Chapters 1 to 4
Name ________________________
Period _____
Revised 7/2013
TABLE OF CONTENTS
Keystone Algebra 1 Exam Eligible Content ………………………………….. 2
Operations with Rational Numbers ……………………………..…………..…. 3
CC Standards: A1.1.1.1.1, A1.1.1.1.1.2, A1.1.1.4.1
Coordinate Plane …………………………………………………………..………13
CC Standards: A1.1.2.1.3, A1.2.2.2.1
Matrices ……………………………………….……………………………..…….. 15
CC Standards: A1.1.1.1.1
Properties ……………………………………………….……………………..……16
CC Standards: A1.1.2.1.2
Algebraic Expressions ……………………………….………………..……..…. 17
CC Standards: A1.1.2.1.2
Distributive Property ………………………………….……………..……….…. 21
CC Standards: A1.1.2.1.2
Solve Equations …………………………………….…………….……………… 22
CC Standards: A1.1.2.1.1, A1.1.2.1.2,
Word Problems and Applications ………………………………..…………… 26
Angle Measure (26), Proportions (27)
CC Standrds: A1.1.2.1.1. A1.1.2.1.3
Pythagorean Theorem …………………………………….……………….……. 32
CC Standrds: A1.1.2.1.1. A1.1.2.1.3
Models 1 to 7 Word Problem Review ……………………….….…..………..…34
CC Standrds: A1.1.2.1.1. A1.1.2.1.3
Function Tables & Graphs ………….………………………….….……….…… 36
CC Standards: A1.2.1.1.1, A1.2.1.1.2, A1.2.1.1.3, A1.2.1.2.1,
A!.2.1.2.2, A1.2.2.1.1, A1.2.2.1.2, A1.2.2.1.3,
A1.2.2.1.3
Scatterplots & Line of Best Fit ………………………………………………… 40
CC Standars: A1.2.2.2, A1.2.2.2.1, A1.2.3.2.2, A1.2.3.2.3
PA State Formula Sheets ………………………………………………………. 41
Vocabulary and Verbal Models ….………………………………….…………. 42
SPECIAL NOTE
This workbook is designed for 8th grade math students at Log College Middle School. Any
person who wishes to copy any part of this book must have written permission from Mrs.
Gismondi, who created, designed and compiled this work.
Keystone Algebra 1 Exam Eligible Content
2
DIRECTIONS FOR RATIONAL NUMBERS
3
Simplify each of the following:
Absolute Value & Opposites
1.
–(–4)
16. – ( – 8 )
31. – [– (– 6 ) ]
46. 3 
2.
–(–9)
17. – ( 7 + 12 )
32. – ( 9  7 )
47. – ( 6  2)
3.
–(7+3)
18. – ( 5 + 2 )
33. – ( 36 / 6 )
48. – ( 7 / 7 )
4.
–(8/4)
19. – ( 15 – 8 )
34. – ( 3  0 )
49. – ( 9 + 6 )
5.
– ( 18 – 11 )
20. – ( 5 – 4 )
35. – ( 6 – 1 )
50. – ( 14 – 8 )
 2
5
6.

7.
 4
8
8.

 6
7
21. 
22.
7
 21
36. 
 3
6
23. 
 5
 15
4
9
51. 
 3
 17
37.
8
 12
52. 
9
15
38.
 6
 24
53. 
 2
 10
9.
1
24.
 41
39.
2
54.
 11
10.
 3
25.
9
40.
 20
55.
5
11.
1 6
26.
5  1
56.
7  16
27.
2  10
57.
14  9
28.
3

58.
12
29.
7

59.
7
60.
32
12.
64 / 8
13.
7
14.
4
15.
18

8

9

6
30.
45
41.

15  5
42.
3  7
4
43.
6
5
44.
3
45.
 24
36
4


4
3
/
8

13

10
/
 16
Add integers
1.
–4 + 3
21.
0+8
41.
–2 
2.
7+–9
22.
17 + – 3
42.
3.
0+3
23.
5+ –2
4.
0+4
24.
5.
18 + – 11
6.

61.
–4+8
–9+–7
62.
–6+–3
43.
36 + – 6
63.
7 + –7
15 + – 7
44.
–3+0
64.
9 
25.
2+ –3
45.
–6+–0
65.
4+–8
–2 + – 1
26.
–8 + 1
46.
–9+–1
66.
6+5
7.
–8 + 4
27.
–6 + 11
47.
–8+ 2
67.
4 
8.
–4 
28.
2+–3
48.
–6+ 8
68.
–4+–2
9.
9+–9
29.
–1 
49.
– 40 + – 10
69.
3 + – 10
10.
–6 
30.
0+–1
50.
–5 
7
70.
63 + 7
11.
0+–2
31.
5+0
51.
12 + – 5
71.
– 13 
12.
8+ –7
32.
5+–6
52.
–7+–4
72.
0+ 2
13.
–2 + 11
33.
7 + – 17
53.
6 
73.
– 2 + – 13
14.
–3 + – 3
34.
0 
54.
–2+–6
74.
– 19 + – 1
15.
8 + –2
35.
6+ –7
55.
–8+ –4
75.
–8 
16.
–13 
36.
–14 
56.
–22 
76.
– 11 
17.
0+ –3
37.
5+ 9
57.
0 
77.
–5+7
18.
0+ –6
38.
–5+ –1
58.
15 + – 5
78.
7 
19.
–64 + – 8
39.
–2 

