Northern Illinois University
Department of Mathematical Sciences

# Math Placement Evaluation

## Intermediate Level

This test, which is self-administered, is NOT an official placement exam. It is for your convenience only, and your name and answers are not stored anywhere. The test is designed to give you additional advice, beyond what you have gotten through the NIU Office of Testing Services.

Back to the introductory page: Math Placement at NIU

## Placement recommendations

If you take this test, you will receive a placement recommendation for one of
Intermediate Algebra,
Introductory Algebra, or
Basic Arithmetic.
IMPORTANT NOTE: These courses are not offered at NIU.

If you tested at level D on the Precalculus Placement test, you can use this recommendation as the first step in deciding what math course to take at a community college. Of course, you must take the math placement test at the college at which you register for the necessary review work.

## Instructions for taking the test

(1) Part One will test your background in basic arithmetic, while Part Two will cover basic algebra.

(2) Each part of the test has 30 questions, and has been designed to take about half an hour, so the total time you spend on the test should be about an hour. You may want to write down your answers as you go, in case you do not have enough time to finish, and need to return later.

(3) If you use a calculator on any part of the test, you will invalidate the recommended placement.

## Part One: Arithmetic

1. 1996 + 28 + 643 =

1667
2557
2667
8344
8454

2. 864 - 77 =

94
787
796
896
897

3. 28 x 17 =

45
376
468
476
484

4. 2406 / 6 =

40
41
401
410
411

5. 1/4 + 2/3 =

3/7
8/3
3/4
5/6
11/12

6. An airplane is flying at an altitude of 7,425 feet. If the plane goes up 450 feet, what is the new altitude?

6,975
7,875
7,975
8,975
11,925

7. Which of the following represents fifty thousand two hundred and seven?

527
5207
5270
50207
52007

8. Find 6 divided by 5/7.

5/42
7/30
30/7
37/5
42/5

9. A job pays \$6 per hour for the first 40 hours per week, and \$9 per hour for overtime. If you work 46 hours a week, what will you earn?

\$276
\$294
\$303
\$396
\$414

10. Which one of these fractions is less than 3/5?

2/3
3/2
3/4
5/3
7/12

11. An airplane traveling from L.A. to New York is carrying 326 passengers. It stops at Chicago, where 78 passengers get off and 93 new passengers get on. How many passengers continue on to New York?

233
248
341
404
419

12. When the number 66,340 is divided by 62, the answer is

1700
1070
107
170
17

13. A woman has an estate of \$10,000. She leaves 1/10 to charity. Her daughter gets 2/3 of the remainder. How much money does her daughter get?

\$6,667
\$6,000
\$3,000
\$667
\$600

14. When the number 71.07 is divided by 2.3, the answer is

30.9
39
3.9
3.7
3.09

15. A handicapped parking space is designed to measure 14 feet wide by 18 feet long. Find its area.

252 square feet
244 square feet
222 square feet
64 square feet
32 square feet

16. Write 65% as a fraction:

100/65
10/65
65/10
65/100
65/1000

17. When the fraction 14/27 is divided by 2/3 , the answer is

28/81
28/27
14/81
7/18
7/9

18. 35% of 160 is

56
560
5600
5.6
.56

19. 9 1/3 - 4 5/6 =
(nine and one third minus four and five sixths)

5 2/3
5 4/9
5 1/2
4 1/2
4 4/9

20. 6.431 x 0.01 =

0.06431
0.6431
6.431
64.31
643.1

21. 15.7 x 4.09 =

64213
642.13
64.213
76.93
7693

22. Which one of these numbers is smallest?

27.799
27.51
27.8
27.503
27.53

23. 12 x 3 1/4 =
(twelve times three and one quarter)

39
40
36
48
84

24. Find the average (arithmetic mean) of these numbers: 6.2, 6.7, 12.3

25.2
12.6
9.6
8.4
6.3

25. The number 8 is 20% of what number?

160
16
1.6
4
40

26. Rounding 12.5362 to the nearest hundredth gives

12.54
12.53
12.536
12.537
12.5362

27. Write 5/8 as a decimal:

6.25
0.625
0.0625
0.375
3.75

28. A car dealer is offering 15% off on all vehicles. If the original cost of a car is \$16,000, what is its sale price?

\$18,400
\$18,000
\$14,500
\$14,000
\$13,600

29. 18 is what percent of 45?

45%
40%
28%
20%
18%

30. A theater owner wants to be able to seat 1250 people. The main floor has 30 rows of 25 seats each. If the balcony has 25 rows, how many seats must be in each row?

