function.
1)
20
2)
y
15
3)
y
14
16
12
12
12
9
10
8
6
8
4
3
6
-20 -16 -12 -8 -4
-4
x
4 8 12 16 20
-2
-3
x
2 4 6 8 10 12 14 16 18
4
2
-8
-6
-12
-9
-2 -1
-2
-16
-12
-4
-20
-15
-6
No
Yes
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y
x
1 2 3 4 5 6 7 8
Yes
Name :
Sheet 2
Functions - Ordered Pairs
A) State whether each set of ordered pairs represents a function.
1) {(–1, –8), (3, –16), (–11, 0), (3, 9)}
2) {(9, –3), (–20, 2), (3, –9), (–7, 18), (–4, 20), (–3, –3)}
3) {(5, 4), (7, –11), (0, –2), (8, –1), (3, 0), (–7, 1), (–8, 0)}
4) {(–4, –5), (–10, 15), (–2, 0), (0, –8), (–2, 9)}
5) {(1, –5), (13, –4), (–11, 3), (–1, 8), (9, –4), (9, 19)}
6) {(3, 9), (12, 0), (–12, 15), (10, 19), (–15, 15)}
7) {(–6, 6), (5, 0), (6, –16), (–8, 1), (2, –14), (–1, 7)}
8) {(–19, –4), (–18, 1), (–9, 2), (–5, –3), (10, 0), (–19, 3)}
B) State whether each set of ordered pairs on the graph represents a function.
1)
8
2)
y
5
3)
y
6
7
4
4
6
3
2
5
2
4
1
3
-5 -4 -3 -2 -1
-1
2
1
-16 -14 -12 -10 -8 -6 -4 -2
-1
-2
x
2 4
-2
-3
-4
-5
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x
1 2 3 4 5
-9 -6 -3
-2
-4
-6
-8
-10
-12
-14
y
x
3 6 9 12 15 18 21
Answer key
Name :
Sheet 2
Functions - Ordered Pairs
A) State whether each set of ordered pairs represents a function.
1) {(–1, –8), (3, –16), (–11, 0), (3, 9)}
2) {(9, –3), (–20, 2), (3, –9), (–7, 18), (–4, 20), (–3, –3)}
No
Yes
3) {(5, 4), (7, –11), (0, –2), (8, –1), (3, 0), (–7, 1), (–8, 0)}
4) {(–4, –5), (–10, 15), (–2, 0), (0, –8), (–2, 9)}
Yes
No
5) {(1, –5), (13, –4), (–11, 3), (–1, 8), (9, –4), (9, 19)}
6) {(3, 9), (12, 0), (–12, 15), (10, 19), (–15, 15)}
No
Yes
7) {(–6, 6), (5, 0), (6, –16), (–8, 1), (2, –14), (–1, 7)}
8) {(–19, –4), (–18, 1), (–9, 2), (–5, –3), (10, 0), (–19, 3)}
Yes
No
B) State whether each set of ordered pairs on the graph represents a function.
1)
8
2)
y
5
6
7
4
4
6
3
2
5
2
4
1
3
-5 -4 -3 -2 -1
-1
2
1
-16 -14 -12 -10 -8 -6 -4 -2
-1
-2
Yes
3)
y
x
2 4
-2
-3
-4
-5
No
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x
1 2 3 4 5
-9 -6 -3
-2
-4
-6
-8
y
x
3 6 9 12 15 18 21
-10
-12
-14
No
Name :
Sheet 3
Functions - Ordered Pairs
A) State whether each set of ordered pairs represents a function.
1) {(0, 2), (15, –2), (3, 7), (2, 5), (–2, –4), (1, 7), (–11, 7)}
2) {(–11, –2), (20, 15), (–12, 0), (19, –13)}
3) {(16, –4), (9, –1), (3, –2), (8, –1), (13, 0), (–17, 16)}
4) {(–8, –13), (–7, 3), (5, –9), (–7, 18), (–4, 3), (0, –10)}
5) {(–9, –5), (–9, –16), (–9, 10), (–9, 9), (–9, 20)}
6) {(14, 11), (0, 11), (–17, 11), (8, 11)}
7) {(4, 14), (–2, –12), (–1, 6), (4, –17), (5, 6), (13, 0)}
8) {(–3, 2), (18, 9), (–19, 1), (2, –3), (5, 0), (1, 1), (–5, 9)}
B) State whether each set of ordered pairs on the graph represents a function.
1)
18
2)
y
3
15
2
12
1
9
6
-40 -35 -30 -25 -20 -15 -10 -5
-1
3
-2
-2 -1
-3
x
1 2 3 4 5 6 7 8
3)
y
15
12
x
5 10
9
6
3
-3
-15 -12 -9 -6 -3
-3
-4
-6
-6
-5
-9
-9
-6
-12
-12
-7
-15
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y
x
3 6 9 12 15
Answer key
Name :
Sheet 3
Functions - Ordered Pairs
A) State whether each set of ordered pairs represents a function.
1) {(0, 2), (15, –2), (3, 7), (2, 5), (–2, –4), (1, 7), (–11, 7)}
2) {(–11, –2), (20, 15), (–12, 0), (19, –13)}
Yes
Yes
3) {(16, –4), (9, –1), (3, –2), (8, –1), (13, 0), (–17, 16)}
4) {(–8, –13), (–7, 3), (5, –9), (–7, 18), (–4, 3), (0, –10)}
Yes
No
5) {(–9, –5), (–9, –16), (–9, 10), (–9, 9), (–9, 20)}
6) {(14, 11), (0, 11), (–17, 11), (8, 11)}
No
Yes
7) {(4, 14), (–2, –12), (–1, 6), (4, –17), (5, 6), (13, 0)}
8) {(–3, 2), (18, 9), (–19, 1), (2, –3), (5, 0), (1, 1), (–5, 9)}
No
Yes
B) State whether each set of ordered pairs on the graph represents a function.
1)
18
2)
y
3
15
2
12
1
9
6
-40 -35 -30 -25 -20 -15 -10 -5
-1
3
-2
-2 -1
-3
x
1 2 3 4 5 6 7 8
3)
y
15
12
x
5 10
9
6
3
-3
-15 -12 -9 -6 -3
-3
-4
-6
-6
-5
-9
-9
-6
-12
-12
-7
-15
No
Yes
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y
No
x
3 6 9 12 15
Name:
Sheet 1
Linear or Nonlinear Functions
A) Determine whether each function is linear or nonlinear.
1) 5 = 7 + 6
3)
–
9
=4+
= 12
4) 2 3 =
= 13
6)
5) 9 4 –
7)
2)
+8=
5
3
– 11
= –5( + 7)
8) 2 = 6 2 –
2
+3
B) 1) Which of the following is a linear function?
i)
= 4 4 + 10
ii)
2=7 –3
iii)
+
5
= 14
iv) 8 = –5 (3 + )
2) Which of the following is a nonlinear function?
i) 2 + 1 =
ii)
= – 3 + 12
9
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iii)
+6 =5
iv)
= –10 – 3
Answer key
Name:
Sheet 1
Linear or Nonlinear Functions
A) Determine whether each function is linear or nonlinear.
1) 5 = 7 + 6
2)
=4+
linear
3)
–
9
nonlinear
4) 2 3 =
= 12
linear
5) 9 4 –
5
3
– 11
nonlinear
= 13
6)
= –5( + 7)
nonlinear
7)
+8=
linear
8) 2 = 6 2 –
2
linear
+3
nonlinear
B) 1) Which of the following is a linear function?
i)
= 4 4 + 10
ii)
2=7 –3
iii)
+
5
= 14
iv) 8 = –5 (3 + )
2) Which of the following is a nonlinear function?
i) 2 + 1 =
ii)
= – 3 + 12
9
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iii)
+6 =5
iv)
= –10 – 3
Name:
Sheet 2
Linear or Nonlinear Functions
A) Determine whether each function is linear or nonlinear.
1) 2 (5 + ) =
2)
3)
=8
4) 6 = 2 + 12
5) 5 + 4 = 0
6) 10 = 9 3 –
7)
=
4
8
= 7 + 15
8) 3 +
6
7
= 14
B) 1) Which of the following is a nonlinear function?
i)
2+2 =
5
3
ii)
= 7( + 4)
iii)
= –6 – 9
iv) 12 +
=
iv)
3
=
2) Which of the following is a linear function?
i)
= 8 3 – 15
ii)
= 10 4 + 14
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iii)
7
+ 11
–2 5=0
Answer key
Name:
Sheet 2
Linear or Nonlinear Functions
A) Determine whether each function is linear or nonlinear.
1) 2 (5 + ) =
2)
= 7 + 15
nonlinear
3)
linear
4) 6 = 2 + 12
=8
linear
nonlinear
5) 5 + 4 = 0
6) 10 = 9 3 –
linear
7)
=
6
7
nonlinear
4
8
8) 3 +
= 14
nonlinear
linear
B) 1) Which of the following is a nonlinear function?
i)
2+2 =
5
3
ii)
= 7( + 4)
iii)
= –6 – 9
iv) 12 +
=
iv)
3
=
2) Which of the following is a linear function?
i)
= 8 3 – 15
ii)
= 10 4 + 14
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iii)
7
+ 11
–2 5=0
Name:
Sheet 3
Linear or Nonlinear Functions
A) Determine whether each function is linear or nonlinear.
1)
2 – 11 = 4
2)
=
3)
+
3
=9
2
4)
=5 –8
5)
– =0
6
6) 7 5 +
+1
= 12
8)
2
+ = 15
4
iii)
(2 + 8 ) =
iv)
= –7 + 2
= 3 + 14
iv)
–
7) 2 (5 + 3 ) = 10
B) 1) Which of the following is a linear function?
i)
2 + 4 = 13
ii)
= 4 – 11
3
2) Which of the following is a nonlinear function?
i)
= (5 – 9 )
ii) 6 – = 1
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iii)
4
=
5
Answer key
Name:
Sheet 3
Linear or Nonlinear Functions
A) Determine whether each function is linear or nonlinear.
1)
2 – 11 = 4
2)
=
6
+1
nonlinear
3)
+
linear
3
=9
2
4)
=5 –8
nonlinear
5)
linear
– =0
6) 7 5 +
linear
= 12
nonlinear
7) 2 (5 + 3 ) = 10
8)
nonlinear
2
+ = 15
4
nonlinear
B) 1) Which of the following is a linear function?
i)
2 + 4 = 13
ii)
= 4 – 11
3
iii)
(2 + 8 ) =
iv)
= –7 + 2
= 3 + 14
iv)
–
2) Which of the following is a nonlinear function?
i)
= (5 – 9 )
ii) 6 – = 1
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iii)
4
=
5
Name:
Sheet 1
Evaluate - Function Table
A) Evaluate each function from the table.
1)
x
–4
2
7
10
f(x)
6
11
0
14
2)
x
5
8
13
19
f(x)
37
–13
–55
22
i)
f(–4)
=
i)
f(13)
=
ii)
f(7)
=
ii)
f(8)
=
3)
x
–17
–16
–11
3
f(x)
–27
–17
1
29
4)
x
0
4
10
14
f(x)
–16
99
0
–8
i)
f(3)
=
i)
f(4)
=
ii)
f(–17) =
ii)
f(14)
=
B) Evaluate the functions from the table.
1)
x
f(x)
g(x)
6
35
13
15
2)
x
f(x)
g(x)
19
–6
–24
14
–19
5
1
4
–4
8
23
4
16
10
i)
f(13)
=
i)
f(4)
=
ii)
f(6)
=
ii)
g(1)
=
iii)
g(15) =
iii)
g(4)
=
iv)
g(13) =
iv)
g(–6) =
v)
For what value of x, f(x) is 35?
v)
For what value of x, f(x) is –24?
vi)
For what value of x, g(x) is 5?
vi)
For what value of x, f(x) is 4?
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Answer key
Name:
Sheet 1
Evaluate - Function Table
A) Evaluate each function from the table.
1)
x
–4
2
7
10
f(x)
6
11
0
14
2)
x
5
8
13
19
f(x)
37
–13
–55
22
i)
f(–4)
=
6
i)
f(13)
=
–55
ii)
f(7)
=
0
ii)
f(8)
=
–13
3)
x
–17
–16
–11
3
f(x)
–27
–17
1
29
4)
x
0
4
10
14
f(x)
–16
99
0
–8
i)
f(3)
=
29
i)
f(4)
=
99
ii)
f(–17) =
–27
ii)
f(14)
=
–8
B) Evaluate the functions from the table.
1)
x
f(x)
g(x)
6
35
13
15
2)
x
f(x)
g(x)
19
–6
–24
14
–19
5
1
4
–4
8
23
4
16
10
i)
f(13)
=
–19
i)
f(4)
=
16
ii)
f(6)
=
35
ii)
g(1)
=
–4
iii)
g(15) =
23
iii)
g(4)
=
10
iv)
g(13) =
5
iv)
g(–6) =
14
v)
For what value of x, f(x) is 35?
v)
For what value of x, f(x) is –24?
6
vi)
For what value of x, g(x) is 5?
13
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–6
vi)
For what value of x, f(x) is 4?
1
Name:
Sheet 2
Evaluate - Function Table
A) Evaluate each function from the table.
1)
x
8
10
15
18
f(x)
0
–4
16
10
2)
x
–18
–4
2
10
f(x)
1
–12
7
15
i)
f(15)
=
i)
f(2)
=
ii)
f(10)
=
ii)
f(10)
=
3)
x
–1
3
5
8
f(x)
11
27
66
–2
4)
x
–10
–6
6
10
f(x)
–10
2
–14
6
i)
f(5)
=
i)
f(–6)
ii)
f(3)
=
ii)
f(–10) =
=
B) Evaluate the functions from the table.
1)
x
f(x)
g(x)
–17
–19
–12
–7
2)
x
f(x)
g(x)
–2
3
14
–4
–22
3
7
20
0
–36
–9
13
10
6
i)
g(–7) =
i)
f(7)
ii)
f(–17) =
ii)
f(13) =
iii)
g(–12) =
iii)
g(3)
=
iv)
f(–12) =
iv)
f(3)
=
v)
For what value of x, f(x) is –36?
v)
For what value of x, g(x) is 0?
vi)
For what value of x, g(x) is –2?
vi)
For what value of x, g(x) is 6?
Printable Worksheets @ www.mathworksheets4kids.com
=
Answer key
Name:
Sheet 2
Evaluate - Function Table
A) Evaluate each function from the table.
1)
x
8
10
15
18
f(x)
0
–4
16
10
2)
x
–18
–4
2
10
f(x)
1
–12
7
15
i)
f(15)
=
16
i)
f(2)
=
7
ii)
f(10)
=
–4
ii)
f(10)
=
15
3)
x
–1
3
5
8
f(x)
11
27
66
–2
4)
x
–10
–6
6
10
f(x)
–10
2
–14
6
i)
f(5)
=
66
i)
f(–6)
=
2
ii)
f(3)
=
27
ii)
f(–10) =
–10
B) Evaluate the functions from the table.
1)
x
f(x)
g(x)
–17
–19
–12
–7
2)
x
f(x)
g(x)
–2
3
14
–4
–22
3
7
20
0
–36
–9
13
10
6
i)
g(–7) =
–9
i)
f(7)
=
20
ii)
f(–17) =
–19
ii)
f(13) =
10
iii)
g(–12) =
3
iii)
g(3)
=
–4
iv)
f(–12) =
–22
iv)
f(3)
=
14
v)
For what value of x, f(x) is –36?
v)
For what value of x, g(x) is 0?
–7
vi)
For what value of x, g(x) is –2?
–17
Printable Worksheets @ www.mathworksheets4kids.com
7
vi)
For what value of x, g(x) is 6?
13
Name:
Sheet 3
Evaluate - Function Table
A) Evaluate each function from the table.
1)
x
12
15
18
20
f(x)
24
33
48
42
2)
x
–14
–10
–7
0
f(x)
–3
–7
7
9
i)
f(18)
=
i)
f(–10) =
ii)
f(12)
=
ii)
f(0)
3)
x
–8
–4
0
4
f(x)
4
8
–4
0
4)
=
x
5
6
8
11
f(x)
17
14
16
20
i)
f(0)
=
i)
f(5)
=
ii)
f(–4)
=
ii)
f(8)
=
B) Evaluate the functions from the table.
1)
x
f(x)
g(x)
8
14
11
13
2)
x
f(x)
g(x)
18
–1
–9
–2
16
29
3
–1
–1
11
15
4
1
–6
i)
g(8)
=
i)
f(3)
=
ii)
g(11) =
ii)
g(4)
=
iii)
g(13) =
iii)
f(–1) =
iv)
f(8)
iv)
g(–1) =
v)
For what value of x, f(x) is 11?
v)
For what value of x, g(x) is –2?
vi)
For what value of x, f(x) is 16?
vi)
For what value of x, f(x) is 1?
=
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Answer key
Name:
Sheet 3
Evaluate - Function Table
A) Evaluate each function from the table.
1)
x
12
15
18
20
f(x)
24
33
48
42
2)
x
–14
–10
–7
0
f(x)
–3
–7
7
9
i)
f(18)
=
48
i)
f(–10) =
–7
ii)
f(12)
=
24
ii)
f(0)
9
3)
x
–8
–4
0
4
f(x)
4
8
–4
0
4)
=
x
5
6
8
11
f(x)
17
14
16
20
i)
f(0)
=
–4
i)
f(5)
=
17
ii)
f(–4)
=
8
ii)
f(8)
=
16
B) Evaluate the functions from the table.
1)
x
f(x)
g(x)
8
14
11
13
2)
x
f(x)
g(x)
18
–1
–9
–2
16
29
3
–1
–1
11
15
4
1
–6
i)
g(8)
=
18
i)
f(3)
=
–1
ii)
g(11) =
29
ii)
g(4)
=
–6
iii)
g(13) =
15
iii)
f(–1) =
–9
iv)
f(8)
14
iv)
g(–1) =
–2
v)
For what value of x, f(x) is 11?
v)
For what value of x, g(x) is –2?
=
13
vi)
For what value of x, f(x) is 16?
11
Printable Worksheets @ www.mathworksheets4kids.com
–1
vi)
For what value of x, f(x) is 1?
4
Name:
Sheet 1
Linear or Nonlinear Functions
A) Determine whether each graph is linear or nonlinear.
1)
2)
10
5
7
8
4
6
6
3
5
4
2
4
3
2
1
-10 -8 -6 -4 -2
1
1 2 3 4 5
-1
-2
4)
5)
2 4 6 8 10
-2
-3 -2 -1
-1
-4
-2
-6
-3
-8
-4
-10
-5
1 2 3 4 5 6 7
6)
9
8
8
7
6
5
4
3
2
1
8
7
6
5
4
3
2
1
-1
-1
8
2
-5 -4 -3 -2 -1
3)
-12 -9 -6 -3
-1
-2
1 2 3 4 5 6 7 8 9
7
6
5
4
3
2
1
-5 -4 -3 -2 -1
3 6 9 12 15 18
-1
-2
1 2 3 4 5
B) 1) Which of the following graphs represents a linear function?
a)
5
4
3
2
1
-10 -8 -6 -4 -2
-1
-2
-3
-4
-5
b)
2 4 6 8 10
5
4
3
2
1
-2 -1
-1
-2
-3
-4
-5
c)
1 2 3 4 5 6 7 8
7
6
5
4
3
2
1
d)
-20 -16 -12 -8 -4
-1
-2
-3
4 8 12 16 20
5
4
3
2
1
-4 -3 -2 -1
-1
-2
-3
-4
-5
1 2 3 4 5 6
2) Which of the following graphs represents a nonlinear function?
3
2
1
a)
-15 -12 -9 -6 -3
-1
-2
-3
-4
-5
-6
-7
3 6 9 12 15
b)
10
8
6
4
2
-6 -5 -4 -3 -2 -1
-2
-4
-6
-8
-10
1 2 3 4
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c)
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
1 2 3 4 5
d)
7
6
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
1 2 3 4 5
Answer key
Name:
Sheet 1
Linear or Nonlinear Functions
A) Determine whether each graph is linear or nonlinear.
1)
2)
10
5
7
8
4
6
6
3
5
4
2
4
3
2
1
-10 -8 -6 -4 -2
1
nonlinear
-3
-4
-10
-5
linear
nonlinear
6)
8
8
7
6
5
4
3
2
1
8
7
6
5
4
3
2
1
-1
-1
1 2 3 4 5 6 7
-8
9
-1
-2
5)
-3 -2 -1
-6
1 2 3 4 5
-1
2 4 6 8 10
-2
-4
-2
4)
8
2
-5 -4 -3 -2 -1
3)
-12 -9 -6 -3
-1
-2
1 2 3 4 5 6 7 8 9
linear
7
6
5
4
3
2
1
-5 -4 -3 -2 -1
3 6 9 12 15 18
nonlinear
-1
-2
1 2 3 4 5
linear
B) 1) Which of the following graphs represents a linear function?
a)
5
4
3
2
1
-10 -8 -6 -4 -2
-1
-2
-3
-4
-5
b)
2 4 6 8 10
5
4
3
2
1
-2 -1
-1
-2
-3
-4
-5
c)
1 2 3 4 5 6 7 8
7
6
5
4
3
2
1
d)
-20 -16 -12 -8 -4
-1
-2
-3
4 8 12 16 20
5
4
3
2
1
-4 -3 -2 -1
-1
-2
-3
-4
-5
1 2 3 4 5 6
2) Which of the following graphs represents a nonlinear function?
3
2
1
a)
-15 -12 -9 -6 -3
-1
-2
-3
-4
-5
-6
-7
3 6 9 12 15
b)
10
8
6
4
2
-6 -5 -4 -3 -2 -1
-2
-4
-6
-8
-10
1 2 3 4
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c)
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
1 2 3 4 5
d)
7
6
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
1 2 3 4 5
Name:
Sheet 2
Linear or Nonlinear Functions
A) Determine whether each graph is linear or nonlinear.
1)
2)
-8 -7 -6 -5 -4 -3 -2 -1
5
7
24
4
6
21
3
5
18
2
4
15
1
3
2
12
9
1
6
-1
1 2
-2
-5 -4 -3 -2 -1
-3
4)
3)
-4
-2
-5
-3
-1
1
-3
2 3 4
6)
5
20
7
4
16
6
3
12
5
2
8
4
1
4
3
-3 -2 -1
-1
-20 -16 -12 -8 -4
1 2 3 4 5 6 7
5 6 7 8 9
-6
5)
3
1 2 3 4 5
-1
2
1
4 8 12 16 20
-4
-2
-8
-3
-12
-4
-16
-2
-5
-20
-3
-5 -4 -3 -2 -1
-1
1 2 3 4 5
B) 1) Which of the following graphs represents a nonlinear function?
a)
5
4
3
2
1
-6 -4 -2
-1
-2
-3
-4
-5
b)
2 4 6 8 10 12 14
8
7
6
5
4
3
2
1
c)
-5 -4 -3 -2 -1
-1
-2
1 2 3 4 5
15
12
9
6
3
-15 -12 -9 -6 -3
-3
-6
-9
-12
-15
d)
3 6 9 12 15
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
1 2 3 4 5
2) Which of the following graphs represents a linear function?
a)
7
6
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
b)
1 2 3 4 5
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
1 2 3 4 5
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c)
10
8
6
4
2
-8 -7 -6 -5 -4 -3 -2 -1
-2
-4
-6
-8
-10
1 2
d)
5
4
3
2
1
-25 -20 -15 -10 -5
-1
-2
-3
-4
-5
5 10 15 20 25
Answer key
Name:
Sheet 2
Linear or Nonlinear Functions
A) Determine whether each graph is linear or nonlinear.
1)
2)
-8 -7 -6 -5 -4 -3 -2 -1
5
7
24
4
6
21
3
5
18
2
4
15
1
3
2
12
9
1
6
-1
1 2
-2
-5 -4 -3 -2 -1
-3
-2
-5
-3
3
1 2 3 4 5
-1
-4
linear
4)
3)
-1
1
-3
2 3 4
-6
nonlinear
5)
linear
6)
5
20
7
4
16
6
3
12
5
2
8
4
1
4
3
-3 -2 -1
-1
-20 -16 -12 -8 -4
1 2 3 4 5 6 7
5 6 7 8 9
2
1
4 8 12 16 20
-4
-2
-8
-3
-12
-4
-16
-2
-5
-20
-3
nonlinear
linear
-5 -4 -3 -2 -1
-1
1 2 3 4 5
nonlinear
B) 1) Which of the following graphs represents a nonlinear function?
a)
5
4
3
2
1
-6 -4 -2
-1
-2
-3
-4
-5
b)
2 4 6 8 10 12 14
8
7
6
5
4
3
2
1
c)
-5 -4 -3 -2 -1
-1
-2
1 2 3 4 5
15
12
9
6
3
-15 -12 -9 -6 -3
-3
-6
-9
-12
-15
d)
3 6 9 12 15
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
1 2 3 4 5
2) Which of the following graphs represents a linear function?
a)
7
6
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
b)
1 2 3 4 5
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
1 2 3 4 5
Printable Worksheets @ www.mathworksheets4kids.com
c)
10
8
6
4
2
-8 -7 -6 -5 -4 -3 -2 -1
-2
-4
-6
-8
-10
1 2
d)
5
4
3
2
1
-25 -20 -15 -10 -5
-1
-2
-3
-4
-5
5 10 15 20 25
Name:
Sheet 3
Linear or Nonlinear Functions
A) Determine whether each graph is linear or nonlinear.
1)
2)
5
5
16
4
4
12
3
3
8
2
2
-9 -8 -7 -6 -5 -4 -3 -2 -1
-4
1
1
5
1
5 10 15 20 25 30 35 40 45
-1
-4 -2
-1
-8
-2
-2
-12
-3
-3
-16
-4
-4
-20
-5
-5
5)
2 4 6 8 10 12 14 16
6)
5
8
5
4
7
4
3
6
3
2
5
2
4
3
1
1
-15 -12 -9 -6 -3
20
4
4)
3)
3 6 9 12 15
-1
-5 -4 -3 -2 -1
-1
2
1
-2
-3
-4
-5 -4 -3 -2 -1
-1
-5
-2
1 2 3 4 5
-2
-3
1 2 3 4 5
-4
-5
B) 1) Which of the following graphs represents a linear function?
a)
-32 -28 -24 -20 -16-12 -8 -4
-1
-2
-3
-4
-5
9
6
3
5
4
3
2
1
4 8
b)
1
-10 -8 -6 -4 -2
-3
-6
-9
-12
-15
-18
-21
2 4 6 8 10
c)
-8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-9
1 2
d)
7
6
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
1 2 3 4 5
2) Which of the following graphs represents a nonlinear function?
2
1
a)
-25 -20 -15 -10 -5
-1
-2
-3
-4
-5
-6
-7
-8
5 10 15 20 25
b)
-5 -4 -3 -2 -1
-1
-2
3
2
1
8
7
6
5
4
3
2
1
c)
1 2 3 4 5
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-20 -16 -12 -8 -4
-1
-2
-3
-4
-5
-6
-7
4 8 12 16 20
d)
15
12
9
6
3
-15 -12 -9 -6 -3
-3
-6
-9
-12
-15
3 6 9 12 15
Answer key
Name:
Sheet 3
Linear or Nonlinear Functions
A) Determine whether each graph is linear or nonlinear.
1)
2)
3)
20
5
5
16
4
4
12
3
3
8
2
2
4
-9 -8 -7 -6 -5 -4 -3 -2 -1
-4
1
1
5
5 10 15 20 25 30 35 40 45
-1
-4 -2
-1
-8
-2
-2
-12
-3
-3
-16
-4
-4
-20
-5
-5
linear
5)
2 4 6 8 10 12 14 16
nonlinear
6)
5
8
5
4
7
4
3
6
3
2
5
2
4
3
1
1
-15 -12 -9 -6 -3
1
linear
4)
3 6 9 12 15
-1
-5 -4 -3 -2 -1
-1
2
1
-2
-3
1 2 3 4 5
-2
-3
-4
-5 -4 -3 -2 -1
-1
1 2 3 4 5
-5
-2
-5
nonlinear
nonlinear
linear
-4
B) 1) Which of the following graphs represents a linear function?
a)
-32 -28 -24 -20 -16-12 -8 -4
-1
-2
-3
-4
-5
9
6
3
5
4
3
2
1
4 8
b)
1
-10 -8 -6 -4 -2
-3
-6
-9
-12
-15
-18
-21
2 4 6 8 10
c)
-8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-9
1 2
d)
7
6
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
1 2 3 4 5
2) Which of the following graphs represents a nonlinear function?
2
1
a)
-25 -20 -15 -10 -5
-1
-2
-3
-4
-5
-6
-7
-8
5 10 15 20 25
b)
-5 -4 -3 -2 -1
-1
-2
3
2
1
8
7
6
5
4
3
2
1
c)
1 2 3 4 5
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-20 -16 -12 -8 -4
-1
-2
-3
-4
-5
-6
-7
4 8 12 16 20
d)
15
12
9
6
3
-15 -12 -9 -6 -3
-3
-6
-9
-12
-15
3 6 9 12 15
Name:
Comparing Linear Functions
Sheet 1
Fill in the table and answer the following questions.
1)
Function A
Function B
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
Function
–1
0
1
–15 –10
–5
-intercept
Slope
-intercept
Slope
-intercept
-intercept
A
1 2 3 4 5
Slope
B
i) Which function has a greater slope?
ii) Which function has a greater -intercept?
iii) Which function has a lesser -intercept?
2)
Function A
Function B
Function
–4
–2
0
8
12
( )=
16
2
–7
5
-intercept
A
B
i) Which function has a greater -intercept?
ii) Which function has a greater rate of change?
iii) Which function has a lesser -intercept?