10
59.
–3+–7
79.
4 + – 19
20.
–7 + – 8
40.
–8 

5
60.
0 + 10
80.
11 + – 11

3

4

5


6
7

7
5


8

6

8
20

6


7


6
9

9
16
Subtract Integers
1.
–6–9
21. 6 – 8
41. 13   8
61. 12 – 8
2.
– 26 – 11
22. – 19 + – 13
42. – 5 + – 11
62. – 7   1
3.
9– 8
23. 9 + – 2
43. 41 – 7
63. 8   3
4.
11 – 41
24. 16 – 13
44. – 9 + 1
64. 4   60
5.
13 – 19
25. 5 – 12
45. – 7 – 16
65. 8 – 18
6.
–9–4
26. – 9 + 20
46. – 11 – 13
66. 45 + 11
7.
– 1 – 13
27. – 8 + 16
47. – 13 – 14
67. 14   7
8.
–2   3
28. 9 + – 3
48. – 26 – 15
68. – 7 + – 2
9.
23 + – 3
29. –17   6
49. – 34 + – 21
69. 23 – 29
10. – 9   4
30. 14 – 0
50. – 35   7
70. 47 – 51
11. 30 + – 6
31. 23 – 4
51. 62 – 53
71. – 14   6
12. 6 + – 8
32. 5 – 7
52. – 25 + – 13
72. 1 – 7
13. –5 – 18
33. 6 – 37
53. 70   6
73. – 39 – 16
14. – 3 – 4
34. 7   7
54. – 51 + – 6
74. – 81 – 1
15. 16 + – 18
35. – 3 + – 5
55. – 72 – 52
75. – 45   5
16. –13   13
36. –14   10
56. –16   8
76. – 19   9
17. 6 + – 6
37. 5 – 11
57. 20   20
77. – 13 + 69
18. 9 – 0
38. – 24 – 1
58. 10 – 15
78. 37   16
19. –12 + – 13
39. –61   10
59. – 7 + – 23
79. 8 – 43
20. – 36 – 16
40. – 14   8
60. 30 + 39
80. 48 + – 24
6
Multiply Integers
1.
–5  7
21. 12  8
41. –5  – 8
61. – 3  3
2.
6  –4
22. 18  – 2
42. – 8  – 7
62. – 11  – 11
3.
9  3
23. 12  – 5
43. 49  – 3
63. 8  – 2
4.
12  4
24. 11  – 10
44. – 19  0
64. 6  – 6
5.
9  – 10
25. 2  – 31
45. – 12  – 1
65. 9  – 8
6.
–6  – 7
26. –9  12
46. – 50  – 5
66. 7  12
7.
–3  8
27. –5  14
47. – 5  21
67. 16   2
8.
–11   3
28. 7  – 9
48. – 9  8
68. – 8  – 8
9.
8  –9
29. –4   6
49. – 61  – 9
69. 4  – 11
10. –7   4
30. 0  – 41
50. – 2  – 2
70. 85  7
11. 6  – 3
31. 8  0
51. 12  – 8
71. – 16  – 7
12. 12  – 10
32. 7  – 1
52. – 4  – 6
72. 0  24
13. –12  11
33. 4  – 32
53. 13  – 8
73. – 6  – 25
14. –13  – 6
34. 1   7
54. – 5  – 6
74. – 87  – 1
15. 33  – 3
35. 0  – 7
55. – 9  – 4
75. –7  – 9
16. –41   7
36. –4  – 11
56. –71  – 8
76. – 81  –4
17. 8  – 3
37. 15  6
57. 10  – 20
77. – 3  12
18. 10  – 99
38. – 4  – 2
58. 7  – 25
78. 0   16
19. –61  – 9
39. –30  – 10
59. – 6  – 7
79. 14  – 2
20. –35  – 4
40. –6  – 5
60. 10  10
80. 12  – 12
7
Divide Integers
1. 3 6   4
2.
45  9
3.
567
Simplify. Write fraction answers in lowest terms.
21.  7 7   1 1
22.
764
23.
9.
10.
64
8
27
9
248
11. 8 5  1 7
12.
13.
18
36
14 2
14.
72
24
15.
9612
16.
427
17.
26
13
18.
7

21
56
8
19.

20.
497
1407

62.
68
4
43.
42 14
63. 5 4   2
24.
6622
44.
366
64.
144 12
25.
9519
45.
15
25
65.

26.

4
18
46.
3913
66.
27.
 2 1 7
47.
 5 1  3
5
70
126
67.
90 18
28.
48.
68.
633
29.
0 11
48
72
30.
 8 1 2 7
49.
29
35
69.

31.
10
120
50.
444
70.
483
51.
262
71. 7 2  2 4
52.
10812
53.
546
7. 3 5  7
61.
19
57
6. 1 6   8
8.
333
42.
4. 6 3  9
5.
41.
32.
33.
808
41
123
34.
844
35.
28

35
36.

8
64
37.
186
38.
90 18
39.
250 10
40.
8
30
60
9
126
72.
15
150
60
12
73.
 8 1 9
54.
888
74.
1005
55.
8
88
75.
707
56.
45
60
13
156
76. 5 2   2
369
57.
987
58.

59.
524
60.
105 15
130
13
24
40
77.

78.
 1 1  1
15
15
80.  1 1 0   1 0
79.

All Operations
1.
–2 + 3
21.
0+5
41.
–1   8
61.
–5+8
2.
8–9
22.
16 + – 3
42.
–1  –9
62.
–6  –1
3.
0+5
23.
6+ –3
43.
30 / – 6
63.
6 / –6
4.
0/7
24.
16 – 7
44.
–1  0
64.
9  1
5.
19 – 10
25.
4–5
45.
–7–0
65.
3–9
6.
–4 – 1
26.
–9 + 1
46.
–5–1
66.
6+8
7.
–7  2
27.
–9 + 10
47.
–6/ 3
67.
4  1
8.
–9   3
28.
6  –3
48.
–2  8
68.
–4/ –1
9.
9/–9
29.
–1   8
49.
– 30 / – 10
69.
2 – 10
10.
–9   4
30.
0–5
50.
–5 6
70.
63 / 9
11.
0/–3
31.
8–0
51.
13 – 5
71.
– 13   7
12.
9+ –7
32.
5  –3
52.
–7  –8
72.
0  6
13.
–2 + 6
33.
6 – 16
53.
0 6
73.
–2–7
14.
–1 – 3
34.
0 9
54.
–3  –6
74.
– 10  – 1
15.
7  –2
35.
4+ –7
55.
–1–4
75.
–8   5
16.
–14   5
36.
–13   7
56.
–23   8
76.
– 11   4
17.
0  –2
37.
2  2
57.
0   10
77.
–5+6
18.
0–8
38.
–5–4
58.
13 – 5
78.
7   12
19.
–56 / – 8
39.
–3   10
59.
–7  –7
79.
4 – 18
20.
–7 – 6
40.
–8   4
60.
0  5
80.
9+ –9
9
Decimal Rationals Review
10
Fractions Rationals Review
11
12
13
14
Matrix Operations
Simplify the following:
 2  8   5 2 
 

