Summer Mathematics Prep
Entering Algebra 1
Chesterfield County Public Schools
Department of Mathematics
SOLUTIONS
NOTE: There are many ways to solve problems in mathematics. The solution shown is just one way to solve
each problem in this document.
Order of Operations
Simplify.
15 ÷ 3 ⋅ 5
1. 5 ⋅ 5
= 25
15 ⋅ 3 ÷ 5 − 36
45 ÷ 5 − 6
2.
9−6
=3
130 − 10  22 − 4 ( 3) 
130 − 10 [ 22 − 12]
3. 130 − 10 [10]
130 − 100
= 30
18 + 3 ( 43 − 54 )
2
18 + 3 ( 64 − 54 )
4. 18 + 3 (10 )
2
2
18 + 3 (100 )
18 + 300
= 318
102 ÷ 52 + 27 ÷ 3 ( 9 )
100 ÷ 25 + 27 ÷ 3 ( 9 )
5. 4 + 9 ( 9 )
4 + 81
= 85
Chesterfield County Public Schools
Department of Mathematics
Page 1 of 4
May 2012
Evaluate each expression.
6. 2(x + y) + 3x when x = 4 & y = – 5
2 ( 4 − 5 ) + 34
2 ( −1) + 81
−2 + 81
= 79
7. Use y = 4 and y = – 4 to evaluate
a. y2 = (4)2 = 16
y2 = (– 4)2 = 16
b. (2y)2 = (2 ● 4)2 = (8)2 = 64
(2y)2 = (2 ● – 4)2 = (– 8)2 = 64
Properties – Name the property of real numbers illustrated by each of the following.
8. 2(x + 3) = (x + 3)2
9. 2(x + 3) = 2x + 6
A – Commutative Property of Multiplication
C – Distributive Property
10. 4 + (7 + 6) = (4 + 7) + 6
B – Associative Property of Addition
11. 4 + (7 + 6) = 4 + (6 + 7)
A – Commutative Property of Addition
12. 7x(5 •
1
) = 7x(1)
5
D – Multiplicative Inverse
13. 7x(1) = 7x
G – Identity Property of Multiplication
14. x + 0 = 0 + x
A – Commutative Property of Addition
15. 5x3 + 0 = 5x3
G – Identity Property of Addition
Combining Like Terms – Apply the distributive property as needed then combine the like terms.
16. 12 – 9x + 15x = 6x + 12
17. 25x – 6x + 13 – 20 = 19x – 7
18. 4(x – 2) + 19 = 4x + 11
Chesterfield County Public Schools
Department of Mathematics
19. 2(x + 3) + 4(x – 1) = 6x + 2
Page 2 of 4
May 2012
Solving Equations – solve for variable.
20. 14x – 20x = 42
21. 2(x – 5) = – 30
–
x= 7
x = – 10
x
= 15
4
x = 48
22. 27 −
23.
Functions
24. Domain: {1, 2, 3, 4}
2
(6 x − 9) = 5 x − 11
3
x=5
Range: {2, 7, 12, 17}
25. C. y = 5x – 3
26. A. {(1,1), (2,2), (3,3)}
C. {(4,2), (-3,2), (2,2), (-9,2)}
F. {(5,-8), (-3,-7), (7,-6), (0,-5)}
27. A, C, D, F
y
28.
29.
x
y
x
Application Problems
30.
A. For every hour Sara works, she earns $5.
C. When she works 10 hours, she earns $50.
3
D. If she works 7 hours, she earns $38.75.
4
F. The more she works, the more she earns.
31. x = 5
32. x = 56
33. h = 16 m
Chesterfield County Public Schools
Department of Mathematics
Page 3 of 4
May 2012
34. State the properties used to simplify the problem.
9(2x + 6) – 18x =
Step
Step
Step
Step
Chesterfield County Public Schools
Department of Mathematics
1: 18x + 54 – 18x
2: 18x – 18x + 54
3:
0 + 54
4:
54
Step
Step
Step
Step
1
2
3
4
Distributive Property
Commutative Property
Additive Inverse
Identity Property
Page 4 of 4
May 2012