3)
Function A
Function B
5
4
3
2
1
( ) = 3 + 12
-16 -14 -12 -10 -8 -6 -4 -2
-1
-2
-3
-4
-5
Function
A
2 4
i) Which function has a lesser -intercept?
ii) Which function has a greater -intercept?
iii) Which function has a lesser slope?
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B
-intercept
Answer key
Name:
Sheet 1
Comparing Linear Functions
Fill in the table and answer the following questions.
1)
Function A
Function B
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
–1
0
1
–15 –10
–5
1 2 3 4 5
Function
Slope
-intercept
A
–
1
2
4
2
B
5
2
–10
i) Which function has a greater slope?
Function B
ii) Which function has a greater -intercept?
Function A
iii) Which function has a lesser -intercept?
Function B
2)
Function A
–4
Function B
–2
0
8
12
( )=
16
2
–7
5
Function
Slope
-intercept
A
2
–8
16
B
2
5
35
2
–7
i) Which function has a greater -intercept?
Function A
ii) Which function has a greater rate of change?
Function A
iii) Which function has a lesser -intercept?
Function A
3)
-intercept
Function A
-intercept
Function B
5
4
3
2
1
( ) = 3 + 12
-16 -14 -12 -10 -8 -6 -4 -2
-1
-2
-3
-4
-5
Function
Slope
-intercept
A
3
–4
12
B
3
10
–10
3
-intercept
2 4
i) Which function has a lesser -intercept?
Function B
ii) Which function has a greater -intercept?
Function A
iii) Which function has a lesser slope?
Function B
Printable Worksheets @ www.mathworksheets4kids.com
Name:
Comparing Linear Functions
Sheet 2
Fill in the table and answer the following questions.
1)
Function A
Function B
4
2
–9
–6
-5 -4 -3 -2 -1
-2
-4
-6
-8
-10
-12
-14
-16
–3
–20 –18 –16
Function
Slope
-intercept
Slope
-intercept
Slope
-intercept
-intercept
1 2 3 4 5
A
B
i) Which function has a lesser -intercept?
ii) Which function has a lesser rate of change?
iii) Which function has a greater -intercept?
2)
Function A
Function B
6
5
4
3
2
1
-15 -12 -9 -6 -3
-1
-2
-3
-4
Function
3 6 9 12 15
( ) = – 5 – 13
4
-intercept
A
B
i) Which function has a greater -intercept?
ii) Which function has a lesser -intercept?
iii) Which function has a greater slope?
3)
Function A
Function B
Function
–5
0
5
( ) = 10 – 11
A
4
5
6
B
i) Which function has a lesser slope?
ii) Which function has a greater -intercept?
iii) Which function has a lesser -intercept?
Printable Worksheets @ www.mathworksheets4kids.com
-intercept
Answer key
Name:
Sheet 2
Comparing Linear Functions
Fill in the table and answer the following questions.
1)
Function A
Function B
4
2
–9
–6
-5 -4 -3 -2 -1
-2
-4
-6
-8
-10
-12
-14
-16
–3
–20 –18 –16
Function
Slope
-intercept
A
2
3
21
–14
B
4
3
–12
i) Which function has a lesser -intercept?
Function B
ii) Which function has a lesser rate of change?
Function A
iii) Which function has a greater -intercept?
Function B
2)
Function A
-intercept
1 2 3 4 5
Function B
6
5
4
3
2
1
-15 -12 -9 -6 -3
-1
-2
-3
-4
3 6 9 12 15
( ) = – 5 – 13
4
Function
Slope
-intercept
A
–
1
2
6
3
B
–
5
4
– 52
5
–13
i) Which function has a greater -intercept?
Function A
ii) Which function has a lesser -intercept?
Function B
iii) Which function has a greater slope?
Function A
3)
Function A
Function B
–5
-intercept
0
4
5
Slope
-intercept
A
10
11
10
–11
B
1
5
–25
5
5
( ) = 10 – 11
Function
6
i) Which function has a lesser slope?
Function B
ii) Which function has a greater -intercept?
Function A
iii) Which function has a lesser -intercept?
Function A
Printable Worksheets @ www.mathworksheets4kids.com
-intercept
Name:
Comparing Linear Functions
Sheet 3
Fill in the table and answer the following questions.
1)
Function A
Function B
Function
5
6
7
8
16
24
( )=9 –
1
3
Slope
-intercept
Slope
-intercept
Slope
-intercept
-intercept
A
B
i) Which function has a greater slope?
ii) Which function has a lesser -intercept?
iii) Which function has a greater -intercept?
2)
Function A
Function B
7
6
5
4
3
2
1
( ) = –7 + 15
Function
-intercept
A
-8 -4
-1
-2
-3
4 8 12 16 20 24 28 32
B
i) Which function has a greater -intercept?
ii) Which function has a lesser -intercept?
iii) Which function has a higher rate of change?
3)
Function A
Function B
14
12
10
8
6
4
2
-35 -30 -25 -20 -15-10 -5
-2
-4
-6
Function
–5
–3
–1
A
0
10
20
B
5 10 15
i) Which function has a lesser slope?
ii) Which function has a lesser -intercept?
iii) Which function has a greater -intercept?
Printable Worksheets @ www.mathworksheets4kids.com
-intercept
Answer key
Name:
Sheet 3
Comparing Linear Functions
Fill in the table and answer the following questions.
1)
Function A
Function B
5
6
7
8
16
24
( )=9 –
1
3
Function
Slope
-intercept
A
8
4
–32
B
9
1
27
–
i) Which function has a greater slope?
Function B
ii) Which function has a lesser -intercept?
Function B
iii) Which function has a greater -intercept?
Function B
2)
Function A
-intercept
1
3
Function B
7
6
5
4
3
2
1
( ) = –7 + 15
Function
Slope
-intercept
A
–7
15
7
15
B
–
3
14
28
6
-8 -4
-1
-2
-3
4 8 12 16 20 24 28 32
i) Which function has a greater -intercept?
Function A
ii) Which function has a lesser -intercept?
Function A
iii) Which function has a higher rate of change?
Function B
3)
-intercept
Function A
Function B
14
12
10
8
6
4
2
-35 -30 -25 -20 -15-10 -5
-2
-4
-6
–5
0
–3
10
Function
Slope
-intercept
A
2
5
–30
12
B
5
–5
25
–1
20
5 10 15
i) Which function has a lesser slope?
Function A
ii) Which function has a lesser -intercept?
Function A
iii) Which function has a greater -intercept?
Function B
Printable Worksheets @ www.mathworksheets4kids.com
-intercept
Name:
ES1
Evaluating Linear Functions
A) Evaluate each function at the specified value.
1)
( )=7 –5 ;
=6
2)
( )=9 +3 ;
2)
( ) = 4 ; find (–15)
= –10
B) Evaluate each function.
1)
( ) = –8 – 9 ; find (–3)
C) If ( ) = 3(–2 + 7) ; find the following.
1)
(–7)
=
2)
(13)
=
3)
(11)
=
4)
(–8)
=
(2)
D) If ( ) = – – 11 ; find the following.
1)
4 (–2) + 5 (1)
=
2)
3 (5)
3)
–5 (12) – 2 (–9) =
4)
(9)
(–6)
=
=
E) What is the value of (4), if ( ) = –4( + 3) – 14?
i)
42
ii)
–24
iii)
Printable Worksheets @ www.mathworksheets4kids.com
–42
iv)
8
Answer key
Name:
ES1
Evaluating Linear Functions
A) Evaluate each function at the specified value.
1)
( )=7 –5 ;
=6
2)
( )=9 +3 ;
37
= –10
–87
B) Evaluate each function.
1)
( ) = –8 – 9 ; find (–3)
2)
( ) = 4 ; find (–15)
15
–60
C) If ( ) = 3(–2 + 7) ; find the following.
1)
(–7)
=
63
2)
(13)
=
–57
3)
(11)
=
–45
4)
(–8)
=
69
(2)
D) If ( ) = – – 11 ; find the following.
1)
4 (–2) + 5 (1)
=
–96
2)
3 (5)
3)
–5 (12) – 2 (–9) =
119
4)
(9)
(–6)
=
624
=
4
E) What is the value of (4), if ( ) = –4( + 3) – 14?
i)
42
ii)
–24
iii)
Printable Worksheets @ www.mathworksheets4kids.com
–42
iv)
8
Name:
ES2
Evaluating Linear Functions
A) Evaluate each function at the specified value.
1)
( ) = 10 + 2 ;
= –8
2)
( )=– +9 ;
2)
( ) = –6 – 12 ; find (11)
=7
B) Evaluate each function.
1)
( ) = –(3 – 1) ; find (–15)
C) If ( ) = –5( – 11) + 8 ; find the following.
1)
(3)
=
2)
(12)
=
3)
(14)
=
4)
(–4)
=
D) If ( ) = –13 + 7
; find the following.
1)
2 (8) + 7 (2)
=
2)
(13)
4 (3)
=
3)
–3 (1)
=
4)
–4 (9) – 6 (0)
=
(–2)
E) What is the value of (–5), if ( ) = –9 – 4?
i)
41
ii)
–49
iii)
Printable Worksheets @ www.mathworksheets4kids.com
–41
iv)
49
Answer key
Name:
ES2
Evaluating Linear Functions
A) Evaluate each function at the specified value.
1)
( ) = 10 + 2 ;
= –8
2)
( )=– +9 ;
–78
=7
2
B) Evaluate each function.
1)
( ) = –(3 – 1) ; find (–15)
2)
( ) = –6 – 12 ; find (11)
46
–78
C) If ( ) = –5( – 11) + 8 ; find the following.
1)
(3)
=
48
2)
(12)
=
3
3)
(14)
=
–7
4)
(–4)
=
83
=
39
16
=
–122
D) If ( ) = –13 + 7
; find the following.
1)
2 (8) + 7 (2)
=
93
2)
(13)
4 (3)
3)
–3 (1)
=
–486
4)
–4 (9) – 6 (0)
(–2)
E) What is the value of (–5), if ( ) = –9 – 4?
i)
41
ii)
–49
iii)
Printable Worksheets @ www.mathworksheets4kids.com
–41
iv)
49
Name:
ES3
Evaluating Linear Functions
A) Evaluate each function at the specified value.
1)
( ) = –2 + 7 ;
= –12
2)
( ) = 5 – 13 ;
2)
( ) = 3( + 15) ; find (0)
= –14
B) Evaluate each function.
1)
( ) = –4 – 10 ; find (6)
C) If ( ) = –(10 + 5) ; find the following.
1)
(–11) =
2)
(4)
=
3)
(–6)
4)
(13)
=
=
2)
–2 (0) – 9 (–1)
=
4)
– (–8) + 5 (–7) =
=
D) If ( ) = –8 ; find the following.
1)
(–3)
3)
–6 (–4)
–3 (2)
(5)
=
E) What is the value of (–2), if ( ) = –14(6 + 3)?
i)
180
ii)
–126
iii)
Printable Worksheets @ www.mathworksheets4kids.com
210
iv)
126
Answer key
Name:
ES3
Evaluating Linear Functions
A) Evaluate each function at the specified value.
1)
( ) = –2 + 7 ;
= –12
2)
( ) = 5 – 13 ;
31
= –14
–83
B) Evaluate each function.
1)
( ) = –4 – 10 ; find (6)
2)
( ) = 3( + 15) ; find (0)
–34
45
C) If ( ) = –(10 + 5) ; find the following.
1)
(–11) =
105
2)
(4)
=
–45
3)
(–6)
55
4)
(13)
=
–135
=
D) If ( ) = –8 ; find the following.
1)
(–3)
3)
–6 (–4)
–3 (2)
(5)
=
–960
2)
–2 (0) – 9 (–1)
=
–72
=
–4
4)
– (–8) + 5 (–7) =
216
E) What is the value of (–2), if ( ) = –14(6 + 3)?
i)
180
ii)
–126
iii)
Printable Worksheets @ www.mathworksheets4kids.com
210
iv)
126
Name :
Score :
T1L1S1
Function Table
Complete the function table. Plot the points and graph the line.
1)
=– –7
2)
=5+
3)
=4 –6
–7
–5
–3
–2
–3
0
–1
3
5
7
0
1
2
3
4
1
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
14
-2
12
-3
10
-4
8
-5
6
-6
4
-7
2
= +4
1 2 3 4 5 6 7
5)
=2–2
0
1 2 3 4 5
= –2 + 3
0
4
6)
–20 –16 –8
-5 -4 -3 -2 -1
-2
-4
-6
-8
-10
-3 -2 -1
-2
-9
10
8
6
4
2
16
1
-8
4)
18
2
4
6
–2
8
–1
0
1
3
4
24
20
16
12
8
4
-24 -20 -16 -12 -8 -4
-4
-8
-12
-16
2
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
-12
-14
-16
4 8 12 16
7)
= –2 + 2
6
5
2 4 6 8 10
4
3
2
1
0
3
4
-3
=6
9)
=3 –6
–8
6
1 2 3 4 5
-2
–4
-5 -4 -3 -2 -1
-1
8)
7
–6
–5
0
1
–5
–4
–3
–2
–1
10
8
6
6
-9 -8 -7 -6 -5 -4 -3 -2 -1
-6
4
-12
2
-4 -3 -2 -1
-2
-4
-6
-8
-10
1 2 3 4 5 6
Printable Math Worksheets @ www.mathworksheets4kids.com
-18
-24
-30
-36
-42
-48
-54
1
6
3
-5 -4 -3 -2 -1
-3
-6
-9
-12
-15
-18
-21
-24
1 2 3 4 5
Name :
Score :
Answer key
T1L1S1
Function Table
Complete the function table. Plot the points and graph the line.
1)
=– –7
2)
=5+
3)
=4 –6
–7
–5
–3
–2
0
0
–2
–4
–5
–7
–3
–1
3
5
7
2
4
8
10 12
-1
1
12
-3
10
-4
8
-5
6
-6
4
-7
2
4
1 2 3 4 5 6 7
=2–2
–16 –12 –4
4
8
4
2
6
10
-5 -4 -3 -2 -1
-2
-4
-6
-8
-10
1 2 3 4 5
6)
= –2 + 3
0
3
10
8
6
4
2
5)
–20 –16 –8
2
-3 -2 -1
-2
–2
14
-2
= +4
–6
16
-9
1
18
-8
4)
1
-9 -8 -7 -6 -5 -4 -3 -2 -1
0
0
2
4
6
8
2
–2
–6 –10 –14
–2
–1
0
1
3
7
5
3
1
–3
4
24
20
16
12
8
4
-24 -20 -16 -12 -8 -4
-4
-8
-12
-16
2
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
-12
-14
-16
4 8 12 16
7)
= –2 + 2
6
5
2 4 6 8 10
4
3
2
1
0
3
4
6
-3
–10 –2
4
6
10
9)
=3 –6
–8
1 2 3 4 5
-2
=6
-5 -4 -3 -2 -1
-1
–4
8)
7
–6
–5
0
1
–48 –36 –30
0
6
–5
–4
–3
–2
–1
–21 –18 –15 –12 –9
10
8
6
6
-9 -8 -7 -6 -5 -4 -3 -2 -1
-6
4
-12
2
-4 -3 -2 -1
-2
-4
-6
-8
-10
1 2 3 4 5 6
Printable Math Worksheets @ www.mathworksheets4kids.com
-18
-24
-30
-36
-42
-48
-54
1
6
3
-5 -4 -3 -2 -1
-3
-6
-9
-12
-15
-18
-21
-24
1 2 3 4 5
Name :
Score :
T1L1S2
Function Table
Complete the function table. Plot the points and graph the line.
1)
= –5
2)
= –4 + 4
3)
=
–1
–6
–8
–4
–2
0
–3
–1
3
5
7
5
6
7
4
3
32
24
16
8
70
60
50
40
30
20
10
-14 -12 -10 -8 -6 -4 -2
-10
4
6
-20
-30
6
5
4
-3 -2 -1
-8
-16
-24
-32
-40
-48
2
7
3
2
1 2 3 4 5 6 7
1
-3 -2 -1
-1
-2
-3
0
2
3
=2 +2
–2
6)
=6+
5)
–2
–3
1 2 3 4 5 6 7
= –2 + 10
4)
–1
0
1
0
3
2
4
6
8
18
16
14
12
10
8
6
4
2
-5 -4 -3 -2 -1
-2
9
18
16
14
12
10
8
6
4
2
8
7
6
5
4
3
2
1
-5 -4 -3 -2 -1
1 2 3 4 5
-1
1 2 3 4 5
-10 -8 -6 -4 -2
-2
=2
8)
=3 –3
12
15
–1
=– –2
21
9)
9
3
2 4 6 8 10
7)
0
1
2
3
–4
–2
0
2
4
54
48
42
36
30
24
18
12
6
-9 -6 -3
-6
8
6
4
2
15
12
9
6
3
3 6 9 12 15 18 21
-4 -3 -2 -1
-3
-6
-9
-12
1 2 3 4 5 6
-15
Printable Math Worksheets @ www.mathworksheets4kids.com
-5 -4 -3 -2 -1
-2
-4
-6
-8
-10
-12
1 2 3 4 5
Name :
Score :
Answer key
T1L1S2
Function Table
Complete the function table. Plot the points and graph the line.
1)
= –5
2)
= –4 + 4
3)
=
–1
–6
–2
0
40 30 20 10
0
–8
–4
–3
–1
3
5
7
–16 –8
8
16 24
3
4
5
6
7
3
4
5
6
2
32
24
16
8
70
60
50
40
30
20
10
-14 -12 -10 -8 -6 -4 -2
-10
4
6
-20
-30
6
5
4
-3 -2 -1
-8
-16
-24
-32
-40
-48
2
7
3
2
1 2 3 4 5 6 7
1
-3 -2 -1
-1
-2
-3
–3
1 2 3 4 5 6 7
= –2 + 10
4)
–2
0
2
3
16 14 10
6
4
6)
=6+
=2 +2
5)
–2
–1
0
1
3
4
5
6
7
9
0
2
4
6
8
2
6
10 14 18
18
16
14
12
10
8
6
4
2
-5 -4 -3 -2 -1
-2
9
18
16
14
12
10
8
6
4
2
8
7
6
5
4
3
2
1
-5 -4 -3 -2 -1
1 2 3 4 5
-1
1 2 3 4 5
-10 -8 -6 -4 -2
-2
=2
8)
=3 –3
9
12
15
6
18 24 30 42
=– –2
21
9)
3
2 4 6 8 10
7)
–1
0
1
2
3
–6
–3
0
3
6
–4
–2
0
2
4
2
0
–2
–4
–6
54
48
42
36
30
24
18
12
6
-9 -6 -3
-6
8
6
4
2
15
12
9
6
3
3 6 9 12 15 18 21
-4 -3 -2 -1
-3
-6
-9
-12
1 2 3 4 5 6
-15
Printable Math Worksheets @ www.mathworksheets4kids.com
-5 -4 -3 -2 -1
-2
-4
-6
-8
-10
-12
1 2 3 4 5
Name :
Score :
T1L1S3
Function Table
Complete the function table. Plot the points and graph the line.
1)
=8
2)
=– –5
3)
=2–4
–5
–3
–1
2
0
4
2
1
3
4
–2
–1
0
1
2
32
24
16
8
1
2
3
-24
-32
-40
-48
3
4
5
-5 -4 -3 -2 -1
-2
-6
-8
-10
–8
–5
–3
–2
–1
0
–6
–2
0
2
–4
-10 -8 -6 -4 -2
-3
-6
-9
-12
-15
-18
-21
1
2
3
4
0
1
14
12
2 4 6 8 10
10
8
6
4
2
-5 -4 -3 -2 -1
-2
1 2 3 4 5
9)
=4 –4
–10 –8
4
16
=5
2
2
0
18
3
–2
6
8)
–1
= –1 + 2
–2
9
7)
= –2 + 8
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
6)
5
4
3
2
1
1 2 3 4 5
-4
=3 +3
5)
= +3
2
4)
1
-3
-4
-5
-6
-7
-8
-9
4
-16
10
8
6
4
2
-5 -4 -3 -2 -1
-1
-2
-6 -5 -4 -3 -2 -1
-8
1
–6
–4
–2
–7
–6
–5
–4
–3
10
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
1
2
3
4
5
-18 -16 -14 -12 -10 -8 -6 -4 -2
-10
-20
-30
-40
-50
-60
-70
-80
-90
Printable Math Worksheets @ www.mathworksheets4kids.com
2
8
4
-9 -8 -7 -6 -5 -4 -3 -2 -1
-4
-8
-12
-16
-20
-24
-28
-32
1
Name :
Score :
Answer key
T1L1S3
Function Table
Complete the function table. Plot the points and graph the line.
1)
=8
2)
=– –5
–3
–1
2
4
0
1
2
3
4
–5
–6
–7
–8
–9
16 32
–40 –24 –8
1
2
3
-40
-48
–3
–2
–1
0
–2
0
1
2
3
–8
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
3
–2
0
2
–21 –15 –3
3
9
–4
–2
0
2
4
16 12
8
4
0
18
16
14
12
2 4 6 8 10
10
8
6
4
2
-5 -4 -3 -2 -1
-2
=5
–2
–1
0
1
2
–5
–3
–1
1
3
1 2 3 4 5
=4 –4
–10 –8
9)
= –2 + 8
8)
1 2 3 4 5
-8
–6
-10 -8 -6 -4 -2
-3
-6
-9
-12
-15
-18
-21
4
–6
-10
3
2
–2
-6
6
1
2
-4
2
-5 -4 -3 -2 -1
-2
9
= –1 + 2
5
7)
4
6)
5
4
3
2
1
3
=3 +3
2
–5
1
5)
1
= +3
6
0
10
8
6
4
2
-3
-4
-5
-6
-7
-8
-9
4
-32
10
-5 -4 -3 -2 -1
-1
-2
-24
–1
1
-16
4)
32
24
16
8
-6 -5 -4 -3 -2 -1
-8
–2
=2–4
–5
3)
–6
–4
–2
–7
–50 –40 –30 –20 –10
–6
–5
–4
–3
–32 –28 –24 –20 –16
10
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
1
2
3
4
5
-18 -16 -14 -12 -10 -8 -6 -4 -2
-10
-20
-30
-40
-50
-60
-70
-80
-90
Printable Math Worksheets @ www.mathworksheets4kids.com
2
8
4
-9 -8 -7 -6 -5 -4 -3 -2 -1
-4
-8
-12
-16
-20
-24
-28
-32
1
Name :
Score :
T1L1S4
Function Table
Complete the function table. Plot the points and graph the line.
1)
= 2 – 16
2)
=4 +8
3)
= 3 – 24
–2
0
2
4
–4
6
–2
–3
–1
0
1
2
3
4
5
16
12
8
4
-3 -2 -1
-4
1 2 3 4 5 6 7
-12
-16
-20
-24
= 12 + 3
1 2 3 4 5
= –2 + 5
–4
–2
0
=
+3
0
4
6)
–8
1 2 3 4 5
-3
-6
-9
-12
-15
-18
-21
-24
5)
-5 -4 -3 -2 -1
-5 -4 -3 -2 -1
-2
-4
-6
-8
-10
-8
4)
6
3
10
8
6
4
2
2
1
3
4
–2
0
1
3
4
-8 -6 -4 -2
-6
-12
-18
-24
-30
5
4
4
3
2
3
2
2 4 6 8 10 12
1
-5 -4 -3 -2 -1
= – – 10
1
-3 -2 -1
-1
1 2 3 4 5
-1
-2
-2
-3
-3
8)
= –8 +
–7
–6
–4
0
4
8
-4
-5
-6
-7
-8
-9
–2
0
1
2
4
1
-3
–4
-2
1 2 3 4 5 6 7
=–
12
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
–4
–3
9)
–8
7
6
5
6
7)
7
30
24
18
12
6
24
20
16
12
8
4
-24 -20 -16 -12 -8 -4
-4
-8
-12
-16
5
4
3
2
1
4 8 12 16
Printable Math Worksheets @ www.mathworksheets4kids.com
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
1 2 3 4
Name :
Score :
Answer key
T1L1S4
Function Table
Complete the function table. Plot the points and graph the line.
1)
= 2 – 16
2)
=4 +8
= 3 – 24
–2
0
2
4
6
–20 –16 –12 –8
–4
–4
–3
–2
–1
0
–8
–4
0
4
8
1
8
4
-3 -2 -1
-4
1 2 3 4 5 6 7
-12
-16
-20
-24
= 12 + 3
–4
–2
0
1 2 3 4 5
= –2 + 5
–12
0
6
12 24
1 2 3 4 5
6)
=
+3
4
-3
-6
-9
-12
-15
-18
-21
-24
–8
5
–21 –18 –15 –12 –9
-5 -4 -3 -2 -1
5)
4
-5 -4 -3 -2 -1
-2
-4
-6
-8
-10
-8
3
6
3
10
8
6
4
2
12
16
4)
2
3)
0
1
2
3
4
5
3
1
–1
–3
–2
0
1
3
4
1
3
4
6
7
-8 -6 -4 -2
-6
-12
-18
-24
-30
5
4
2
2 4 6 8 10 12
1
-5 -4 -3 -2 -1
1
-3 -2 -1
-1
1 2 3 4 5
-1
-2
-2
-3
-3
8)
= –8 +
4
3
2
3
= – – 10
7
6
5
6
7)
7
30
24
18
12
6
–7
–6
–4
–3
–2
–3
–4
–6
–7
4
8
12
–12 –8
–4
0
4
-3
-4
-5
-6
-7
-8
-9
–4
–2
0
4
2
0
1
4
–2
–4
24
20
16
12
8
4
-24 -20 -16 -12 -8 -4
-4
-8
-12
-16
2
1
-2
=–
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
1 2 3 4 5 6 7
0
–4
9)
–8
5
4
3
2
1
4 8 12 16
Printable Math Worksheets @ www.mathworksheets4kids.com
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
1 2 3 4
Name :
Score :
T1L1S5
Function Table
Complete the function table. Plot the points and graph the line.
1)
=3
2)
= 33 + 3
3)
=– –8
2
6
8
–7
–9
14
10
–5
–3
–1
0
2
4
–2
–4
-6 -4 -2
-6
8
6
4
2
48
42
36
30
18
12
6
2 4 6 8 10 12 14
-9 -8 -7 -6 -5 -4 -3 -2 -1
-6
= 4 + 16
1
= 3 – 21
5)
–8
–7
1 2 3 4 5
= –2 –
2
0
–5
–6
6)
–9
-5 -4 -3 -2 -1
-2
-4
-6
-8
-10
-12
24
4)
54
54
48
42
36
30
24
18
12
6
4
6
–2
8
–1
0
1
2
4
-9 -8 -7 -6 -5 -4 -3 -2 -1
-4
-8
-12
-16
-20
-24
-28
-32
3
1
-10 -8 -6 -4 -2
-3
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-9
2 4 6 8 10
-6
-9
-12
-15
-18
-21
= –2
8)
=2–4
–3
–2
–1
2
1
1 2 3 4 5
=2 +6
0
9)
–4
1
6
7)
9
8
3
4
5
–4
–3
–1
0
2
18
16
14
12
10
8
6
4
2
-5 -4 -3 -2 -1
-2
2
-3 -2 -1
-2
1 2 3 4 5 6 7
-4
-6
-8
-10
-12
1 2 3 4 5
-14
-16
-18
Printable Math Worksheets @ www.mathworksheets4kids.com
10
8
6
4
2
-4 -3 -2 -1
-2
-4
-6
-8
-10
1 2 3 4 5 6
Name :
Score :
Answer key
T1L1S5
Function Table
Complete the function table. Plot the points and graph the line.
1)
=3
2)
= 33 + 3
=– –8
2
6
8
10
14
6
18 24 30 42
–9
–7
–5
–3
–1
6
12 18 24 30
–6
–8 –10 –12
30
18
12
6
-9 -8 -7 -6 -5 -4 -3 -2 -1
-6
1
= 3 – 21
5)
–8
–6
–5
–20 –16 –12 –8
–4
–7
1 2 3 4 5
6)
= –2 –
2
4
6
8
–21 –15 –9
–3
3
0
-5 -4 -3 -2 -1
-2
-4
-6
-8
-10
-12
24
4
36
2 4 6 8 10 12 14
2
8
6
4
2
–4
42
0
48
= 4 + 16
–9
–2
54
4)
54
48
42
36
30
24
18
12
6
-6 -4 -2
-6
–4
3)
–2
–1
0
1
2
0
–1
–2
–3
–4
4
-9 -8 -7 -6 -5 -4 -3 -2 -1
-4
-8
-12
-16
-20
-24
-28
-32
3
1
-10 -8 -6 -4 -2
-3
2 4 6 8 10
-6
-12
-15
-18
-21
8)
=2–4
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-9
-9
= –2
1
6
7)
9
8
–3
–2
–1
0
8
6
4
2
0
1 2 3 4 5
=2 +6
9)
–4
1
2
3
4
5
–2
–6 –10 –14 –18
–4
–3
–2
0
–1
0
2
4
6
10
18
16
14
12
10
8
6
4
2
-5 -4 -3 -2 -1
-2
2
-3 -2 -1
-2
1 2 3 4 5 6 7
-4
-6
-8
-10
-12
1 2 3 4 5
-14
-16
-18
Printable Math Worksheets @ www.mathworksheets4kids.com
10
8
6
4
2
-4 -3 -2 -1
-2
-4
-6
-8
-10
1 2 3 4 5 6
Name :
Score :
T2L1S1
Function Table
Complete the function table. Plot the points and graph the line.