6   9 1 
1.
 6 4 8 1

 

 3 5  5 7 
12. 
9
2.
  5  4    6  1

 

 6  2   7  3
13.
3.
4.
5.
6.
7.
8.
 5  6   3 4 

 

0 3    2 8 
 8  4   9 6 

 

 2  2   6  4
  3  5   7 9 

 

 4  3   2  5
14.
  3 31   8  6 

 

 18  7    2  8 
15.
  8  4   3 14 

 

 2 16    9 0 
6  2  7  9 7 
5

16.   8 5 1  6  5 12
 4 10  7   6  8 7 
  4 29   2  3 

 

 14  5    7  9 
  4  7  4 0 

 

1    5 11
 5
 3 7  8 5  2 6 

 

  4 9 6    8  9 10 
 3 0  5  4  6 9 
9  2   5  4 8 
7

 

 5  4 6    1  3  5
  8 0  3   5  5 1 
17.
  5 10 
4

 2  3
18.
 4 9 
8

  5 12 
19.
 7 3 


  4 19 
5
6
 8 12 
20. 7 

 1  20 15  3 
9.
8
 2  2  7  2
4

 

  5  9 1   5  8 13 
 4  10  9    1  3  8 
21.
  13 10   13 8 
 

 7    9 23 
10. 
 14
11.
7  12   7
5
 8
 6

 

  25  3 11    14  23  1
 2
20  4    5 14 11 
6
3 
 3  6 8 1 8
 4 7 2 8

  

  5 5 7  2 1
 1 6 9  3  5
3
7
 5  4  2 

 5  11
22. 
  
