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Algebra 1 CC
Review
Unit 1: Properties, Expressions, Equations, and Applications
_____1. What is the value of the expression 5 x  12 when x  5 ?
(1) 13
(2) 13
(3) 22
(4) 37
_____2.. Which expression is an example of the commutative property?
(1) (x + y) + z = x + (y + z)
(3) x(y + z) = xy + xz
(2) x + y + z = z + y + x
(4) x • 1 = x
_____3. Which of the following shows the Identity Property of Multiplication?
(1) 10 + (-10) = 0
(3) 10 x 0 = 0
(2) 10 x 1 = 10
(4) 10 + 0 = 10
_____4. Which property of real numbers is illustrated by the equation  3  3  0?
(1) additive identity
(3) associative property of addition
(2) commutative property of addition (4) additive inverse
5. In your own words explain what the property of equality is and why it is useful in solving equations.
5
6. What is the additive inverse of  ?
6
5
7. What is the multiplicative inverse of  ?
6
For #8 – 11, simplify using order of operations.
8. 
1
 96  12
2
10. 8  10 4  7  2  
9.
50  25  5  2
 2  6
2
8
11. 20   10   52  2


2
For questions #12 – 15, evaluate the following expressions. Let a  6, b   1 and c  3
12.
 ab 
2
c
14. 4a  b  3c
2
13. ab c
15. 5 b  3c  a
16. 2 y  7  3 y  12
17. 5(2 x  7)  15x  10
18.
m2 5

8
4
19. 8 y  2 y  5  8  6 y
20.
x  1 2x 1

4
5
21. 6r  (3  4r )  5r  12
22. 5  x  6   2  x  1  3  x  9   1
23. 2 x  4  x  9   8  2  x  4 
Translate each of the following into algebraic expressions.
24. 5 more than a number
25. 6 less than x
26. The product of a number and 12
27. 3 less than the product of a number and 4
28. 10 more than twice a number
29. The quotient of 7 and x
Solve each of the following literal equations.
30. Solve for y:
3d  y  9
31. Solve for x:
6x  2  x  m
32. Solve for N:
A  S 1  DN 
33. Solve for a:
34. Solve for x:
35. Solve for P:
11
D   P  15
5
9 x  24a  6a  4 x
36. Solve for a:
4 p 100a

5
t
6 x  y  2H
37. Solve for x:
3
y  x  20
2
38. Solve for F:
5
C   F  32 
9
39. The width of a rectangle is 2 less than 5 times the length. If the perimeter is 68, find its
dimensions. (Draw and label an appropriate diagram.)
40. Five times the second of three consecutive even integers is six more than twice the sum of
the first and third integers. Find the middle even integer.
41. Mrs. Jones is 3 times as old as her son. Ten years ago, she was 5 times as old as her son
was then. What are their current ages?
42. Bike riders Brent and Jane started at noon from points 60 miles apart and rode toward each
other, meeting at 1:30PM. Brent’s speed was 4mph greater than Jane’s speed. Find their
speeds.