1)
=7
2)
=– –8
3)
=6–3
2
4
–4
5
7
21
8
16
–10
–6
–2
–12
–20
30
18
16
12
8
4
42
35
28
21
14
7
1 2 3 4 5
4)
30
24
= +4
12
4 8 12 16 20
6
= –9 –
2
4
6
2 4 6 8 10
= –2 + 5
–6
1
6)
–1
-10 -8 -6 -4 -2
-6
-12
-18
-24
5)
18
-20 -16 -12 -8 -4
-4
-8
-12
-16
-20
-24
-5 -4 -3 -2 -1
-7
-14
-21
-28
36
–3
0
3
6
–12
4
5
3
–5
6
12
5
5
9
4
4
6
3
3
2
-15 -12 -9 -6 -3
1
-5 -4 -3 -2 -1
-3
-15
-4
-18
=5
1
–6
–4
1
2
3
4
5
=4 –8
–4
3
9)
–2
8)
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-9
-12
= –4 + 2
1
3 6 9 12 15
-3
-2
7)
2
-6
1 2 3 4 5
-1
3
2
–2
–25
0
15
4
8
–8
16
10
8
6
4
2
40
32
24
16
8
25
20
15
10
5
-5 -4 -3 -2 -1
-2
-4
-6
-8
-10
1 2 3 4 5
-5 -4 -3 -2 -1
-5
-10
-15
-20
-25
1 2 3 4 5
Printable Math Worksheets @ www.mathworksheets4kids.com
-10 -8 -6 -4 -2
-8
-16
-24
-32
-40
2 4 6 8 10
Name :
Score :
Answer key
T2L1S1
Function Table
Complete the function table. Plot the points and graph the line.
1)
=7
2)
=– –8
3)
=6–3
1
2
3
4
5
–4
7
14
21
28 35
8
4
12
16
–10 –8
–6
–4
–2
30
24
18
12
–4 –12 –16 –20 –24
36
16
12
8
4
42
35
28
21
14
7
1 2 3 4 5
4)
30
24
= +4
12
4 8 12 16 20
6
= –9 –
–1
0
1
2
2
3
4
5
6
2 4 6 8 10
6)
= –2 + 5
–2
-10 -8 -6 -4 -2
-6
-12
-18
-24
5)
18
-20 -16 -12 -8 -4
-4
-8
-12
-16
-20
-24
-5 -4 -3 -2 -1
-7
-14
-21
-28
36
–6
–3
0
–3
–6
–9 –12 –15
3
6
0
1
3
4
5
5
3
–1
–3
–5
6
12
5
5
9
4
4
6
3
3
2
-15 -12 -9 -6 -3
1
-5 -4 -3 -2 -1
-3
-15
-4
-18
=5
8)
–1
0
1
3
–8
–6
–4
–2
2
1
2
3
4
5
=4 –8
–4
0
2
3
–25 –20
0
10
15
–5
9)
–2
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-9
-12
= –4 + 2
1
3 6 9 12 15
-3
-2
7)
2
-6
1 2 3 4 5
-1
3
–2
0
4
6
8
8
16
24
–16 –8
10
8
6
4
2
40
32
24
16
8
25
20
15
10
5
-5 -4 -3 -2 -1
-2
-4
-6
-8
-10
1 2 3 4 5
-5 -4 -3 -2 -1
-5
-10
-15
-20
-25
1 2 3 4 5
Printable Math Worksheets @ www.mathworksheets4kids.com
-10 -8 -6 -4 -2
-8
-16
-24
-32
-40
2 4 6 8 10
Score :
Name :
T2L1S2
Function Table
Complete the function table. Plot the points and graph the line.
1)
=– –7
2)
=3 –6
3)
=9
0
–2
1
–5
–9
–6
–3
–1
4
6
8
–18
–12
45
63
1
-5 -4 -3 -2 -1
1 2 3 4 5
-1
81
9
6
3
72
63
-2
-5 -4 -3 -2 -1
-3
-4
-5
-6
-7
-8
-9
= –3
4)
54
1 2 3 4 5
-3
-6
-9
-12
-15
-18
-21
45
36
27
18
9
-2 -1
-9
=– +3
5)
–18
9
1
1 2 3 4 5 6 7 8
= +5
6)
9
3
–6
5
–2
5
4
0
3
2
7
9
5
54
45
36
27
18
9
3
2
1
3 6 9 12 15
-18
-27
-36
= –8 – 4
0
16
–32
1 2 3 4 5
=4–2
–3
9)
4
–4
-5 -4 -3 -2 -1
-1
= –2 + 2
8)
1 2 3 4 5
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-15 -12 -9 -6 -3
-9
7)
9
8
7
6
5
4
3
2
1
4
–2
2
5
–10
2
4
–2
2
–6
32
24
16
8
-10 -8 -6 -4 -2
-8
-16
-24
-32
-40
-48
2 4 6 8 10
10
8
6
4
2
-5 -4 -3 -2 -1
-2
3
2
1
1 2 3 4 5
-5 -4 -3 -2 -1
-1
-2
-3
-4
-4
-6
-5
-8
-6
-10
-7
Printable Math Worksheets @ www.mathworksheets4kids.com
1 2 3 4 5
Name :
Score :
Answer key
T2L1S2
Function Table
Complete the function table. Plot the points and graph the line.
1)
=– –7
2)
=3 –6
3)
=9
–2
–1
0
1
2
–5
–5
–6
–7
–8
–9
–3
–4
–2
–1
4
5
6
7
8
45
54
63
72
–21 –18 –15 –12 –9
36
1
-5 -4 -3 -2 -1
1 2 3 4 5
-1
81
9
6
3
72
63
-2
-5 -4 -3 -2 -1
-3
-4
-5
-6
-7
-8
-9
= –3
4)
54
1 2 3 4 5
-3
-6
-9
-12
-15
-18
-21
45
36
27
18
9
-2 -1
-9
=– +3
5)
–3
3
18
9
–9 –18 –27
6
1 2 3 4 5 6 7 8
= +5
9
6)
–6
–2
–1
1
3
5
5
4
2
0
–2
–3
–2
2
3
2
3
4
7
8
9
5
54
45
36
27
18
9
3
2
1
3 6 9 12 15
-18
-27
-36
= –8 – 4
–4
–2
4
16
0
8
–24 –32
1 2 3 4 5
=4–2
–3
–2
2
5
–10 –8
–6
2
8
–4
6
9)
–6
-5 -4 -3 -2 -1
-1
= –2 + 2
8)
1 2 3 4 5
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-15 -12 -9 -6 -3
-9
7)
9
8
7
6
5
4
3
2
1
4
1
2
2
0
3
4
5
–2
–4
–6
32
24
16
8
-10 -8 -6 -4 -2
-8
-16
-24
-32
-40
-48
2 4 6 8 10
10
8
6
4
2
-5 -4 -3 -2 -1
-2
3
2
1
1 2 3 4 5
-5 -4 -3 -2 -1
-1
-2
-3
-4
-4
-6
-5
-8
-6
-10
-7
Printable Math Worksheets @ www.mathworksheets4kids.com
1 2 3 4 5
Name :
Score :
T2L1S3
Function Table
Complete the function table. Plot the points and graph the line.
1)
2)
= –8 + 4
= +9
3)
= –2 + 4
–1
0
–4
–6
–8
2
–20
–1
0
2
2
7
–10 –6
10
16
12
8
4
-5 -4 -3 -2 -1
1 2 3 4 5
-4
-8
-12
-16
-20
-24
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
10
8
6
4
2
-5 -4 -3 -2 -1
-2
-4
-6
-8
-10
1
5)
= –6 – 2
2
–4
–12
–5
–2
–4
2
=
–2
6)
= –8
1 2 3 4 5
4)
5
–3
–32
24
3
0
–6
–10
2
-5 -4 -3 -2 -1
-2
-4
-6
-8
-10
-12
1 2 3 4 5
-8
-16
-24
-32
-40
8)
=3–3
–36
–12
24
=– –5
–3
1
–4
1 2 3 4 5
2
9)
–4
-5 -4 -3 -2 -1
4
8
=6
6
24
1 2 3 4 5
-2
-4
-6
-8
-10
-12
32
16
-5 -4 -3 -2 -1
7)
8
40
8
6
4
2
12
18
–3
–2
1
2
–4
60
18
48
15
36
12
-5 -4 -3 -2 -1
9
24
12
-10 -8 -6 -4 -2
-12
-24
-36
-48
-60
1
2 4 6 8 10
6
3
-5 -4 -3 -2 -1
-3
-6
-9
-12
1 2 3 4 5
Printable Math Worksheets @ www.mathworksheets4kids.com
-1
-2
-3
-4
-5
-6
-7
-8
-9
1 2 3 4 5
Name :
Score :
Answer key
T2L1S3
Function Table
Complete the function table. Plot the points and graph the line.
1)
2)
= –8 + 4
= +9
3)
= –2 + 4
–1
0
1
12
4
–4 –12 –20
2
3
–8
–7
–6
–2
–1
1
2
3
7
8
–2
0
2
3
–2
6
10
–1
–10 –6
16
12
8
4
-5 -4 -3 -2 -1
1 2 3 4 5
-4
-8
-12
-16
-20
-24
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
10
8
6
4
2
-5 -4 -3 -2 -1
-2
-4
-6
-8
-10
1
5)
= –6 – 2
–2
–1
2
2
–2
–4 –10 –12
–5
3
=
–4
6)
= –8
1 2 3 4 5
4)
–4
–3
–2
32
24
16 –32 –40
4
5
–3
–1
3
5
–10 –8
–6
–2
0
–5
2
-5 -4 -3 -2 -1
-2
-4
-6
-8
-10
-12
1 2 3 4 5
-8
-16
-24
-32
-40
8)
=3–3
–4
4
–36 –24 –12 12
24
–2
1 2 3 4 5
9)
=– –5
2
–6
-5 -4 -3 -2 -1
4
8
=6
6
24
1 2 3 4 5
-2
-4
-6
-8
-10
-12
32
16
-5 -4 -3 -2 -1
7)
8
40
8
6
4
2
–5
–4
–3
1
2
18
15
12
0
–3
–3
–2
–2
–3
–1
1
2
–4
–6
–7
60
18
48
15
36
12
-5 -4 -3 -2 -1
9
24
12
-10 -8 -6 -4 -2
-12
-24
-36
-48
-60
1
2 4 6 8 10
6
3
-5 -4 -3 -2 -1
-3
-6
-9
-12
1 2 3 4 5
Printable Math Worksheets @ www.mathworksheets4kids.com
-1
-2
-3
-4
-5
-6
-7
-8
-9
1 2 3 4 5
Name :
Score :
T2L1S4
Function Table
Complete the function table. Plot the points and graph the line.
1)
2)
= 24 – 6
= +2
18
24
0
–2
2
6
-5 -4 -3 -2 -1
1
1 2 3 4
-45 -36 -27 -18 -9
1 2 3 4 5
-4
-5
–3
–1
3 6 9 12 15
-9
-2
-12
-3
-15
-4
-18
-5
-21
-6
-24
-7
-27
–4
0
–1
8
6
4
2
-4
-6
-8
-10
2
1
0
4
3
–7
–4
10
-2
= –8
-10 -8 -6 -4 -2
9)
–3
2 4 6 8 10
5
–2
1 2 3 4
-6
-12
-18
-24
-30
=4+2
-5 -4 -3 -2 -1
8)
–8
–24
30
24
18
12
6
–6
-6
1
0
-15 -12 -9 -6 -3
-3
3
=
–6
3
1
2
–15
–3
2
12
7)
= –6
3
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
9 18 27 36 45
-9
3
–3
–3
6)
= –3 – 2
5)
–5
–18
-18
-27
-36
-45
-3
0
-2
18
18
-5 -4 -3 -2 -1
-1
5
+1
–6
45
36
27
18
9
=
5
4
3
2
1
4)
0
-12
-18
-24
-30
2
-6
1
30
24
18
12
6
=– +9
–1
3)
12
10
8
6
4
2
-5 -4 -3 -2 -1
-2
-4
-6
-8
–3
1
-5 -4 -3 -2 -1
-1
-2
-3
1 2 3 4 5
Printable Math Worksheets @ www.mathworksheets4kids.com
-4
-5
-6
-7
-8
-9
1 2 3 4 5
Name :
Score :
Answer key
T2L1S4
Function Table
Complete the function table. Plot the points and graph the line.
1)
2)
= 24 – 6
= +2
–1
0
1
2
3
30
24
18
12
6
–2
–1
0
1
2
0
1
2
3
4
-5 -4 -3 -2 -1
1 2 3 4
-5
–6
–5
–4
–3
–2
–5
–4
–3
–2
–1
0
3
3
–3
–9 –15 –27
-12
-3
-15
-4
-18
-5
-21
-6
-24
-7
-27
–6
–4
–2
0
–8
–6
–4
–2
0
6
4
2
-8
-10
0
–6 –12 –18 –24
3 6 9 12 15
2 4 6 8 10
-5 -4 -3 -2 -1
-6
-12
-18
-24
-30
1 2 3 4
5
3
4
5
–5
–4
–3
9)
= –8
–3
–2
–1
0
1
–2
0
2
4
6
1
2
–7
–6
8
4
30
24
18
12
6
10
3
1
=4+2
-6
2
0
–8
-4
-9
-2
8)
-2
9 18 27 36 45
-9
-6
1
-10 -8 -6 -4 -2
12
-15 -12 -9 -6 -3
-3
=
6
3
2
–9 –18
= –6
0
27
–3
3
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
6)
= –3 – 2
1
18
5)
+1
9
-18
-27
-36
-45
-4
7)
9
-45 -36 -27 -18 -9
1 2 3 4 5
18
-3
0
45
36
27
18
9
–9
-2
=
-5 -4 -3 -2 -1
-1
5
-12
-18
-24
-30
4)
5
4
3
2
1
-6
30
24
18
12
6
=– +9
3)
12
10
8
6
4
2
-5 -4 -3 -2 -1
-2
-4
-6
-8
1
-5 -4 -3 -2 -1
-1
-2
-3
1 2 3 4 5
Printable Math Worksheets @ www.mathworksheets4kids.com
-4
-5
-6
-7
-8
-9
1 2 3 4 5
Name :
Score :
T2L1S5
Function Table
Complete the function table. Plot the points and graph the line.
1)
2)
=3
=– +7
–2
–3
14
0
0
3
-5 -4 -3 -2 -1
0
1 2 3 4 5
-6
-15
-18
-21
15
–3
15
12
12
8
9
4
1 2 3 4 5
-3
-12
=– –6
-5 -4 -3 -2 -1
–2
–6
–10
-8
-10
-12
-14
-16
-18
-2
-4
-6
-8
-10
-12
9)
=9+3
–3
3
20
10
30
–2
1 2 3 4 5
-5
3
12
30
25
20
15
10
5
-5 -4 -3 -2 -1
2
2
1 2 3 4 5
-2
-6
1 2 3 4 5
1
2
–4
-4
= 5 + 10
-5 -4 -3 -2 -1
–8
–16
–2
1
2
8)
–8
-5 -4 -3 -2 -1
-4
-8
-12
-16
-20
-24
-9
–1
16
-6
–1
–16
6
7)
= –8 + 2
-5 -4 -3 -2 -1
6)
18
3
1 2 3 4 5
3
-5 -4 -3 -2 -1
-2
–5
2
–9
16
6
18
16
14
12
10
8
6
4
2
0
0
7 14 21 28 35
=4
4
5)
= –3 + 6
-7
-14
-21
-28
-35
-12
–14
-35 -28 -21 -14 -7
-9
4)
3
35
28
21
14
7
-3
28
9
6
3
=2 +6
–3
3)
1 2 3 4 5
18
15
12
9
6
3
-5 -4 -3 -2 -1
-3
-14
-10
-16
-15
-9
-18
-20
-12
Printable Math Worksheets @ www.mathworksheets4kids.com
-6
1 2 3 4 5
Name :
Score :
Answer key
T2L1S5
Function Table
Complete the function table. Plot the points and graph the line.
1)
2)
=3
=– +7
–3
–2
–1
0
1
–9
–6
–3
0
3
0
7
14
7
0
–7 –14 –21
-5 -4 -3 -2 -1
1 2 3 4 5
-6
-15
-18
-21
0
1
2
3
–9
–3
3
9
15
–3
–2
–1
–20 –16 –12 –8
–4
–4
15
12
12
8
9
4
1 2 3 4 5
-9
-12
=– –6
0
2
–2 –4
–6
–8 –10
-6
-8
-10
-12
1
2
–16 –10 –8
–6
–4
1 2 3 4 5
1 2 3 4 5
-2
-4
-6
1 2 3 4 5
-8
-10
-12
-14
-16
-18
9)
=9+3
0
1
2
3
4
10
15
20
25
30
–3
–2
0
3
-5
2
3
12
15 18
30
25
20
15
10
5
-5 -4 -3 -2 -1
1
2
-4
0
-2
–1
-5 -4 -3 -2 -1
4
1 2 3 4 5
= 5 + 10
-5 -4 -3 -2 -1
–2
–4
8)
2
-5 -4 -3 -2 -1
-4
-8
-12
-16
-20
-24
-3
16
16
-6
–4
18
3
12 14
= –8 + 2
6
6)
7)
6
5
–5
–1
-5 -4 -3 -2 -1
0
4
3
18
16
14
12
10
8
6
4
2
0
-5 -4 -3 -2 -1
-2
=4
–3
5)
= –3 + 6
4)
7 14 21 28 35
-7
-14
-21
-28
-35
-12
-35 -28 -21 -14 -7
-9
28
35
28
21
14
7
-3
21
9
6
3
=2 +6
3)
1 2 3 4 5
18
15
12
9
6
3
-5 -4 -3 -2 -1
-3
-14
-10
-16
-15
-9
-18
-20
-12
Printable Math Worksheets @ www.mathworksheets4kids.com
-6
1 2 3 4 5
Name:
Sheet 1
Linear or Nonlinear Functions
A) Determine whether each function table is linear or nonlinear.
1)
–16
–3
11
15
–24
–11
3
7
–7
0
9
12
–10
–3
6
9
–3
2
13
17
–21
–26
59
41
–18
–14
–12
0
2
4
5
11
2)
1
4
6
7
–7
23
63
89
–9
–6
–1
14
–7
–7
2
16
–14
–10
–5
–4
–11
–7
–2
–1
–16
3
8
21
25
–11
44
51
( )
3)
( )
4)
( )
5)
( )
6)
( )
7)
( )
8)
( )
( )
B) 1) Which of the following tables represents a linear function?
a)
( )
–2
0
6
9
0
–4
45
96
b)
( )
3
7
11
14
17
37
57
72
c)
( )
–7
–6
1
3
40
16
0
7
–8
–3
4
6
65
2
17
37
2) Which of the following tables represents a nonlinear function?
a)
( )
1
3
9
10
–3
–1
5
6
b)
( )
–10
2
15
20
–51
9
74
99
Printable Worksheets @ www.mathworksheets4kids.com
c)
( )
Answer key
Name:
Sheet 1
Linear or Nonlinear Functions
A) Determine whether each function table is linear or nonlinear.
1)
–16
–3
11
15
–24
–11
3
7
2)
1
4
6
7
–7
23
63
89
( )
( )
nonlinear
linear
3)
–7
0
9
12
–10
–3
6
9
4)
–9
–6
–1
14
–7
–7
2
16
( )
( )
linear
5)
nonlinear
–3
2
13
17
–21
–26
59
41
6)
–14
–10
–5
–4
–11
–7
–2
–1
( )
( )
nonlinear
7)
linear
–18
–14
–12
0
2
4
5
11
8)
–16
3
8
21
25
–11
44
51
( )
( )
linear
nonlinear
B) 1) Which of the following tables represents a linear function?
a)
( )
–2
0
6
9
0
–4
45
96
b)
( )
3
7
11
14
17
37
57
72
c)
( )
–7
–6
1
3
40
16
0
7
–8
–3
4
6
65
2
17
37
2) Which of the following tables represents a nonlinear function?
a)
( )
1
3
9
10
–3
–1
5
6
b)
( )
–10
2
15
20
–51
9
74
99
Printable Worksheets @ www.mathworksheets4kids.com
c)
( )
Name:
Sheet 2
Linear or Nonlinear Functions
A) Determine whether each function table is linear or nonlinear.
1)
–13
3
8
10
12
–11
44
80
2
5
9
11
–6
–3
1
3
–16
0
17
21
–13
3
20
24
–19
–15
6
12
36
20
21
19
2)
–18
–14
–11
3
–15
–11
–8
6
–8
0
15
18
34
–30
17
29
–11
–9
–5
–4
18
90
15
6
–17
1
7
14
–7
11
17
24
( )
3)
( )
4)
( )
5)
( )
6)
( )
7)
( )
8)
( )
( )
B) 1) Which of the following tables represents a linear function?
a)
( )
1
7
8
10
12
54
61
75
b)
( )
–4
0
2
9
–6
2
4
18
c)
( )
–11
–5
2
5
–9
–3
0
3
–8
–7
6
–19
–3
–4
–1
24
2) Which of the following tables represents a nonlinear function?
a)
( )
–10
3
9
15
27
1
–11
–23
b)
( )
–18
4
12
20
27
5
–3
–11
Printable Worksheets @ www.mathworksheets4kids.com
c)
( )
Answer key
Name:
Sheet 2
Linear or Nonlinear Functions
A) Determine whether each function table is linear or nonlinear.
1)
–13
3
8
10
12
–11
44
80
2)
–18
–14
–11
3
–15
–11
–8
6
( )
( )
linear
nonlinear
3)
2
5
9
11
–6
–3
1
3
4)
–8
0
15
18
34
–30
17
29
( )
( )
linear
5)
nonlinear
–16
0
17
21
–13
3
20
24
6)
–11
–9
–5
–4
18
90
15
6
( )
( )
linear
7)
nonlinear
–19
–15
6
12
36
20
21
19
8)
–17
1
7
14
–7
11
17
24
( )
( )
nonlinear
linear
B) 1) Which of the following tables represents a linear function?
a)
( )
1
7
8
10
12
54
61
75
b)
( )
–4
0
2
9
–6
2
4
18
c)
( )
–11
–5
2
5
–9
–3
0
3
–8
–7
6
–19
–3
–4
–1
24
2) Which of the following tables represents a nonlinear function?
a)
( )
–10
3
9
15
27
1
–11
–23
b)
( )
–18
4
12
20
27
5
–3
–11
Printable Worksheets @ www.mathworksheets4kids.com
c)
( )
Name:
Sheet 3
Linear or Nonlinear Functions
A) Determine whether each function table is linear or nonlinear.
1)
–19
–15
–7
–5
–16
–12
–4
–2
–9
0
2
7
77
–4
0
45
1
3
8
14
10
18
9
25
–16
–12
–9
4
–12
–8
–5
8
2)
–3
9
13
17
4
76
19
28
–18
–16
7
10
–13
–11
12
15
–12
–10
11
15
–20
–18
3
7
–17
0
4
12
–15
2
6
14
( )
3)
( )
4)
( )
5)
( )
6)
( )
7)
( )
8)
( )
( )
B) 1) Which of the following tables represents a nonlinear function?
a)
( )
–5
–1
6
8
–3
1
8
10
b)
( )
–21
–17
–4
0
–18
–14
–1
3
c)
( )
5
7
11
15
21
45
17
21
–7
–6
10
19
39
26
0
31
2) Which of the following tables represents a linear function?
a)
( )
9
12
13
22
6
9
10
19
b)
( )
–10
–6
–2
3
91
27
–5
0
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c)
( )
Answer key
Name:
Sheet 3
Linear or Nonlinear Functions
A) Determine whether each function table is linear or nonlinear.
1)
–19
–15
–7
–5
–16
–12
–4
–2
2)
–3
9
13
17
4
76
19
28
( )
( )
nonlinear
linear
3)
–9
0
2
7
77
–4
0
45
4)
–18
–16
7
10
–13
–11
12
15
( )
( )
nonlinear
5)
linear
1
3
8
14
10
18
9
25
6)
–12
–10
11
15
–20
–18
3
7
( )
( )
nonlinear
7)
linear
–16
–12
–9
4
–12
–8
–5
8
8)
–17
0
4
12
–15
2
6
14
( )
( )
linear
linear
B) 1) Which of the following tables represents a nonlinear function?
a)
( )
–5
–1
6
8
–3
1
8
10
b)
( )
–21
–17
–4
0
–18
–14
–1
3
c)
( )
5
7
11
15
21
45
17
21
–7
–6
10
19
39
26
0
31
2) Which of the following tables represents a linear function?
a)
( )
9
12
13
22
6
9
10
19
b)
( )
–10
–6
–2
3
91
27
–5
0
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c)
( )
Name:
Sheet 1
Evaluating Functions - Graphing
A) Evaluate.
1)
2)
( )
3)
5
2
4
1
5
4
3
3
-15 -12 -9 -6 -3
2
1
-5 -4 -3 -2 -1
1 2 3 4 5
-1
-2
-3
-4
-5
3 6 9 12 15
-1
-2
-3
-4
-5
-6
-7
-8
2
1
( )
-20 -16 -12 -8 -4
4 8 12 16 20
-1
-2
-3
( )
-4
-5
i)
(–2) =
i)
(12) =
i)
(–16) =
ii)
(2) =
ii)
(–9) =
ii)
(8) =
B) Evaluate.
i)
3 (–2)
(3)
ii)
iii)
8 (–5) + 2 (1)
iv)
–5 (1) – (–4)
20
16
12
( )
8
4
-5 -4 -3 -2 -1
1 2 3 4 5
-4
-8
7 (0)
(–3)
-12
-16
-20
C) For what values of , ( ) = ( )
1)
2)
3)
14
12
10
8
6
( )
15
12
9
6
3
8
( )
6
5
4
( )
2
-3 -2 -1
-2
1 2 3 4 5 6 7
-6
( )
-3
3 6 9 12 15
( )
-6
4
3
2
1
( )
-4
-15 -12 -9 -6 -3
7
-9
-12
-15
Printable Worksheets @ www.mathworksheets4kids.com
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
1
Answer key
Name:
Sheet 1
Evaluating Functions - Graphing
A) Evaluate.
1)
2)
( )
3)
5
2
4
1
5
4
3
3
-15 -12 -9 -6 -3
2
1
-5 -4 -3 -2 -1
1 2 3 4 5
-1
-2
-3
-4
-5
3 6 9 12 15
-1
-2
-3
-4
-5
-6
-7
-8
2
1
( )
-20 -16 -12 -8 -4
4 8 12 16 20
-1
-2
-3
( )
-4
-5
i)
(–2) =
3
i)
(12) =
1
i)
(–16) =
3
ii)
(2) =
–4
ii)
(–9) =
–6
ii)
(8) =
–1
B) Evaluate.
i)
3 (–2)
(3)
ii)
–5 (1) – (–4)
20
16
12
( )
8
4
-5 -4 -3 -2 -1
–96
28
1 2 3 4 5
-4
iii)
-8
8 (–5) + 2 (1)
iv)
7 (0)
(–3)
-12
-16
-20
48
–14
C) For what values of , ( ) = ( )
1)
2)
3)
14
12
10
8
6
( )
15
12
9
6
3
8
( )
6
5
4
3
2
4
( )
2
-3 -2 -1
-2
1 2 3 4 5 6 7
( )
-3
3 6 9 12 15
( )
-6
1
( )
-9
-9 -8 -7 -6 -5 -4 -3 -2 -1
-12
-15
-6
=3
-4
-15 -12 -9 -6 -3
7
= –6 ;
Printable Worksheets @ www.mathworksheets4kids.com
=9
= –5 ;
= –2
-1
-2
1
Name:
Sheet 2
Evaluating Functions - Graphing
A) Evaluate.
1)
2)
3)
16
10
14
8
12
6
10
4
8
2
2
1
( )
-20 -16 -12 -8 -4
6
-25 -20 -15 -10 -5
4
-2
-4
-6
-8
-10
( )
2
-5 -4 -3 -2 -1
1 2 3 4 5
-2
-4
( )
5 10 15 20 25
i)
(–3) =
i)
(10) =
i)
(–12) =
ii)
(2) =
ii)
(–5) =
ii)
(0) =
4
-1
-2
-3
-4
-5
-6
-7
-8
8 12 16 20
B) Evaluate.
2 (2)
i)
( )
ii)
5 (–14)
(–6)
iv)
–9 (–12) + 7 (–8)
3 (0)
15
12
9
6
3
-16 -14 -12 -10 -8 -6 -4 -2
-3
2 4
iii)
-6
6 (–10) – 4 (–4)
-9
-12
-15
C) For what values of , ( ) = ( )
1)
2)
5
4
( )
3
2
1
-5 -4 -3 -2 -1
-1
-2
( )
-3
1 2 3 4 5
3)
5
14
12
10
8
( ) 6
4
2
4
3
( )
2
-3 -2 -1
-2
( )
( )1
-20 -16 -12 -8 -4
1 2 3 4 5 6 7
-1
-2
-3
-4
-4
-4
-5
-6
-5
Printable Worksheets @ www.mathworksheets4kids.com
4 8 12 16 20
Answer key
Name:
Sheet 2
Evaluating Functions - Graphing
A) Evaluate.
1)
2)
3)
16
10
14
8
12
6
10
4
8
2
2
1
( )
-20 -16 -12 -8 -4
6
-25 -20 -15 -10 -5
4
( )
2
-5 -4 -3 -2 -1
1 2 3 4 5
-2
-4
( )
5 10 15 20 25
-2
-4
-6
-8
-10
4
-1
-2
-3
-4
-5
-6
-7
-8
8 12 16 20
i)
(–3) =
10
i)
(10) =
6
i)
(–12) =
–2
ii)
(2) =
0
ii)
(–5) =
–4
ii)
(0) =
1
B) Evaluate.
