ALEKS Math Placement Assessment — Questions and Answers

Question 1: What is the mean of the data set: 4, 7, 10, 13, 16?

7
13
9
10 (Correct answer)

Correct answer: 10

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

Question 2: Which subject areas does the ALEKS Math Placement Assessment typically cover?

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

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 3: Which value represents the middle 50% of a data set in a box plot?

Standard deviation
Range
Mean
Interquartile range (IQR) (Correct answer)

Correct answer: Interquartile range (IQR)

The IQR is the difference between Q3 and Q1, representing the spread of the middle 50% of data.

Question 4: Solve for x: 3x + 7 = 22

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

Correct answer: x = 5

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

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

100
60
50 (Correct answer)
40

Correct answer: 50

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

Question 6: Which of the following is an exponential growth function?

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

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

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

Correct answer: 5/6

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

Question 8: What is the absolute value of -17?

-17
1/17
0
17 (Correct answer)

Correct answer: 17

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

Question 9: What is the value of 2⁴ ÷ 2²?

2
8
1
4 (Correct answer)

Correct answer: 4

2⁴ ÷ 2² = 16 ÷ 4 = 4, or using exponent rules, 2^(4-2) = 2² = 4.

Question 10: What is log₂(32)?

6
5 (Correct answer)
3
4

Correct answer: 5

log₂(32) = 5 because 2⁵ = 32.

Question 11: Which of the following is equivalent to 0.35?

3/5
7/20 (Correct answer)
35/10
1/3

Correct answer: 7/20

0.35 = 35/100, which simplifies to 7/20 by dividing numerator and denominator by 5.

Question 12: What does ALEKS do when a student reaches 100% on their pie?

The student has mastered all topics in the course and ALEKS may offer review or extended content (Correct answer)
ALEKS assigns the student a tutor
ALEKS restarts the course from the beginning
Nothing happens — the student waits for class to end

Correct answer: The student has mastered all topics in the course and ALEKS may offer review or extended content

A complete pie means mastery of all course topics; ALEKS may then offer cumulative review or the next level of content.

Question 13: Convert 5/4 to a mixed number.

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

Correct answer: 1 1/4

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

Question 14: What is tan(45°)?

0
√3/2
√2
1 (Correct answer)

Correct answer: 1

tan(45°) = sin(45°)/cos(45°) = (√2/2)/(√2/2) = 1.

Question 15: What is the volume of a cube with side length 4 cm?

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

Correct answer: 64 cm³

Volume = side³ = 4³ = 64 cm³.

Question 16: A line segment has endpoints A(1, 2) and B(5, 6). What is the midpoint?

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

Correct answer: (3, 4)

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

Question 17: If two triangles are similar and their sides are in a ratio of 2:3, what is the ratio of their areas?

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

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: Which number is a prime number?

39
37 (Correct answer)
51
49

Correct answer: 37

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

Question 19: What happens during an ALEKS Initial Knowledge Check?

ALEKS creates a study schedule for you
ALEKS assigns a practice test
ALEKS gives you your first assignment
ALEKS assesses what topics you already know before beginning coursework (Correct answer)

Correct answer: ALEKS assesses what topics you already know before beginning coursework

The Initial Knowledge Check uses adaptive questioning to determine a student's existing mathematical knowledge before starting.

Question 20: What are the solutions to x² - 5x + 6 = 0?

x = -2 and x = -3
x = 2 and x = 3 (Correct answer)
x = 1 and x = 6
x = 2 and x = -3

Correct answer: x = 2 and x = 3

Factor as (x - 2)(x - 3) = 0, giving solutions x = 2 and x = 3.

Question 21: A card is drawn at random from a standard 52-card deck. What is the probability of drawing a king?

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

Correct answer: 1/13

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

Question 22: What does the ALEKS Pie represent for a student?

The student's overall grade in the course
The time spent on the platform
The topics a student has mastered versus what remains to be learned (Correct answer)
The number of questions answered correctly

Correct answer: The topics a student has mastered versus what remains to be learned

The ALEKS Pie visually shows mastered topics (filled) and topics remaining to be learned in the course.

Question 23: Which value is a solution to 2x − 3 > 7?

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

Correct answer: x = 6

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

Question 24: Solve: log₃(x) = 4

x = 64
x = 12
x = 34
x = 81 (Correct answer)

Correct answer: x = 81

log₃(x) = 4 means 3⁴ = x = 81.

Question 25: A right triangle has legs of 6 and 8. What is the length of the hypotenuse?

10 (Correct answer)
7
14
12

Correct answer: 10

Using the Pythagorean theorem: √(6² + 8²) = √(36 + 64) = √100 = 10.

Question 26: 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 27: What type of learning system is ALEKS based on?

Video-based passive instruction
Fixed curriculum with set lesson order
Adaptive learning using knowledge space theory (Correct answer)
Peer-to-peer tutoring

Correct answer: Adaptive learning using knowledge space theory

ALEKS is grounded in Knowledge Space Theory, which maps all possible states of student knowledge and adapts accordingly.

Question 28: If f(x) = x + 2 and g(x) = x², what is f(g(3))?

25
15
9
11 (Correct answer)

Correct answer: 11

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

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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