 3 1 0
2
15
Properties
Identity Property of Addition:
For all real numbers, a, a + 0 = a and 0 + a = a
Additive Inverse Property
For every real number, there is exactly one real number – a, such that a + (-a) = 0 and
– a + a = 0.
Closure
Take two numbers from a set and perform an operation.
If the answer is always in the set, then the set is closed.
Identity Property of Multiplication
For all real numbers a, a  1 = a and
1  a = a.
Multiplicative Inverse Property
For every non-zero real number a, there is exactly one number
The number
1
a
1
a
, such that a  a1  1 and
1
a
 a  1.
is called the reciprocal or multiplicative inverse of a.
Multiplicative Property of Zero
The product of any real number and zero is zero.
Other Properties of Zero
Zero divided by any nonzero real number is zero.
0
a
a  0= 0
0
Division by zero is undefined. (Division by zero cannot be done.)
Commutative Property. For all real numbers and b, a + b = b + a and
ab=ba
Associative Property
For all real numbers a, b and c, (a + b) + c = a + (b + c) and
(a  b)  c = a  (b  c).
Distributive Property
For all real numbers a, b and c, a(b + c) = ab + ac and a(b – c) = ab – ac.
Properties of Equality
For all real numbers a, b and c:
Reflexive Property
a=a
(A number equals itself.)
Symmetric Property
If a = b, then b = a.
Transitive Property
If a = b and b = c, then a = c.
Substitution Property If a = b, then a can be replaced by b and b can be replaced by a.
Additive Property of Equality: If a = b then a + c = b + c.
Multiplicative Property of Equality: If a = b then a  c = b  c.
16
17
Name the property used in each step.
Algebraic Proofs
18
Evaluate Algebraic Expressions
Evaluate the following showing all math steps and the matching steps in order of operations.
Do work in your spirals.
Examples:
Evaluate the following when a = 3, x = 6, y = – 5.
x+y
6+5
11
substitution
+ –
ax – y
3 6 – (–5) subst
18 + 5
/
23
+ –
4 ( xy – 7 )
4( 6(–5) – 7 ) subst.
4  – 37
( )N
– 148
/
Evaluate the following when a = – 3, b = 4, c = – 2, h = 10, k = 16, x = – 6, y = 5, z = 8.
1. ax + b
2. | cy – b |
3. b ( x – a )
4.
a2b
5. ab2
6. | bc + ax |
7.
(x–b)(y+a)
8. 59 – abc
9. x / a + b / c
10. y2 – ab
11. ( hk ) / ( cb )
12. h2 / y2
13. x2 + ax + k
14. y3 – ch
15. c ( bk – h )
16. ( h – b )2
17.
19. zh + bk + ax
20. kz – cx – hb
21. zx – ab + ck
22. k / b + h / y
23. z / c + k / c
24. yz / | bc |
25. k2 – bk + a
26. h2 + ak – b
27. z2 + cz + hx
28. c2 + 9c – 11
29. 13h2 + 11y2
30. 12b2 – b
31. ( kx ) / ( ab )
32. k x / a b
33. ( kx ) / c2
| ch – ax |4
18. z ( abh – cxy )
19
Algebraic Expressions
Write a P for positive or N for negative above each term then simplify the following:
1. 2a + 4a + 8a
28. –x – x
55. 23m + 4n – –16m
2.
5x + 6x + 9x
29. x – – 2x
56. 5y – 9 – 3y + 11
3.
3n + 9n + 11n
30. c + 3c
57. 5q – 2w + 9w – 8g
4.
5y + 6y + 14y
31. 5x – 2x
58. 24b – 4b – 6b – –9b
5.
6p + 9p – 5p
32. 3x – – 2x
59. 6h – v + 27v + 5h
6.
2w + w + w + 4w
33. 4w – 9w
60. 13f – 7g + 18f + 4f
7.
8x + 17x + x
34. – 5p – p
61. 2k – 7 + 11k – –14k
8.
4g + 9g + 8q
35. 6k – – 5k
62. 7m –- 2m – 8m – m
9.
3c + 9c + c + 7c
36. x – 9x
63. –15 + 12x + 11 – 13x
10. 8w + 8f + 8w
37. – 8x –
64. 6c + 2h – –9c + 3h
11. 9a + 8m + 3m
38. 5 + x – 3
65. 12 + 5v + 4v – 8 – 9v
12. 5w + 15v + 8w + 6
39. 3 – – j – 10
66. 26 + 36b + 4b + 30b
13. 4j + 9h + 9j + 7j
40. g – 5 – 3g
67. 2x + 6 – x – 5
14. 2x + x + 3x + 5
41. 12 – 3q –
15. 9f + 5y + 3f + 4y
42. 5 – x – 6
69. – x – 1 – 2x – 3
16. 4x + 7y + x + y
43. 3 + x + 6
70. – 3r + 4s – 7r – s
17. 18x + 14 + x + 17x + 6
44. 7 – –k – 4
71. 12m – n – 23m – 4n
18. 5c + 2c + 8c + c
45. 8g – 2 – 2g
72. 2y – 7 – 4y + 16
19. 9w – 4w
46. 4q – 15
73. 9g – 8w + 2w – 4g
20. 4x – 3x
47. 7 – 5x – –6x
74. 14b – 3b – b – – 5b
21. 2c + –6c
48. 8 + 9p – 6 – 2p
75. 3h – v + 9v + 17v + 9h
22. 5x – 8x
49. 4x + 7 – 4x – 7
76. 4f – 5q + 13f – 6f
23. 3x – –12x
50. 3w – 6 + 3w – 8
77. 9k + 5 + 13k – – 18k
24. 3w – 8w
51. – x + 7 – 4x – 5