2 (2)
i)
( )
ii)
5 (–14)
(–6)
3 (0)
15
12
9
6
2
3
-16 -14 -12 -10 -8 -6 -4 -2
-3
–180
2 4
iii)
-6
6 (–10) – 4 (–4)
iv)
–9 (–12) + 7 (–8)
-9
-12
-15
–36
48
C) For what values of , ( ) = ( )
1)
2)
5
4
( )
3
2
1
-5 -4 -3 -2 -1
-1
1 2 3 4 5
-2
( )
5
14
12
10
8
( ) 6
4
2
4
-2
3
( )
2
( )1
-20 -16 -12 -8 -4
1 2 3 4 5 6 7
-1
-4
-5
-6
-5
=4
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4 8 12 16 20
-3
-4
=1
-2
-4
= –3 ;
( )
-3 -2 -1
-3
3)
= –12 ;
= 12
Name:
Sheet 3
Evaluating Functions - Graphing
A) Evaluate.
1)
2)
3)
5
15
20
4
12
16
3
9
12
6
8
3
4
( )
( )
2
1
-5 -4 -3 -2 -1
1 2 3 4 5
-1
-16 -14 -12 -10 -8 -6 -4 -2
-2
( )
2
-3
-6
-9
-12
-15
-3
-4
-5
-25 -20 -15 -10 -5
4
-8
-12
-16
-20
i)
(–4) =
i)
(0) =
ii)
(–10) =
i)
(–4) =
ii)
(–5) =
ii)
5 10 15 20 25
-4
(10) =
B) Evaluate.
i)
6 (–25)
5 (20) + 8 (15)
ii)
(–5)
10
8
( )
6
4
2
-25 -20 -15 -10 -5
5 10 15 20 25
-2
iii)
-4
9 (0)
(–10)
iv)
–7 (–10) – (5)
-6
-8
-10
C) For what values of , ( ) = ( )
1)
2)
( )
( )
15
12
9
6
3
16
14
12
10
8
6
4
2
-5 -4 -3 -2 -1
-2
-4
3)
2
1
-20 -16 -12 -8 -4
( )
( )
-1
4 8 12 16 20
-2
( )
-15 -12 -9 -6 -3
-3
3 6 9 12 15
-6
1 2 3 4 5
-9
-3
-4
-5
( )
-6
-12
-15
Printable Worksheets @ www.mathworksheets4kids.com
-7
-8
Answer key
Name:
Sheet 3
Evaluating Functions - Graphing
A) Evaluate.
1)
2)
3)
5
15
20
4
12
16
3
9
12
6
8
3
4
( )
( )
2
1
-5 -4 -3 -2 -1
1 2 3 4 5
-1
-16 -14 -12 -10 -8 -6 -4 -2
-2
( )
2
-3
-6
-9
-12
-15
-3
-4
-5
-25 -20 -15 -10 -5
4
-8
-12
-16
-20
i)
(–4) =
3
i)
(0) =
–1
ii)
(–10) =
9
i)
(–4) =
0
ii)
ii)
5 10 15 20 25
-4
(–5) =
–8
(10) =
16
B) Evaluate.
i)
6 (–25)
5 (20) + 8 (15)
ii)
(–5)
10
8
( )
6
4
94
2
-25 -20 -15 -10 -5
24
5 10 15 20 25
-2
iii)
-4
9 (0)
(–10)
iv)
–7 (–10) – (5)
-6
-8
-10
–72
20
C) For what values of , ( ) = ( )
1)
2)
( )
( )
15
12
9
6
3
16
14
12
10
8
6
4
2
-5 -4 -3 -2 -1
-2
-4
= –3 ;
3)
2
1
-20 -16 -12 -8 -4
( )
( )
-1
4 8 12 16 20
-2
( )
-15 -12 -9 -6 -3
-3
3 6 9 12 15
-6
1 2 3 4 5
-9
-4
-5
( )
-6
-12
-15
=2
-3
= –9 ;
Printable Worksheets @ www.mathworksheets4kids.com
-7
-8
=6
=0
Name :
L1ES1
Function Table - Linear Function
A) Complete each function table.
1)
f(x) = x – 4
x
2)
f(x) = 15 – 6x
f(x)
x
3)
f(x) = –3 – 2x
f(x)
x
–10
0
–6
–9
1
–3
–8
2
–2
–7
3
–1
0
6
2
f(x)
B) Complete the function table using the function rule f(x) = 5x and answer the
following questions.
x
–4
1
2
3
6
f(x)
ii) What is the value of f(x), if x is –8?
i) What is the value of f(–3)?
C) Complete the function table.
f(x)
x – 11
f(–3)
f(–2)
f(4)
Printable Worksheets @ www.mathworksheets4kids.com
–7x + 1
x+8
Answer key
Name :
L1ES1
Function Table - Linear Function
A) Complete each function table.
1)
f(x) = x – 4
2)
f(x) = 15 – 6x
3)
f(x) = –3 – 2x
x
f(x)
x
f(x)
x
f(x)
–10
–14
0
15
–6
9
–9
–13
1
9
–3
3
–8
–12
2
3
–2
1
–7
–11
3
–3
–1
–1
0
–4
6
–21
2
–7
B) Complete the function table using the function rule f(x) = 5x and answer the
following questions.
x
–4
1
2
3
6
f(x)
–20
5
10
15
30
ii) What is the value of f(x), if x is –8?
i) What is the value of f(–3)?
–15
–40
C) Complete the function table.
f(x)
x – 11
–7x + 1
x+8
f(–3)
–14
22
5
f(–2)
–13
15
6
f(4)
–7
–27
12
Printable Worksheets @ www.mathworksheets4kids.com
Name :
L1ES2
Function Table - Linear Function
A) Complete each function table.
1)
f(x) = 2x + 9
x
2)
f(x) = 3x
f(x)
x
3)
f(x) = 10x – 6
x
f(x)
–1
10
–7
2
–8
–5
4
–6
0
5
–5
3
6
2
5
f(x)
B) Complete the function table using the function rule f(x) = –5x – 7 and answer the
following questions.
x
–3
6
7
9
10
f(x)
i) What is the value of f(x), if x is 1?
ii) What is the value of f(–5)?
C) Complete the function table.
f(x)
4+x
f(6)
f(9)
f(11)
Printable Worksheets @ www.mathworksheets4kids.com
9x – 12
–1 – 2x
Answer key
Name :
L1ES2
Function Table - Linear Function
A) Complete each function table.
1)
f(x) = 2x + 9
2)
f(x) = 3x
3)
f(x) = 10x – 6
x
f(x)
x
f(x)
x
f(x)
–1
7
10
30
–7
–76
2
13
–8
–24
–5
–56
4
17
–6
–18
0
–6
5
19
–5
–15
3
24
6
21
2
6
5
44
B) Complete the function table using the function rule f(x) = –5x – 7 and answer the
following questions.
x
–3
6
7
9
10
f(x)
8
–37
–42
–52
–57
i) What is the value of f(x), if x is 1?
ii) What is the value of f(–5)?
–12
18
C) Complete the function table.
f(x)
4+x
9x – 12
–1 – 2x
f(6)
10
42
–13
f(9)
13
69
–19
f(11)
15
87
–23
Printable Worksheets @ www.mathworksheets4kids.com
Name :
L1ES3
Function Table - Linear Function
A) Complete each function table.
1)
f(x) = 7 – 2x
x
2)
f(x) = 12 + x
x
f(x)
3)
f(x) = –4x
f(x)
x
2
–3
–8
3
–1
–6
6
0
–3
8
4
–2
10
6
–1
f(x)
B) Complete the function table using the function rule f(x) = –8x – 13 and answer the
following questions.
x
–2
0
3
4
7
f(x)
ii) What is the value of f(x), if x is –9?
i) What is the value of f(8)?
C) Complete the function table.
f(x)
15 + 4x
f(–1)
f(2)
f(5)
Printable Worksheets @ www.mathworksheets4kids.com
x – 10
2 – 9x
Answer key
Name :
L1ES3
Function Table - Linear Function
A) Complete each function table.
1)
f(x) = 7 – 2x
2)
f(x) = 12 + x
3)
f(x) = –4x
x
f(x)
x
f(x)
x
f(x)
2
3
–3
9
–8
32
3
1
–1
11
–6
24
6
–5
0
12
–3
12
8
–9
4
16
–2
8
10
–13
6
18
–1
4
B) Complete the function table using the function rule f(x) = –8x – 13 and answer the
following questions.
x
–2
0
3
4
7
f(x)
3
–13
–37
–45
–69
ii) What is the value of f(x), if x is –9?
i) What is the value of f(8)?
–77
59
C) Complete the function table.
f(x)
15 + 4x
x – 10
2 – 9x
f(–1)
11
–11
11
f(2)
23
–8
–16
f(5)
35
–5
–43
Printable Worksheets @ www.mathworksheets4kids.com
Name:
Sheet 1
Function Rule
A) Identify the function rule for each function table.
1)
–7
2
4
13
–25
11
19
55
–16
0
–8
8
–2
0
–1
1
–14
–19
11
12
–70
–95
55
60
2)
0
3
15
14
–7
11
83
77
–18
–3
1
10
–35
–5
3
21
–17
–11
–9
–4
41
23
17
2
( )
3)
( )
4)
( )
5)
( )
6)
( )
( )
B) 1) Which of the following function rules determines the function table?
–8
0
6
14
–4
0
3
7
1
2
i)
( )= +4
ii)
( )=
iii)
( )=4 −8
iv)
( ) = −2 + 1
( )
2) Which of the following function rules determines the function table?
( )
–10
–9
–5
0
–70
–63
–35
0
i)
( )=7
ii)
( ) = −2 − 7
iii)
( )=2 +3
iv)
( ) = −7
3) Which of the following function rules determines the function table?
( )
3
5
6
16
–3
–13
–18
–68
i)
( ) = −9 + 12
ii)
( ) = 7 − 12
iii)
( )=5
iv)
( ) = −5 + 12
Printable Worksheets @ www.mathworksheets4kids.com
Answer key
Name:
Sheet 1
Function Rule
A) Identify the function rule for each function table.
1)
–7
2
4
13
–25
11
19
55
2)
0
3
15
14
–7
11
83
77
( )
( )
( )=6 −7
( )=4 +3
3)
–16
0
–8
8
–2
0
–1
1
4)
–18
–3
1
10
–35
–5
3
21
( )
( )=
5)
( )
1
8
( )=2 +1
–14
–19
11
12
–70
–95
55
60
6)
–17
–11
–9
–4
41
23
17
2
( )
( )
( )=5
( ) = −3 − 10
B) 1) Which of the following function rules determines the function table?
–8
0
6
14
–4
0
3
7
1
2
i)
( )= +4
ii)
( )=
iii)
( )=4 −8
iv)
( ) = −2 + 1
( )
2) Which of the following function rules determines the function table?
( )
–10
–9
–5
0
–70
–63
–35
0
i)
( )=7
ii)
( ) = −2 − 7
iii)
( )=2 +3
iv)
( ) = −7
3) Which of the following function rules determines the function table?
( )
3
5
6
16
–3
–13
–18
–68
i)
( ) = −9 + 12
ii)
( ) = 7 − 12
iii)
( )=5
iv)
( ) = −5 + 12
Printable Worksheets @ www.mathworksheets4kids.com
Name:
Sheet 2
Function Rule
A) Identify the function rule for each function table.
1)
–11
–10
–8
0
73
66
52
–4
–13
2
16
14
–77
13
97
85
1
4
6
10
9
36
54
90
2)
–18
–15
3
12
–24
–20
4
16
–17
9
11
15
93
–37
–47
–67
–7
0
5
7
3
10
15
17
( )
3)
( )
4)
( )
5)
( )
6)
( )
( )
B) 1) Which of the following function rules determines the function table?
( )
–8
–5
3
17
22
13
–11
–53
i)
( )=3
ii)
( )=− +8
iii)
( ) = −3 − 2
iv)
( )=2 −8
2) Which of the following function rules determines the function table?
0
4
8
16
0
1
2
4
1
4
i)
( ) = −8 − 5
ii)
( )=
iii)
( )=8 −3
iv)
( )=7 +5
( )
3) Which of the following function rules determines the function table?
–20
–18
–6
–2
80
72
24
8
i)
( ) = −4
ii)
( )=4
iii)
( ) = 6 + 11
iv)
( ) = −3 − 10
( )
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Answer key
Name:
Sheet 2
Function Rule
A) Identify the function rule for each function table.
1)
–11
–10
–8
0
73
66
52
–4
2)
–18
–15
3
12
–24
–20
4
16
( )
( )
3)
4
3
( )=
( ) = −7 − 4
–13
2
16
14
–77
13
97
85
4)
–17
9
11
15
93
–37
–47
–67
( )
( )
( )=6 +1
5)
( ) = −5 + 8
1
4
6
10
9
36
54
90
6)
–7
0
5
7
3
10
15
17
( )
( )
( )=9
( )=
+ 10
B) 1) Which of the following function rules determines the function table?
( )
–8
–5
3
17
22
13
–11
–53
i)
( )=3
ii)
( )=− +8
iii)
( ) = −3 − 2
iv)
( )=2 −8
2) Which of the following function rules determines the function table?
0
4
8
16
0
1
2
4
1
4
i)
( ) = −8 − 5
ii)
( )=
iii)
( )=8 −3
iv)
( )=7 +5
( )
3) Which of the following function rules determines the function table?
–20
–18
–6
–2
80
72
24
8
i)
( ) = −4
ii)
( )=4
iii)
( ) = 6 + 11
iv)
( ) = −3 − 10
( )
Printable Worksheets @ www.mathworksheets4kids.com
Name:
Sheet 3
Function Rule
A) Identify the function rule for each function table.
1)
–12
0
3
4
96
0
–24
–32
–15
–13
–8
2
–14
–12
–7
3
–9
–6
–5
–1
–51
–30
–23
5
2)
5
9
12
15
21
41
56
71
–11
–7
0
6
22
10
–11
–29
–20
–10
5
10
–4
–2
1
2
( )
3)
( )
4)
( )
5)
( )
6)
( )
( )
B) 1) Which of the following function rules determines the function table?
7
8
13
16
14
16
26
32
i)
( )=2
iii)
( )=
ii)
( ) = −7 − 2
iv)
( )=2 +7
( )
−7
2) Which of the following function rules determines the function table?
–17
–14
–4
–3
–69
–57
–17
–13
i)
( ) = −8 + 4
ii)
( )=4
iii)
( )=4 −1
iv)
( )=6 −4
( )
3) Which of the following function rules determines the function table?
( )
–12
0
14
20
6
0
–7
–10
i)
( )= 5 −9
ii)
( )=−1
2
iii)
( )=3 +5
iv)
( ) = −6 − 12
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Answer key
Name:
Sheet 3
Function Rule
A) Identify the function rule for each function table.
1)
–12
0
3
4
96
0
–24
–32
2)
5
9
12
15
21
41
56
71
( )
( )
( )=5 −4
( ) = −8
3)
–15
–13
–8
2
–14
–12
–7
3
4)
–11
–7
0
6
22
10
–11
–29
( )
+1
( )=
5)
( )
( ) = −3 − 11
–9
–6
–5
–1
–51
–30
–23
5
6)
–20
–10
5
10
–4
–2
1
2
( )
( )
( )= 1
( ) = 7 + 12
5
B) 1) Which of the following function rules determines the function table?
7
8
13
16
14
16
26
32
i)
( )=2
iii)
( )=
ii)
( ) = −7 − 2
iv)
( )=2 +7
( )
−7
2) Which of the following function rules determines the function table?
–17
–14
–4
–3
–69
–57
–17
–13
i)
( ) = −8 + 4
ii)
( )=4
iii)
( )=4 −1
iv)
( )=6 −4
( )
3) Which of the following function rules determines the function table?
( )
–12
0
14
20
6
0
–7
–10
i)
( )= 5 −9
ii)
( )=−1
2
iii)
( )=3 +5
iv)
( ) = −6 − 12
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Name :
ES1
Function Table - Quadratic Function
A) Complete each function table.
1)
f(x) = 3x(x – 1)
2)
f(x) = x2 – 5x + 6
f(x)
x
x
3)
f(x) = 4x2 + 13
f(x)
x
0
–6
–7
1
–4
–5
2
–3
–2
3
–2
0
5
–1
2
f(x)
B) Complete the function table using the function rule f(x) = (x + 6)(x – 8) and
answer the following questions.
–6
x
–1
0
5
8
f(x)
i) What is the value of f(9)?
ii) What is the value of f(x), if x is 3?
C) Complete the function table.
f(x)
3x2 – 14
f(–4)
f(0)
f(6)
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x2
2x2 – 7x + 5
Answer key
Name :
ES1
Function Table - Quadratic Function
A) Complete each function table.
1)
f(x) = 3x(x – 1)
2)
f(x) = x2 – 5x + 6
3)
f(x) = 4x2 + 13
x
f(x)
x
f(x)
x
f(x)
0
0
–6
72
–7
209
1
0
–4
42
–5
113
2
6
–3
30
–2
29
3
18
–2
20
0
13
5
60
–1
12
2
29
B) Complete the function table using the function rule f(x) = (x + 6)(x – 8) and
answer the following questions.
x
–6
–1
0
5
8
f(x)
0
–45
–48
–33
0
i) What is the value of f(9)?
ii) What is the value of f(x), if x is 3?
15
–45
C) Complete the function table.
f(x)
3x2 – 14
x2
2x2 – 7x + 5
f(–4)
34
16
65
f(0)
–14
0
5
f(6)
94
36
35
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Name :
ES2
Function Table - Quadratic Function
A) Complete each function table.
1)
f(x) = 4x(3 – 2x)
2)
f(x) = 3x2 – 8x + 5
f(x)
x
x
3)
f(x) = (3x – 2)(3x + 2)
f(x)
f(x)
x
–7
–2
–9
–5
–1
–8
–3
8
–4
0
9
–3
1
10
–2
B) Complete the function table using the function rule f(x) = 6x2 and answer the
following questions.
–3
x
–1
0
2
5
f(x)
i) What is the value of f(x), if x is –7?
ii) What is the value of f(9)?
C) Complete the function table.
f(x)
14 – x2
f(–4)
f(3)
f(6)
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x2 – 7x + 12
8x + 2x2
Answer key
Name :
ES2
Function Table - Quadratic Function
A) Complete each function table.
1)
f(x) = 4x(3 – 2x)
2)
f(x) = 3x2 – 8x + 5
3)
f(x) = (3x – 2)(3x + 2)
x
f(x)
x
f(x)
x
f(x)
–7
–476
–2
33
–9
725
–5
–260
–1
16
–8
572
–3
–108
8
133
–4
140
0
0
9
176
–3
77
1
4
10
225
–2
32
B) Complete the function table using the function rule f(x) = 6x2 and answer the
following questions.
x
–3
–1
0
2
5
f(x)
54
6
0
24
150
i) What is the value of f(x), if x is –7?
ii) What is the value of f(9)?
294
486
C) Complete the function table.
f(x)
14 – x2
x2 – 7x + 12
8x + 2x2
f(–4)
–2
56
0
f(3)
5
0
42
f(6)
–22
6
120
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Name :
ES3
Function Table - Quadratic Function
A) Complete each function table.
1)
f(x) = 12 – 3x2
2)
f(x) = 6x2 + 5x – 1
f(x)
x
x
3)
f(x) = x(x – 5)
f(x)
x
–8
–4
–9
–5
0
–7
0
6
–3
1
8
4
2
10
5
f(x)
B) Complete the function table using the function rule f(x) = –10x2 and answer the
following questions.
–3
x
–2
–1
1
2
f(x)
i) What is the value of f(x), if x is 4?
ii) What is the value of f(–8)?
C) Complete the function table.
f(x)
(x – 13)(x + 1)
f(–6)
f(–3)
f(–1)
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x2 + 12
3x2 + 5x – 8
Answer key
Name :
ES3
Function Table - Quadratic Function
A) Complete each function table.
1)
f(x) = 12 – 3x2
2)
f(x) = 6x2 + 5x – 1
3)
f(x) = x(x – 5)
x
f(x)
x
f(x)
x
f(x)
–8
–180
–4
75
–9
126
–5
–63
0
–1
–7
84
0
12
6
245
–3
24
1
9
8
423
4
–4
2
0
10
649
5
0
B) Complete the function table using the function rule f(x) = –10x2 and answer the
following questions.
x
–3
–2
–1
1
2
f(x)
–90
–40
–10
–10
–40
i) What is the value of f(x), if x is 4?
ii) What is the value of f(–8)?
–160
–640
C) Complete the function table.
f(x)
(x – 13)(x + 1)
x2 + 12
3x2 + 5x – 8
f(–6)
95
48
70
f(–3)
32
21
4
f(–1)
0
13
–10
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Name:
T1ES1
Evaluating Quadratic Functions
A) Evaluate each function at the specified value.
1)
( ) = ( + 3)2 – 2 2 ;
= –12
2)
( ) = –5 + 4 2 ;
( ) = (3 – 14)2 ; find (11)
2)
( ) = – 2 ; find (–5)
= –6
B) Evaluate each function.
1)
C) If ( ) = 2 – 7 – 13 ; find the following.
1)
(–15) =
2)
(12)
=
3)
(0)
4)
(6)
=
=
D) If ( ) = ( – 2)2 ; find the following.
1)
4 (1)
6 (0)
=
2)
–8 (2) + 3 (4)
=
3)
–7 (7) + (–8)
=
4)
–3 (–1)
(3)
=
E) What is the value of (–3), if ( ) = 10 2 + 8?
i)
91
ii)
–88
iii)
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–96
iv)
98
Answer key
Name:
T1ES1
Evaluating Quadratic Functions
A) Evaluate each function at the specified value.
1)
( ) = ( + 3)2 – 2 2 ;
= –12
2)
( ) = –5 + 4 2 ;
–207
= –6
174
B) Evaluate each function.
1)
( ) = (3 – 14)2 ; find (11)
2)
( ) = – 2 ; find (–5)
361
–25
C) If ( ) = 2 – 7 – 13 ; find the following.
1)
(–15) =
317
2)
(12)
=
47
3)
(0)
–13
4)
(6)
=
–19
=
D) If ( ) = ( – 2)2 ; find the following.
1)
4 (1)
6 (0)
=
96
2)
–8 (2) + 3 (4)
=
12
3)
–7 (7) + (–8)
=
–75
4)
–3 (–1)
(3)
=
–27
E) What is the value of (–3), if ( ) = 10 2 + 8?
i)
91
ii)
–88
iii)
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–96
iv)
98
Name:
T1ES2
Evaluating Quadratic Functions
A) Evaluate each function at the specified value.
1)
( ) = 3 2 – 5 + 15 ;
= –1
2)
( ) = ( – 4)2 – 6 ;
2)
( ) = 8( + 4)2 – 12 ; find (–3)
=7
B) Evaluate each function.
1)
( ) = 2 – 9 ; find (8)
C) If ( ) = –2 2 + 6 ; find the following.
1)
(0)
=
2)
(14)
=
3)
(10)
=
4)
(1)
=
D) If ( ) = 2 – 10 – 7 ; find the following.
1)
3 (15) + 5 (2)
=
2)
2 (11)
(4)
=
3)
(–3)
4 (–1)
=
4)
–6 (9) – (12)
=
E) What is the value of (–13), if ( ) = (3 + 9) + 11?
i)
401
ii)
–396
iii)
Printable Worksheets @ www.mathworksheets4kids.com
410
iv)
–398
Answer key
Name:
T1ES2
Evaluating Quadratic Functions
A) Evaluate each function at the specified value.
1)
( ) = 3 2 – 5 + 15 ;
= –1
2)
( ) = ( – 4)2 – 6 ;
23
=7
–33
B) Evaluate each function.
1)
( ) = 2 – 9 ; find (8)
2)
( ) = 8( + 4)2 – 12 ; find (–3)
–8
44
C) If ( ) = –2 2 + 6 ; find the following.
1)
(0)
=
6
2)
(14)
=
–386
3)
(10)
=
–194
4)
(1)
=
4
D) If ( ) = 2 – 10 – 7 ; find the following.
1)
3 (15) + 5 (2)
=
89
2)
2 (11)
(4)
=
–248
3)
(–3)
4 (–1)
=
2
4)
–6 (9) – (12)
=
79
E) What is the value of (–13), if ( ) = (3 + 9) + 11?
i)
401
ii)
–396
iii)
Printable Worksheets @ www.mathworksheets4kids.com
410
iv)
–398
Name:
T1ES3
Evaluating Quadratic Functions
A) Evaluate each function at the specified value.
1)
( ) = ( – 13) ;
=9
2)
( ) = 6( + 3)2 + 3 ;
2)
( ) = 2 + ; find (15)
B) Evaluate each function.
1)
( ) = 8 – 2 2 ; find (12)
C) If ( ) = (7 + 1)(– + 6) ; find the following.
1)
(1)
=
2)
(–5)
=
3)
(–4)
=
4)
(0)
=
=
2)
9 (–8) + (2)
=
4)
–7 (–3) – (10) =
D) If ( ) = 2 – 9 ; find the following.
1)
2 (–11)
(11)
3)
3 (5)
(0)
=
E) What is the value of (6), if ( ) = 5 2?
i)
150
ii)
–150
iii)
Printable Worksheets @ www.mathworksheets4kids.com
180
iv)
–180
= –14
Answer key
Name:
T1ES3
Evaluating Quadratic Functions
A) Evaluate each function at the specified value.
1)
( ) = ( – 13) ;
=9
( ) = 6( + 3)2 + 3 ;
2)
–36
= –14
684
B) Evaluate each function.
1)
( ) = 8 – 2 2 ; find (12)
2)
( ) = 2 + ; find (15)
–280
240
C) If ( ) = (7 + 1)(– + 6) ; find the following.
1)
(1)
=
40
2)
(–5)
=
–374
3)
(–4)
=
–270
4)
(0)
=
6
D) If ( ) = 2 – 9 ; find the following.
1)
2 (–11)
(11)
3)
3 (5)
(0)
=
2
2)
9 (–8) + (2)
=
490
=
–432
4)
–7 (–3) – (10) =
–91
E) What is the value of (6), if ( ) = 5 2?
i)
150
ii)
–150
iii)
Printable Worksheets @ www.mathworksheets4kids.com
180
iv)
–180
Name:
Sheet 1
Evaluating Rational Functions
A) Evaluate each function at the specified value.
1)
( )=
7
2 –4
;
2)
= –2
–6
( )=
+4
;
=1
B) Evaluate each function.
1)
( )=
C) If ( ) =
1)
3)
²–8
3 + 15
( )=
3
9 ²–7
; find (0)
10
; find the following.
– –5
(–8)
=
2)
(9)
=
D) If ( ) =
(3)
=
4)
(–7)
=
=
2)
–5 (7) – 9 (–1)
=
=
4)
7 (4)
=
+1
; find the following.
( – 2)( + 3)
4 (–2) + 8 (–4)
1)
2)
; find (10)
–6 (–6)
3)
(5)
E) What is the value of (–3), if ( ) =
i)
3
5
ii)
–3
5
3 (0)
9
?
²+6
iii)
Printable Worksheets @ www.mathworksheets4kids.com
–9
iv)
3
Answer key
Name:
Sheet 1
Evaluating Rational Functions
A) Evaluate each function at the specified value.
1)
( )=
7
;
2 –4
2)
= –2
–6
( )=
+4
;
–7
8
=1
–1
B) Evaluate each function.
1)
( )=
²–8
3 + 15
2)
; find (10)
( )=
3
9 ²–7
4
9
C) If ( ) =
1)
3)
10
; find the following.
– –5
(–8)
=
(9)
=
– 45 or –6 3
7
7
(3)
=
– 15 or –3 3
4
4
4)
(–7)
=
–35
2)
–5 (7) – 9 (–1)
4)
7 (4)
2)
+1
; find the following.
( – 2)( + 3)
4 (–2) + 8 (–4)
1)
–3
7
– 80 or –26 2
3
3
D) If ( ) =
; find (0)
–6 (–6)
=
–3
=
–4
5
=
– 5 or –1 1
4
4
3)
(5)
=
5
E) What is the value of (–3), if ( ) =
i)
3
5
ii)
–3
5
3 (0)
9
?
²+6
iii)
Printable Worksheets @ www.mathworksheets4kids.com
–9
iv)
3
Name:
Sheet 2
Evaluating Rational Functions
A) Evaluate each function at the specified value.
1)
5 +4
( )=
9 +3
;
2)
=2
² + 25
( )=
;
² – 9 – 10
=0
B) Evaluate each function.
1)
C) If ( ) =
1)
²–2
( )=
3)
7
2)
; find (–5)
– 11
; find (7)
+1
; find the following.
( + 8)²
(–6)
=
2)
(1)
=
D) If ( ) =
–4
( )=
(–9)
=
4)
(–7)
=
=
2)
4 (–2)
9 (–3)
=
=
4)
8 (–10) – 3 (0)
=
; find the following.
6–
5 (–8)
1)
2 (4)
–6 (–6) + 7 (–1)
3)
E) What is the value of (–4), if ( ) =
i)
– 11
8
ii)
–1
8
+7
?
2
iii)
Printable Worksheets @ www.mathworksheets4kids.com
–3
8
iv)
2
Answer key
Name:
Sheet 2
Evaluating Rational Functions
A) Evaluate each function at the specified value.
1)
5 +4
( )=
9 +3
;
2)
=2
² + 25
( )=
;
² – 9 – 10
2
3
=0
– 5 or –2 1
2
2
B) Evaluate each function.
1)
²–2
( )=
7
2)
; find (–5)
–4
( )=
– 11
–1
C) If ( ) =
1)
3)
+1
; find the following.
