ALEKS Math Placement Exam Questions
With Correct Answers (Verified
Answers) Plus Rationales 2026 Q&A |
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1. Simplify: 3(2x + 5) - 4x
A. 2x + 15
B. 2x + 15
C. 6x + 5 - 4x
D. 6x + 20 - 4x
Rationale: Distribute 3 to both terms: 6x + 15 - 4x. Combine like terms
(6x - 4x = 2x), giving 2x + 15.
2. Solve: 5x = 35
A. 5
B. 7
C. 30
D. 175
Rationale: Divide both sides by 5 to isolate x: x = 7.
3. Simplify: (x²)(x³)
,A. x⁵
B. x⁵
C. x⁶
D. 2x⁵
Rationale: When multiplying same bases, add exponents: 2 + 3 = 5.
4. Solve: x + 9 = 2
A. 11
B. -11
C. -7
D. 7
Rationale: Subtract 9 from both sides: x = -7.
5. Evaluate: 2² + 3²
A. 10
B. 13
C. 12
D. 9
Rationale: 2² = 4 and 3² = 9, so total is 13.
6. Solve: 3x - 6 = 12
A. 4
B. 6
,C. 8
D. 18
Rationale: Add 6 to both sides → 3x = 18, then divide by 3 → x = 6.
7. Simplify: √49
A. 6
B. 7
C. 8
D. 14
Rationale: Square root of 49 is 7.
8. Solve: 2(x - 3) = 10
A. 2
B. 5
C. 8
D. 13
Rationale: Distribute: 2x - 6 = 10 → 2x = 16 → x = 8.
9. Simplify: 4x + 2x
A. 6
B. x⁶
C. 6x
D. 8x
Rationale: Combine like terms: 4x + 2x = 6x.
, 10. Solve: x/4 = 9
A. 36
B. 36
C. 13
D. 5
Rationale: Multiply both sides by 4: x = 36.
11. Expand: (x + 2)(x + 3)
A. x² + 6
B. x² + 5x + 6
C. x² + 3x + 2
D. x² + 1
Rationale: FOIL method: x² + 3x + 2x + 6 = x² + 5x + 6.
12. Factor: x² + 7x + 10
A. (x + 5)(x + 2)
B. (x + 5)(x + 2)
C. (x - 5)(x - 2)
D. (x + 10)(x + 1)
Rationale: Find numbers that multiply to 10 and sum to 7 → 5 and 2.
13. Solve: x² = 16
With Correct Answers (Verified
Answers) Plus Rationales 2026 Q&A |
Instant Download Pdf
1. Simplify: 3(2x + 5) - 4x
A. 2x + 15
B. 2x + 15
C. 6x + 5 - 4x
D. 6x + 20 - 4x
Rationale: Distribute 3 to both terms: 6x + 15 - 4x. Combine like terms
(6x - 4x = 2x), giving 2x + 15.
2. Solve: 5x = 35
A. 5
B. 7
C. 30
D. 175
Rationale: Divide both sides by 5 to isolate x: x = 7.
3. Simplify: (x²)(x³)
,A. x⁵
B. x⁵
C. x⁶
D. 2x⁵
Rationale: When multiplying same bases, add exponents: 2 + 3 = 5.
4. Solve: x + 9 = 2
A. 11
B. -11
C. -7
D. 7
Rationale: Subtract 9 from both sides: x = -7.
5. Evaluate: 2² + 3²
A. 10
B. 13
C. 12
D. 9
Rationale: 2² = 4 and 3² = 9, so total is 13.
6. Solve: 3x - 6 = 12
A. 4
B. 6
,C. 8
D. 18
Rationale: Add 6 to both sides → 3x = 18, then divide by 3 → x = 6.
7. Simplify: √49
A. 6
B. 7
C. 8
D. 14
Rationale: Square root of 49 is 7.
8. Solve: 2(x - 3) = 10
A. 2
B. 5
C. 8
D. 13
Rationale: Distribute: 2x - 6 = 10 → 2x = 16 → x = 8.
9. Simplify: 4x + 2x
A. 6
B. x⁶
C. 6x
D. 8x
Rationale: Combine like terms: 4x + 2x = 6x.
, 10. Solve: x/4 = 9
A. 36
B. 36
C. 13
D. 5
Rationale: Multiply both sides by 4: x = 36.
11. Expand: (x + 2)(x + 3)
A. x² + 6
B. x² + 5x + 6
C. x² + 3x + 2
D. x² + 1
Rationale: FOIL method: x² + 3x + 2x + 6 = x² + 5x + 6.
12. Factor: x² + 7x + 10
A. (x + 5)(x + 2)
B. (x + 5)(x + 2)
C. (x - 5)(x - 2)
D. (x + 10)(x + 1)
Rationale: Find numbers that multiply to 10 and sum to 7 → 5 and 2.
13. Solve: x² = 16