78. – 6m – 4m – 8m – m
25. –6p – 2p
52. 9 + 6x + 5x – l
79. –16 + 14x + 17 – 14x
26. 3k – –9k
53. 9 – 4 + 17k – 3
80. 5c + 3h – – 5c + 4h
27. 15x – 19x
54. 13r + 5s – 6r – 2s
81. 4x – 6x – 7x – 9x
x
20
9
68. w – 5 – 3w – – 7
Simplify the following using the Distributive Property:
3m – 8 ( 7w + 6m )
1.
2(x+6)
18. 4 ( 2x + 5 ) + 11
35.
2.
5(x–8)
19. 2 ( 4 + 8x ) + 12
36. 4x + 8 ( 3x – 4 )
3.
6(8–x)
20. 5 ( x + 13 ) + x
37.
6w – 5 ( 9w + 6 )
4.
3(2–g)
21. 4 ( 5x + 12 ) + 6x
38.
7 – 3 ( 2 + 3n )
5.
8(4+2x)
22. 2 ( x – 11 ) + 1
39.
1 + 5 ( 7n – 8 )
6.
9 ( 5 + 8x )
23. 2m – 7( 8w + 9m )
40.
3 – 8 ( 11x – 4 }
7.
8 ( 9 – 3y )
24. 6x – 6 ( 6x – 7 )
41.
16 – 5 ( 4 – 8x )
8.
4 ( 8 – 6y )
25. 2w + 7 ( 7w – 9 )
42.
6 ( 4z + 8 ) + ( 11z + 4 )
9.
–5 ( 3x + 7 )
26. 9 – 4 ( 2n + 3 )
43.
2 ( 6 + 5x ) + 3 ( 4 + 8x )
10.
–4 ( 8x + 7 )
27. 6 – 5 ( 3 – 9c )
44.
– 3 ( 5 – 3w) – ( 5w + 4 )
11.
–3 ( 2 – 3x )
28. 3 ( 2x + 8 ) – 6
45. 7 ( 2c + 8 ) – ( 9 – 5c )
12.
–3 ( 7 – 4x )
29.
7 ( 4 + 7x ) – 5
46. – 6( 3y – 3p ) + 2(5p + 4y )
13.
–5 (–3x – 7 )
30.
3 ( 2x – 11 ) – 10x
47. 9 ( 3x + 7 ) + ( 5x – 4 )
14.
–2 (–x – 5 )
31.
3( 5+x ) – 6
48. – 11 ( 8 – 3h ) – 3 ( h – 2 )
15.
–3 (–9 – 11x )
32.
5 ( 6x + 8 ) – 3x
49. 9 ( 5 – 8d ) + 7 ( d + 9 )
16.
–11 (–2 – 5x )
33.
9 ( 3x – 2y ) + 9y
50. 8 ( k + m ) – ( k + m )
17.
–5 ( 3x + 2y )
34.
7y – 4 ( 2y – 9 )
51. 4(2x – 7) – 5 (6 – 3x)
21
Solve the following equations showing all the work.
1. a – 11 = 15
30. 61 = – y – 4
2. b – 8 = 17
31. 36x = 72
3. y + 7 = 29
32. 10y = – 10
4. x + 18 = 31
33. 3c = – 21
5. – 76 + m = 92
34. – 8a = 32
6. – 49 + n = 63
35.
1
b4
2
36.
1
3
55. – 4 = – 8 – 2z
56.
7. c – 30 = – 19
8. d – 24 = – 15
9. p + 18 = – 32
58. 18 = 2c + 10
59. 17 – 3y = – 10
1
37.  10
r5
10. s + 90 = – 55
38. 
11. 24 + t = 0
39. 0 = – 4 k
12. 0 = z – 14
40. – 7 = – 7p
13. v – 37 = – 54
57. – 6x + 25 = – 11
t7
41.
c
4
9
1
s
9
 1
14. w – 94 = – 110
60.
8n – 14 = – 22
61.
–x+3 = –4
62.
5 – m = 12
63.
–6 – z = –2
64.
– 4 = 6 – 2x
2
65.
43. – 11f = – 88
66.
44. – 27p = – 81
67.
18. 39 = y + 12
45. 4  
u
3
68.
19. – 19 – a = – 23
46.  1 
n
13
69.
15. – 7 + k = – 17
16. – 18 + h = – 38
17. 45 = x + 16
20. b – 32 = – 82
42.
d
2
– 7 = 3 + 5a
x
 9  13
5
x
7  9 
3
y
5 
 4
3
1
x 72
3
3
6 
y  9
5
3
z
4
47. 5x – 1 = 26
70.
17   10 
48. 4y – 2 = 14
71.
32 = 7x + 8 – 5x
49. 2z + 4 = 8
72.
6y + 8 – 5y = – 11
50. 6 + 2a = 10
73.
– 3 = 8z + 8 – 9z
51. 9z – 5 = 4
74.
5 = 5x – 7x + 25
27. 45 – m = 15
52. 4y – 7 = 21
75.
3y + 7 – 5y = – 9
28. 34 – r = 34
53. 6 = – 4x – 2
76. – 7 = 3p – 9 – 7p
21. 1 – x = 4
22. 16 = 3 – a
23. 18 = 5 – g
24. 3 – h = – 26
25. 25 = 18 – k
26. 4 = – p – 6
29. 52 = 81 – z
54. 4 – 3y = 13
22
Solve the following equations. Show all work for each.
77. 9y – 18 = 3y
98. y + 11 = – 2y + 6
78. 7c – 9 = 8c
99. – 2y + 3 – y = 11 + y
79. 8n – 12 = 5n
100.
16 – x = 4x + 8 + 3x
80. – 11m = 14 – 9m
101.
2 ( y + 7 ) = 16
81. – 6x = 10 – 4x
102.
3 ( x – 2 ) = 18
82. – 4z = 35 – 9z
103.
– 5 ( a + 2 ) = 30
83. 8p = – 5p + 65
104.
x + 9 = 2(x–3)
84. – 84 + 15r = 3r
105.
2 ( y + 3 ) = 12 – y
85. 11c + 36 = 8c
106.
25 – 5a = 3 ( 2a + 1 )
86. 7z – 9 = 3z + 19
107.
– 2 ( 3 – 2c ) = 10 – 4c
87. 6 + 10t = 8t + 12
108.
23 = 12 – ( 6 + c )
88. 3x + 7 = 16 + 6x
109.
5 ( x – 1 ) = 2x + 4 ( x – 1 )
89. 18 + 3y = 5y – 4
110.
13 – ( 2x – 5 ) = 2 ( x + 2 ) + 3x
90. 11a + 8 = – 2 + 9a
111.
– ( 3 – 2n ) + 7n = 3 ( n + 3 )
91. 9x – 5 = 6x + 13
112.
– ( y + 8 ) – 5 = 4 ( y + 2 ) – 6y
92. 5 – x = x + 9
113.
3 ( c + 4 ) – 6c = 2 ( 4 – 2c )
93. 14 + 3n = n – 14
114.
8y – 3 ( 4 – 2y ) = 6 ( y + 1 ) – 2
94. 7 – x = 5 + 3x
115.
– 2 ( 3 – 4z ) + 7z = 12z – ( z + 2 )
95. 4y + 2 = 2y + 4 + 3y
116.
– 3 ( 6 – 2x ) + 4x = – ( 2x – 6 )
96. 8c – 12 = 15c – 4c
117.
7x – ( 9 – 4x ) = 3 ( x – 11 )
97. 5x – 3 = 7x + 7 + 3x
118.
7r + 3 ( 7 – r ) = – ( r + 4 )
23.
LCM Method
Solve the following using the LCM Method. Show all work in your notebook.
1.
3
c 15
4
2.
3
2
y 
 y
5
15
3.
5
2
 c  6
9
3
4.
1
2
1
c 