( + 8)²
(–6)
=
(1)
=
2
81
(–9)
=
–8
4)
(–7)
=
–6
=
–5
7
2)
4 (–2)
9 (–3)
=
3
2 (4)
–6 (–6) + 7 (–1)
=
2
4)
8 (–10) – 3 (0)
=
–5
– 11
8
E) What is the value of (–4), if ( ) =
i)
3)
2)
; find the following.
6–
5 (–8)
1)
7
– 5 or –1 1
4
4
D) If ( ) =
; find (7)
ii)
–1
8
+7
?
2
iii)
Printable Worksheets @ www.mathworksheets4kids.com
–3
8
iv)
2
Name:
Sheet 3
Evaluating Rational Functions
A) Evaluate each function at the specified value.
1)
5+
( )=
;
2)
= –9
( )=
–3
2 –8
;
=7
B) Evaluate each function.
1)
+3
( )=
+ 14
1)
3)
3 ² – 12
C) If ( ) =
2)
; find (0)
² – 8 + 16
9–7 ²
2
; find (–5)
; find the following.
(6)
=
2)
(–4)
=
4)
D) If ( ) =
( )=
(3)
=
(–1)
=
5 +8
; find the following.
–1
2 (2)
1)
–8 (–7) – 6 (–2)
=
2)
(0)
=
4)
3)
4 (–3)
i)
6
5
–3 (4) + 9 (10)
E) What is the value of (5), if ( ) =
ii)
–1
=
7 (–6)
=
–6
?
+ 25
iii)
Printable Worksheets @ www.mathworksheets4kids.com
–6
5
iv)
–6
Answer key
Name:
Sheet 3
Evaluating Rational Functions
A) Evaluate each function at the specified value.
1)
5+
( )=
;
2)
= –9
( )=
–3
2 –8
4
9
;
=7
–1
2
B) Evaluate each function.
1)
+3
( )=
+ 14
2)
; find (0)
( )=
9–7 ²
1)
3)
–83
3 ² – 12
; find the following.
² – 8 + 16
(6)
=
9
2)
(–4)
=
3 or 1 1
2
2
4)
D) If ( ) =
2
3
14
C) If ( ) =
; find (–5)
(3)
=
–9
(–1)
=
3
5
5 +8
; find the following.
–1
2 (2)
=
18 or 1 7
11
11
=
30
1)
–8 (–7) – 6 (–2)
=
–31
2)
(0)
=
–56
4)
3)
4 (–3)
6
5
–3 (4) + 9 (10)
E) What is the value of (5), if ( ) =
i)
7 (–6)
ii)
–1
–6
?
+ 25
iii)
Printable Worksheets @ www.mathworksheets4kids.com
–6
5
iv)
–6
Name:
Sheet 4
Evaluating Rational Functions
A) Evaluate each function at the specified value.
8
– –7
1)
( )=
;
–5
2)
=4
( )=
²–9
;
= –1
B) Evaluate each function.
1)
( )=
² + 7 + 10
; find (2)
² – 16
3 +6
2)
( )=
2
5 –4
; find the following.
12 +
C) If ( ) =
1)
(5)
=
2)
(–2)
=
3)
(0)
=
4)
(8)
=
–10 (1) + 6 (6)
D) If ( ) =
–4 ² + 9
10
; find the following.
1)
3 (5)
2 (–4)
=
2)
3)
2 (–1) – 8 (3)
=
4)
E) What is the value of (–3), if ( ) =
i)
2
3
; find (–6)
ii)
–2
3
( + 1)( – 3)
– 15
iii)
Printable Worksheets @ www.mathworksheets4kids.com
=
(7)
=
(–2)
?
–2
iv)
–3
2
Answer key
Name:
Sheet 4
Evaluating Rational Functions
A) Evaluate each function at the specified value.
8
– –7
1)
( )=
;
–5
2)
=4
( )=
²–9
;
= –1
3
4
–32
B) Evaluate each function.
1)
( )=
² + 7 + 10
; find (2)
² – 16
3 +6
2)
( )=
2
– 7 or –2 1
3
3
1
5 –4
; find the following.
12 +
C) If ( ) =
1)
(5)
=
21 or 1 4
17
17
3)
(0)
=
–1
3
D) If ( ) =
3 (5)
1)
–4 ² + 9
10
; find the following.
2 (–4)
=
2 (–1) – 8 (3)
3)
–
33 or –16 1
2
2
=
2
3
ii)
–2
3
2)
(–2)
=
– 7 or –1 2
5
5
4)
(8)
=
9 or 1 4
5
5
2)
–10 (1) + 6 (6)
4)
5
E) What is the value of (–3), if ( ) =
i)
; find (–6)
( + 1)( – 3)
– 15
iii)
Printable Worksheets @ www.mathworksheets4kids.com
(7)
(–2)
=
–14
=
– 19 or –1 2
17
17
?
–2
iv)
–3
2
Name:
Sheet 5
Evaluating Rational Functions
A) Evaluate each function at the specified value.
1)
–10
( )=
²–4
;
6–9 ²
2)
= –3
( )=
8
;
=6
B) Evaluate each function.
4 +5
20
1)
( )=
C) If ( ) =
13 –
2)
; find (–8)
( )=
( – 1)²
²
7 + 18
; find the following.
1)
(–4)
=
2)
(–9)
=
3)
(3)
=
4)
(10)
=
=
2)
(5)
=
4)
3 (0) – 7 (–6)
D) If ( ) =
–6
; find the following.
4– ²
–2 (–5) + (1)
1)
4 (–1)
3)
(8)
E) What is the value of (4), if ( ) =
i)
6
5
; find (2)
ii)
16
8 (7)
=
=
–16 – 5 ²
?
–4
iii)
Printable Worksheets @ www.mathworksheets4kids.com
–9
iv)
6
Answer key
Name:
Sheet 5
Evaluating Rational Functions
A) Evaluate each function at the specified value.
1)
–10
( )=
²–4
;
6–9 ²
2)
= –3
( )=
8
;
=6
2
15
2
3
B) Evaluate each function.
4 +5
20
1)
( )=
13 –
2)
; find (–8)
( )=
( – 1)²
– 9 or –1 2
7
7
C) If ( ) =
²
7 + 18
20
; find the following.
1)
(–4)
=
– 8 or –1 3
5
5
3)
(3)
=
3
13
D) If ( ) =
4 (–1)
3)
(8)
6
7
=
=
6
5
(–9)
=
4)
(10)
=
25 or 1 3
22
22
2)
4)
10
E) What is the value of (4), if ( ) =
i)
2)
– 9 or –1 4
5
5
–6
; find the following.
4– ²
–2 (–5) + (1)
1)
; find (2)
ii)
16
(5)
8 (7)
3 (0) – 7 (–6)
=
32 or 10 2
3
3
=
63 or 7 7
8
8
–16 – 5 ²
?
–4
iii)
Printable Worksheets @ www.mathworksheets4kids.com
–9
iv)
6
Name :
ES1
Interior Angles
Find the value of each indicated angle.
1)
2)
650
1140
=
=
3)
4)
1200
740
=
=
5)
6)
710
550
=
=
7)
8)
1490
400
=
Printable Worksheets @ www.mathworksheets4kids.com
=
Answer key
Name :
ES1
Interior Angles
Find the value of each indicated angle.
1)
2)
650
1140
=
=
650
3)
660
4)
1200
740
=
=
1060
5)
1200
6)
710
550
=
=
1250
7)
710
8)
1490
400
=
1490
Printable Worksheets @ www.mathworksheets4kids.com
=
1400
Name :
ES2
Interior Angles
Find the value of each indicated angle.
1)
2)
1150
1130
=
3)
=
4)
410
890
=
5)
=
6)
880
710
=
7)
=
8)
620
1060
=
Printable Worksheets @ www.mathworksheets4kids.com
=
Answer key
Name :
ES2
Interior Angles
Find the value of each indicated angle.
1)
2)
1150
1130
=
1150
3)
=
670
4)
410
890
=
890
5)
=
1390
6)
880
710
=
1090
7)
=
880
8)
620
1060
=
620
Printable Worksheets @ www.mathworksheets4kids.com
=
740
Name :
ES3
Interior Angles
Find the value of each indicated angle.
1)
2)
920
560
=
3)
=
4)
80
13
760
=
5)
=
6)
133
850
=
7)
=
8)
1220
820
=
Printable Worksheets @ www.mathworksheets4kids.com
=
0
Answer key
Name :
ES3
Interior Angles
Find the value of each indicated angle.
1)
2)
920
560
=
880
3)
=
560
=
420
4)
80
13
760
=
760
5)
6)
133
850
=
950
7)
=
0
1330
8)
1220
820
=
1220
Printable Worksheets @ www.mathworksheets4kids.com
=
980
Name :
ES1
Exterior Angles
Find the value of each indicated angle.
2)
11
50
1)
1130
=
=
3)
4)
410
890
=
5)
=
6)
88
0
71
0
=
7)
=
8)
620
740
=
Printable Worksheets @ www.mathworksheets4kids.com
=
Answer key
Name :
ES1
Exterior Angles
Find the value of each indicated angle.
2)
11
50
1)
1130
=
650
3)
=
1130
4)
410
890
=
890
5)
=
1390
6)
88
0
71
0
=
1090
7)
=
880
8)
620
740
=
620
Printable Worksheets @ www.mathworksheets4kids.com
=
1060
Name :
ES2
Exterior Angles
Find the value of each indicated angle.
1)
2)
1200
750
=
3)
=
4)
0
114
650
=
5)
=
6)
700
1490
=
7)
=
8)
550
=
Printable Worksheets @ www.mathworksheets4kids.com
=
400
Answer key
Name :
ES2
Exterior Angles
Find the value of each indicated angle.
1)
2)
1200
750
=
1200
3)
=
1050
4)
0
114
650
=
1150
5)
=
660
6)
700
1490
=
1490
7)
=
1100
8)
550
=
550
Printable Worksheets @ www.mathworksheets4kids.com
=
1400
400
Name :
ES3
Exterior Angles
Find the value of each indicated angle.
1)
2)
560
920
=
=
3)
4)
760
1380
=
=
5)
6)
0
133
850
=
=
7)
8)
780
1210
=
Printable Worksheets @ www.mathworksheets4kids.com
=
Answer key
Name :
ES3
Exterior Angles
Find the value of each indicated angle.
1)
2)
560
920
=
=
920
3)
1240
4)
760
1380
=
=
1040
5)
1380
6)
0
133
850
=
=
850
7)
470
8)
780
1210
=
590
Printable Worksheets @ www.mathworksheets4kids.com
=
780
Name :
MS1
Interior and Exterior Angles
Find the value of .
1)
2)
800
(6
76
0
+
10
)0
( + 25)0
=
=
3)
4)
(5 + 12)0
1090
1170
(2 – 1)0
=
=
5)
6)
1070
(12 )0
1320
(4 + 15)0
=
=
7)
8)
(7 )0
570
(8
+1
)0
750
=
Printable Worksheets @ www.mathworksheets4kids.com
=
Answer key
Name :
MS1
Interior and Exterior Angles
Find the value of .
1)
2)
800
(6
76
0
+
10
)0
( + 25)0
=
75
3)
=
11
4)
(5 + 12)0
1090
1170
(2 – 1)0
=
21
5)
=
36
6)
1070
(12 )0
1320
(4 + 15)0
=
4
7)
=
23
8)
(7 )0
570
(8
+1
)0
750
=
7
Printable Worksheets @ www.mathworksheets4kids.com
=
15
Name :
MS2
Interior and Exterior Angles
Find the value of .
1)
2)
1230
960
(6 )
0
(3 – 3)0
=
=
3)
4)
(4 +
1)0
950
1090
1)0
(2 –
=
=
5)
6)
(2 + 9)0
540
(4 –
6)0
630
=
=
7)
8)
(3
+ 1)
0
108
0
(6 )
0
850
=
Printable Worksheets @ www.mathworksheets4kids.com
=
Answer key
Name :
MS2
Interior and Exterior Angles
Find the value of .
1)
2)
1230
960
(6 )
0
(3 – 3)0
=
42
3)
=
14
4)
(4 +
1)0
950
1090
1)0
(2 –
=
21
5)
=
36
6)
(2 + 9)0
540
(4 –
6)0
630
=
54
7)
=
15
8)
(3
+ 1)
0
108
0
(6 )
0
850
=
12
Printable Worksheets @ www.mathworksheets4kids.com
=
28
Name :
MS3
Interior and Exterior Angles
Find the value of .
1)
2)
560
(3 – 1)0
1020
( + 27)0
=
=
3)
4)
)0
(10
)0
10
40
(4
–8
140
0
=
=
5)
6)
(5 – 20
)0
67
0
(2
–7
1150
)0
=
=
7)
8)
(7 – 12)0
(11 )0
700
=
Printable Worksheets @ www.mathworksheets4kids.com
1140
=
Answer key
Name :
MS3
Interior and Exterior Angles
Find the value of .
1)
2)
560
(3 – 1)0
1020
( + 27)0
=
19
3)
=
75
4)
)0
(10
)0
10
40
(4
–8
140
0
=
21
5)
=
4
6)
(5 – 20
)0
67
0
(2
–7
1150
)0
=
60
7)
=
27
8)
(7 – 12)0
(11 )0
700
=
10
Printable Worksheets @ www.mathworksheets4kids.com
1140
=
18
Name :
DS1
Angle Pairs - Transversal
Find the value of .
1)
2)
+
(8
)0
19
(9
+
(3 – 31)0
0
9)
( + 59)0
=
=
4)
(5
3)
0
3)
–3
(6
(2 )0
+
0
4)
6)0
(3 – 2
=
(7
–1
2)
0
( +5
0)0
(6
+
3)
0
6)
( +
10)0
5)
=
=
7)
=
8)
(3
(
(3 +
19)0
1)0
(4 – 2
)0
=
Printable Worksheets @ www.mathworksheets4kids.com
+1
=
+1
)0
Answer key
Name :
DS1
Angle Pairs - Transversal
Find the value of .
1)
2)
+
(8
)0
19
(9
+
(3 – 31)0
0
9)
( + 59)0
=
=
45
4)
(5
3)
10
0
3)
–3
(6
(2 )0
+
0
4)
6)0
(3 – 2
=
19
=
26
=
(7
–1
2)
0
( +5
0)0
(6
+
3)
0
6)
( +
10)0
5)
60
7)
=
15
8)
(3
(
(3 +
19)0
=
1)0
(4 – 2
)0
21
Printable Worksheets @ www.mathworksheets4kids.com
+1
=
42
+1
)0
Name :
DS2
Angle Pairs - Transversal
Find the value of .
2)
(2 + 9)0
1)
(7 )0
(4 – 41
)0
(5 + 12)0
=
=
4)
( + 5)0
+
)0
3)
(
+1
1)0
(39
(75 – )0
=
=
5)
6)
(8
+
(3 + 25)0
1)
0
(4
+
11
)0
(4 – 5)0
=
=
7)
8)
(3
–1
00
(2 + 6)0
( + 55)0
=
Printable Worksheets @ www.mathworksheets4kids.com
(2
=
–2
0)0
)0
Answer key
Name :
DS2
Angle Pairs - Transversal
Find the value of .
2)
(2 + 9)0
1)
(7 )0
(4 – 41
)0
(5 + 12)0
=
=
14
4)
( + 5)0
+
)0
3)
25
(
+1
1)0
(39
(75 – )0
=
=
65
5)
35
6)
(8
+
1)
0
(3 + 25)0
(4
+
11
)0
(4 – 5)0
=
=
14
7)
30
8)
(3
–1
00
(2 + 6)0
( + 55)0
=
49
Printable Worksheets @ www.mathworksheets4kids.com
(2
=
–2
0)0
80
)0
Name :
DS3
Angle Pairs - Transversal
Find the value of .
1)
2)
(5 + 10)0
(6
+8
(4 – 10)0
)0
(7
–5
)0
=
=
4)
(8 –
12)0
3)
(7 + 10)0 (26 + 5)0
(3 +
28)0
=
=
5)
6)
(6 )0
(2 +
39)0
( +
64)0
(3 )0
=
=
7)
8)
(2
)0
0)0
–1
14
(5 –
0
54)
( +
=
Printable Worksheets @ www.mathworksheets4kids.com
(3
=
+ 18
)0
Answer key
Name :
DS3
Angle Pairs - Transversal
Find the value of .
1)
2)
(5 + 10)0
(6
+8
)0
(4 – 10)0
(7
–5
)0
=
20
13
4)
(8 –
12)0
3)
=
(3 +
28)0
(7 + 10)0 (26 + 5)0
=
8
5)
=
5
6)
(6 )0
(2 +
39)0
( +
64)0
(3 )0
=
20
7)
=
25
8)
(2
)0
0)0
–1
14
(5 –
0
54)
( +
=
64
Printable Worksheets @ www.mathworksheets4kids.com
(3
=
+ 18
)0
22
Name :
Sheet 1
Triangle - Interior Angles
Find the measure of the indicated angle in each triangle.
1)
2)
3)
T
C
B
Q
370
510
460
630
360
R
A
V
U
mÐU =
mÐB =
4)
mÐQ =
5)
6)
Z
G
V
Y
1180
860
W
420
330
470
E
F
640
X
mÐF =
U
mÐY =
7)
mÐV =
8)
9)
L
E
U
600
M
600
350
530
350
T
S
770
C
K
mÐK =
P
mÐU =
Printable Worksheets @ www.mathworksheets4kids.com
mÐC =
D
Name :
Answer key
Sheet 1
Triangle - Interior Angles
Find the measure of the indicated angle in each triangle.
1)
2)
3)
T
C
B
Q
370
510
460
630
800
mÐU =
360
R
A
V
U
440
mÐB =
4)
mÐQ =
5)
Z
V
Y
1180
860
W
420
330
470
E
F
640
X
470
U
290
mÐY =
7)
mÐV =
8)
E
U
600
600
530
350
350
T
S
600
770
C
K
mÐK =
740
9)
L
M
930
6)
G
mÐF =
P
mÐU =
Printable Worksheets @ www.mathworksheets4kids.com
1100
mÐC =
D
500
Name :
Sheet 2
Triangle - Interior Angles
Find the measure of the indicated angle in each triangle.
1)
2)
3)
Y
D
U
E
450
1230
780
X
320
720
680
S
T
F
Z
mÐX =
mÐS =
4)
mÐD =
5)
6)
M
C
Q
540
A
400
530
N
620
260
400
R
P
B
L
mÐL =
mÐC =
7)
mÐQ =
8)
9)
Y
V
H
830
710
G
U
660
380
F
T
mÐU =
mÐH =
Printable Worksheets @ www.mathworksheets4kids.com
W
850
610
X
mÐY =
Name :
Answer key
Sheet 2
Triangle - Interior Angles
Find the measure of the indicated angle in each triangle.
1)
2)
3)
Y
D
U
E
450
1230
780
X
320
720
680
S
T
F
Z
670
mÐX =
mÐS =
4)
300
250
mÐD =
5)
6)
M
C
Q
540
A
400
530
N
R
P
B
L
730
mÐL =
620
260
400
mÐC =
7)
1000
920
mÐQ =
8)
9)
Y
V
H
830
710
G
U
660
380
F
T
mÐU =
590
mÐH =
Printable Worksheets @ www.mathworksheets4kids.com
430
W
850
610
X
mÐY =
340
Name :
Sheet 3
Triangle - Interior Angles
Find the measure of the indicated angle in each triangle.
1)
2)
3)
G
S
R
410
V
580
580
H
310
470
490
W
Q
U
F
mÐS =
mÐF =
4)
mÐV =
5)
6)
N
Z
Y
390
M
U
1040
910
1140
380
370
X
S
T
L
mÐY =
mÐT =
7)
mÐN =
8)
F
9)
C
X
440
570
450
D
mÐF =
E
600
W
A
600
Y
mÐX =
Printable Worksheets @ www.mathworksheets4kids.com
B
mÐB =
Name :
Answer key
Sheet 3
Triangle - Interior Angles
Find the measure of the indicated angle in each triangle.
1)
2)
3)
G
S
R
410
V
580
580
H
310
470
490
W
Q
U
F
1080
mÐS =
mÐF =
4)
640
mÐV =
5)
840
6)
N
Z
Y
390
M
U
1040
910
1140
380
370
X
S
T
L
mÐY =
270
mÐT =
7)
520
mÐN =
8)
F
9)
C
X
440
450
mÐF =
E
450
600
W
A
570
D
380
600
Y
mÐX =
Printable Worksheets @ www.mathworksheets4kids.com
B
790
mÐB =
600
Name :
Sheet 1
Triangle - Exterior Angles
Find the measure of the indicated angle in each triangle.
1)
2)
3)
V
X
R
H
1030
T
390
530
X
800
490
P
U
Q
mÐQRX =
4)
F
X
mÐVUX =
mÐHFX =
5)
6)
X
C
K
B
300
X
V
X
440
930
210
J
L
W
A
mÐJKX =
mÐACX =
9)
E
M
X
T
X
850
R
630
470
D
660
F
mÐDFX =
U
mÐWVX =
8)
X
710
350
7)
G
260
750 750
N
mÐLMX =
Printable Worksheets @ www.mathworksheets4kids.com
S
L
mÐSTX =
Name :
Answer key
Sheet 1
Triangle - Exterior Angles
Find the measure of the indicated angle in each triangle.
1)
2)
3)
V
X
R
H
1030
T
390
530
X
800
490
P
U
Q
1290
mÐQRX =
4)
F
X
1560
mÐVUX =
650
mÐHFX =
5)
6)
X
C
K
B
300
X
V
X
440
930
210
J
W
A
1370
510
mÐACX =
7)
8)
M
mÐWVX =
1060
X
T
X
850
R
630
U
9)
E
470
D
660
F
750 750
X
mÐDFX =
710
350
L
mÐJKX =
G
260
1480
S
N
L
mÐLMX =
1500
Printable Worksheets @ www.mathworksheets4kids.com
mÐSTX =
1130
Name :
Sheet 2
Triangle - Exterior Angles
Find the measure of the indicated angle in each triangle.
1)
2)
3)
E
X
400
K
L
U
X
910
1100
F
X
330
640
S
400
T
J
D
mÐLKX =
mÐEFX =
4)
mÐUTX =
5)
6)
M
C
X
480
D
T
N
670
X
460
410
X
B
540
730
R
mÐCBX =
S
L
mÐRTX =
7)
mÐLNX =
8)
9)
R
X
H
W
320
830
Q
580
P
mÐPQX =
X
940
450
V
F
X
U
mÐVWX =
Printable Worksheets @ www.mathworksheets4kids.com
mÐGFX =
280
G
Name :
Answer key
Sheet 2
Triangle - Exterior Angles
Find the measure of the indicated angle in each triangle.
1)
2)
3)
E
X
400
K
L
U
X
910
1100
F
X
330
640
S
400
T
J
D
1550
mÐLKX =
800
mÐEFX =
4)
mÐUTX =
5)
6)
M
C
X
480
D
1430
T
N
670
X
460
410
X
B
540
R
940
mÐCBX =
730
7)
S
L
1270
mÐRTX =
mÐLNX =
8)
1080
9)
R
X
H
W
320
830
Q
580
X
P
mÐPQX =
900
940
450
V
F
280
X
U
mÐVWX =
Printable Worksheets @ www.mathworksheets4kids.com
1390
mÐGFX =
1110
G
Name :
Sheet 3
Triangle - Exterior Angles
Find the measure of the indicated angle in each triangle.
1)
2)
3)
C
X
L
B
560
X
R
M
1040
X
270
430
380
620
Q
P
K
A
mÐACX =
4)
mÐRPX =
mÐKLX =
5)
S
6)
W
360
V
810
E
590
X
600
R
600
360
X
U
X
D
C
T
mÐSRX =
mÐWUX =
7)
mÐECX =
8)
L
290
9)
G
X
K
U
X
370
690
310
520
J
F
V
420
E
mÐJKX =
mÐEGX =
Printable Worksheets @ www.mathworksheets4kids.com
T
X
mÐVTX =
Name :
Answer key
Sheet 3
Triangle - Exterior Angles
Find the measure of the indicated angle in each triangle.
1)
2)
3)
C
X
L
B
560
X
R
M
1040
X
270
430
380
620
Q
P
K
A
mÐACX =
4)
830
1420
mÐRPX =
mÐKLX =
5)
S
6)
W
360
1050
V
810
E
590
X
600
R
600
360
X
U
X
D
C
T
mÐSRX =
720
1400
mÐWUX =
7)
mÐECX =
8)
L
290
9)
G
X
K
1200
U
X
370
690
310
V
520
J
F
420
T
X
E
mÐJKX =
600
mÐEGX =
Printable Worksheets @ www.mathworksheets4kids.com
1210
mÐVTX =
790
Name :
Sheet 1
Triangle - Exterior Angles
Find the value of x in each triangle.
1)
2)
3)
X
U
810
C
E
(4x)0
(–4x – 26)0
310
V
X
T
840
B
700
(12 + 10x)0
X
A
580
F
x=
x=
4)
x=
5)
6)
X
S
C
R
(–6x + 51)0
G
U
1050
X
E
(2x – 13)0
(x + 46)0
D
300
800
X
430
P
T
Q
x=
x=
7)
x=
8)
W
9)
X
V
350
500
(–3 + x)0
X
x=
1340
L
S
R
(5x – 8)0
(3x + 42)0
670
990
U
460
M
T
440
X
N
x=
Printable Worksheets @ www.mathworksheets4kids.com
x=
Name :
Answer key
Sheet 1
Triangle - Exterior Angles
Find the value of x in each triangle.
1)
2)
3)
X
U
810
C
E
(4x)0
(–4x – 26)0
310
V
X
T
840
B
700
(12 + 10x)0
X
A
580
G
F
x=
x=
10
4)
x=
–45
5)
6)
X
S
C
R
(–6x + 51)0
37
U
1050
X
E
(2x – 13)0
(x + 46)0
D
300
800
X
430
P
x=
T
Q
x=
–12
7)
x=
74
8)
W
X
500
(–3 + x)0
X
x=
88
21
9)
V
350
1340
L
S
R
(5x – 8)0
(3x + 42)0
670
990
U
460
T
440
M
X
N
x=
Printable Worksheets @ www.mathworksheets4kids.com
16
x=
8
Name :
Sheet 2
Triangle - Exterior Angles
Find the value of x in each triangle.
1)
2)
3)
B
R
S
X
(3x – 4)0
(–10x)0
510
X
U
860
300
240
C
1300
T
D
x=
X
x=
4)
6)
X
X
L
V
(6x + 15)0
(–9 + 2x)0
A
980
W
750
420
B
M
x=
C
x=
8)
9)
E
480
640
X
X
L
S
(4x – 20)0
(x + 78)0
(7x – 32)0
X
x=
F
G
260
(–5x – 14)0
1260
820
R
T
M
X
x=
U
310
590
7)
Q
x=
5)
K
(–8x + 23)0
P
x=
Printable Worksheets @ www.mathworksheets4kids.com
x=
490
N
Name :
Answer key
Sheet 2
Triangle - Exterior Angles
Find the value of x in each triangle.
1)
2)
3)
B
R
S
X
(3x – 4)0
(–10x)0
510
X
U
860
300
240
C
T
D
x=
1300
X
x=
38
4)
L
X
V
(6x + 15)0
A
980
W
750
420
B
M
x=
17
8)
F
E
X
X
L
S
(4x – 20)0
(x + 78)0
260
G
(–5x – 14)0
1260
820
R
T
M
X
x=
34
23
9)
480
640
(7x – 32)0
X
C
x=
79
7)
U
310
590
x=
–7
6)
X
(–9 + 2x)0
Q
x=
–12
5)
K
(–8x + 23)0
P
x=
Printable Worksheets @ www.mathworksheets4kids.com
43
x=
–29
490
N
Name :
Sheet 3
Triangle - Exterior Angles
Find the value of x in each triangle.
1)
2)
3)
X
W
R
C
(2x + 6)0
450
65 0
(4x − 52)0
470
B
A
(8x)0
X
830
770
T
S
X
V
790
U
x=
x=
4)
x=
5)
6)
X
E
X
(5x − 26)0
S
(−x + 44)0
N
920
250
T
F
360
L
(x + 68)0
X
800
M
640
G
x=
x=
7)
x=
8)
P
9)
X
L
D
(3x − 10)0
150
E
X
1250
(9x + 8)0
C
Q
X
x=
x=
Printable Worksheets @ www.mathworksheets4kids.com
1350
980
R
(−6x − 7)0
230
M
x=
K
U
Name :
Answer key
Sheet 3
Triangle - Exterior Angles
Find the value of x in each triangle.
1)
2)
3)
X
W
R
C
(2x + 6)0
450
65 0
(4x − 52)0
470
B
A
(8x)0
X
830
770
T
S
X
V
790
U
x=
x=
41
4)
x=
16
5)
6)
X
E
X
(5x − 26)0
S
(−x + 44)0
N
75
920
250
T
F
360
L
(x + 68)0
X
800
M
640
G
x=
x=
–82
7)
x=
34
8)
P
49
9)
X
L
D
(3x − 10)0
150
E
X
(9x + 8)0
C
1250
Q
R
(−6x − 7)0
X
x=
3
x=
Printable Worksheets @ www.mathworksheets4kids.com
1350
980
K
230
M
–20
x=
56
U
Name :
Sheet 1
Triangle - Exterior Angles
A) Solve for x in each triangle and find the measure of the indicated angle.
1)
2)
P
C
(76 – x)0
X
(17 + 4x)0
Q
B
(–x + 20)0
(70 – 6x)0
(–10x)0
R
A
(25 + 7x)0
X
x=
x=
mÐQRP =
mÐA =
4)
3)
K
X
W
(11 + 3x)0
(–2x + 21)0
(19 + x)0
L
M
(5x + 2)0
(–71 – 3x)0
(–x – 2)0
U
X
V
x=
x=
mÐU =
mÐXLM =
B) Solve for x in each triangle and find the measure of the indicated angles.
