ALEKS Math Placement Assessment — Questions and Answers

Question 1: How does ALEKS determine which problems to present to a student?

Randomly from a large question bank
By the student choosing topics manually
Based on the student's current knowledge state and mastered prerequisites (Correct answer)
By following a fixed textbook chapter order

Correct answer: Based on the student's current knowledge state and mastered prerequisites

ALEKS continuously updates its model of the student's knowledge and presents problems appropriate for their current learning frontier.

Question 2: Which display best shows the distribution of a large data set?

Pie chart
Line graph
Bar graph
Histogram (Correct answer)

Correct answer: Histogram

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

Question 3: Solve: −3x + 9 = 0

x = −3
x = −9
x = 27
x = 3 (Correct answer)

Correct answer: x = 3

Subtracting 9 gives −3x = −9, and dividing both sides by −3 gives x = 3.

Question 4: If f(x) = x + 2 and g(x) = x², what is f(g(3))?

25
9
15
11 (Correct answer)

Correct answer: 11

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

Question 5: What is the distance between points (1, 1) and (4, 5)?

4
7
3
5 (Correct answer)

Correct answer: 5

Distance = √((4-1)² + (5-1)²) = √(9 + 16) = √25 = 5.

Question 6: Which transformation shifts f(x) = x² three units to the right?

f(x) = x² + 3
f(x) = (x - 3)² (Correct answer)
f(x) = (x + 3)²
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 7: What is the sum of the arithmetic series: 3 + 7 + 11 + 15 + 19?

60
50
45
55 (Correct answer)

Correct answer: 55

Sum = n/2 × (first + last) = 5/2 × (3 + 19) = 5/2 × 22 = 55.

Question 8: Which decimal is equivalent to 7/25?

0.32
0.28 (Correct answer)
0.35
0.27

Correct answer: 0.28

7/25 = 28/100 = 0.28.

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

18 (Correct answer)
54
12
3

Correct answer: 18

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

Question 10: A card is drawn at random from a standard 52-card deck. What is the probability of drawing a king?

1/13 (Correct answer)
1/4
4/13
4/52

Correct answer: 1/13

There are 4 kings in 52 cards: P = 4/52 = 1/13.

Question 11: Which number is a prime number?

37 (Correct answer)
49
39
51

Correct answer: 37

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

Question 12: Two angles are supplementary. If one angle measures 65°, what is the other?

115° (Correct answer)
295°
90°
25°

Correct answer: 115°

Supplementary angles sum to 180°, so 180° - 65° = 115°.

Question 13: Solve for x: 3x + 7 = 22

x = 3
x = 5 (Correct answer)
x = 9
x = 7

Correct answer: x = 5

Subtract 7 from both sides to get 3x = 15, then divide by 3 to get x = 5.

Question 14: Two fair coins are tossed. What is the probability of getting exactly one head?

1/4
1/2 (Correct answer)
2/3
3/4

Correct answer: 1/2

Outcomes with exactly one head: HT, TH — that's 2 out of 4 total outcomes = 1/2.

Question 15: Simplify: 4x + 3y - 2x + y

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

Correct answer: 2x + 4y

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

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

9
13
10 (Correct answer)
7

Correct answer: 10

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

Question 17: A recipe calls for 2/3 cup of sugar. If you triple the recipe, how much sugar do you need?

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

Correct answer: 2 cups

Triple 2/3: 3 × 2/3 = 6/3 = 2 cups.

Question 18: What is the domain of f(x) = √(x - 4)?

x > 4
x ≥ 4 (Correct answer)
x ≤ 4
all real numbers

Correct answer: x ≥ 4

The expression under a square root must be non-negative: x - 4 ≥ 0, so x ≥ 4.

Question 19: How many attempts at the ALEKS Placement Assessment are typically allowed?

Only 1 attempt is allowed
Unlimited attempts with no restrictions
Up to 5 attempts, with required prep work between attempts (Correct answer)
2 attempts with no prep required

Correct answer: Up to 5 attempts, with required prep work between attempts

Most institutions allow up to 5 ALEKS placement attempts, but require students to spend time in the prep module between retakes.

Question 20: Which number line correctly shows the solution to x + 2 ≤ 6?

An open circle at 8, shaded to the left
A closed circle at 4, shaded to the right
A closed circle at 4, shaded to the left (Correct answer)
An open circle at 4, shaded to the left

Correct answer: A closed circle at 4, shaded to the left

Subtracting 2 from both sides gives x ≤ 4; the closed circle includes 4, and shading left shows all values less than or equal to 4.

Question 21: What is the greatest common factor (GCF) of 36 and 48?

6
12 (Correct answer)
24
4

Correct answer: 12

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

Question 22: What type of triangle has all three sides of equal length?

Isosceles
Equilateral (Correct answer)
Right
Scalene

Correct answer: Equilateral

An equilateral triangle has all three sides equal and all angles measuring 60°.

Question 23: What is the range of f(x) = x² - 1?

y ≤ -1
y ≥ 0
y ≥ -1 (Correct answer)
all real numbers

Correct answer: y ≥ -1

Since x² ≥ 0 for all x, x² - 1 ≥ -1, so the range is y ≥ -1.

Question 24: 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 25: A survey of 200 people found 60 prefer brand A. What is the relative frequency of brand A preference?

60%
0.30 (Correct answer)
0.60
30/100

Correct answer: 0.30

Relative frequency = 60/200 = 0.30.

Question 26: What is the circumference of a circle with radius 5? (Use π ≈ 3.14)

78.5
31.4 (Correct answer)
15.7
25

Correct answer: 31.4

Circumference = 2πr = 2 × 3.14 × 5 = 31.4.

Question 27: What is the x-intercept of y = 3x - 9?

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

Correct answer: (3, 0)

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

Question 28: A trapezoid has bases of 8 and 12 and a height of 5. What is its area?

40
50 (Correct answer)
100
60

Correct answer: 50

Area = ½ × (b₁ + b₂) × h = ½ × (8 + 12) × 5 = ½ × 100 = 50.

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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