ALEKS Math Placement Assessment — Questions and Answers

Question 1: What is the least common multiple (LCM) of 6 and 9?

3
12
54
18 (Correct answer)

Correct answer: 18

The LCM of 6 and 9 is 18 because it is the smallest number divisible by both 6 and 9.

Question 2: What is the area of a circle with diameter 10? (Use π ≈ 3.14)

50
157
78.5 (Correct answer)
31.4

Correct answer: 78.5

Radius = 5, Area = πr² = 3.14 × 25 = 78.5.

Question 3: A standard die is rolled. What is the probability of rolling a number greater than 4?

2/3
1/3 (Correct answer)
1/2
1/6

Correct answer: 1/3

Numbers greater than 4 are 5 and 6, so P = 2/6 = 1/3.

Question 4: What is the x-intercept of y = 3x - 9?

(3, 0) (Correct answer)
(-9, 0)
(0, 3)
(0, -9)

Correct answer: (3, 0)

Set y = 0: 3x - 9 = 0, so x = 3; the x-intercept is (3, 0).

Question 5: What is the greatest common factor (GCF) of 36 and 48?

12 (Correct answer)
6
24
4

Correct answer: 12

The GCF of 36 and 48 is 12 because 12 is the largest number that divides both evenly.

Question 6: What is the x-intercept of y = 2x − 8?

(0, −8)
(4, 0) (Correct answer)
(−4, 0)
(8, 0)

Correct answer: (4, 0)

Setting y = 0 gives 2x = 8, so x = 4, making the x-intercept the point (4, 0).

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

63
197.82 (Correct answer)
131.88
66

Correct answer: 197.82

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

Question 8: What is 15% of 240?

48
36 (Correct answer)
30
24

Correct answer: 36

15% of 240 = 0.15 × 240 = 36.

Question 9: What is the recommended number of topics a student should work on per week in a typical ALEKS course?

As many as possible in one sitting
It varies by instructor settings, but goals are often set around 5-10 or more topics per week (Correct answer)
Only topics assigned by the teacher
Exactly 3 topics per week

Correct answer: It varies by instructor settings, but goals are often set around 5-10 or more topics per week

Instructors customize weekly goals in ALEKS, but a common target is progressing at least 5-10 topics to stay on pace.

Question 10: What is 5.6 × 10²?

0.056
560 (Correct answer)
5600
56

Correct answer: 560

5.6 × 10² = 5.6 × 100 = 560.

Question 11: A line segment has endpoints A(1, 2) and B(5, 6). What is the midpoint?

(2, 3)
(6, 8)
(3, 4) (Correct answer)
(4, 8)

Correct answer: (3, 4)

Midpoint = ((1+5)/2, (2+6)/2) = (3, 4).

Question 12: 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)?

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

Correct answer: 68%

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

Question 13: A store sells apples for $1.25 each. How much do 8 apples cost?

$11.00
$10.00 (Correct answer)
$8.25
$9.25

Correct answer: $10.00

Multiply 8 × $1.25 = $10.00.

Question 14: What is the amplitude of y = -4sin(x)?

1
-4
2
4 (Correct answer)

Correct answer: 4

The amplitude is the absolute value of the coefficient: |-4| = 4.

Question 15: A survey of 200 people found 60 prefer brand A. What is the relative frequency of brand A preference?

0.30 (Correct answer)
30/100
60%
0.60

Correct answer: 0.30

Relative frequency = 60/200 = 0.30.

Question 16: Which of the following is an exponential growth function?

y = 3x + 5
y = 3x²
y = 3(0.5)ˣ
y = 3(1.5)ˣ (Correct answer)

Correct answer: y = 3(1.5)ˣ

Exponential growth occurs when the base is greater than 1; y = 3(1.5)ˣ has base 1.5 > 1.

Question 17: 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
2:3
8:27

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 18: What is the mode of: 2, 4, 4, 6, 7, 9, 9, 9?

7
4
9 (Correct answer)
6

Correct answer: 9

9 appears three times, more than any other value, making it the mode.

Question 19: What is log₂(32)?

6
5 (Correct answer)
4
3

Correct answer: 5

log₂(32) = 5 because 2⁵ = 32.

Question 20: Which of the following is NOT a function?

y = x²
x = 3 (Correct answer)
y = |x|
y = 2x + 1

Correct answer: x = 3

x = 3 is a vertical line, which fails the vertical line test and is not a function.

Question 21: What is the y-intercept of the line y = −2x + 4?

2
−2
4 (Correct answer)
−4

Correct answer: 4

In slope-intercept form y = mx + b, the y-intercept is the constant b = 4.

Question 22: Which display best shows the distribution of a large data set?

Line graph
Pie chart
Histogram (Correct answer)
Bar graph

Correct answer: Histogram

A histogram is designed to display the frequency distribution of continuous numerical data.

Question 23: What is the perimeter of a regular hexagon with side length 6 cm?

24 cm
30 cm
36 cm (Correct answer)
42 cm

Correct answer: 36 cm

A regular hexagon has 6 equal sides, so perimeter = 6 × 6 = 36 cm.

Question 24: Which value is a solution to 2x − 3 > 7?

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

Correct answer: x = 6

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

Question 25: Which transformation shifts f(x) = x² three units to the right?

f(x) = (x - 3)² (Correct answer)
f(x) = (x + 3)²
f(x) = x² - 3
f(x) = x² + 3

Correct answer: f(x) = (x - 3)²

Replacing x with (x - h) shifts the graph h units to the right.

Question 26: Solve for x: 3x − 7 = 2x + 5

x = 7
x = 12 (Correct answer)
x = −2
x = 2

Correct answer: x = 12

Subtracting 2x from both sides gives x − 7 = 5, and adding 7 to both sides gives x = 12.

Question 27: Simplify: 4x + 3y - 2x + y

4x + 4y
2x + 2y
6x + 4y
2x + 4y (Correct answer)

Correct answer: 2x + 4y

Combine like terms: (4x - 2x) + (3y + y) = 2x + 4y.

Question 28: 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
f⁻¹(x) = (x + 6)/3 (Correct answer)

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.

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

Checking for saved progress...

Exam Rules

You can skip questions and return to them later
Flag questions for review before submitting
No feedback shown until you submit the entire exam
Unanswered questions count as wrong — answer everything
10 pretest questions are mixed in and don't affect your score
Timer auto-submits when time runs out
Your progress is auto-saved every 30 seconds