5)
6)
E
X
(x + 37)0
T
(7x + 55)0
(–2 + 3x)0
(x – 1)0
F
G
R
X
x=
(7 + 9x)0
x=
mÐFGE =
; mÐF =
mÐXTR =
; mÐR =
mÐEGX =
; mÐE =
mÐRTS =
; mÐS =
Printable Worksheets @ www.mathworksheets4kids.com
(2x)0
S
Name :
Answer key
Sheet 1
Triangle - Exterior Angles
A) Solve for x in each triangle and find the measure of the indicated angle.
1)
2)
P
C
(76 – x)0
X
(17 + 4x)0
Q
B
(–x + 20)0
(70 – 6x)0
(–10x)0
R
A
(25 + 7x)0
X
x=
17
x=
–10
mÐQRP =
360
mÐA =
1000
4)
3)
K
X
W
(11 + 3x)0
(–2x + 21)0
(19 + x)0
L
M
(5x + 2)0
(–71 – 3x)0
(–x – 2)0
U
X
V
x=
–47
x=
28
mÐU =
700
mÐXLM =
1420
B) Solve for x in each triangle and find the measure of the indicated angles.
5)
6)
E
X
(x + 37)0
T
(7x + 55)0
(–2 + 3x)0
(x – 1)0
F
G
R
X
(7 + 9x)0
(2x)0
x=
38
mÐFGE =
680
; mÐF =
370
mÐXTR =
1390
; mÐR =
1150
mÐEGX =
1120
; mÐE =
750
mÐRTS =
410
; mÐS =
240
x=
Printable Worksheets @ www.mathworksheets4kids.com
12
S
Name :
Sheet 2
Triangle - Exterior Angles
A) Solve for in each triangle and find the measure of the indicated angle.
1)
2)
X
S
(31 + 9 )0
V
R
(4 + 1)0
(28 + 6 )0
(–9 + 7 )0
Q
( + 5)0
(10 + 59)0
U
W
X
=
=
mÐU =
mÐXQR =
4)
3)
X
D
F
(34 – 3 )0
(5 )0
(8 – 25)0
(55 – )0
B
C
X
(–2 + 4)0
(82 + )0
G
=
=
mÐBCD =
mÐH =
H
B) Solve for in each triangle and find the measure of the indicated angles.
5)
6)
N
L
(– + 91)0
(–2 – 15)0
( + 8)0
L
M
(9 )0
(–66 – 4 )0
X
(– – 11)0
J
K
X
=
=
mÐXJL =
; mÐK =
mÐLMX =
; mÐN =
mÐLJK =
; mÐL =
mÐNML =
; mÐL =
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 2
Triangle - Exterior Angles
A) Solve for in each triangle and find the measure of the indicated angle.
1)
2)
X
S
(31 + 9 )0
V
R
(4 + 1)0
(28 + 6 )0
(–9 + 7 )0
Q
( + 5)0
(10 + 59)0
U
W
X
=
16
=
mÐU =
210
mÐXQR =
9
1490
4)
3)
X
D
F
(34 – 3 )0
(5 )0
(8 – 25)0
(55 – )0
B
C
X
(–2 + 4)0
(82 + )0
=
20
mÐBCD =
450
G
=
–26
mÐH =
560
H
B) Solve for in each triangle and find the measure of the indicated angles.
5)
6)
N
L
(– + 91)0
(–2 – 15)0
( + 8)0
L
M
(9 )0
(–66 – 4 )0
X
(– – 11)0
J
K
=
X
–40
=
11
mÐXJL =
940
; mÐK =
290
mÐLMX =
990
; mÐN =
800
mÐLJK =
860
; mÐL =
650
mÐNML =
810
; mÐL =
190
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 3
Triangle - Exterior Angles
A) Solve for x in each triangle and find the measure of the indicated angle.
1)
2)
X
(3 + 8x)0
E
L
D
X
(–2 + 3x)0
(36 + 10x)0
(9x + 20)0
M
(6x)0
(4x – 29)0
C
N
x=
x=
mÐMLX =
mÐE =
4)
3)
X
X
(–7 + 5x)0
(3x – 11)0
(x + 24)0
P
W
R
Q
U
(–x + 11)0
x=
x=
mÐP =
mÐUWV =
(–60 – 5x)0
(3 – 2x)0
V
B) Solve for x in each triangle and find the measure of the indicated angles.
5)
6)
A
(2 + 3x)0
(2x – 57)0
F
C
(61 – x)0
(–15 + 4x)0
B
G
X
x=
(9x – 9)0
(6x – 26)0
E
x=
mÐABX =
; mÐA =
mÐFEX =
; mÐG =
mÐABC =
; mÐC =
mÐGEF =
; mÐF =
Printable Worksheets @ www.mathworksheets4kids.com
X
Name :
Answer key
Sheet 3
Triangle - Exterior Angles
A) Solve for x in each triangle and find the measure of the indicated angle.
1)
2)
X
(3 + 8x)0
E
L
D
X
(–2 + 3x)0
(36 + 10x)0
(9x + 20)0
M
(6x)0
(4x – 29)0
C
N
x=
16
x=
9
mÐMLX =
1310
mÐE =
250
4)
3)
X
X
(–7 + 5x)0
(3x – 11)0
(x + 24)0
P
W
R
Q
U
(–x + 11)0
(3 – 2x)0
x=
20
x=
–37
mÐP =
440
mÐUWV =
550
(–60 – 5x)0
V
B) Solve for x in each triangle and find the measure of the indicated angles.
5)
6)
A
(2 + 3x)0
(2x – 57)0
F
C
(61 – x)0
(–15 + 4x)0
B
G
X
x=
40
(9x – 9)0
(6x – 26)0
E
x=
11
X
mÐABX =
1450
; mÐA =
1220
mÐFEX =
900
; mÐG =
400
mÐABC =
350
; mÐC =
230
mÐGEF =
900
; mÐF =
500
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 1
Triangle - Angles
1) In the figure, DABD is an isosceles triangle with AB = AD. Find mÐACB.
A
440
D
B
2) In the figure, KLMN is a square. Determine mÐMKJ.
290
C
L
K
M
N
490
J
3) Triangle OPQ and triangle ORS are acute triangles. What is mÐP?
Q
R
670
630
O
640
S
P
4) If DEGH is an isosceles triangle with EG = EH, determine mÐFGH and mÐEHG.
G
F
600
H
300
460
E
5) DRSU is an equilateral triangle. What is mÐQTP and mÐTOU?
R
Q
550
O
S
Printable Worksheets @ www.mathworksheets4kids.com
T
U
P
Name :
Answer key
Sheet 1
Triangle - Angles
1) In the figure, DABD is an isosceles triangle with AB = AD. Find mÐACB.
A
440
D
B
390
2) In the figure, KLMN is a square. Determine mÐMKJ.
290
C
L
K
M
N
490
860
J
3) Triangle OPQ and triangle ORS are acute triangles. What is mÐP?
Q
R
670
630
O
640
600
S
P
4) If DEGH is an isosceles triangle with EG = EH, determine mÐFGH and mÐEHG.
G
F
600
H
300
460
1570 ; 670
E
5) DRSU is an equilateral triangle. What is mÐQTP and mÐTOU?
R
Q
550
O
S
350 ; 850
Printable Worksheets @ www.mathworksheets4kids.com
T
U
P
Name :
Sheet 2
Triangle - Angles
1) If DCED is an equilateral triangle, determine mÐAED.
C
E
B
1200
190
A
D
2) DJKM is an isosceles triangle. Find mÐLMK, if mÐLMJ = 900.
L
K
860
J
M
B
3) If DABC is a right triangle, determine mÐB.
250
320
C
D
A
4) DEFG is an equilateral triangle. If EH = HF, find mÐHEF and mÐGFH.
G
H
1040
E
5) If DVYZ and DXYW are right triangles, then find mÐVYZ and mÐZYX.
F
Y
440
W
440
Z
Printable Worksheets @ www.mathworksheets4kids.com
V
X
Name :
Answer key
Sheet 2
Triangle - Angles
1) If DCED is an equilateral triangle, determine mÐAED.
C
E
B
1200
190
A
D
790
2) DJKM is an isosceles triangle. Find mÐLMK, if mÐLMJ = 900.
L
K
860
J
M
430
B
3) If DABC is a right triangle, determine mÐB.
250
320
C
D
A
330
4) DEFG is an equilateral triangle. If EH = HF, find mÐHEF and mÐGFH.
G
H
1040
E
380 ; 220
5) If DVYZ and DXYW are right triangles, then find mÐVYZ and mÐZYX.
F
Y
440
W
440
Z
460 ; 920
Printable Worksheets @ www.mathworksheets4kids.com
V
X
Name :
Sheet 3
Triangle - Angles
1) In the figure, DDEF and DHGF are right triangles. Find mÐDFH.
F
G
E
230
290
H
D
2) DXYZ and DXWZ are isosceles triangles. Determine mÐYZW, if mÐWXY = 900.
Y
Z
X
W
3) DKLM is an equilateral triangle. Find mÐKOL.
L
P
O
M
N
K
4) DOPQ and DORS are isosceles triangles with OP = PQ and OR = OS. Find mÐOPQ and mÐROQ.
R
660
O
S
Q
P
5) In the figure, triangle TVS is a right triangle. Determine mÐUTS and mÐVST.
T
240
400
U
Printable Worksheets @ www.mathworksheets4kids.com
V
S
Name :
Answer key
Sheet 3
Triangle - Angles
1) In the figure, DDEF and DHGF are right triangles. Find mÐDFH.
F
G
E
230
290
H
520
D
2) DXYZ and DXWZ are isosceles triangles. Determine mÐYZW, if mÐWXY = 900.
Y
Z
X
W
1350
3) DKLM is an equilateral triangle. Find mÐKOL.
L
P
O
M
N
K
1200
4) DOPQ and DORS are isosceles triangles with OP = PQ and OR = OS. Find mÐOPQ and mÐROQ.
R
660
O
S
Q
P
840 ; 1320
5) In the figure, triangle TVS is a right triangle. Determine mÐUTS and mÐVST.
T
240
400
740 ; 660
Printable Worksheets @ www.mathworksheets4kids.com
U
V
S
Name :
Sheet 1
Identify the right triangles
Apply the Pythagorean theorem. Find whether each triangle has a right angle.
1)
2)
A
E
V
L
M 9 ft
t
in
W
4)
f
15
11
9 in
7 in
G
5 yd
12 ft
4 ft
U
F
C
3 ft
6 yd
t
3)
8y
d
5f
B
N
5) In triangle XYZ, the sides XY, YZ and XZ measure 12 ft, 16 ft and 20 ft respectively.
Prove that XYZ is a right triangle.
6) In triangle PQR, the sides PQ, QR and PR measure 15 in, 20 in and 25 in respectively.
Prove that PQR is a right triangle.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer Key
Sheet 1
Identify the right triangles
Apply the Pythagorean theorem. Find whether each triangle has a right angle.
1)
2)
A
E
F
C
right triangle
U
7 in
V
not a right triangle
4)
L
M 9 ft
t
in
W
not a right triangle
f
15
11
9 in
3)
G
5 yd
12 ft
4 ft
3 ft
6 yd
t
8y
d
5f
B
N
right triangle
5) In triangle XYZ, the sides XY, YZ and XZ measure 12 ft, 16 ft and 20 ft respectively.
Prove that XYZ is a right triangle.
XY2 = 144 ft, YZ2 = 256 ft, XZ2 = 400 ft
XY2 + YZ2 = XZ2
XYZ is a right triangle.
6) In triangle PQR, the sides PQ, QR and PR measure 15 in, 20 in and 25 in respectively.
Prove that PQR is a right triangle.
PQ2 = 225 in, QR2 = 400 in, PR2 = 625 in
PQ2 + QR2 = PR2
PQR is a right triangle.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 2
Identify the right triangles
Apply the Pythagorean theorem. Find whether each triangle has a right angle.
1)
2)
S
J
L
T
3)
4 yd
d
7y
13
5 ft
ft
12 ft
X
Q
R
K
8 in
4)
P
in
6 in
10
Y
6 yd
3 yd
6y
d
5 yd
R
Z
5) In triangle ABC, the sides AB, BC and AC measure 24 yd, 10 yd and 26 yd respectively.
Prove that ABC is a right triangle.
6) In triangle EFG, the sides EF, FG and EG measure 15 ft, 17 ft and 8 ft respectively.
Prove that EFG is a right triangle.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer Key
Sheet 2
Identify the right triangles
Apply the Pythagorean theorem. Find whether each triangle has a right angle.
1)
2)
S
J
L
T
not a right triangle
3)
right triangle
4 yd
d
7y
13
5 ft
ft
12 ft
X
Q
R
right triangle
K
8 in
4)
P
in
6 in
10
Y
6 yd
3 yd
6y
d
5 yd
R
Z
not a right triangle
5) In triangle ABC, the sides AB, BC and AC measure 24 yd, 10 yd and 26 yd respectively.
Prove that ABC is a right triangle.
AB2 = 576 yd, BC2 = 100 yd, AC2 = 676 yd
AB2 + BC2 = AC2
ABC is a right triangle.
6) In triangle EFG, the sides EF, FG and EG measure 15 ft, 17 ft and 8 ft respectively.
Prove that EFG is a right triangle.
EF2 = 225 ft, FG2 = 289 ft, EG2 = 64 ft
EF2 + EG2 = FG2
EFG is a right triangle.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 3
Identify the right triangles
Apply the Pythagorean theorem. Find whether each triangle has a right angle.
1)
2)
G
8 in
15 in
3)
A
18 ft
ft
F
in
30
17
24 ft
C
E
B
4)
J
10 yd
7 yd
L
n
Q
i
17
12 in
yd
12
K
P
13 in
R
5) In triangle UVW, the sides UV, VW and UW measure 10 yd, 8 yd and 6 yd respectively.
Prove that UVW is a right triangle.
6) In triangle LMN, the sides LM, MN and LN measure 9 in, 15 in and 12 in respectively.
Prove that LMN is a right triangle.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer Key
Sheet 3
Identify the right triangles
Apply the Pythagorean theorem. Find whether each triangle has a right angle.
1)
2)
G
8 in
15 in
right triangle
3)
A
18 ft
ft
F
in
30
17
24 ft
C
E
B
right triangle
4)
J
10 yd
7 yd
L
not a right triangle
n
Q
i
17
12 in
yd
12
K
P
13 in
R
not a right triangle
5) In triangle UVW, the sides UV, VW and UW measure 10 yd, 8 yd and 6 yd respectively.
Prove that UVW is a right triangle.
UV2 = 100 yd, VW2 = 64 yd, UW2 = 36 yd
VW2 + UW2 = UV2
UVW is a right triangle.
6) In triangle LMN, the sides LM, MN and LN measure 9 in, 15 in and 12 in respectively.
Prove that LMN is a right triangle.
LM2 = 81 in, MN2 = 225 in, LN2 = 144 in
LM2 + LN2 = MN2
LMN is a right triangle.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 1
Pythagorean Triples
Determine whether each set of numbers form a Pythagorean triple.
1) 12, 20, 16
2) 1, 7, 5
3) 8, 15, 17
4) 5, 11, 9
5) 29, 20, 21
6)
7) 24, 18, 30
8) 3, 1, 5
9) 6, 10, 8
3, 14 , 10
10) Determine whether the sides of the triangle form a Pythagorean triple.
A
Printable Worksheets @ www.mathworksheets4kids.com
2 ft
6 ft
11
f
t
C
B
Name :
Answer Key
Sheet 1
Pythagorean Triples
Determine whether each set of numbers form a Pythagorean triple.
1) 12, 20, 16
Pythagorean triple
4) 5, 11, 9
Not a Pythagorean triple
7) 24, 18, 30
Pythagorean triple
2) 1, 7, 5
3) 8, 15, 17
Pythagorean triple
Not a Pythagorean triple
5) 29, 20, 21
6)
Not a Pythagorean triple
Pythagorean triple
8) 3, 1, 5
3, 14 , 10
9) 6, 10, 8
Pythagorean triple
Not a Pythagorean triple
10) Determine whether the sides of the triangle form a Pythagorean triple.
6 ft
11
f
t
C
Not a Pythagorean triple
A
Printable Worksheets @ www.mathworksheets4kids.com
2 ft
B
Name :
Sheet 2
Pythagorean Triples
Determine whether each set of numbers form a Pythagorean triple.
1) 13, 8, 14
2) 24, 32, 40
3)
4) 20, 15, 25
5) 1, 10, 4
6) 15, 9, 12
7) 12, 6, 7
8) 35, 21, 28
9) 5, 4, 11
8, 5 , 12
10) Determine whether the sides of the triangle form a Pythagorean triple.
R
12 in
20
P
Printable Worksheets @ www.mathworksheets4kids.com
in
16 in
Q
Name :
Answer Key
Sheet 2
Pythagorean Triples
Determine whether each set of numbers form a Pythagorean triple.
1) 13, 8, 14
Not a Pythagorean triple
4) 20, 15, 25
Pythagorean triple
7) 12, 6, 7
Not a Pythagorean triple
2) 24, 32, 40
3)
Not a Pythagorean triple
Pythagorean triple
5) 1, 10, 4
6) 15, 9, 12
Pythagorean triple
Not a Pythagorean triple
8) 35, 21, 28
8, 5 , 12
9) 5, 4, 11
Not a Pythagorean triple
Pythagorean triple
10) Determine whether the sides of the triangle form a Pythagorean triple.
R
12 in
20
in
Pythagorean triple
P
Printable Worksheets @ www.mathworksheets4kids.com
16 in
Q
Name :
Sheet 3
Pythagorean Triples
Determine whether each set of numbers form a Pythagorean triple.
1) 36, 27, 45
2) 13, 12, 5
4) 9, 8, 12
5)
7)
3, 7 , 1
15, 5, 14
8) 3, 4, 5
3)
6 , 7, 1
6) 7, 24, 25
9)
6, 2, 13
10) Determine whether the sides of the triangle form a Pythagorean triple.
5 ft
32
ft
U
V 3 ft W
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Name :
Answer Key
Sheet 3
Pythagorean Triples
Determine whether each set of numbers form a Pythagorean triple.
1) 36, 27, 45
2) 13, 12, 5
Pythagorean triple
4) 9, 8, 12
Not a Pythagorean triple
7)
3, 7 , 1
Not a Pythagorean triple
3)
Not a Pythagorean triple
Pythagorean triple
5)
15, 5, 14
6) 7, 24, 25
Pythagorean triple
Not a Pythagorean triple
8) 3, 4, 5
Pythagorean triple
6 , 7, 1
9)
6, 2, 13
Not a Pythagorean triple
10) Determine whether the sides of the triangle form a Pythagorean triple.
5 ft
32
ft
U
Not a Pythagorean triple
V 3 ft W
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 1
Pythagorean Theorem
Determine the missing length in each right triangle using the Pythagorean theorem. Round
the answer to the nearest tenth.
2)
3)
?
U
?
Q 2 in R
C
BC =
V
W
PQ =
4)
6 ft
t
yd
15
B
?
P
9f
12 yd
A
5 in
1)
UW =
5)
6)
E
J
F
?
?
K
17 yd
ft
13 yd
10
3 in
?
8 ft
X
Z
14 in
Y
G
XZ =
EF =
7)
JL =
8)
9)
E
S
N
?
?
M
T 1 yd U
MN =
ST =
Printable Worksheets @ www.mathworksheets4kids.com
C
CE =
?
11 in
16 ft
4 yd
8 ft
L
L
7 in
D
Name :
Answer Key
Sheet 1
Pythagorean Theorem
Determine the missing length in each right triangle using the Pythagorean theorem. Round
the answer to the nearest tenth.
2)
3)
?
?
Q 2 in R
C
9 yd
BC =
U
4)
V
W
29 » 5.4 in
PQ =
6 ft
t
yd
15
B
?
P
9f
12 yd
A
5 in
1)
5)
UW =
45 » 6.7 ft
6)
E
J
F
?
?
K
17 yd
ft
13 yd
10
3 in
?
8 ft
X
Z
14 in
Y
G
XZ = 205 » 14.3 in
7)
6 ft
EF =
8)
JL =
458 » 21.4 yd
9)
E
S
N
?
?
M
MN = 320 » 17.9 ft
ST =
?
11 in
16 ft
4 yd
8 ft
L
L
D
T 1 yd U
C
7 in
15 » 3.9 yd
CE =
170 » 13 in
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 2
Pythagorean Theorem
Determine the missing length in each right triangle using the Pythagorean theorem. Round
the answer to the nearest tenth.
1)
2)
7 yd T
?
?
5 in
14 yd
K
10
G
L
3 ft
S
3)
in
J
E
KL =
FG =
U
SU =
4)
5)
N
F
15 yd
M
T
?
25
yd
?
2 in
6 in
9 ft
?
4 ft
6)
B
R
?
S
A 4 ft
L
AB =
NL =
8)
7)
9)
Z
U
?
8y
d
R
3 yd
?
13 ft
P
12 in
RT =
C
?
W
16 in
Q
Y
YZ =
11 ft
X
PR =
Printable Worksheets @ www.mathworksheets4kids.com
UV =
V
Name :
Answer Key
Sheet 2
Pythagorean Theorem
Determine the missing length in each right triangle using the Pythagorean theorem. Round
the answer to the nearest tenth.
1)
2)
7 yd T
?
?
5 in
14 yd
K
10
G
L
3 ft
S
3)
in
J
E
U
245 » 15.7 yd
4)
KL =
75 » 8.7 in
5)
FG =
N
5 ft
15 yd
M
T
?
?
25
2 in
6 in
9 ft
?
F
6)
B
R
4 ft
yd
SU =
?
S
A 4 ft
32 » 5.7 in
7)
AB =
L
97 » 9.8 ft
8)
20 yd
9)
Z
U
?
8y
d
R
3 yd
13 ft
P
?
NL =
12 in
RT =
C
?
W
16 in
Q
Y
YZ =
11 ft
X
290 » 17 ft
PR =
55 » 7.4 yd
Printable Worksheets @ www.mathworksheets4kids.com
UV =
20 in
V
Name :
Sheet 3
Pythagorean Theorem
Determine the missing length in each right triangle using the Pythagorean theorem. Round
the answer to the nearest tenth.
1)
2)
3)
L
yd
7 ft
15 in
X
26
11
ft
?
Z
2 in
U
?
Y
V
W
?
M 10 yd
N
LM =
VW =
4)
XY =
5)
6)
3 in
F
G
T
S
8 yd
5 ft
?
Q
U
1 ft
?
17 in
6 yd
P
R
?
E
TU =
EG =
7)
QR =
8)
K
D
DE =
Printable Worksheets @ www.mathworksheets4kids.com
?
T
4 yd S
10 yd
ft
12 ft
in
14 in
16
L
JK =
C
13
?
J
9)
?
R
E
RS =
Name :
Answer Key
Sheet 3
Pythagorean Theorem
Determine the missing length in each right triangle using the Pythagorean theorem. Round
the answer to the nearest tenth.
1)
2)
3)
L
yd
7 ft
15 in
X
26
11
ft
?
Z
2 in
U
?
Y
V
?
W
VW =
72 » 8.5 ft
M 10 yd
4)
N
XY = 229 » 15.1 in
24 yd
LM =
5)
6)
3 in
F
G
T
S
8 yd
5 ft
?
U
1 ft
?
17 in
6 yd
P
Q
?
R
QR =
24 » 4.9 ft
E
EG = 298 » 17.3 in
10 yd
7)
8)
K
60 » 7.7 in
12 ft
in
14 in
16
L
JK =
ft
C
13
?
J
9)
D
DE =
Printable Worksheets @ www.mathworksheets4kids.com
T
4 yd S
10 yd
TU =
?
R
E
?
5 ft
RS =
116 » 10.8 yd
Name :
Sheet 1
Diagonals of a Rectangle
A) Find the length of the diagonal of each rectangle. Round your answer to the nearest tenth.
1)
length = 33 in, width = 8 in
2)
diagonal =
diagonal =
3)
width = 16 ft, length = 21.6 ft
width = 48 yd, length = 90 yd
4)
diagonal =
length = 6 in, width = 5 in
diagonal =
B) Find the length of the diagonal of each rectangle. Round your answer to the nearest tenth.
6)
4.4 ft
3.5 ft
7 yd
5)
24 yd
diagonal =
diagonal =
8)
7)
25 ft
15 in
47 ft
10 in
diagonal =
diagonal =
9) The length and width of a rectangle are 73.5 yards and 53.7 yards respectively. What is the length
of the diagonal?
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 1
Diagonals of a Rectangle
A) Find the length of the diagonal of each rectangle. Round your answer to the nearest tenth.
1)
length = 33 in, width = 8 in
34 in
diagonal =
3)
width = 48 yd, length = 90 yd
diagonal =
2)
width = 16 ft, length = 21.6 ft
diagonal =
4)
102 yd
26.9 ft
length = 6 in, width = 5 in
diagonal =
7.8 in
B) Find the length of the diagonal of each rectangle. Round your answer to the nearest tenth.
6)
4.4 ft
3.5 ft
7 yd
5)
24 yd
diagonal =
5.6 ft
diagonal =
25 yd
8)
7)
25 ft
15 in
47 ft
10 in
diagonal =
18 in
diagonal =
53.2 ft
9) The length and width of a rectangle are 73.5 yards and 53.7 yards respectively. What is the length
of the diagonal?
91 yards
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 2
Diagonals of a Rectangle
A) Find the length of the diagonal of each rectangle. Round your answer to the nearest tenth.
1)
width = 25.6 ft, length = 65.8 ft
2)
diagonal =
diagonal =
3)
length = 12 yd, width = 9 yd
length = 7 in, width = 4 in
4)
diagonal =
width = 8.9 ft, length = 40 ft
diagonal =
B) Find the length of the diagonal of each rectangle. Round your answer to the nearest tenth.
6)
83 in
31.8 in
27 yd
5)
36 yd
diagonal =
diagonal =
7)
8)
6 ft
9 yd
3.1 ft
8 yd
diagonal =
diagonal =
9) Find the length of the diagonal of a rectangle whose length and width are 52 inches and 45 inches
respectively.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Diagonals of a Rectangle
A) Find the length of the diagonal of each rectangle. Round your answer to the nearest tenth.
1)
width = 25.6 ft, length = 65.8 ft
diagonal =
3)
70.6 ft
length = 7 in, width = 4 in
diagonal =
2)
length = 12 yd, width = 9 yd
diagonal =
4)
8.1 in
15 yd
width = 8.9 ft, length = 40 ft
diagonal =
41 ft
B) Find the length of the diagonal of each rectangle. Round your answer to the nearest tenth.
6)
83 in
31.8 in
27 yd
5)
36 yd
diagonal =
45 yd
7)
diagonal =
88.9 in
8)
6 ft
9 yd
3.1 ft
8 yd
diagonal =
6.8 ft
diagonal =
12 yd
9) Find the length of the diagonal of a rectangle whose length and width are 52 inches and 45 inches
respectively.
68.8 inches
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Diagonals of a Rectangle
Sheet 3
A) Find the length of the diagonal of each rectangle. Round your answer to the nearest tenth.
1)
2)
length = 5 yd, width = 2 yd
diagonal =
diagonal =
3)
length = 9.2 in, width = 3 in
4)
width = 18 ft, length = 38 ft
diagonal =
width = 68 yd, length = 82.6 yd
diagonal =
B) Find the length of the diagonal of each rectangle. Round your answer to the nearest tenth.
5)
6)
6 in
28.7 ft
35 in
8.9 ft
diagonal =
diagonal =
8)
9 yd
25 in
7)
49 in
50 yd
diagonal =
diagonal =
9) A rectangle has a length of 18.4 feet and a width of 12 feet. Determine the length of the diagonal.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 3
Diagonals of a Rectangle
A) Find the length of the diagonal of each rectangle. Round your answer to the nearest tenth.
1)
diagonal =
3)
2)
length = 5 yd, width = 2 yd
5.4 yd
diagonal =
4)
width = 18 ft, length = 38 ft
diagonal =
length = 9.2 in, width = 3 in
42 ft
9.7 in
width = 68 yd, length = 82.6 yd
diagonal =
107 yd
B) Find the length of the diagonal of each rectangle. Round your answer to the nearest tenth.
5)
6)
6 in
28.7 ft
35 in
8.9 ft
diagonal =
35.5 in
30 ft
8)
9 yd
25 in
7)
diagonal =
49 in
50 yd
diagonal =
50.8 yd
diagonal =
55 in
9) A rectangle has a length of 18.4 feet and a width of 12 feet. Determine the length of the diagonal.
22 feet
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Name :
Level 1: S1
Pythagorean Theorem
Solve the word problems. Round the answer to the nearest tenth.
1)
Mark is on his way home from work. He drives 35 miles due North and then 42 miles due
West. Find the shortest distance he can cover to reach home early.
N
35 mi
42 mi
?
W
E
S
2)
Mr. Richard owns an orchard that has a rectangular fence. The orchard is 36 yards long and
18 yards wide. If he walks across the diagonal length of the orchard, how much distance
would he cover?
?
18
36
yd
yd
Joey made a sandwich that was 2 inches long and 4 inches high. If he cuts the sandwich
in half as shown in the figure, what would be the diagonal length of the sandwich?
4 in
?
3)
2 in
A 15 feet tree casts a shadow that is 8 feet long. What is the distance from the tip of the
tree to the tip of its shadow?
15 ft
4)
?
