Name: ______________________________________
Damascus
High School
Summer Math Packet
Algebra
DUE AUGUST 29, 2014
The problems in this packet are designed to help you review topics from previous
mathematics courses that are important for your success in Algebra 1.
Directions: Show all of your work. You may use your notes from previous
mathematics courses to help you. Additional copies of this packet may be obtained
from the counseling office.
Helpful website:
http:/ /www.khanacademy.org/
By the time you enter Algebra, you should be able to:
A. Apply the order of operations to integer computations.
B. Add, subtract, multiply and divide integers.
C. Work with fractions.
D. Simplify algebraic expressions.
E. Solve equations that contain multiple steps.
F. Create algebraic equations from verbal expressions.
G. Evaluate expressions.
H. Find the slope of a line.
I. Graph linear equations.
A. You should be able to: Apply the Order of Operations to integer computations.
Refer to video tutorials at http://www.khanacademy.org/
Evaluate the following expressions without a calculator using Order of Operations.
(PEMDAS)
1.
4 ∙ 12 + 8 − 10 ÷ 5
2.
8(3 + 4) − 3 ∙ 2 ÷ (12 − 9)
3.
[52 + (12 − 8)2 ] − 17
B. You should be able to: Add, subtract, multiply and divide integers.
Refer to video tutorials at http://www.khanacademy.org/
Simplify the following expressions without a calculator. Show work when necessary.
4.
27 − 12 =
5.
−13 − 9 =
6. 27 − 100 =
7.
−15 − (−18) =
8.
−10 ∙ (−3 ∙ 6) =
9. (−5)2 =
11.
−12
=
−4
12. 81 ÷ (−9) =
10. −44 ÷ 4 =
C. You should be able to: Work with fractions.
Refer to video tutorials at http://www.khanacademy.org/
Simplify the following without a calculator. Make sure to show all of your work.
13.
3 6 15
∙ ∙
=
2 5 30
14.
15.
3
÷8=
4
16.
17.
1 5 4
∙ ∙ =
2 8 5
18.
3 5 1
+ + =
5 8 4
5 2
− =
4 3
−
16
÷8=
9
D. You should be able to: Simplify algebraic expressions.
Refer to video tutorials at http://www.khanacademy.org/
Simplify the following algebraic expressions. Show all work.
19.
−2(3𝑥 + 2) =
20.
21.
4(3𝑥 − 2) − (5𝑥 − 6) =
22.
3(2𝑥 − 3) + (𝑥 − 5) =
3
(𝑥 − 5) =
4
E. You should be able to: Solve equations.
Refer to video tutorials at http://www.khanacademy.org/
Solve the following equations. Show all work.
23.
𝑥 + 12 = 62
24.
48 − 𝑥 = 23
25.
𝑥 − 2 = 14 + 6
26.
13𝑥 = 195
27.
6𝑦 − 11 = 25
28.
8=
29.
𝑥
6
=
42 7
30.
3𝑥 + 7 = 2𝑥 − 1
−8 + 7𝑥 − 2 = 3𝑥 + 4 + 2𝑥
32.
−2 − 3(1 − 𝑥) = 4(−2𝑥 + 7)
31.
𝑥
5
F. You should be able to: Create algebraic equations from verbal expressions.
Refer to video tutorials at http://www.khanacademy.org/
Write an algebraic equation for each. Then, solve each equation showing all work.
33.
Three times a number, increased by 4, is 25. What is the number?
34.
A number divided by 6 is 14. What is the number?
35.
One third of a number is equal to 24. What is the number?
36.
Eight less than twice a number is twenty. What is the number?
Solve the following word problems by setting up an algebraic equation. Then, solve the
equations showing all work.
37. A $180 leather jacket is going on sale for a 25% discount. How much will the jacket cost on
sale?
38. Mike bought 3 CD's at a cost of $13.99 for each CD. What will he pay in total including a
7% sales tax?