4
3
3
5.
2
1
5
y 

3
2
3
6.
5
3
1

a 
8
2
4
7.
2
x79
3
8. 9 
1
3
9.
x6 
x3
2
4
1
x  6
2
10.
1
1
y  4 
y  7
2
5
11.
3
2
x  3 
x  2
2
3
12.
1
2
r  1 
r  2
3
5
13.
3a  4
5
2a  1


12
3
2
14.
2x  3
x
x3


7
2
14
15.
3y
2y  9
y1


4
3
5
16.
3b
2b  1
b7


4
2
6
18.
6x  5
2x  7
9 x


8
12
3
17.
4x  3
5x  4

9
6
5
24.
Decimal Method
Solve the following using the Decimal Method. Show all work in notebook.
1.
0.2 x = 1.8
3.
8.2 – 3.2c =
– 7.8
2.
2.6 x =
4.
0.05 m = 7.45
5. 0.02 d – 2.6 = 0.84
6.
1.3 = 0.15 x – 3.2
7. 0.006 x – 7.3
8. 0.08 – 0.2y =
0.7 z – 0.1071
9.
– 17.4
=
0.14
=
0.07z
11.
0.112 y + 2 = 0.012 y – 4
13.
0.5 n + 0.02
=
– 0.2 – 0.6 n
– 4.4
10.
– 0.09
–
12.
0.7 x – 0.11 =
= 5.2
0.1 x
– 0.03 x
14. 0.23 z + 119.7 = 0.8 z
15. 1.2 x + 0.004 = 1.4 x – 2
16. 0.09 c – 5.1 = 1.5 – 0.24 c
Solve the following using the LCM and Decimal Methods. Show all work in your notebook.
17.
19.
1c =
6
18. – k
8
8 +c
5
x–3 = 5
6
3
20.
=
– 7 + 3k
10
h + h = 1
5
7
21.
7y + 1 = 5 y – 4
9
2
6
3
22. 14 x + 8 = 2 x – 10
7
3
23.
9y + 5 –
15
24. x + 5
8
7y + 2
3
= 6
5
25.
+
x+9
4
=
6
Use the verbal model format to solve the following. Show all work.
1. Seven more than three times a number is eighteen. Find the number.
2. Jason has fourteen more than three times Evelyn’s amount. Together they have 130 marbles. How many
marbles does each have?
3. Seven times the difference between eleven and twelve times a number is four. Find the number.
4. April has 9 computer games. This is seven less than twice the number of Sam’s games. How many does
Sam have?
5. The quotient of nine times a number and fourteen is seven. Find the number.
6. George has twelve books more than Jonathan. Together, they have 44 books. How many books does
each have?
7. Six more than half a number is forty-two. Find the number.
8. Arthur has 23 books. This is twelve books less than Jonathan. How many books does Jonathan have?
9. One number is sixteen more than five times a second number. Their sum is 58. Find the numbers.
10. Eleven is twice the sum of eight times a number and twelve. Find the number.
11. Greg earned 4 more points than twice Matt’s amount. Together, they earned 19 points. How many points
has each earned?
12. Find the radius of a circle with the circumference of 13.65 feet.
13. The measures of two angles of a triangle are 41° and 83°. Find the measure of the third angle.
14. Find the height of a prism if its volume is 2295 ft3, its width is 15 ft and its length is 17 ft.
15. A triangle has a height of 38.2 m and an area of 324.7 m2. Find its base.
16. Find the measure of each angle in a regular octagon.
26.
Use the verbal model format to solve the following. Show all work.
17. Find the sum of the angles of a polygon with 19 sides.
18. Four of the angles in a pentagon measure 89°, 109°, 73°, 154°. Find the measure of the other angle.
19. What was the cost of the meal if an 18% tip was $10.99?
20. What was the original cost of a dress during a 25% off sale if the savings was $22.50?
21. How many towels did Stephanie purchase for $89.70, if each towel cost $5.98?
22. The sum of five and six times a number divided by three is the same as the difference between seven
times the same number and four divided by eight. Find the number.
23. The sum of a number divided by four and nine times a number divided by six is the same as the difference
between five times a number and seven divided by two. Find the number.
24. A company reimburses $49 plus forty-five cent for each mile a salesman drives. If the reimbursement
check was for $121, how many miles did the salesman drive?
25. A coat, originally marked $159, was sold for $135.15 during a sale. What was the rate of the discount?
26. A stereo cost $289. The final bill after sales tax was $306.34. What was the rate of the sales tax?
27. The check in a restaurant came to $58.45 and Mr. Jones left $69. What was the rate of the tip?
28. Marcy paid $146 for her purchases including a 7% sales tax. What was the original cost of her purchases
before the sales tax?
29. Mr. Brown paid $136 for a suit during a 25% off sale. What was the original price of the suit?
30. A repair man charges a service fee of $60 plus $35 for each hour he works on the item. If the final bill was
$147.50, for how many hours did he work on the item?
31. The page of your school yearbook is 8 ½ inches by 11 inches. The left and right margins are ¾ inch and
2 78 inches, respectively. The space between pictures is 163 inch. How wide should you make each picture to
fit three across the page?
32. You are shopping for earrings. The sales tax is 5%. You have a total of $18.37. What is your price limit
for the earrings?
33. You want to include four photos on the cover of a program for the school play, two across the page. The
cover is 6 1/2 inches wide, and the left and right margins are ¾ inches each. The space between the pictures
is ½ inches. How wide would you make the pictures?
27.
1.
28.
29.
∆ABC and ∆DEF are similar. For each set of measures given, find the measures of the
remaining sides.
B
21. c = 11, f = 6, d = 5, e = 4
a
c
22. a = 5, d = 7, f = 6, e = 5
23. a = 17, b = 15, c = 10, f = 6
A
C
b
24. a = 16, e = 7, b = 13, c = 12
E
25. d = 2.1, b = 4.5, f = 3.2, e = 3.4
d
f
26. f = 12, d = 18, c = 18, e = 16
27. c = 5, a = 12.6, e = 8.1, f = 2.5
D
e
F
Glencoe Algebra 1, p. 204
Solve the following using the verbal model format. Show all work.
1. Seven is to nine as fourteen is to what number?
2. Eleven is to thirty-three as what number is to twenty?
3. What number is to forty-nine as three is to seven?
4. Fifty-one is to what number as thirty-four is to two?
5. Three is to four as what number is to twenty-four?
6. Twenty-seven is to eighteen as six is to what number?
