ALEKS Math Placement Assessment — Questions and Answers

Question 1: A car travels 180 miles in 3 hours. What is its average speed?

90 mph
45 mph
54 mph
60 mph (Correct answer)

Correct answer: 60 mph

Speed = distance ÷ time = 180 ÷ 3 = 60 mph.

Question 2: Solve: (x + 3)/2 = 5

x = 10
x = 4
x = 7 (Correct answer)
x = 13

Correct answer: x = 7

Multiplying both sides by 2 gives x + 3 = 10, and subtracting 3 gives x = 7.

Question 3: Two parallel lines are cut by a transversal. Which angle pair is always equal?

Supplementary angles
Adjacent angles
Co-interior angles
Alternate interior angles (Correct answer)

Correct answer: Alternate interior angles

Alternate interior angles are congruent when formed by parallel lines and a transversal.

Question 4: What type of correlation is shown when one variable increases as the other decreases?

Positive correlation
No correlation
Negative correlation (Correct answer)
Zero correlation

Correct answer: Negative correlation

A negative correlation means one variable increases while the other decreases.

Question 5: An angle measures 130°. What is its complement?

230°
No complement exists (Correct answer)
40°
50°

Correct answer: No complement exists

Complementary angles add to 90°; since 130° > 90°, it has no complementary angle.

Question 6: If f(x) = x + 2 and g(x) = x², what is f(g(3))?

9
15
11 (Correct answer)
25

Correct answer: 11

g(3) = 9, then f(9) = 9 + 2 = 11.

Question 7: Convert 5/4 to a mixed number.

4/5
1 1/2
2 1/4
1 1/4 (Correct answer)

Correct answer: 1 1/4

5 ÷ 4 = 1 remainder 1, so 5/4 = 1 1/4.

Question 8: What is the probability of NOT rolling a 6 on a fair die?

4/6
1/6
1/3
5/6 (Correct answer)

Correct answer: 5/6

P(not 6) = 1 - P(6) = 1 - 1/6 = 5/6.

Question 9: What is the mean of the data set: 4, 7, 10, 13, 16?

7
10 (Correct answer)
13
9

Correct answer: 10

Mean = (4 + 7 + 10 + 13 + 16) ÷ 5 = 50 ÷ 5 = 10.

Question 10: What does the ALEKS instructor module allow teachers to do?

Schedule in-person tutoring
Track individual student progress, set assignments, and customize course content (Correct answer)
Only view class averages
Automatically grade paper tests

Correct answer: Track individual student progress, set assignments, and customize course content

The instructor module provides detailed analytics, assignment tools, and content customization for managing student learning.

Question 11: What is the absolute value of -17?

17 (Correct answer)
1/17
-17
0

Correct answer: 17

The absolute value of any number is its distance from zero, so |-17| = 17.

Question 12: Find the inverse of f(x) = 3x - 6.

f⁻¹(x) = 3x + 6
f⁻¹(x) = x/3 - 6
f⁻¹(x) = (x + 6)/3 (Correct answer)
f⁻¹(x) = (x - 6)/3

Correct answer: f⁻¹(x) = (x + 6)/3

Replace f(x) with y, swap x and y, then solve: x = 3y - 6 → y = (x + 6)/3.

Question 13: A bag has 3 red, 5 blue, and 2 green marbles. What is the probability of picking a blue marble?

1/2 (Correct answer)
5/3
3/10
1/5

Correct answer: 1/2

P(blue) = 5/10 = 1/2.

Question 14: Which is true about even functions?

f(-x) = f(x) (Correct answer)
f(0) = 0
f(-x) = -f(x)
f(x) = f(2x)

Correct answer: f(-x) = f(x)

A function is even if f(-x) = f(x) for all x, meaning it is symmetric about the y-axis.

Question 15: If y varies directly with x and y = 15 when x = 3, what is y when x = 7?

35 (Correct answer)
30
14
21

Correct answer: 35

The constant of variation k = y/x = 15/3 = 5, so y = 5(7) = 35.

