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Mathematics Placement Sample Questions

1. If the odometer of your car read 32,765 when you bought it and 76,438 when you
sold it, how many miles did you drive your car while you owned it?
A. 109,203     B. 43,673     C. 44,333     D. 43,808     E. – 43,673

2. Which decimal below represents the smallest number?
A. 0.434     B. 0.444     C. 4.44     D. 0.4     E. 0.4444

3. If a recipe calls for 2/3 cup of flour and 1/4 cup of sugar, how many total cups of
ingredients does this recipe call for?
A. 11/12    B. 3/7    C. 3/12    D. 2/12    E. 8/3

4. The shaded region represents what fraction of the whole rectangle:

A.
2
1
B.
4
1
C.
3
1
D.
8
1
E.
5
2
5. 47 is between
A. 2 and 3 B. 3 and 4 C. 4 and 5 D. 5 and 6 E. 6 and 7
6. If - 3x + 2 = 14 , then x equals:
A. – 4 B. – 3 C.
3
16 - D. 19 E.
3
16
7. Which of the following ordered pairs is a solution to 3x + 2y = 12 ?
A. ( 0, 4 ) B. ( – 4, 0 ) C. ( 4, 0 ) D. ( 0, – 4 ) E. ( 0, 0 )
8. What is the slope of the line whose equation is 3x - 4y = 8 ?
A. 3 B. – 4 C.
4
3
D.
3
4
E.
4
3 -
9. 4 + 5 · 2 ¸ 2 - 3 + 1 =
A.
3
14
B. 10 C. 20 D. 16 E. 7
10. If x = 4 and y = -3 then 3x - 2y =
A. 18 B. 6 C. – 17 D. 17 E. 0
11.   4x ( 4)2
=
A. 4x8 B. 16x8 C. 4x6 D. 16x6 E. 256x8
12. What is the solution to the following system:
2x + y = 7
x - y = 2
ì
í
î
A.
9
2
, - 5
2
æ
è
ö
ø  B. ( 1, 3 ) C. ( 3, -1 ) D. ( 3, 1 ) E.
( 1, - 3 )
13. Factor x2 + 8x - 48
A. (x + 4)(x -12) B. (x + 4)(x + 8) C. (x - 4)(x - 8) D. ( )2 x + 4 E. (x - 4)(x +12)
14. The roots of x2 - 3x - 7 = 0 are:
A.
2
3 ± 37
B.
2
3 ± i 19
C. – 3 and – 5 D.
2
- 3 ± 37
E. 3 and 5
15. If 2 + x = 5 then x =
A. 9 B. 3 C. 49 D. 7 E. 3
16. The length of a rectangle is twice the width. The perimeter of the rectangle is 48.
If w stands for the width of the rectangle, which of the following equations could
be used to find w ?
A. 3w = 48 B. 2(2w) = 48 C. 2w + 2(2w) = 48 D. 2w2 = 48 E. 3w2 = 48
17. If ( )
x
x
f x
-
= -
7
3 4
, then f (2)=
A.
9
2
B.
5
1
C.
x
x
14 2
6 8
-
-
D.
5
2
E. 2
18. What is the distance between the points ( 2, - 3 ) and ( 5, 4 ) ?
A. 10 B. 58 C. 10 D. 58 E.
3
7
19. Which of the following curves best resembles f (x)= x2 + 4 ?
A. B. C. D.
20. In the right triangle shown, tan q =
2
x
q
A.
2
x
B.
4 x2
x
-
C.
x
4 - x 2
D.
x
2
E.
4 x2
x
+
ANSWERS:
1. B; 2. D; 3. A; 4. B; 5. E; 6. A; 7. C; 8. C; 9. E; 10. A; 11. B; 12. D; 13. E;
14. A; 15. A; 16. C; 17. D; 18. B; 19. A; 20. B