8 ft
Rachel bought a rug for her apartment. The rug is 11 feet long and 9 feet wide. Find the
diagonal length of the rug.
?
11 ft
Printable Worksheets @ www.mathworksheets4kids.com
9 ft
5)
Name :
Answer Key
Level 1: S1
Pythagorean Theorem
Solve the word problems. Round the answer to the nearest tenth.
1)
Mark is on his way home from work. He drives 35 miles due North and then 42 miles due
West. Find the shortest distance he can cover to reach home early.
N
35 mi
42 mi
?
W
E
54.7 miles
2)
S
Mr. Richard owns an orchard that has a rectangular fence. The orchard is 36 yards long and
18 yards wide. If he walks across the diagonal length of the orchard, how much distance
would he cover?
?
36
18
40.2 yards
yd
yd
Joey made a sandwich that was 2 inches long and 4 inches high. If he cuts the sandwich
in half as shown in the figure, what would be the diagonal length of the sandwich?
4 in
?
3)
4.5 inches
A 15 feet tree casts a shadow that is 8 feet long. What is the distance from the tip of the
tree to the tip of its shadow?
15 ft
4)
2 in
?
17 feet
8 ft
Rachel bought a rug for her apartment. The rug is 11 feet long and 9 feet wide. Find the
diagonal length of the rug.
?
14.2 feet
Printable Worksheets @ www.mathworksheets4kids.com
11 ft
9 ft
5)
Name :
Level 1: S2
Pythagorean Theorem
Solve the word problems. Round the answer to the nearest tenth.
1)
There are two buildings beside each other that are 47 feet and 31 feet high. The buildings
are 12 feet apart. What is the distance between the rooftops of the buildings?
31 ft
47 ft
?
12 ft
2)
Joshua won a laptop in a school raffle. The laptop screen measures 15 inches in length and
11 inches in width. Find the diagonal length of the laptop screen.
11 in
15 in
?
Carol pitches a tent at a Girl Scout camp. She ties a rope from the tip of the pole to the peg
nailed into the ground, as shown. The pole is 8 feet high and the distance between the base
of the pole and the peg is 7 feet. Determine the length of the rope.
?
8 ft
3)
7 ft
4)
Ross and Monica are playing on a seesaw. Monica’s seat is grounded. The height of the
fulcrum is 2 feet. The distance from grounded end of the seesaw to the fulcrum is 4 feet.
What is the length of the seesaw?
2 ft
?
4 ft
The roof rafter of a house has been raised to a height of 13 yards at the ridge. Half the
length of the run measures 9 yards. Find the length of the rafter.
?
9 yd
Printable Worksheets @ www.mathworksheets4kids.com
13 yd
5)
Name :
Answer Key
Level 1: S2
Pythagorean Theorem
Solve the word problems. Round the answer to the nearest tenth.
1)
There are two buildings beside each other that are 47 feet and 31 feet high. The buildings
are 12 feet apart. What is the distance between the rooftops of the buildings?
31 ft
47 ft
?
20 feet
12 ft
2)
Joshua won a laptop in a school raffle. The laptop screen measures 15 inches in length and
11 inches in width. Find the diagonal length of the laptop screen.
11 in
15 in
?
18.6 inches
Carol pitches a tent at a Girl Scout camp. She ties a rope from the tip of the pole to the peg
nailed into the ground, as shown. The pole is 8 feet high and the distance between the base
of the pole and the peg is 7 feet. Determine the length of the rope.
?
8 ft
3)
10.6 feet
7 ft
4)
Ross and Monica are playing on a seesaw. Monica’s seat is grounded. The height of the
fulcrum is 2 feet. The distance from grounded end of the seesaw to the fulcrum is 4 feet.
What is the length of the seesaw?
2 ft
?
9 feet
4 ft
The roof rafter of a house has been raised to a height of 13 yards at the ridge. Half the
length of the run measures 9 yards. Find the length of the rafter.
?
9 yd
15.8 yards
Printable Worksheets @ www.mathworksheets4kids.com
13 yd
5)
Name :
Pythagorean Theorem
Level 1: S3
Solve the word problems. Round the answer to the nearest tenth.
John wins a tripod projector screen in a lucky draw. The screen is 6 feet long and 4 feet
6 ft
wide. What is the diagonal length of the projector screen?
4 ft
1)
?
The mast of a sailboat is 12 feet high. A sturdy rope that supports the mast to the deck is
5 feet away from the base of the mast. Determine the length of the rope.
?
12 ft
2)
5 ft
Ben props a ladder against the wall of a building. The distance between the base of the
building and the foot of the ladder is 11 feet. The top of the ladder touches the wall at a
height of 27 feet. What is the length of the ladder?
27 ft
3)
?
11 ft
Sandra builds a dog house in the shape of a tent. The ridge is 98 inches high and the base
of the tent is 70 inches wide. Find the slant height of the tent.
?
98 in
4)
70 in
5)
Anne was given a sheet of paper during her math class. She was asked to fold the paper,
so as to get the adjacent sides to meet, as shown in the figure. The paper was 15 inches
long and 15 inches wide. How much would the diagonal edge of the paper measure?
?
Printable Worksheets @ www.mathworksheets4kids.com
15 in
15 in
Name :
Answer Key
Pythagorean Theorem
Level 1: S3
Solve the word problems. Round the answer to the nearest tenth.
John wins a tripod projector screen in a lucky draw. The screen is 6 feet long and 4 feet
6 ft
wide. What is the diagonal length of the projector screen?
4 ft
1)
?
7.2 feet
The mast of a sailboat is 12 feet high. A sturdy rope that supports the mast to the deck is
5 feet away from the base of the mast. Determine the length of the rope.
?
12 ft
2)
5 ft
13 feet
Ben props a ladder against the wall of a building. The distance between the base of the
building and the foot of the ladder is 11 feet. The top of the ladder touches the wall at a
height of 27 feet. What is the length of the ladder?
27 ft
3)
?
29.2 feet
11 ft
Sandra builds a dog house in the shape of a tent. The ridge is 98 inches high and the base
of the tent is 70 inches wide. Find the slant height of the tent.
?
98 in
4)
104.1 inches
70 in
5)
Anne was given a sheet of paper during her math class. She was asked to fold the paper,
so as to get the adjacent sides to meet, as shown in the figure. The paper was 15 inches
long and 15 inches wide. How much would the diagonal edge of the paper measure?
?
21.2 inches
Printable Worksheets @ www.mathworksheets4kids.com
15 in
15 in
Name :
Sheet 1
Area of a Square
A)
Find the area of each square. Round your answer to the nearest hundredth.
2)
18
.7
15
ft
1)
Area =
yd
Area =
3)
The diagonal of a square measures 24 inches. Find the area of the square.
4)
The diagonal of a square measures 31.3 feet. Determine the area of the square.
B)
Find the length of the diagonal of each square. Round your answer to the nearest tenth.
5)
6)
Area = 392 yd2
Diagonal =
Area = 474.3 in2
Diagonal =
7)
The area of a square is 338 square feet. Determine the length of the diagonal.
8)
A square has an area of 111.01 square yards. Find the length of the diagonal.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 1
Area of a Square
A)
Find the area of each square. Round your answer to the nearest hundredth.
2)
1)
15
ft
18
.7
112.5 ft2
Area =
3)
yd
174.85 yd2
Area =
The diagonal of a square measures 24 inches. Find the area of the square.
288 square inches
4)
The diagonal of a square measures 31.3 feet. Determine the area of the square.
489.85 square feet
B)
Find the length of the diagonal of each square. Round your answer to the nearest tenth.
5)
6)
Area = 392 yd2
Diagonal =
7)
28 yd
Area = 474.3 in2
Diagonal =
30.8 in
The area of a square is 338 square feet. Determine the length of the diagonal.
26 feet
8)
A square has an area of 111.01 square yards. Find the length of the diagonal.
14.9 yards
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 2
Area of a Square
Find the area of each square. Round your answer to the nearest hundredth.
1)
2)
yd
ft
9
17
A)
Area =
Area =
3)
The diagonal of a square measures 21.3 feet. Determine the area of the square.
4)
What is the area of the square, if the length of the diagonal is 34 yards?
B)
Find the length of the diagonal of each square. Round your answer to the nearest tenth.
5)
6)
Area = 134.48 ft2
Diagonal =
Area = 200 in2
Diagonal =
7)
A square has an area of 677.12 square yards. Find the length of the diagonal.
8)
If the area of a square is 396.92 square feet, what is the length of the diagonal?
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 2
Area of a Square
A)
Find the area of each square. Round your answer to the nearest hundredth.
1)
2)
ft
40.5 yd2
Area =
3)
yd
17
9
144.5 ft2
Area =
The diagonal of a square measures 21.3 feet. Determine the area of the square.
226.85 square feet
4)
What is the area of the square, if the length of the diagonal is 34 yards?
578 square yards
B)
Find the length of the diagonal of each square. Round your answer to the nearest tenth.
5)
6)
Area = 134.48 ft2
Diagonal =
7)
16.4 ft
Area = 200 in2
Diagonal =
20 in
A square has an area of 677.12 square yards. Find the length of the diagonal.
36.8 yards
8)
If the area of a square is 396.92 square feet, what is the length of the diagonal?
28.2 feet
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 3
Area of a Square
A)
Find the area of each square. Round your answer to the nearest hundredth.
1)
2)
.2
36
22
in
Area =
yd
Area =
3)
What is the area of the square, if the length of the diagonal is 29.1 feet?
4)
The diagonal of a square measures 16 inches. Find the area of the square.
B)
Find the length of the diagonal of each square. Round your answer to the nearest tenth.
5)
6)
Area = 760 yd2
Diagonal =
Area = 117.08 ft2
Diagonal =
7)
If the area of a square is 28.9 square inches, what is the length of the diagonal?
8)
The area of a square is 312 square yards. Determine the length of the diagonal.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 3
Area of a Square
A)
Find the area of each square. Round your answer to the nearest hundredth.
1)
2)
.2
36
655.22 in2
Area =
3)
22
in
yd
242 yd2
Area =
What is the area of the square, if the length of the diagonal is 29.1 feet?
423.41 square feet
4)
The diagonal of a square measures 16 inches. Find the area of the square.
128 square inches
B)
Find the length of the diagonal of each square. Round your answer to the nearest tenth.
5)
6)
Area = 760 yd2
Diagonal =
7)
39 yd
Area = 117.08 ft2
Diagonal =
15.3 ft
If the area of a square is 28.9 square inches, what is the length of the diagonal?
7.6 inches
8)
The area of a square is 312 square yards. Determine the length of the diagonal.
25 yards
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 4
Area of a Square
A)
Find the area of each square. Round your answer to the nearest hundredth.
2)
yd
1)
10
19
Area =
in
Area =
3)
The diagonal of a square measures 13.5 feet. Find the area of the square.
4)
What is the area of the square, if the length of the diagonal is 17.3 yards?
B)
Find the length of the diagonal of each square. Round your answer to the nearest tenth.
5)
6)
Area = 512 yd2
Diagonal =
Area = 327.68 in2
Diagonal =
7)
The area of a square is 283.22 square feet. Determine the length of the diagonal.
8)
If the area of a square is 637.25 square inches, what is the length of the diagonal?
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 4
Area of a Square
A)
Find the area of each square. Round your answer to the nearest hundredth.
2)
yd
1)
10
19
50 yd2
Area =
3)
in
180.5 in2
Area =
The diagonal of a square measures 13.5 feet. Find the area of the square.
91.13 square feet
4)
What is the area of the square, if the length of the diagonal is 17.3 yards?
149.65 square yards
B)
Find the length of the diagonal of each square. Round your answer to the nearest tenth.
5)
6)
Area = 512 yd2
Diagonal =
7)
32 yd
Area = 327.68 in2
Diagonal =
25.6 in
The area of a square is 283.22 square feet. Determine the length of the diagonal.
23.8 feet
8)
If the area of a square is 637.25 square inches, what is the length of the diagonal?
35.7 inches
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 5
Area of a Square
A)
Find the area of each square. Round your answer to the nearest hundredth.
1)
2)
7
.9
11
9.
in
ft
Area =
Area =
3)
The diagonal of a square measures 27 yards. Determine the area of the square.
4)
What is the area of the square, if the length of the diagonal is 29.6 inches?
B)
Find the length of the diagonal of each square. Round your answer to the nearest tenth.
5)
6)
Area = 557.78 ft2
Diagonal =
Area = 800 yd2
Diagonal =
7)
A square has an area of 75.65 square inches. Find the length of the diagonal.
8)
The area of a square is 648 square feet. Determine the length of the diagonal.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 5
Area of a Square
A)
Find the area of each square. Round your answer to the nearest hundredth.
1)
2)
in
ft
47.05 ft2
Area =
3)
7
.9
11
9.
70.81 in2
Area =
The diagonal of a square measures 27 yards. Determine the area of the square.
364.5 square yards
4)
What is the area of the square, if the length of the diagonal is 29.6 inches?
438.08 square inches
B)
Find the length of the diagonal of each square. Round your answer to the nearest tenth.
5)
6)
Area = 557.78 ft2
Diagonal =
7)
33.4 ft
Area = 800 yd2
Diagonal =
40 yd
A square has an area of 75.65 square inches. Find the length of the diagonal.
12.3 inches
8)
The area of a square is 648 square feet. Determine the length of the diagonal.
36 feet
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 1
Area of a Rectangle
Find the area of each rectangle for the given measurements. Round your answer to two decimal places.
1)
2)
25 f
t
20
in
12 in
A)
19 ft
Area =
3)
The diagonal of a rectangle measures 30 yards. What is the area of the rectangle, if the length is
24 yards?
4)
Find the area of the rectangle whose diagonal measures 14 feet and has a width of 7 feet.
Find the length of the diagonal of each rectangle for the given measurements. Round your answer to
the nearest tenth.
2)
24 in
1)
Area = 390.69 in2
Diagonal =
Area = 48 yd2
8 yd
B)
Area =
Diagonal =
3)
The area of a rectangle is 96 square feet. Find the length of the diagonal, if the width is 6 feet.
4)
The length of a rectangle is 31 inches. If the area of the rectangle is 626.17 square inches, find the
length of the diagonal.
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 1
Area of a Rectangle
Find the area of each rectangle for the given measurements. Round your answer to two decimal places.
1)
2)
25 f
t
20
in
12 in
A)
19 ft
308.71 ft2
Area =
3)
192 in2
Area =
The diagonal of a rectangle measures 30 yards. What is the area of the rectangle, if the length is
24 yards?
432 square yards
4)
Find the area of the rectangle whose diagonal measures 14 feet and has a width of 7 feet.
84.87 square feet
Find the length of the diagonal of each rectangle for the given measurements. Round your answer to
the nearest tenth.
2)
24 in
1)
Area = 390.69 in2
Diagonal =
3)
29 in
Area = 48 yd2
Diagonal =
8 yd
B)
10 yd
The area of a rectangle is 96 square feet. Find the length of the diagonal, if the width is 6 feet.
17.1 feet
4)
The length of a rectangle is 31 inches. If the area of the rectangle is 626.17 square inches, find the
length of the diagonal.
37 inches
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 2
Area of a Rectangle
Find the area of each rectangle for the given measurements. Round your answer to two decimal places.
2)
in
d
.3 y
21
17
Area =
B)
11.7 yd
5.9 in
1)
Area =
3)
Find the area of the rectangle whose diagonal measures 31 feet and has a length of 27 feet.
4)
The length of a rectangle is 23 inches. If the diagonal measures 24.5 inches, determine the area of
the rectangle.
Find the length of the diagonal of each rectangle for the given measurements. Round your answer to
the nearest tenth.
1)
2)
Area = 455.9 yd2
Area = 411.7 ft2
18.3 ft
A)
16.7 yd
Diagonal =
Diagonal =
3)
The length of a rectangle is 27 inches. If it has an area of 642.9 square inches, find the length of the
diagonal.
4)
The area of a rectangle is 624.4 square yards. Determine the length of the diagonal, if the rectangle
has a width of 21 yards.
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 2
Area of a Rectangle
A)
Find the area of each rectangle for the given measurements. Round your answer to two decimal places.
1)
2)
5.9 in
94.07 in2
Area =
3)
in
d
.3 y
21
17
11.7 yd
208.25 yd2
Area =
Find the area of the rectangle whose diagonal measures 31 feet and has a length of 27 feet.
411.25 square feet
4)
The length of a rectangle is 23 inches. If the diagonal measures 24.5 inches, determine the area of
the rectangle.
194.14 square inches
Find the length of the diagonal of each rectangle for the given measurements. Round your answer to
the nearest tenth.
1)
2)
Area = 455.9 yd2
Area = 411.7 ft2
18.3 ft
B)
16.7 yd
Diagonal =
3)
32 yd
Diagonal =
29 ft
The length of a rectangle is 27 inches. If it has an area of 642.9 square inches, find the length of the
diagonal.
36 inches
4)
The area of a rectangle is 624.4 square yards. Determine the length of the diagonal, if the rectangle
has a width of 21 yards.
36.4 yards
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 3
Area of a Rectangle
Find the area of each rectangle for the given measurements. Round your answer to two decimal places.
1)
2)
21
yd
29
ft
15 ft
A)
16 yd
Area =
3)
The diagonal of a rectangle measures 35 inches. What is the area of the rectangle, if the length is
30 inches?
4)
The width of a rectangle is 24 yards. If the diagonal measures 40 yards, determine the area of the
rectangle.
Find the length of the diagonal of each rectangle for the given measurements. Round your answer to
the nearest tenth.
2)
Area = 60 ft2
12 ft
Diagonal =
23 in
1)
Area = 325.3 in2
B)
Area =
Diagonal =
3)
A rectangle has a length of 25 yards. If it has an area of 391.51 square yards, determine the length
of the diagonal.
4)
The area of a rectangle is 360 square feet. Find the length of the diagonal, if the width is 9 feet.
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 3
Area of a Rectangle
Find the area of each rectangle for the given measurements. Round your answer to two decimal places.
1)
2)
21
yd
29
ft
15 ft
A)
16 yd
217.62 yd2
Area =
3)
Area =
372.29 ft2
The diagonal of a rectangle measures 35 inches. What is the area of the rectangle, if the length is
30 inches?
540.83 square inches
4)
The width of a rectangle is 24 yards. If the diagonal measures 40 yards, determine the area of the
rectangle.
768 square yards
Find the length of the diagonal of each rectangle for the given measurements. Round your answer to
the nearest tenth.
2)
Area = 60 ft2
12 ft
13 ft
Diagonal =
3)
Diagonal =
23 in
1)
Area = 325.3 in2
B)
27 in
A rectangle has a length of 25 yards. If it has an area of 391.51 square yards, determine the length
of the diagonal.
29.5 yards
4)
The area of a rectangle is 360 square feet. Find the length of the diagonal, if the width is 9 feet.
41 feet
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 4
Area of a Rectangle
Find the area of each rectangle for the given measurements. Round your answer to two decimal places.
2)
ft
in
18
34
Area =
B)
12.4 in
13.5 ft
1)
Area =
3)
The width of a rectangle is 20 yards. What is the area of the rectangle, if the diagonal measures
33 yards?
4)
The length of the diagonal of a rectangle is 36.7 feet. Find the area of the rectangle, if the length is
33.4 feet.
Find the length of the diagonal of each rectangle for the given measurements. Round your answer to
the nearest tenth.
1)
2)
Area = 389.1 in2
Area = 398.5 ft2
19 ft
A)
26 in
Diagonal =
Diagonal =
3)
The area of a rectangle is 496 square inches. Find the length of the diagonal, if the width is 22 inches.
4)
The length of a rectangle is 30 yards. If the area of the rectangle is 586.07 square yards, determine
the length of the diagonal.
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 4
Area of a Rectangle
A)
Find the area of each rectangle for the given measurements. Round your answer to two decimal places.
1)
2)
13.5 ft
421.27 ft2
Area =
3)
ft
in
18
34
12.4 in
161.79 in2
Area =
The width of a rectangle is 20 yards. What is the area of the rectangle, if the diagonal measures
33 yards?
524.98 square yards
4)
The length of the diagonal of a rectangle is 36.7 feet. Find the area of the rectangle, if the length is
33.4 feet.
508 square feet
Find the length of the diagonal of each rectangle for the given measurements. Round your answer to
the nearest tenth.
1)
2)
Area = 389.1 in2
Area = 398.5 ft2
19 ft
B)
26 in
Diagonal =
3)
30 in
Diagonal =
28.3 ft
The area of a rectangle is 496 square inches. Find the length of the diagonal, if the width is 22 inches.
31.5 inches
4)
The length of a rectangle is 30 yards. If the area of the rectangle is 586.07 square yards, determine
the length of the diagonal.
35.8 yards
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 5
Area of a Rectangle
Find the area of each rectangle for the given measurements. Round your answer to two decimal places.
35 in
37
23
Area =
B)
yd
16 yd
2)
in
1)
Area =
3)
The length of the diagonal of a rectangle is 40 feet. Find the area of the rectangle, if the length is
36 feet.
4)
Determine the area of the rectangle whose diagonal measures 25 inches and has a width of 7 inches.
Find the length of the diagonal of each rectangle for the given measurements. Round your answer to
the nearest tenth.
1)
2)
Area = 480.5 yd2
Area = 120 ft2
8 ft
A)
22 yd
Diagonal =
Diagonal =
3)
The width of a rectangle is 9 inches. If it has an area of 119.06 square inches, find the length of the
diagonal.
4)
The area of a rectangle is 137.7 square yards. Determine the length of the diagonal, if the rectangle
has a length of 21 yards.
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 5
Area of a Rectangle
Find the area of each rectangle for the given measurements. Round your answer to two decimal places.
1)
37
420 in2
Area =
3)
23
35 in
in
2)
yd
16 yd
A)
264.36 yd2
Area =
The length of the diagonal of a rectangle is 40 feet. Find the area of the rectangle, if the length is
36 feet.
627.68 square feet
4)
Determine the area of the rectangle whose diagonal measures 25 inches and has a width of 7 inches.
168 square inches
Find the length of the diagonal of each rectangle for the given measurements. Round your answer to
the nearest tenth.
1)
2)
Area = 480.5 yd2
Area = 120 ft2
8 ft
B)
22 yd
Diagonal =
3)
31 yd
Diagonal =
17 ft
The width of a rectangle is 9 inches. If it has an area of 119.06 square inches, find the length of the
diagonal.
16 inches
4)
The area of a rectangle is 137.7 square yards. Determine the length of the diagonal, if the rectangle
has a length of 21 yards.
22 yards
Printable Math Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 1
Perimeter of a Rectangle
A) Find the diagonal of each rectangle. Round your answer to the nearest tenth.
1)
perimeter = 50 in, length = 15 in
2)
Diagonal =
3)
perimeter = 72 ft, width = 13.8 ft
Diagonal =
perimeter = 180.9 yd, width = 30.2 yd
4)
Diagonal =
perimeter = 230 in, length = 60 in
Diagonal =
B) Find the perimeter of each rectangle. Round your answer to the nearest tenth.
1)
2)
19
22.
10.6 ft
.9 ft
8y
d
20 yd
Perimeter =
Perimeter =
3)
4)
44 yd
72
in
43
yd
35 in
Perimeter =
Perimeter =
C) The perimeter of a rectangle is 145.3 feet. Determine the length of the diagonal, if the
width of the rectangle is 27.5 feet. Round your answer to the nearest tenth.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 1
A) Find the diagonal of each rectangle. Round your answer to the nearest tenth.
1)
perimeter = 50 in, length = 15 in
18 in
Diagonal =
3)
2)
Diagonal =
perimeter = 180.9 yd, width = 30.2 yd
Diagonal =
perimeter = 72 ft, width = 13.8 ft
4)
67.4 yd
26.1 ft
perimeter = 230 in, length = 60 in
Diagonal =
81.4 in
B) Find the perimeter of each rectangle. Round your answer to the nearest tenth.
1)
2)
19
22.
10.6 ft
.9 ft
8y
d
20 yd
Perimeter =
Perimeter =
54.9 ft
3)
61.9 yd
4)
44 yd
72
in
43
yd
35 in
Perimeter =
120 in
Perimeter =
202 yd
C) The perimeter of a rectangle is 145.3 feet. Determine the length of the diagonal, if the
width of the rectangle is 27.5 feet. Round your answer to the nearest tenth.
52.9 feet
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Perimeter of a Rectangle
Sheet 2
A) Find the diagonal of each rectangle. Round your answer to the nearest tenth.
1)
perimeter = 102 ft, width = 16 ft
2)
Diagonal =
3)
perimeter = 19.1 yd, length = 6.3 yd
Diagonal =
perimeter = 78 in, length = 22 in
4)
Diagonal =
perimeter = 188.7 ft, width = 39 ft
Diagonal =
B) Find the perimeter of each rectangle. Round your answer to the nearest tenth.
1)
2)
14.6
in
ft
47
7.5 ft
36 in
Perimeter =
Perimeter =
3)
4)
n
yd
i
7.2
63
55 yd
6 in
Perimeter =
Perimeter =
C) Find the perimeter of the rectangle, if the diagonal measures 70.1 yards and its length is
68 yards. Round your answer to the nearest tenth.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 2
Perimeter of a Rectangle
A) Find the diagonal of each rectangle. Round your answer to the nearest tenth.
1)
perimeter = 102 ft, width = 16 ft
38.5 ft
Diagonal =
3)
2)
perimeter = 78 in, length = 22 in
7.1 yd
Diagonal =
4)
27.8 in
Diagonal =
perimeter = 19.1 yd, length = 6.3 yd
perimeter = 188.7 ft, width = 39 ft
67.7 ft
Diagonal =
B) Find the perimeter of each rectangle. Round your answer to the nearest tenth.
1)
2)
14.6
in
ft
47
7.5 ft
36 in
Perimeter =
Perimeter =
132.4 in
3)
40.1 ft
4)
6 in
n
63
55 yd
yd
i
7.2
Perimeter =
171.4 yd
Perimeter =
20 in
C) Find the perimeter of the rectangle, if the diagonal measures 70.1 yards and its length is
68 yards. Round your answer to the nearest tenth.
170.1 yards
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 3
Perimeter of a Rectangle
A) Find the diagonal of each rectangle. Round your answer to the nearest tenth.
1)
perimeter = 46.4 yd, width = 8 yd
2)
Diagonal =
3)
perimeter = 223 in, length = 72 in
Diagonal =
perimeter = 84 ft, length = 26 ft
4)
Diagonal =
perimeter = 118 yd, width = 14 yd
Diagonal =
B) Find the perimeter of each rectangle. Round your answer to the nearest tenth.
1)
2)
64.6 in
yd
74
57
.9
.4 i
n
32 yd
Perimeter =
Perimeter =
3)
4)
Perimeter =
ft
ft
21
2
11.
19 ft
10 ft
Perimeter =
C) The width of a rectangle is 7 inches. What is the length of the diagonal, if the perimeter
of the rectangle is 42 inches? Round your answer to the nearest tenth.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 3
Perimeter of a Rectangle
A) Find the diagonal of each rectangle. Round your answer to the nearest tenth.
1)
perimeter = 46.4 yd, width = 8 yd
17.2 yd
Diagonal =
3)
2)
perimeter = 84 ft, length = 26 ft
82.1 in
Diagonal =
4)
30.5 ft
Diagonal =
perimeter = 223 in, length = 72 in
perimeter = 118 yd, width = 14 yd
47.1 yd
Diagonal =
B) Find the perimeter of each rectangle. Round your answer to the nearest tenth.
1)
2)
64.6 in
yd
74
57
.9
.4 i
n
32 yd
Perimeter =
Perimeter =
160.5 yd
3)
203 in
4)
30.1 ft
Perimeter =
ft
Perimeter =
ft
21
2
11.
19 ft
10 ft
55.9 ft
C) The width of a rectangle is 7 inches. What is the length of the diagonal, if the perimeter
of the rectangle is 42 inches? Round your answer to the nearest tenth.
15.7 inches
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 4
Perimeter of a Rectangle
A) Find the diagonal of each rectangle. Round your answer to the nearest tenth.
1)
perimeter = 177 in, length = 53 in
2)
Diagonal =
3)
perimeter = 95 ft, width = 18.5 ft
Diagonal =
perimeter = 48 yd, width = 7.6 yd
4)
Diagonal =
perimeter = 100.4 ft, length = 30.2 ft
Diagonal =
B) Find the perimeter of each rectangle. Round your answer to the nearest tenth.
1)
2)
in
15
80
.4
yd
70 in
8.2 yd
Perimeter =
Perimeter =
3)
4)
27.6 in
ft
.8
54
22
in
18 ft
Perimeter =
Perimeter =
C) What is the perimeter of the rectangle, if the diagonal measures 42.6 yards and its width
is 27.3 yards? Round your answer to the nearest tenth.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 4
Perimeter of a Rectangle
A) Find the diagonal of each rectangle. Round your answer to the nearest tenth.
1)
perimeter = 177 in, length = 53 in
63.8 in
Diagonal =
3)
2)
perimeter = 48 yd, width = 7.6 yd
34.4 ft
Diagonal =
4)
18.1 yd
Diagonal =
perimeter = 95 ft, width = 18.5 ft
perimeter = 100.4 ft, length = 30.2 ft
36.2 ft
Diagonal =
B) Find the perimeter of each rectangle. Round your answer to the nearest tenth.
1)
2)
in
15
80
.4
yd
70 in
8.2 yd
Perimeter =
Perimeter =
217.5 in
3)
42.5 yd
4)
27.6 in
ft
.8
54
22
in
18 ft
Perimeter =
61.3 ft
Perimeter =
149.9 in
C) What is the perimeter of the rectangle, if the diagonal measures 42.6 yards and its width
is 27.3 yards? Round your answer to the nearest tenth.
