Download Algebra Review

Name: ________________________ Class: ___________________ Date: __________
ID: A
Algebra Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
____
____
____
1. Simplify -(3 - x) as far as possible.
a. -2x
b. x - 3
c.
-3 - x
d.
x+3
2. Simplify -(x - 3) as far as possible.
a. 2x
b. -x - 3
c.
3-x
d.
-4x
3. Simplify -(3x - 2) as far as possible.
a. -x
b. -3x - 2
c.
5x
d.
-3x + 2
4. Simplify -(-3x + 2) as far as possible.
a. x
b. 3x - 2
c.
5x
d.
3x + 2
5. The following diagram illustrates an equation. Which of the following is a reasonable first step in order to
solve the equation?
a.
____
b.
add 2 to both
sides
c.
subtract 2x from
both sides
d.
divide both sides
by 2
6. The following diagram illustrates an equation. Which of the following is a reasonable first step in order to
solve the equation?
a.
____
add x to both
sides
add x to both
sides
b.
subtract 2x from
both sides
c.
add 2x to both
sides
d.
divide both sides
by -2
7. The following diagram illustrates an equation. Which of the following is a reasonable first step in order to
solve the equation?
a.
subtract 3x from
both sides
b.
add 3x to both
sides
c.
1
add x to both
sides
d.
divide both sides
by -3
Name: ________________________
____
ID: A
8. The following diagram illustrates an equation. Which of the following is a reasonable first step in order to
solve the equation?
a.
add 4 to both
sides
c.
add 2 to both
sides
d.
divide both sides
by 3
9. If 3x - 1 = 11, then x =
a. 4
b.
10
3
c.
9
d.
7
____ 10. If 2x + 5 = 1, then x =
a. 3
b.
-2
c.
1.5
d.
-6
____ 11. If 2x - 4 = 2, then x =
a. -1
b.
4
c.
3
d.
-4
____ 12. If 5 - x = 7, then x =
a. 2
b.
12
c.
-12
d.
-2
____ 13. If 1 - 2x = 3, then x =
a. 2
b.
-1
c.
-3
d.
-2
____
add 3x to both
sides
b.
x−2
= 5, then x =
3
a. 21
b.
13
c.
17
d.
10
x+1
= 2, then x =
3
a. 7
b.
3
c.
4
d.
5
6
= −2, then x =
x+1
a. -4
b.
-3
c.
1
d.
2
6
+ 2 = 0, then x =
x
a. 12
-3
c.
-12
d.
3
x = 1 + 2y
c.
x=
4
+ 2y
3
d.
x=
c.
x=
−2
y
3
d.
x = −2y
____ 14. If
____ 15. If
____ 16. If
____ 17. If
b.
____ 18. Solve 3x - 2y = 4 for x
4 + 2y
a. x =
b.
3
____ 19. Solve 3x + 2y = -4 for x
4 + 2y
a. x =
b.
3
x=
−4 − 2y
3
2
4 − 2y
3
Name: ________________________
____ 20. Solve 2x + 3y = -4 for x
−4 + 3y
b.
a. x =
2
____ 21. Solve -2x + 3y = 4 for x
−4 − 3y
b.
a. x =
2
ID: A
x = −2 + 1.5y
x = 2−
3y
2
3y
2
c.
x = −2 − 1.5y
d.
x = 2−
c.
x = −2 − 1.5y
d.
x = −2 + 1.5y
____ 22. The following diagram illustrates that...
a.
b.
(x + 1)(x − 2) = x 2 − x − 2
c.
2
2
x + 1 + x − 2 + x − 2x + x − 2 = x + x − 3 d.
x2 − x − 2 = x + 1 + x − 2
(x − 2) − (x + 1) = x 2 + 2x − x − 2
____ 23. The following diagram illustrates that...
a.
b.
(x − 1)(x − 2) = 2x 2 − 2x
x − 1 + 2x + 2x 2 − 2x = 2x 2 + x − 1
c.
d.
2x 2 − 2x = 2x(x − 1)
(x − 1) − (2x) = x 2 − 2x
____ 24. The following diagram illustrates that...
a.
b.
(x − 1)(x − 2) = 2x 2 − 2x
−x(2x + 1) = −2x 2 − x
c.
d.
3
−2x 2 + x = (2x + 1)(x − 1)
(−x) + (2x + 1) = −2x 2 − x
Name: ________________________
ID: A
____ 25. The following diagram illustrates that...
a.
b.
c.
d.