G. You should be able to: Evaluate expressions.
Refer to video tutorials at http://www.khanacademy.org/
39. Complete the following table by evaluating each expression for the given values.
Expression
3𝑥 + 1
𝑥=4
𝑥 = −3
3(4) + 1 = 13 3(−3) + 1 = −8
𝑥2
2𝑥
𝑥+6
H. You should be able to find the slope of a line.
Refer to video tutorials at http://www.khanacademy.org/
40.) Find the slope of the line depicted in the graph below.
41.) Find the slope of the line depicted in the graph below.
42.) Find the slope of the line passing through (2, 4) and (5, 3).
43.) Find the slope of the line passing through (-2, -5) and (2, 3).
I.
You should be able to graph linear equations.
Refer to video tutorials at http://www.khanacademy.org/
Directions:
Procedure 1
1. Put the equation in slope-intercept form (𝑦 = 𝑚𝑥 + 𝑏).
2. Identify the y-intercept (𝑏).
3. Plot the y-intercept.
4. Identify the slope of the line (𝑚).
5. Use the slope to graph more points. Use 𝑚 = 𝑟𝑖𝑠𝑒 .
𝑟𝑢𝑛
6. Draw the line.
Or use Procedure 2
1. Set up a table of values and graph ordered pairs.
Note:
• Horizontal lines are written as 𝑦 = 𝑐, where 𝑐 is a real number. To graph, plot the
y-intercept (0, c) and draw a horizontal line through that point.
• Vertical lines are written as 𝑥 = 𝑐, where 𝑐 is a real number. To graph, plot the
x-intercept (c, O) and draw a vertical line through that point.
44.
𝑦 = 2𝑥 + 3
45.
1
𝑦 = 3𝑥 − 4
𝑚 = __________
𝑚 = __________
𝑏 = __________
𝑏 = __________
46.
48.
2𝑥 + 3𝑦 = 12
47.
−4𝑥 = 2𝑦 − 8
𝑚 = __________
𝑚 = __________
𝑏 = __________
𝑏 = __________
3
𝑦 = −2𝑥 + 5
49.
𝑦=𝑥
𝑚 = __________
𝑚 = __________
𝑏 = __________
𝑏 = __________
50.
52.
𝑦 = −𝑥 − 1
51.
𝑦=2
𝑚 = __________
𝑚 = __________
𝑏 = __________
𝑏 = __________
𝑦 = −6
53.
𝑥=3
𝑚 = __________
𝑚 = __________
𝑏 = __________
𝑏 = __________
Answers to ALGEBRA I summer packet
1)
54
2)
54
3)
24
4)
15
5)
-22
6)
-73
7)
3
8)
180
9)
25
10)
-11
11)
3
12)
-9
13)
17)
9
14)
10
1
18)
4
59
15)
40
−
3
2
9
15
3
32
16)
7
12
19)
−6𝑥 − 4
20)
7𝑥 − 14
23)
𝑥 = 50
24)
𝑥 = 25
21)
7𝑥 − 2
22)
25)
𝑥 = 22
26)
𝑥 = 15
27)
𝑦=6
28)
𝑥 = 40
29)
𝑥 = 36
30)
𝑥 = −8
31)
𝑥=7
32)
𝑥=3
33)
3𝑥 + 4 = 25; 𝑥 = 7
34)
35)
𝑥
4
𝑥−
4
= 14; 𝑥 = 84
6
1
3
𝑥 = 24; 𝑥 = 72
36)
2𝑥 − 8 = 20; 𝑥 = 14
37)
180(0.75) = 𝑥 𝑜𝑟 180 − 180(0.25) = 𝑥; 𝑥 = $135
38)
3(13.99) + .07(3 ∙ 13.99) = 𝑥; 𝑥 = $44.91
39)
Expression
3𝑥 + 1
𝑥2
2𝑥
𝑥+6
40)
41)
-2
2
3
1
42)
−3
43)
2
𝑥=4
𝑥 = −3
16
8
10
9
-6
3
44)
45)
46)
47)
48)
49)
50)
51)
52)
53)
I I