7. What number compared to 10 is the same as 3 compared to 5?
8. At the rate of 3 items for $.10, how many items can you buy for $.50?
9. At the rate of $9.50 for 19 items, how much will 8 items cost?
10. How much will 8 items cost at the rate of 6 items for $9?
11. How many items can you get for $4.50 at the rate of 8 items for $.75?
Simple Interest = Principle • rate • time
12. How much simple interest did Simon earn by depositing $5800 for 4 years at an interest rate of 2.4%?
13. John invested some money at 6% for 1.75 years and received $777 in simple interest. What was his initial
investment amount?
14. Alex had $580 invested for 2.5 years and earned $62.64 in simple interest. What was the interest rate?
15. How long did it take Pat to earn $137.10 in simple interest by investing $952 at an annual rate of 4.8%?
30.
Model 6 Review
31.
Pythagorean Theorem:
c2 = a2 + b2
32.
Which of the following are right triangles?
1. 3, 4, 5
2. 6, 4, 5
3. 13, 12, 5
4. 11, 6, 9
5. 7, 24, 25
6. 13, 10, 8
7. 6, 11,
8. 9, 14,
9. 9, 7,
32
10. 12, 20, 24
11. 9, 40, 41
13. 16,
356 , 10
14.
15.
150 , 4, 13
15 ,
157
7,
115
12. 2, 2.5, 1.5
8
16. 1.7, 1.5, 0.8
Solve the following using the Pythagorean Theorem. Draw a picture.
1.
A fire truck parks 15 ft away from a building. The fire truck extends its ladder 39 ft. How far up the building from the
truck's roof does the extension ladder reach?
2.
Carson found an old tent in the attic of his house and decided to set it up in the back yard. However, the support
sticks for the tent are missing. If the tent is 60 inches across on the bottom and 34 inches on each side, how tall of a
stick does he need to set up the tent?
3.
A television has a rectangular screen with a diagonal measurement of 30 inches. If the screen has a height of 18
inches, what is the width of the screen?
4.
Two ships leave port at the same time. Ship X is heading due north and Ship Y is heading due east. Six hours later
they are 300 miles apart. If the Ship X had traveled 240 miles from the port, how many miles had Ship Y traveled?
5.
Jeremy goes to White Water Amusement Park. While there he decides to go down the park's huge waterslide called
Lightning. If the slide is 120 feet high and the base of the slide is 90 feet from the pool, then what is the length of the
slide?
In #6 to 10, find the length of each of these lines in a coordinate plane.
7
6
9
1
8
33.
0
Solve completely the following word problems using the verbal model format:
Verbal Models 1 to 7 Review
1. The volume of a rectangular prism is 43200 m 3. If its length is 36 m and its height is 48 m, find its width.
2. Alice earned $54, which is $36 less than three times Sue’s amount. How much does Sue earn?
3. John drives 450 miles in 7.4 hours. At the same rate, how long will it take him to travel 780 miles?
4. The final cost of a refrigerator (including an 8% tax) was $744. What was the original cost of the refrigerator?
5. The sum of the measures of the angles of a polygon is 9720°. How many sides does the polygon have?
6. Find the number such that six times a number less than nine is the same as four times the same number subtract one
7. The hypotenuse of a right triangle measures 36 feet and one leg measures 8 feet. Find the length of the other leg.
8. A tree cast a 25-foot shadow at the same time as a 6-foot pole casts a 2.5-foot shadow. How tall is the tree?
9. The waiter received a tip of $29.67, which represented 20% of the food check. How much was the check for the food?
10. Convert 456 liters to kiloliters.
11. A pair of jeans went on sale for $38.86. What was their original cost if the discount rate during the sale was 33%?
12. The first number is twelve more than five times the second number. Their sum is 432. Find each number.
13. A simple recipe calls for 4 cups of flour for every 1.5 cups of sugar. Amanda only has 3 cups of flour. How much
sugar must she use with 3 cups of sugar to keep the taste the same?
14. Julie saved $11.62 on an item that was marked $64.58. What was the rate of discount?
15. Find the missing sides in these sets
of similar triangles.
19 ft
A.
8 ft
y ft
12 ft
26 m
B.
10 m
32m
wm
12 m
xm
14 ft
k ft
16. Sloan made 35 more cards than five times Monica’s amount. If he made 245 cards, how many did Monica make?
17. Seven times the difference between eight times a number and five is the same as four times the sum of eleven times
that number and twelve. Find the number.
18. Jeanne ran 15 miles more than twice Alison’s distance. Together they ran 72 miles. How far did each girl run?
19. Two boats left the same dock at the same time. One traveled due north at 11 knots per hour. The second traveled
due south at 14 knots per hour. After how many hours were the boats 150 knots apart? How far had each boat gone?
20. What number is 84% of 26?
21. The sum of nine times a number plus three is to eight as the difference between seven and six times the same
number is to six. Find the number.
22. A square has an area of 990 square feet. How long is one of its sides?
23. Fifty-five is to thirty-three as twelve is to what number?
24. A rancher rode 32 miles on horseback over 8 hours. At this rate, how far can he go in 10 hours?
25. Emily worked nine hours longer than five times Liz. If Emily worked 44 hours, how long did Liz work?
34.
Solve completely the following word problems using the verbal model format:
Verbal Models 1 to 7 Review
26. Two boats left the same dock at the same time. One traveled due north at 16 knots per hour. The second traveled
due east at 15 knots per hour. After nine hours, how far apart were the boats?
27. Alex earned $46.58 in simple interest over 3 years at a rate of 2.3%. How much money did she invest?