Question 16: If two triangles are similar and their sides are in a ratio of 2:3, what is the ratio of their areas?

4:9 (Correct answer)
1:3
8:27
2:3

Correct answer: 4:9

The ratio of areas of similar figures equals the square of the ratio of corresponding sides: (2:3)² = 4:9.

Question 17: A cylinder has radius 3 and height 7. What is its volume? (Use π ≈ 3.14)

197.82 (Correct answer)
63
131.88
66

Correct answer: 197.82

Volume = πr²h = 3.14 × 9 × 7 = 197.82.

Question 18: What is the volume of a cube with side length 4 cm?

16 cm³
64 cm³ (Correct answer)
48 cm³
12 cm³

Correct answer: 64 cm³

Volume = side³ = 4³ = 64 cm³.

Question 19: A data set has mean 50 and standard deviation 5. What percentage of data falls within one standard deviation of the mean (using the empirical rule)?

68% (Correct answer)
99.7%
95%
50%

Correct answer: 68%

The empirical rule states approximately 68% of data falls within one standard deviation of the mean.

Question 20: After an ALEKS Placement Assessment, what opportunity do students typically have?

Automatic placement into the highest course
No opportunity to retake
A mandatory tutoring session
A Prep and Learning module to improve their score before retaking the assessment (Correct answer)

Correct answer: A Prep and Learning module to improve their score before retaking the assessment

ALEKS PPL includes Prep and Learning modules that allow students to strengthen skills and improve their placement score.

Question 21: What is 30° in radians?

π/2
π/6 (Correct answer)
π/4
π/3

Correct answer: π/6

30° × (π/180°) = π/6.

Question 22: Which subject areas does the ALEKS Math Placement Assessment typically cover?

Arithmetic, algebra, geometry, trigonometry, and pre-calculus topics (Correct answer)
Only calculus
Grammar and essay writing
Statistics and computer science only

Correct answer: Arithmetic, algebra, geometry, trigonometry, and pre-calculus topics

The ALEKS placement exam spans a wide range of math topics to accurately assess where a student should be placed.

Question 23: Solve: x/4 + 3 = 7

x = 28
x = 10
x = 4
x = 16 (Correct answer)

Correct answer: x = 16

Subtracting 3 from both sides gives x/4 = 4, and multiplying both sides by 4 gives x = 16.

Question 24: What is (-5) × (-8)?

-13
13
-40
40 (Correct answer)

Correct answer: 40

A negative times a negative equals a positive, so (-5) × (-8) = 40.

Question 25: What is the horizontal asymptote of y = 3/(x + 2)?

y = 2
y = 0 (Correct answer)
x = -2
y = 3

Correct answer: y = 0

As x → ±∞, 3/(x + 2) → 0, so the horizontal asymptote is y = 0.

Question 26: Solve the inequality: 2x - 4 > 10

x > 7 (Correct answer)
x < 7
x > 14
x > 3

Correct answer: x > 7

Add 4 to both sides: 2x > 14, then divide by 2: x > 7.

Question 27: Which value is a solution to 2x − 3 > 7?

x = 5
x = 6 (Correct answer)
x = 3
x = 4

Correct answer: x = 6

Adding 3 gives 2x > 10, so x > 5; only x = 6 satisfies this condition.

Question 28: Which number is a prime number?

51
37 (Correct answer)
49
39

Correct answer: 37

37 is prime because it has no divisors other than 1 and itself.

ALEKS Math Placement Assessment

The ALEKS (Assessment and Learning in Knowledge Spaces) PPL is an adaptive online math placement assessment used by colleges and universities. It consists of 20 to 30 open-response questions and typically takes 45 to 90 minutes. Your score (0–100) represents the percentage of topics mastered across 314 math topics from arithmetic through pre-calculus, and is used to place you into the appropriate math course.

Questions

90 min

Time Limit

61%

To Pass

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