120 yards
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 5
Perimeter of a Rectangle
A) Find the diagonal of each rectangle. Round your answer to the nearest tenth.
1)
perimeter = 88 yd, width = 19.4 yd
2)
Diagonal =
3)
perimeter = 240 yd, length = 70 yd
Diagonal =
perimeter = 133.5 ft, length = 41.3 ft
4)
Diagonal =
perimeter = 82 in, width = 18 in
Diagonal =
B) Find the perimeter of each rectangle. Round your answer to the nearest tenth.
1)
.2
12
ft
16
in
10 in
2)
7 ft
Perimeter =
Perimeter =
3)
4)
d
70 y
Perimeter =
25 ft
69 yd
39
.1
ft
Perimeter =
C) The perimeter of a rectangle is 142 inches. If the length of the rectangle is 45.3 inches,
find the length of the diagonal. Round your answer to the nearest tenth.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 5
Perimeter of a Rectangle
A) Find the diagonal of each rectangle. Round your answer to the nearest tenth.
1)
perimeter = 88 yd, width = 19.4 yd
31.3 yd
Diagonal =
3)
2)
perimeter = 133.5 ft, length = 41.3 ft
Diagonal =
4)
48.5 ft
Diagonal =
perimeter = 240 yd, length = 70 yd
86 yd
perimeter = 82 in, width = 18 in
Diagonal =
29.2 in
B) Find the perimeter of each rectangle. Round your answer to the nearest tenth.
1)
.2
12
ft
16
in
10 in
2)
7 ft
Perimeter =
Perimeter =
34 ft
3)
45 in
4)
d
70 y
Perimeter =
161.6 yd
25 ft
69 yd
Perimeter =
39
.1
ft
110.1 ft
C) The perimeter of a rectangle is 142 inches. If the length of the rectangle is 45.3 inches,
find the length of the diagonal. Round your answer to the nearest tenth.
52.1 inches
Printable Worksheets @ www.mathworksheets4kids.com
Name :
T1S1
Area of an Isosceles Triangle
Example:
t
12
f
t
f
12
Area = ?
In an isosceles triangle, altitude drawn to the base is a median.
Median divides base into equal line segments.
b = 10 ft , h = 119 ft
height = 122 – 52
Area = 1 x b x h
2
= 144 – 25
= 1 x 10 x 119
2
= 119 ft
= 54.54 ft2
10 ft
Find the area of each isosceles triangle. Round your answer to two decimal places.
1)
2)
3)
16
in
9 yd
11
ft
6 yd
ft
16 in
11
9 yd
12
in
4 ft
Area =
Area =
Area =
5)
4)
6)
8 in
15 ft
15
Area =
7)
10 yd
13
ft
Area =
yd
n
12 i
n
12 i
8 ft
13
yd
Area =
8)
9)
19
ft
22 y
d
21
16 in
ft
12
19
n
21 i
in
d
22 y
yd
15 ft
Area =
Area =
Printable Worksheets @ www.mathworksheets4kids.com
Area =
Name :
Answer key
T1S1
Area of an Isosceles Triangle
Example:
t
12
f
t
f
12
Area = ?
In an isosceles triangle, altitude drawn to the base is a median.
Median divides base into equal line segments.
b = 10 ft , h = 119 ft
height = 122 – 52
Area = 1 x b x h
2
= 144 – 25
= 1 x 10 x 119
2
= 119 ft
= 54.54 ft2
10 ft
Find the area of each isosceles triangle. Round your answer to two decimal places.
1)
2)
3)
16
in
9 yd
11
ft
6 yd
ft
16 in
11
9 yd
12
in
4 ft
25.46 yd2
21.63 ft2
Area =
5)
4)
6)
8 in
15 ft
8 ft
13
12 i
n
13
ft
57.83 ft2
Area =
7)
Area =
yd
n
12 i
15
88.99 in2
Area =
10 yd
Area =
45.25 in2
8)
Area =
yd
60 yd2
9)
19
ft
22 y
d
21
16 in
ft
12
19
n
21 i
in
d
22 y
yd
15 ft
Area =
155.33 in2
Area =
127 yd2
Printable Worksheets @ www.mathworksheets4kids.com
Area =
130.93 ft2
Name :
T1S2
Area of an Isosceles Triangle
i
14
14
in
Example:
n
Area = ?
In an isosceles triangle, altitude drawn to the base is a median.
Median divides base into equal line segments.
b = 12 in , h = 160 in
height = 142 – 62
Area = 1 x b x h
2
= 196 – 36
= 1 x 12 x 160
2
= 160 in
= 75.89 in2
12 in
Find the area of each isosceles triangle. Round your answer to two decimal places.
1)
2)
3)
n
24 i
10 yd
8 yd
24 i
n
21 f
t
t
21 f
15
10 y
d
in
14 ft
Area =
Area =
Area =
5)
4)
6)
7 ft
5 in
t
7 in
yd
12 f
26
26
yd
12 ft
7 in
30 yd
Area =
Area =
7)
Area =
8)
14 i
n
ft
27
27
20 yd
15
11 in
yd
ft
20
9)
yd
14
14 ft
Area =
Area =
Printable Worksheets @ www.mathworksheets4kids.com
Area =
in
Name :
Answer key
T1S2
Area of an Isosceles Triangle
In an isosceles triangle, altitude drawn to the base is a median.
Median divides base into equal line segments.
b = 12 in , h = 160 in
height = 142 – 62
Area = 1 x b x h
2
= 196 – 36
= 1 x 12 x 160
2
= 160 in
= 75.89 in2
i
14
14
in
Example:
n
Area = ?
12 in
Find the area of each isosceles triangle. Round your answer to two decimal places.
1)
2)
3)
n
24 i
10 yd
8 yd
24 i
n
21 f
t
t
21 f
15
10 y
d
in
14 ft
Area =
138.59 ft2
Area =
170.99 in2
5)
4)
36.66 yd2
Area =
6)
7 ft
5 in
t
7 in
yd
12 f
26
26
yd
12 ft
7 in
30 yd
16.35 in2
7)
Area = 318.55 yd2
8)
14 i
n
yd
ft
27
27
20 yd
15
40.17 ft2
9)
ft
20
Area =
11 in
Area =
yd
14
in
14 ft
Area = 139.05 yd2
Area =
182.54 ft2
Printable Worksheets @ www.mathworksheets4kids.com
Area =
70.81 in2
Name :
T1S3
Area of an Isosceles Triangle
Area = ?
d
5y
5y
d
Example:
In an isosceles triangle, altitude drawn to the base is a median.
Median divides base into equal line segments.
b = 9 yd , h = 4.75 yd
height = 52 – 4.52
Area = 1 x b x h
2
= 25 – 20.25
= 1 x 9 x 4.75
2
= 4.75 yd
= 9.81 yd2
9 yd
Find the area of each isosceles triangle. Round your answer to two decimal places.
2)
25 in
ft
t
13 y
d
26 f
19
d
13 y
in
26
19
in
3)
8 yd
1)
16 ft
Area =
Area =
Area =
5)
4)
6)
24 ft
23
30 y
d
ft
20
yd
in
22
20
23
in
d
30 y
ft
12 in
Area =
7)
Area =
8)
9)
t
18 in
ft
18
9 ft
13
Area =
10
yd
11 in
13 f
10 yd
Area =
d
7y
in
Area =
Printable Worksheets @ www.mathworksheets4kids.com
Area =
Name :
Answer key
T1S3
Area of an Isosceles Triangle
Area = ?
d
5y
5y
d
Example:
In an isosceles triangle, altitude drawn to the base is a median.
Median divides base into equal line segments.
b = 9 yd , h = 4.75 yd
height = 52 – 4.52
Area = 1 x b x h
2
= 25 – 20.25
= 1 x 9 x 4.75
2
= 4.75 yd
= 9.81 yd2
9 yd
Find the area of each isosceles triangle. Round your answer to two decimal places.
2)
25 in
ft
t
13 y
d
26 f
19
d
13 y
in
26
19
in
3)
8 yd
1)
16 ft
178.86 in2
Area =
Area =
49.48 yd2
Area =
5)
4)
197.91 ft2
6)
24 ft
23
30 y
d
ft
20
yd
in
22
20
23
in
d
30 y
ft
12 in
307.02 yd2
7)
Area =
192 ft2
Area =
8)
9)
t
18 in
ft
18
9 ft
13
Area =
10
yd
11 in
13 f
54.88 ft2
133.22 in2
Area =
10 yd
Area =
d
7y
in
94.27 in2
Printable Worksheets @ www.mathworksheets4kids.com
Area =
32.79 yd2
Name :
T1S4
Area of an Isosceles Triangle
Example:
8 in
n
8i
Area = ?
In an isosceles triangle, altitude drawn to the base is a median.
Median divides base into equal line segments.
b = 6 in, h = 55 in
height = 82 – 32
Area = 1 x b x h
2
= 64 – 9
= 1 x 6 x 55
2
= 55 in
= 22.25 in2
6 in
Find the area of each isosceles triangle. Round your answer to two decimal places.
1)
2)
ft
5 in
33
26 ft
23
n
6i
yd
33
yd
23
3)
ft
5 in
18 yd
Area =
Area =
Area =
5)
4)
6)
15 in
28
14 yd
15 in
10
d
9y
32 f
t
ft
9y
d
in
32 f
Area =
Area =
7)
Area =
8)
9)
24 ft
10
10
ft
11
yd
30
in
24 ft
11
in
yd
12 in
14 yd
Area =
t
Area =
Printable Worksheets @ www.mathworksheets4kids.com
Area =
Name :
Answer key
T1S4
Area of an Isosceles Triangle
Example:
8 in
n
8i
Area = ?
In an isosceles triangle, altitude drawn to the base is a median.
Median divides base into equal line segments.
b = 6 in, h = 55 in
height = 82 – 32
Area = 1 x b x h
2
= 64 – 9
= 1 x 6 x 55
2
= 55 in
= 22.25 in2
6 in
Find the area of each isosceles triangle. Round your answer to two decimal places.
1)
2)
ft
5 in
33
26 ft
23
n
6i
yd
33
yd
23
3)
ft
5 in
18 yd
Area =
246.66 ft2
Area = 285.74 yd2
Area =
5)
4)
12 in2
6)
15 in
28
14 yd
15 in
10
d
9y
32 f
t
ft
9y
d
in
32 f
Area =
39.6 yd2
7)
Area =
70.71 in2
Area =
8)
t
402.85 ft2
9)
24 ft
10
10
ft
11
yd
30
in
24 ft
11
in
yd
12 in
14 yd
Area =
55.32 in2
Area =
281.02 ft2
Printable Worksheets @ www.mathworksheets4kids.com
Area =
49.99 yd2
Name :
T1S5
Area of an Isosceles Triangle
In an isosceles triangle, altitude drawn to the base is a median.
Median divides base into equal line segments.
b = 10 ft , h = 134.75 ft
height = 152 – 9.52
Area = 1 x b x h
2
= 225 – 90.25
1
= x 19 x 134.75
2
= 134.75 ft
= 110.28 ft2
Example:
ft
15
ft
15
Area = ?
19 ft
Find the area of each isosceles triangle. Round your answer to two decimal places.
1)
2)
3)
30 ft
yd
f
32
26
30 ft
16
in
in
16
22 yd
22 yd
t
10 in
Area =
Area =
Area =
5)
4)
6)
8 yd
yd
14
yd
14
15
15 in
15 in
18 ft
15
ft
14
ft
Area =
Area =
7)
Area =
8)
9)
27 in
d
0y
in
30
27 in
t
t
23 yd
9f
9f
2
12 ft
23 y
d
Area =
in
Area =
Printable Worksheets @ www.mathworksheets4kids.com
Area =
Name :
Answer key
T1S5
Area of an Isosceles Triangle
In an isosceles triangle, altitude drawn to the base is a median.
Median divides base into equal line segments.
b = 10 ft , h = 134.75 ft
height = 152 – 9.52
Area = 1 x b x h
2
= 225 – 90.25
1
= x 19 x 134.75
2
= 134.75 ft
= 110.28 ft2
Example:
ft
15
ft
15
Area = ?
19 ft
Find the area of each isosceles triangle. Round your answer to two decimal places.
1)
2)
3)
30 ft
yd
Area =
230.73 yd2
f
32
26
30 ft
16
in
in
16
22 yd
22 yd
t
10 in
75.99 in2
Area =
Area =
406.03 ft2
5)
4)
6)
8 yd
14
yd
Area =
53.67 yd2
14
in
ft
108 ft2
Area =
yd
14
15
15 in
15 in
18 ft
15
ft
7)
8)
Area =
9)
27 in
d
0y
30
in
27 in
t
t
23 yd
9f
9f
2
12 ft
23 y
d
Area = 207.12 yd2
92.87 in2
Area =
336.75 in2
Printable Worksheets @ www.mathworksheets4kids.com
Area =
40.25 ft2
Name :
Sheet 1
Kite
A) Find the indicated side length in each kite. Round your answer to the nearest tenth.
1)
2)
M
C
N
D
L
O
B
O
A
K
OC = 7 in ; OD = 9 in
ON = 5 ft ; OK = 15 ft
CD =
KL =
4)
3)
Z
V
Y
O
U
W
O
T
S
X
OV = 19 yd ; SU = 14 yd
OW = 6 in ; OZ = 8 in
UV =
WZ =
B) Find the indicated side lengths in each kite. Round your answer to the nearest tenth.
5)
6)
G
R
S
O
H
Q
O
F
P
E
OE = 2 ft ; OF = 4 ft ; EG = 14 ft
EF =
; GH =
Printable Worksheets @ www.mathworksheets4kids.com
RP = 10 yd ; OQ = 6 yd ; OS = 10 yd
RQ =
; PS =
Name :
Answer key
Sheet 1
Kite
A) Find the indicated side length in each kite. Round your answer to the nearest tenth.
1)
2)
M
C
N
D
B
O
A
K
OC = 7 in ; OD = 9 in
CD =
L
O
ON = 5 ft ; OK = 15 ft
11.4 in
15.8 ft
KL =
4)
3)
Z
V
Y
O
U
W
O
T
S
X
OV = 19 yd ; SU = 14 yd
UV =
OW = 6 in ; OZ = 8 in
20.3 yd
WZ =
10 in
B) Find the indicated side lengths in each kite. Round your answer to the nearest tenth.
5)
6)
G
R
S
O
H
Q
O
F
P
E
OE = 2 ft ; OF = 4 ft ; EG = 14 ft
EF =
4.5 ft
; GH =
12.6 ft
Printable Worksheets @ www.mathworksheets4kids.com
RP = 10 yd ; OQ = 6 yd ; OS = 10 yd
RQ =
7.8 yd
; PS =
11.2 yd
Name :
Sheet 2
Kite
A) Find the indicated side length in each kite. Round your answer to the nearest tenth.
1)
2)
U
L
M
V
O
O
N
W
K
T
OL = 5 ft ; OK = 12 ft
VT = 16 yd ; OW = 7 yd
KN =
TW =
3)
4)
F
S
G
R
O
O
E
T
Q
H
EG = 4 in ; OH = 9 in
OT = 11 ft ; OQ = 13 ft
EH =
RQ =
B) Find the indicated side lengths in each kite. Round your answer to the nearest tenth.
5)
6)
C
Y
O
Z
X
O
D
W
B
A
OZ = 6 yd ; WY = 6 yd ; OX = 8 yd
YZ =
; XY =
Printable Worksheets @ www.mathworksheets4kids.com
AC = 26 in ; OB = 6 in ; OC = 22 in
AB =
; AD =
Name :
Answer key
Sheet 2
Kite
A) Find the indicated side length in each kite. Round your answer to the nearest tenth.
1)
2)
U
L
M
V
O
O
N
W
K
OL = 5 ft ; OK = 12 ft
VT = 16 yd ; OW = 7 yd
13 ft
KN =
T
10.6 yd
TW =
3)
4)
F
S
G
R
O
O
E
T
Q
H
EG = 4 in ; OH = 9 in
OT = 11 ft ; OQ = 13 ft
9.2 in
EH =
17 ft
RQ =
B) Find the indicated side lengths in each kite. Round your answer to the nearest tenth.
5)
6)
C
Y
O
Z
X
O
D
W
B
A
OZ = 6 yd ; WY = 6 yd ; OX = 8 yd
YZ =
6.7 yd
; XY =
8.5 yd
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AC = 26 in ; OB = 6 in ; OC = 22 in
AB =
7.2 in
; AD =
7.2 in
Name :
Sheet 3
Kite
A) Find the indicated side length in each kite. Round your answer to the nearest tenth.
1)
2)
R
F
S
O
G
E
O
Q
H
P
QS = 12 yd ; OP = 15 yd
OG = 3 in ; OH = 4 in
PS =
FG =
4)
3)
C
X
D
O
Y
W
B
O
Z
A
OZ = 5 ft ; OW = 9 ft
OA = 16 yd ; OD = 7 yd
WX =
AD =
B) Find the indicated side lengths in each kite. Round your answer to the nearest tenth.
5)
6)
M
V
L
U
O
O
N
W
K
KM = 34 in ; OM = 10 in ; ON = 8 in
LM =
; KN =
Printable Worksheets @ www.mathworksheets4kids.com
T
OT = 14 ft ; OV = 21 ft ; UW = 20 ft
TU =
; UV =
Name :
Answer key
Sheet 3
Kite
A) Find the indicated side length in each kite. Round your answer to the nearest tenth.
1)
2)
R
F
S
O
G
E
O
Q
H
P
QS = 12 yd ; OP = 15 yd
OG = 3 in ; OH = 4 in
16.2 yd
PS =
5 in
FG =
4)
3)
C
X
D
O
Y
W
B
O
Z
A
OZ = 5 ft ; OW = 9 ft
OA = 16 yd ; OD = 7 yd
10.3 ft
WX =
AD =
17.5 yd
B) Find the indicated side lengths in each kite. Round your answer to the nearest tenth.
5)
6)
M
V
L
U
O
O
N
W
K
KM = 34 in ; OM = 10 in ; ON = 8 in
LM =
12.8 in
; KN =
25.3 in
Printable Worksheets @ www.mathworksheets4kids.com
T
OT = 14 ft ; OV = 21 ft ; UW = 20 ft
TU =
17.2 ft
; UV =
23.3 ft
Name :
Sheet 1
Perimeter of a Square
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
Perimeter = 208 yd
2)
Diagonal =
3)
Perimeter = 156.3 ft
Diagonal =
Perimeter = 92.5 in
4)
Diagonal =
Perimeter = 56 yd
Diagonal =
B) Find the perimeter of each square. Round your answer to the nearest tenth.
5)
6)
ft
54
in
.6
15
Perimeter =
Perimeter =
7)
8)
82
.2
27
yd
Perimeter =
9)
ft
Perimeter =
The perimeter of a square is 356 inches. Determine the length of the diagonal.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 1
Perimeter of a Square
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
Perimeter = 208 yd
Diagonal =
3)
2)
73.5 yd
Perimeter = 92.5 in
55.3 ft
Diagonal =
4)
32.7 in
Diagonal =
Perimeter = 156.3 ft
Perimeter = 56 yd
19.8 yd
Diagonal =
B) Find the perimeter of each square. Round your answer to the nearest tenth.
5)
6)
ft
54
in
.6
15
Perimeter =
Perimeter =
44.1 ft
7)
8)
82
27
.2
yd
Perimeter =
9)
152.7 in
232.5 yd
Perimeter =
ft
76.4 ft
The perimeter of a square is 356 inches. Determine the length of the diagonal.
125.9 inches
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Name :
Perimeter of a Square
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
Perimeter = 100.7 in
2)
Diagonal =
3)
Perimeter = 52 yd
Diagonal =
Perimeter = 144 ft
4)
Diagonal =
Perimeter = 164 in
Diagonal =
B) Find the perimeter of each square. Round your answer to the nearest tenth.
5)
6)
91
yd
.5
38
Perimeter =
Perimeter =
7)
8)
in
.1
yd
Perimeter =
53
10
9)
ft
Perimeter =
If the length of the diagonal of a square is 29 feet, determine the perimeter.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 2
Perimeter of a Square
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
Perimeter = 100.7 in
Diagonal =
3)
2)
35.6 in
Perimeter = 144 ft
18.4 yd
Diagonal =
4)
50.9 ft
Diagonal =
Perimeter = 52 yd
Perimeter = 164 in
58 in
Diagonal =
B) Find the perimeter of each square. Round your answer to the nearest tenth.
5)
6)
91
yd
.5
38
Perimeter =
108.9 ft
8)
.1
yd
Perimeter =
in
53
10
9)
Perimeter =
257.4 yd
7)
ft
28.3 in
Perimeter =
150.2 yd
If the length of the diagonal of a square is 29 feet, determine the perimeter.
82 feet
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 3
Perimeter of a Square
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
Perimeter = 188 ft
2)
Diagonal =
3)
Perimeter = 84.5 in
Diagonal =
Perimeter = 40.4 yd
4)
Diagonal =
Perimeter = 136 ft
Diagonal =
B) Find the perimeter of each square. Round your answer to the nearest tenth.
5)
6)
29
in
74
Perimeter =
Perimeter =
7)
8)
.8
11
46
in
ft
Perimeter =
9)
yd
Perimeter =
The perimeter of a square is 220.2 yards. Find the length of the diagonal.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 3
Perimeter of a Square
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
Perimeter = 188 ft
Diagonal =
3)
2)
66.5 ft
Perimeter = 40.4 yd
29.9 in
Diagonal =
4)
14.3 yd
Diagonal =
Perimeter = 84.5 in
Perimeter = 136 ft
48.1 ft
Diagonal =
B) Find the perimeter of each square. Round your answer to the nearest tenth.
5)
6)
29
in
74
Perimeter =
Perimeter =
82 in
7)
209.3 yd
8)
.8
11
46
132.4 ft
in
ft
Perimeter =
9)
yd
Perimeter =
31.1 in
The perimeter of a square is 220.2 yards. Find the length of the diagonal.
77.9 yards
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 4
Perimeter of a Square
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
Perimeter = 76 in
2)
Diagonal =
3)
Perimeter = 180 yd
Diagonal =
Perimeter = 204 ft
4)
Diagonal =
Perimeter = 104.9 in
Diagonal =
B) Find the perimeter of each square. Round your answer to the nearest tenth.
5)
6)
in
ft
12
57
Perimeter =
Perimeter =
7)
8)
70
yd
Perimeter =
9)
.5
39
ft
Perimeter =
What is the perimeter of the square, if the length of the diagonal is 43.4 inches?
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 4
Perimeter of a Square
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
Perimeter = 76 in
2)
Diagonal =
3)
26.9 in
Perimeter = 204 ft
63.6 yd
Diagonal =
4)
72.1 ft
Diagonal =
Perimeter = 180 yd
Perimeter = 104.9 in
37.1 in
Diagonal =
B) Find the perimeter of each square. Round your answer to the nearest tenth.
5)
6)
in
ft
12
57
Perimeter =
7)
33.9 in
8)
70
Perimeter =
9)
Perimeter =
161.2 ft
yd
.5
39
198 yd
Perimeter =
ft
111.7 ft
What is the perimeter of the square, if the length of the diagonal is 43.4 inches?
122.8 inches
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Perimeter of a Square
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
Perimeter = 140.5 yd
2)
Diagonal =
3)
Perimeter = 232 ft
Diagonal =
Perimeter = 172.8 in
4)
Diagonal =
Perimeter = 68 yd
Diagonal =
B) Find the perimeter of each square. Round your answer to the nearest tenth.
5)
6)
66
in
.1
yd
13
Perimeter =
Perimeter =
7)
8)
24
ft
49
Perimeter =
9)
in
Perimeter =
If the diagonal of a square measures 64 feet, determine the perimeter.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Perimeter of a Square
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
Perimeter = 140.5 yd
Diagonal =
3)
2)
49.7 yd
Perimeter = 172.8 in
82 ft
Diagonal =
4)
61.1 in
Diagonal =
Perimeter = 232 ft
Perimeter = 68 yd
24 yd
Diagonal =
B) Find the perimeter of each square. Round your answer to the nearest tenth.
5)
6)
66
in
yd
Perimeter =
.1
13
Perimeter =
36.8 in
7)
8)
24
49
ft
Perimeter =
9)
187 yd
67.9 ft
Perimeter =
in
138.6 in
If the diagonal of a square measures 64 feet, determine the perimeter.
181 feet
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 1
Diagonal of a Square
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
side length = 2 yd
2)
Diagonal =
Diagonal =
3)
side length = 17.3 in
side length = 53 ft
4)
Diagonal =
side length = 95 yd
Diagonal =
B) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
5)
48.7 ft
6)
32 in
Diagonal =
Diagonal =
70 yd
88.5 ft
8)
7)
Diagonal =
Diagonal =
9) The side length of a square is 22 yards. What is the length of the diagonal?
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 1
Diagonal of a Square
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
Diagonal =
3)
2)
side length = 2 yd
2.8 yd
side length = 17.3 in
Diagonal =
side length = 53 ft
75 ft
Diagonal =
4)
24.5 in
side length = 95 yd
Diagonal =
134.4 yd
B) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
5)
6)
48.7 ft
32 in
Diagonal =
68.9 ft
Diagonal =
45.3 in
Diagonal =
125.2 ft
8)
70 yd
88.5 ft
7)
Diagonal =
99 yd
9) The side length of a square is 22 yards. What is the length of the diagonal?
31.1 yards
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Diagonal of a Square
Sheet 2
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
side length = 85 in
2)
Diagonal =
3)
side length = 72.4 ft
Diagonal =
side length = 55 ft
4)
Diagonal =
side length = 45.2 yd
Diagonal =
B) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
6)
7 yd
36.3 yd
5)
Diagonal =
7)
Diagonal =
8)
63 ft
29 in
Diagonal =
Diagonal =
9) Determine the length of the diagonal of the square, if its side length is 99 inches.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 2
Diagonal of a Square
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
side length = 85 in
Diagonal =
3)
2)
120.2 in
side length = 55 ft
Diagonal =
side length = 72.4 ft
Diagonal =
4)
77.8 ft
102.4 ft
side length = 45.2 yd
Diagonal =
63.9 yd
B) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
6)
Diagonal =
7 yd
36.3 yd
5)
51.3 yd
7)
Diagonal =
9.9 yd
8)
63 ft
29 in
Diagonal =
41 in
Diagonal =
89.1 ft
9) Determine the length of the diagonal of the square, if its side length is 99 inches.
140 inches
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Diagonal of a Square
Sheet 3
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
side length = 58 ft
2)
Diagonal =
3)
side length = 1.1 in
Diagonal =
side length = 23 yd
4)
Diagonal =
side length = 90 in
Diagonal =
B) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
6)
84 ft
12 in
5)
Diagonal =
Diagonal =
8)
62.7 ft
7)
Diagonal =
34 yd
Diagonal =
9) If the side length of a square is 47.6 feet, determine the length of the diagonal.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 3
Diagonal of a Square
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
side length = 58 ft
2)
82 ft
Diagonal =
3)
side length = 23 yd
Diagonal =
side length = 1.1 in
1.6 in
Diagonal =
4)
32.5 yd
side length = 90 in
Diagonal =
127.3 in
B) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
6)
84 ft
12 in
5)
Diagonal =
17 in
118.8 ft
8)
62.7 ft
7)
Diagonal =
Diagonal =
88.7 ft
34 yd
48.1 yd
Diagonal =
9) If the side length of a square is 47.6 feet, determine the length of the diagonal.
67.3 feet
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 4
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
side length = 50.9 yd
2)
Diagonal =
3)
side length = 75 ft
side length = 33 ft
Diagonal =
4)
Diagonal =
side length = 19.4 in
Diagonal =
B) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
6)
92.1 yd
5)
26 in
Diagonal =
60.5 yd
8)
41 ft
7)
Diagonal =
Diagonal =
Diagonal =
9) Find the length of the diagonal of the square, if its side length is 3 yards.
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 4
Diagonal of a Square
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
side length = 50.9 yd
Diagonal =
3)
72 yd
side length = 75 ft
Diagonal =
2)
side length = 33 ft
Diagonal =
4)
106.1 ft
46.7 ft
side length = 19.4 in
Diagonal =
27.4 in
B) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
6)
92.1 yd
5)
26 in
Diagonal =
Diagonal =
130.2 yd
8)
60.5 yd
41 ft
7)
36.8 in
Diagonal =
85.6 yd
Diagonal =
58 ft
9) Find the length of the diagonal of the square, if its side length is 3 yards.
4.2 yards
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Sheet 5
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
side length = 82 in
2)
Diagonal =
3)
side length = 94 yd
Diagonal =
side length = 73.8 yd
4)
Diagonal =
side length = 6 ft
Diagonal =
B) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
5)
11 yd
6)
56 ft
Diagonal =
Diagonal =
Diagonal =
43.5 yd
8)
39 in
7)
Diagonal =
9) What is the length of the diagonal of the square whose side length is 22.9 feet?
Printable Worksheets @ www.mathworksheets4kids.com
Name :
Answer key
Sheet 5
Diagonal of a Square
A) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
1)
side length = 82 in
Diagonal =
3)
2)
116 in
side length = 73.8 yd
Diagonal =
side length = 94 yd
Diagonal =
4)
104.4 yd
132.9 yd
side length = 6 ft
Diagonal =
8.5 ft
B) Find the length of the diagonal of each square. Round your answer to the nearest tenth.
5)
11 yd
6)
56 ft
Diagonal =
79.2 ft
15.6 yd
Diagonal =
55.2 in
43.5 yd
8)
39 in
7)
Diagonal =
Diagonal =
61.5 yd
9) What is the length of the diagonal of the square whose side length is 22.9 feet?
32.4 feet
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