(x − 1) + (x − 2) + x 2 − 3x + 2 = x 2 − x − 1
−x(2x + 1) = −2x 2 − x
x 2 − 3x − 2 = (x − 2)(x − 1)
(x − 1)(x − 2) = x 2 − 3x + 2
____ 26. Simplify x + x + x + x
a. 4x 4
b.
4x
c.
x4
d.
4x 2
Ê ˆÊ ˆÊ ˆ
____ 27. Simplify ÁÁ x 2 ˜˜ ÁÁ x 2 ˜˜ ÁÁ x 2 ˜˜
Ë ¯Ë ¯Ë ¯
2
a. 3x
b.
x6
c.
x5
d.
3x 6
____ 28. Simplify 6x 2 − 2x 2
a. 6x 2 − 2x 2
b.
4
c.
4x 2
d.
3
b.
4
c.
4x 2
d.
3
____ 30. Simplify x 2 + x 2 + x 2
a. 3x 2
b.
x5
c.
x6
d.
3x 6
____ 31. Simplify 2x 2 + 2x 2 + 2x 2
a. 6x 6
b.
2x 6
c.
6x 2
d.
2x 5
____ 32. Simplify 2x + 2x + 2x
a. 6x 3
b.
2x 3
c.
6x 2
d.
6x
Ê
ˆÊ
ˆÊ
ˆ
____ 33. Simplify ÁÁ 2x 2 ˜˜ ÁÁ 2x 2 ˜˜ ÁÁ 2x 2 ˜˜
Ë
¯Ë
¯Ë
¯
a. 8x 6
b. 6x 5
c.
8x 8
d.
6x 6
____ 34. Simplify (2x) (2x) (2x)
a. 6x 3
b.
6x
c.
8x
d.
8x 3
____ 35. Simplify (3x) (3x)
a. 9x
6x 2
c.
9x 2
d.
6x
____ 29. Simplify
a.
6x 2
2x 2
3x 2
b.
4
Name: ________________________
ID: A
____ 36. Simplify 6x 2 − 2x
a. 3x
b.
4x
c.
4x 2
d.
6x 2 − 2x
____ 37. Simplify 6x 3 − 2x 3
a. 4x 3
b.
4x
c.
4x 2
d.
6x 3 − 2x 3
____ 38. Simplify 6x 3 − 2x 2
a. 4x
b.
6x 3 − 2x 2
c.
4x 2
d.
3x
b.
5x 3
c.
6x
d.
5
b.
3x 2
c.
6x 3
2x
d.
4x 2
b.
2x 2
c.
2
d.
3x 2
____ 42. Simplify 2w 2 + w − 3 − 3w 2 + w − 1
a. −w 2 + 2w − 4
b. 3w 3 − 6w 2 − 1
c.
−3w 6
d.
5w 2 + 2
____ 43. Simplify w 2 − 4w + 5 − w 2 + 4w − 3
a. 2w 2 − 8w + 2
b. 2
c.
−8w + 2
d.
−w 2 + 2
____ 44. Simplify 3w 2 − w − 1 − w 2 + 2w − 3
a. 2w 2 − 3w − 2
b. 2w 2 − 3w − 4
c.
2w 2 + w − 4
d.
−3w − 1
____ 45. Simplify −w 2 + 3w − 1 − w 2 − 4w + 3
a. −w − 4
b. −2w 2 − w − 4
c.
−2w 2 + 7w + 2
d.
−2w 2 − w + 2
____ 46. Simplify x - 2y - 1 -2x +y -3
b. -3x - 3y - 4
a. -x - y - 4
c.
-2xy - 4
d.
-x - y - 2
____ 47. Simplify -x + 2y + 1 -2x +y -3
a. x +3y - 2
b. -3x + 3y - 2
c.
x +3y - 4
d.
-3x + 3y - 4
____ 48. Simplify 3x + 2y -1 -2x -y -3
a. x + y - 2
b. x - 3y - 2
c.
x +y - 4
d.
x + 3y - 4
____ 49. Simplify -x - 2y +1 +2x + y -3
a. -3x -3y - 2
b. x - 3y - 2
c.
-3x - y - 2
d.
x-y-2
____ 39. Simplify
a.
6
____ 40. Simplify
a.
6x 3
2x
3x 3
____ 41. Simplify
a.
6x 3
x3
3
6x 2
3x 2
5
ID: A
Algebra Review
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
B
C
D
B
A
C
B
C
A
B
C
D
B
C
D
A
B
A
B
C
D
A
C
B
D
B
B
C
D
A
C
D
A
D
C
D
A
B
A
1
ID: A
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
B
C
A
B
C
D
A
B
C
D
2