40
30
25
20
15

## Part Two: Basic Algebra

31. -1 + (-2) =

-3
-1
1
2
3

32. 12 - (-9) =

-21
-17
3
17
21

33. 3 + 2 x 2 - 5 =

-15
-5
2
5
7

34. (-2)3 =

-8
-6
-5
5
8

35. Choose the largest of the following numbers:
(use the relation > on the number line)

-6
-3/2
16/3
9/2
5

36. (1/3)(-18)(-6) =

-36
-12
12
24
36

37. Find \/ 28
(the square root of 28)

4 \/ 7
2 \/ 7
7 \/ 2
14 \/ 2
14

38. Solve for x: 3x + 1 = 6

x = 3/7
x = 7/3
x = 3/5
x = 5/3
x = 2
39. 4x - a - 2x + a =
6x
2x
2x - 2a
6x - 2a
2a - 6x

40. If x = 3, then (x-1)2 + 1 =

-3
2
5
10
17

41. Solve for x: 2x - 3 = 5x + 4

x = -7/3
x = -3/7
x = 1/7
x = 1/3
x = 3/7

42. The statement `` x is 2 more than y '' is written as

x + 2 = y
x = 2 + y
x + y = 2
x + 2 > y
x > 2 + y

43. 4x2 - y2 =

(2x - y)2
(2x + y)2
(4x - y)2
(2x - y) (2x + y)
(4x - y) (4x + y)

44. If it costs \$ . 25 per mile to drive a car, how much will it cost (in dollars) to drive d miles?

d - . 25
d + . 25
d / . 25
. 25 d
. 25 / d

45. (x2 y3)(x y)(x4 y) =

x8 y5
x7 y5
x8 y3
x7 y3
x6 y3

46. A box with a square base has a volume of 16 cubic feet. If the base of the box measures 2 feet by 2 feet, how tall is the box?

2 feet
4 feet
8 feet
32 feet
64 feet

47. x6 - 3x4 + x2 =

x2 (x4 - 3x2 + 1)
x2 (x4 - 3x2)
x4 (x2 - 3)
x2 (x3 - 3x2 + 1)
x2 (x3 - 3x2)

48. Find \/(36 x16)
(the square root of 36x16)

6 x4
18 x4
6 x8
18 x8
20 x

49. If y = | x | - 2, and x = -3, then

y = -6
y = -5
y = -1
y = 1
y = 5

50. The y-intercept of the line y - 3x = 2 is

5
-3
3
-2
2

51. The area of the base of a cube is 5 square inches. What is the total surface area of the cube?

20 square inches
25 square inches
30 square inches
100 square inches
150 square inches

52. Solve for x: 3x > x + 12

x < 6
x < 3
x > 6
x > 4
x > 3

53. (x - 2y)2 =

x2 - 4y2
x2 - 2y2
x2 + 4y2
x2 + 4xy + 4y2
x2 - 4xy + 4y2

54. Which one of the following is a factor of x2 + x - 12 ?

x - 4
x - 2
x + 2
x + 4
x + 6

55. Which one of these points is not included in the graph of -2 < 2x - 3 ?

0
1
2
3
4

56. Solve for x: 3x + 7 < 12

x > 19/3
x > 4
x > 5/3
x < 5/3
x < 19/3

57. The graph of the line 2x + y = 6

has a positive slope
has a negative slope
is horizontal
is vertical
None of these

58. Which one of these points lies on the line x - 3y = 5 ?

(-1, 2)
(0, -2)
(1, 2)
(2, 1)
(2, -1)

59. In a mixture of concrete, there are 3 pounds of cement mix for each pound of gravel. If the mixture contains a total of x pounds, which one of the following expressions gives the amount of gravel?

x/4
x/3
x-3
x-4
3x

60. After the 1990 election, there were 14 more Democrats than Republicans in the U.S. Senate. Which one of the following equations can be used to find the number x of Democrats?

x - 14 = 100
x + 14 = 100
x + 28 = 100
2x + 14 = 100
2x - 14 = 100

## Scoring

Placement in Intermediate Algebra is recommended for those scoring above

24/30 on Part One (arithmetic) AND 16/30 on Part Two (algebra)
Placement in Introductory Algebra is recommended at a level of
16/30 on Part One (arithmetic) AND 8/30 on Part Two (algebra)
Placement in Basic Arithmetic is recommended for those scoring
below 16 on Part One (arithmetic)