ALEKS Math Placement Assessment — Questions and Answers

Question 1: A survey of 200 people found 60 prefer brand A. What is the relative frequency of brand A preference?

30/100
0.30 (Correct answer)
60%
0.60

Correct answer: 0.30

Relative frequency = 60/200 = 0.30.

Question 2: What type of learning system is ALEKS based on?

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

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 3: In a stem-and-leaf plot, which part represents the ones digit?

Leaf (Correct answer)
Median line
Title
Stem

Correct answer: Leaf

In a stem-and-leaf plot, the leaf represents the last digit (ones), while the stem represents leading digits.

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

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

Correct answer: x ≥ 4

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

Question 5: What is the perimeter of a regular hexagon with side length 6 cm?

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

Correct answer: 36 cm

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

Question 6: A trapezoid has bases of 8 and 12 and a height of 5. What is its area?

40
100
50 (Correct answer)
60

Correct answer: 50

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

Question 7: 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 8: A car travels 180 miles in 3 hours. What is its average speed?

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

Correct answer: 60 mph

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

Question 9: If f(x) = x + 2 and g(x) = x², what is f(g(3))?

15
25
9
11 (Correct answer)

Correct answer: 11

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

Question 10: Simplify: (x³)⁴

x³⁴
4x³
x⁷
x¹² (Correct answer)

Correct answer: x¹²

When raising a power to a power, multiply the exponents: (x³)⁴ = x^(3×4) = x¹².

Question 11: Solve the inequality: 2x - 4 > 10

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

Correct answer: x > 7

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

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

115° (Correct answer)
25°
90°
295°

Correct answer: 115°

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

Question 13: A card is drawn at random from a standard 52-card deck. What is the probability of drawing a king?

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

Correct answer: 1/13

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

Question 14: What is (-5) × (-8)?

-13
13
40 (Correct answer)
-40

Correct answer: 40

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

Question 15: A store sells apples for $1.25 each. How much do 8 apples cost?

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

Correct answer: $10.00

Multiply 8 × $1.25 = $10.00.

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

1:3
2:3
8:27
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 17: Simplify: 4x + 3y - 2x + y

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

Correct answer: 2x + 4y

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

Question 18: Solve for x: 3x + 7 = 22

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

Correct answer: x = 5

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

Question 19: Which sequence is geometric: 2, 6, 18, 54, ...?

No, it is arithmetic
Yes, with common ratio 2
No, it has no pattern
Yes, with common ratio 3 (Correct answer)

Correct answer: Yes, with common ratio 3

Each term is multiplied by 3: 2×3 = 6, 6×3 = 18, so it is geometric with ratio 3.

Question 20: Solve for x: 3x − 7 = 2x + 5

x = −2
x = 7
x = 12 (Correct answer)
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 21: What is the value of 3/4 + 5/8?

8/12
11/8 (Correct answer)
1/2
2/3

Correct answer: 11/8

Convert 3/4 to 6/8, then add 6/8 + 5/8 = 11/8.

Question 22: Find the inverse of f(x) = 3x - 6.

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

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 23: Which value satisfies −4x + 8 = 0?

x = 2 (Correct answer)
x = 4
x = −4
x = −2

Correct answer: x = 2

Adding 4x to both sides gives 8 = 4x, and dividing both sides by 4 gives x = 2.

Question 24: A bag has 3 red, 5 blue, and 2 green marbles. What is the probability of picking a blue marble?

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

Correct answer: 1/2

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

Question 25: What is tan(45°)?

√3/2
√2
0
1 (Correct answer)

Correct answer: 1

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

Question 26: Which transformation shifts f(x) = x² three units to the right?

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

Correct answer: f(x) = (x - 3)²

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

Question 27: What is the mode of: 2, 4, 4, 6, 7, 9, 9, 9?

7
4
6
9 (Correct answer)

Correct answer: 9

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

Question 28: What is the value of 2⁴ ÷ 2²?

4 (Correct answer)
2
8
1

Correct answer: 4

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

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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