Practice Problems for the IU South Bend Mathematics Placement Exam
The following sample questions will be indicative of some of the topics that are covered by the
mathematics placement examination. For information regarding the Math Placement Exam,
schedules, or to register, please go to the website
https://www.iusb.edu/exams/math.php
Part A
1. The figure below shows a circle divided into 6 equal parts. How many parts should be
8
shaded to illustrate 12 of the circle?
A. 2
B. 3
C. 4
D. 6
3
E. 5
2
2. Pat’s mom gave him 4 of an apple pie. He ate 3 of what was given to him. How much of the
whole pie did he eat?
1
A. 2
5
B. 7
5
C. 12
17
D. 12
8
E. 9
3. −2 – 5 ● ( −1 + 3 ) =
A. −14
B. 20
C. −20
D. 14
E. −12
3
4. If 4 ounce of a substance costs $52, then how many ounces can you buy with $78?
A. 1
B. 1.25
C. 1.5
D. 1.125
E. 2
5. Fran is now making $2356.25 per month thanks to a big 45% raise. How much was Fran
making per month before the raise?
A. $1295.94
B. $1060.31
C. $1625
D. $2311.25
E. $2211.25
1
6. A field is in the shape of a square. If the area of the field is 48,400 square yards, find the
number of yards of fence needed to enclose the field.
A. 193,600 yards
B. 220 yards
C. 96,800 yards
D. 880 yards
E. 440 yards
Part B
7. If 𝑥 = −2, then – 𝑥 2 + 3𝑥 – 5 =
A. −7
B. −15
C. 50
D. −50
E. 10
8. If 2𝑥 – 3𝑦 = 12 and 𝑥 = 9, then find y.
A. 2
B. −10
C. 10
D. −2
E. −3
9. Given 5 – 2 (−3𝑥 + 4) – (−𝑥 + 2) = 3 + (2𝑥 – 1), then x =
5
A. 7
B. . 6
10. Given
−5𝑥
17
A. - 65
2
C. . 8
D. 1.4
13
E. 14
2
– 1.25 = .75 − 5 then x =
B. .2615384
C. .5076923
D. -.5076923
E. -.4857142
3
11. Simplify
A.
−𝑥 5
3𝑦 11
(−3 𝑥 2 𝑦 3 )
81𝑥𝑦 20
B. .
−𝑥 6
3𝑦 11
=
C. .
−𝑥 4
3𝑦 14
D.
−𝑥 5
9𝑦 11
E.
𝑥3
−19683𝑦 51
12. Multiply (2𝑥 – 1)(𝑥 + 1)2 =
A. 4𝑥 4 + 4𝑥 3 − 3𝑥 2 – 2x + 1
B. 2𝑥 3 – 1
D. 2𝑥 3 + 3𝑥 − 1
E. 4𝑥 4 + 1
C. 2𝑥 3 − 𝑥 2 + 2𝑥 − 1
2
13. Consider the picture below. How far is it, by boat, across the lake from the campgrounds
to the store?
A. 8 miles
B. 4 miles
C. 15 miles
D. 34 miles
E. √34 miles
Part C
14. Find the coordinates of the x intercept for 5𝑥 − 3𝑦 = −15
A. ( 0 , 5 )
B. ( −3 , 0 )
C. ( 0 , 0 )
D. ( 3 , 10 )
E. ( 5 , −3 )
15. Determine the slope of this line from the graph below:
A.
−1
3
1
B. 3
C. −3
D. 3
E. 6
3
2
16. The graph below that looks most like the graph of 𝑦 = − x+1 is
3
4
17. Simplify:
A. 𝑥 2
B. 𝑥 4
C. 𝑥 −2
D. 𝑥 −3
E. 𝑥 −5
18. Solve the system
3𝑥 − 4𝑦 = 18
2𝑥 − 5𝑦 = 19
Add your answers as 𝑥 + 𝑦
A. −1
B. 1
C. 5
D. −5
E. 0
19. If 𝑦 = |5𝑥 − 10|, we know that 𝑦 > 0. One branch of the graph is 𝑦 = 5𝑥 − 10. The
other is 𝑦 =
A. 5𝑥 + 10
B. −5𝑥 − 10
C. 10𝑥 + 5
D. 10𝑥 − 5
E. −5𝑥 + 10
20. Solve |−5𝑥 + 10| < 25
A. 𝑥 < 7
B. 𝑥 > −3
C. −3 < 𝑥 < 7
D. 𝑥 < −3
E. −7 < 𝑥 < 0
21. Solve the following equation for all x and then add your answers together.
−16𝑥+3
𝑥 2 +𝑥−6
3
A. 2
1
B. 2
C.
−
−3
2
−2(−𝑥+4)
𝑥−2
D. 0
E.
=
−13
𝑥+3
−1
2
5
22. Given 𝑦 = −𝑥 2 − 10𝑥 + 15, find the x coordinate of the vertex.
A. 5
B. 0
C. −5
D. −10
E. 15
23. Find the radius of the circle with equation 𝑥 2 − 6𝑥 + 𝑦 2 + 10𝑦 + 18 = 0
A. √18
B. 4
C. −6
D. 10
E. 18
24. Solve for all x: 12𝑥 3 + 2𝑥 2 = 30𝑥. Choose the best answer.
A. 0
3
B. 2
C.
−5
3
D. 30
E. A, B, and C
Part D
25. If 𝑓(𝑥) = 3𝑥 − 1 and 𝑥 = 2, then find 𝑓(𝑓(𝑥))
A. 14
B. 5
C. 18
D. 15
E. . 5
26. Find the range of 𝑓(𝑥) = 3 + √4𝑥 − 8
A. 𝑥 ≥ 2
B. 𝑦 ≥ 3
C. 𝑦 > 3
D. 𝑦 > 5
E. 𝑥 < 2
27. Simplify ln(𝑒 𝑥 )
A. 𝑒
B. 𝑒 𝑥
C. 𝑥
D. 𝑙𝑛 𝑒
E. 𝑙𝑛 𝑥
6
28. If 𝑦 = 𝑓(𝑥) = 𝑥 2 − 4 with 𝑥 ≥ 0, find the inverse function where 𝑦 = 𝑓 −1 (𝑥)
A. 𝑦 = 2𝑥
B. 𝑦 = 2𝑥 − 4
C. 𝑦 = √𝑥
D. 𝑦 = √𝑥 + 4
E. 𝑦 = 𝑥
29. If sin 𝑥 = −.6 and 𝑐𝑜𝑠𝑥 < 0, then find 𝑡𝑎𝑛𝑥
A. . 8
B. . 6
C. −.75
D. . 75
E. −.8
30. If 𝑐𝑜𝑠𝑥 = .5 and 𝑐𝑜𝑡𝑥 < 0, then find x.
A. 240°
B. 210°
C. 30°
D. 300°
E. 330°
7