28. Convert 45.6°F to Celsius temperature.
29. A 25-feet high statue and casts a 6-feet shadow while a building casts a 14-foot shadow. How high is the building?
30. The perimeter of a rectangle is 86 feet. Its length is 25 feet more than five times its width. What is the length and
width of the rectangle?
31. John bought a $24.99 frying pan, a $48.89 set of dishes, and $19.56 of assorted cooking utensils. If he purchased all
of these items during a 15% off sale, what was the final cost of all the items?
32. The diagonal of a rectangle measures 38 feet while the length is 21 feet. What is the width of the rectangle?
33. 25.5% of what number is 42.9?
34. One angle of a regular polygon measures 172.5°. How many sides does the polygon have?
35. The first number is twelve times a second number while a third is three more than fourteen times the second number.
The sum of all three numbers is 65.1. Find the values of all three numbers.
36. A rectangular prism has a surface area of 1778.18 feet2, a length of 18.5 feet and a height of 20.1 feet. Find its width.
37. Twelve times a number less than fifteen equals twenty-four times the same number plus one. Find the number.
38. Matt mows the 1200 ft2 lawn in 85 minutes. At the same rate, how long will it take him to mow a 1600 ft2 lawn?
39. Find the sum of the measures of the angles of a polygon with 49 sides.
40. Can the following dimensions form a right triangle? Prove your conclusion. 6 inches, 7 inches,
13 inches.
41. Jen works 4 hours less than twice Maggie’s hours. If Jen works 42 hours this week, how long did Maggie work?
42. How far can a car travel on 14 gallons of gas if at the same rate, it can travel 1584 miles on 49.5 gallons of gas?
43. In a pentagon, the measures of four of the angles are 146, 78, 92, and 81. Find the measure of the fifth angle.
44. $2954 is invested over a four-year period and earned $425.38 in simple interest. What was the interest rate?
45. What is the original cost of a dress if you paid $110.49 during a 15% off sale?
46. How many of the same priced items can you purchase for $100 if each item cost $16.25?
47. The area of a triangle is 123.58 yard2. If its base measures 14.8 yards, what is its height?
48. An antique fire truck cost $16.32 less than a dollhouse. Together they cost $135.58. How much did each cost?
49. Joan purchased 17 of the same items for $61.03. What was the unit cost per item?
50. Mr. Roman is going to paint his house using a 20-foot ladder. He sets the base of the ladder 15 feet away from the
house. How far up the side of the house will the ladder reach?
51. The length of a rectangle is 42 meters less than six times its width. If the perimeter measures 1134 meters, find the
length and width of the rectangle.
35.
Chapters 1 & 4
Write an Equation for a Function
•
•
•
Find the first difference for x.
Find the first difference for y.
Find: Changein y   y
Changein x  x
•
Find the y-intercept: the y-coordinate in (0,
•
Write equation in the form: y =  x x + original value
)
y
Find the missing values in this table:
x
0
y
1
2
3
4
-9
-20
-31
-42
-53
Change in y
Change in x
Find the missing values in each of these tables and, if possible, find the equation for the table.
1.
2.
x
-5
-4
-1
y
14
6
-3
-4
0
2
3.
3
-10 -7
-1
y
-19 -16 -13 -10
0
0
y
-12 -15
x
x
2
4.
x
y
-7
36.
0
1
2
3
4
-15
-20
1
2
3
4
17
24
31
38
-25 -30
Find the missing values in each of these tables and, if possible, find the equation for the table.
5.
6.
7.
x
-6
-4
-1
y
9
5
-1
x
4
5
6
7
y
29
36
43
50
x
0
-10
-11
-12
84
92
100 116
0
-5
-11
-15
31
61
81
y
8.
x
7
y
-29
0
5
9.
-13
0
10.
11.
-14
12.
37.
x
-8
-5
-3
0
9
y
-31
-19
-11
x
-1
0
4
8
12
y
-6
9
21
33
37
x
-13
-9
-6
y
19
11
5
x
-7
-1
0
y
12
6
0
8
-23
6
8
-1
-3
Relationship to Model 5 & 7 Problems
Number of
DVDs
purchased
Total Cost
Find the equation that corresponds to these tables.
1.
6.
x
1
3
5
7
9
x
8
6
4
2
0
y
5
9
13
17
21
y
15
13
11
9
7
2.
7.
x
-6
-5
-4
-2
0
x
0
-2
-3
-5
-9
y
-36
-31
-26
-16
-6
y
-5
-21
-29
-45
-77
3.
8.
x
-4
-2
0
2
4
x
-20
-15
-10
-5
5
y
7
3
-1
-5
-9
y
39
29
19
9
-11
x
0
4
8
9
12
y
4
40
76
85
112
4.
9.
x
-6
-3
0
3
6
y
20
11
2
-7
-16
5.
10.
x
-3
-2
-1
0
1
x
2
3
5
8
13
y
-17
-13
-9
-5
-1
y
4
6
10
16
28
38.
39.
Scatterplots & Line of Best Fit
The 1990 earnings per share and dividends per share for 35 electric utility companies (in the central
United States) are shown in the table.
1.
2.
3.
4.
Enter the data into L1 and L2.
Create a scatterplot.
Write the line of best fit in space to right.
_______________________
Write Correlation coefficient, r = _______
Earnings
Dividend
Earnings
Dividend
Earnings
Dividend
Earnings
Dividend
1.67
1.73
1.77
1.79
1.84
1.90
1.92
1.97
1.99
1.73
1.46
1.48
1.42
1.63
1.60
1.83
1.46
1.56
1.99
2.00
2.00
2.00
2.23
2.23
2.25
2.38
2.48
1.67
1.72
1.65
1.86
1.74
1.56
1.80
2.20
1.60
2.55
2.56
2.58
2.69
2.74
2.77
2.79
3.02
3.26
2.35
2.00
1.80
2.46
2.10
1.74
2.30
1.90
1.78
3.32
3.38
3.45
3.54
3.70
3.79
4.12
4.40
2.62
2.51
2.81
2.28
2.50
2.76
2.40
2.96
The data in the table shows the age in years and the number of hours slept in a day by 28 infants
who are less than one year old.
1.
2.
3.
4.
Enter the data into L1 and L2.
Create a scatterplot.
Write the line of best fit in space to right.
_______________________
Write Correlation coefficient, r = _______
.03
Sleep
(hrs)
15.0
.21
Sleep
(hrs)
14.5
.52
Sleep
(hrs)
14.4
.05
15.8
.26
15.4
.69
.05
16.4
.34
15.2
.08
16.2
.35
.10
14.9
.11
.19
Age (yrs)
.86
Sleep
(hrs)
13.9
13.2
.90
13.7
.70
14.1
.91
13.1
15.3
.75
14.2
.94
13.7
.35
14.4
.80
13.4
.97
12.7
14.8
.44
13.9
.82
14.3
.98
13.7
14.7
.52
13.4
.82
13.2
.98
13.6
Age (yrs)
Age (yrs)
40.
Age (yrs)
41.
VOCABULARY
42.
VERBAL MODELS
43.
44.