ALEKS MATH EXAM — 2025/2026 200 Practice Questions with Answers & Rationales

ALEKS MATH EXAM — 2025/2026
200 Practice Questions with Answers & Rationales
EXAM PREPARATION SUMMARY
Section Questions Key Topics
Whole Numbers & Number Order of operations, GCF, LCM, primes,
1–20
Sense exponents
Fractions, Decimals & Operations on fractions, percent change, scientific
21–45
Percentages notation
Algebra — Expressions & Linear/quadratic equations, factoring, functions,
46–80
Equations logarithms
Geometry & Measurement 81–115 Area, volume, Pythagorean theorem, trig, circles
Mean, median, mode, probability, standard
Statistics & Probability 116–135
deviation
Ratios, Proportions & Word Direct/inverse variation, rates, interest, work
136–155
Problems problems
Sequences, calculus preview, matrices, complex
Advanced Topics 156–200
numbers




SECTION 1: WHOLE NUMBERS & NUMBER SENSE
(Questions 1–20)


1. What is the value of 7 × 8 + 3²?

 A) 59
 B) 65 ✅ (correct answer)
 C) 71
 D) 48

Rationale: Following order of operations (PEMDAS): First, 3² = 9. Then, 7 × 8 = 56. Finally,
56 + 9 = 65.



2. What is the greatest common factor (GCF) of 36 and 48?

,  A) 6
 B) 9
 C) 12 ✅ (correct answer)
 D) 18

Rationale: Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
The greatest common factor is 12.



3. What is the least common multiple (LCM) of 8 and 12?

 A) 16
 B) 20
 C) 24 ✅ (correct answer)
 D) 96

Rationale: Multiples of 8: 8, 16, 24, 32... Multiples of 12: 12, 24, 36... The smallest shared
multiple is 24.



4. Which of the following is a prime number?

 A) 27
 B) 33
 C) 41 ✅ (correct answer)
 D) 51

Rationale: 27 = 3×9, 33 = 3×11, 51 = 3×17. The number 41 has no factors other than 1 and
itself — it is prime.



5. What is 2⁵ × 2³?

 A) 2⁸ ✅ (correct answer)
 B) 2¹⁵
 C) 4⁸
 D) 2⁶

Rationale: When multiplying powers with the same base, add the exponents: 2⁵ × 2³ = 2^(5+3)
= 2⁸ = 256.

,6. Evaluate: 144 ÷ 12 + 5 × 3 − 7

 A) 20
 B) 15
 C) 22
 D) 20 ✅ (correct answer)

Rationale: Order of operations: 144 ÷ 12 = 12. Then 5 × 3 = 15. So 12 + 15 − 7 = 20.



7. What is the absolute value of −15?

 A) −15
 B) 15 ✅ (correct answer)
 C) 0
 D) 1/15

Rationale: The absolute value represents distance from zero on the number line. |−15| = 15
because distance is always non-negative.



8. Which number is divisible by both 4 and 9?

 A) 24
 B) 36 ✅ (correct answer)
 C) 28
 D) 45

Rationale: 36 ÷ 4 = 9 and 36 ÷ 9 = 4. Both divide evenly. LCM of 4 and 9 = 36 since they share
no common factors.



9. What is 3⁴?

 A) 12
 B) 64
 C) 81 ✅ (correct answer)
 D) 27

Rationale: 3⁴ = 3 × 3 × 3 × 3 = 9 × 9 = 81.

, 10. Simplify: −3 + (−8) − (−5)

 A) −16
 B) −6 ✅ (correct answer)
 C) 0
 D) −11

Rationale: −3 + (−8) − (−5) = −3 − 8 + 5. Adding: −3 − 8 = −11. Then −11 + 5 = −6.



11. What is the prime factorization of 72?

 A) 2² × 3³
 B) 2³ × 3² ✅ (correct answer)
 C) 2⁴ × 3
 D) 6² × 2

Rationale: 72 = 8 × 9 = 2³ × 3². Breaking down: 72 → 2 × 36 → 2 × 2 × 18 → 2 × 2 × 2 × 9
→ 2³ × 3².



12. Which of the following is between −3 and 0 on the number line?

 A) −4
 B) 1
 C) −1.5 ✅ (correct answer)
 D) 3

Rationale: Between −3 and 0 are negative values closer to zero. −1.5 falls between −3 and 0.
The others fall outside this range.



13. What is 7! (7 factorial)?

 A) 49
 B) 720
 C) 5040 ✅ (correct answer)
 D) 2520

Rationale: 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.