Math ACCUPLACER Practice Test – 2026 Edition
Total questions: 156
Sections: Arithmetic (Q1–52), Quantitative Reasoning &
Algebra (Q53–104), Advanced Algebra & Functions (Q105–
156)
Arithmetic (Questions 1–52)
1. What is the value of 15 + 6 × 2?
A) 27
B) 42
C) 21
D) 33
ANSWER: A) 27
Rationale: Order of operations (PEMDAS): multiply first: 6×2=12, then add 15 → 27.
B) 42 is incorrect if you add first then multiply. C) 21 is incorrect (15+6=21, then ×2? No). D) 33 is
incorrect (15+18).
2. ¾ + ⅖ = ?
A) ⁷⁄₂₀
B) ²³⁄₂₀
C) ¹⁷⁄₂₀
D) ¹⁄₂₀
ANSWER: B) ²³⁄₂₀
Rationale: Common denominator 20: (15/20 + 8/20)=23/20.
A) 7/20 is sum of numerators without common denom. C) 17/20 is 15+2 over 20? No. D) 1/20 is
difference.
3. 0.08 × 0.5 = ?
A) 0.4
B) 0.04
C) 0.004
D) 0.0004
,ANSWER: B) 0.04
Rationale: 8×5=40, decimal places: 2+1=3 → 0.040 = 0.04.
A) 0.4 is 0.8×0.5. C) 0.004 is 4 decimal places wrong. D) 0.0004 is 4 decimal places wrong.
4. What is ⅝ as a decimal?
A) 0.625
B) 0.6
C) 0.63
D) 0.58
ANSWER: A) 0.625
Rationale: 5÷8=0.625. B) 0.6 is 3/5. C) 0.63 rounded but exact is 0.625. D) 0.58 is 58/100.
5. 7 - 2 × (3 + 1) = ?
A) 20
B) -1
C) 5
D) -9
ANSWER: B) -1
Rationale: Parentheses first: 3+1=4, multiply 2×4=8, subtract 7-8=-1.
A) 20 is 7-2=5×(4)=20 wrong order. C) 5 is 7-2=5 then +1? No. D) -9 is 7-16.
6. Which fraction is largest? ³⁄₄, ⁵⁄₈, ²⁄₃, ⁷⁄₁₂
A) ³⁄₄
B) ⁵⁄₈
C) ²⁄₃
D) ⁷⁄₁₂
ANSWER: A) ³⁄₄
Rationale: Convert to decimals: 0.75, 0.625, 0.666..., 0.583. Largest is 0.75.
B) 0.625 smaller. C) 0.667 smaller. D) 0.583 smallest.
7. 48 ÷ 0.6 = ?
A) 8
B) 80
C) 0.8
D) 800
ANSWER: B) 80
Rationale: 48 ÷ 0.6 = 48 ÷ (6/10) = 48 × (10/6) = 480/6 = 80.
A) 8 is 48÷6. C) 0.8 is 48×0.016. D) 800 is 48÷0.06.
8. What is 15% of 200?
A) 30
B) 15
C) 20
D) 25
,ANSWER: A) 30
Rationale: 0.15 × 200 = 30.
B) 15 is 7.5% of 200. C) 20 is 10%. D) 25 is 12.5%.
9. 5² + 3³ = ?
A) 34
B) 52
C) 25
D) 27
ANSWER: B) 52
Rationale: 5²=25, 3³=27, sum=52.
A) 34 is 25+9. C) 25 only. D) 27 only.
**10. A shirt costs $40. It is on sale for 25% off. What is the sale price?**
A) $10
B) $30
C) $20
D) $35
**ANSWER: B) $30**
Rationale: 25% of 40 = $10, subtract: $40-$10=$30.
A) $10 is discount. C) $20 is 50% off. D) $35 is 12.5% off.
11. ⁷⁄₈ - ¹⁄₄ = ?
A) ⁶⁄₈
B) ⁵⁄₈
C) ³⁄₄
D) ¹⁄₂
ANSWER: B) ⁵⁄₈
Rationale: 1/4=2/8, 7/8-2/8=5/8. A) 6/8=3/4 incorrect. C) 3/4=6/8. D) 1/2=4/8.
12. 0.75 × 0.2 = ?
A) 1.5
B) 0.15
C) 0.015
D) 0.0015
ANSWER: B) 0.15
Rationale: 75×2=150, decimal places 2+1=3 → 0.150=0.15.
A) 1.5 is 0.75×2. C) 0.015 is 3 decimal places? Actually 150 with 3 places=0.150, not 0.015. Wait
150→0.150=0.15, not 0.015. So C is wrong. D) 0.0015 is 4 places.
13. What is the average of 12, 15, 18, 21?
A) 15
B) 16.5
, C) 17
D) 18
ANSWER: B) 16.5
Rationale: Sum=66, divide by 4=16.5. A) 15 too low. C) 17 sum=68 no. D) 18 sum=72 no.
14. ⅖ ÷ ⅓ = ?
A) ²⁄₁₅
B) ⁶⁄₅
C) ⁵⁄₆
D) ¹⁄₅
ANSWER: B) ⁶⁄₅
Rationale: (2/5)×(3/1)=6/5. A) 2/15 is multiply instead of divide. C) 5/6 is reciprocal. D) 1/5 is 2/5 × 1/2
wrong.
15. 3.6 + 0.84 = ?
A) 4.44
B) 3.44
C) 4.4
D) 3.64
ANSWER: A) 4.44
Rationale: 3.60+0.84=4.44. B) 3.44 is subtract. C) 4.4 is rounding. D) 3.64 is wrong addition.
16. ⅓ of 60 is what percent of 40?
A) 20%
B) 50%
C) 25%
D) 30%
ANSWER: B) 50%
Rationale: 1/3 of 60=20, 20/40=0.5=50%. A) 20% is 8/40. C) 25% is 10/40. D) 30% is 12/40.
17. 8 - 3 × (2 + 1) + 4 = ?
A) 3
B) 19
C) 11
D) 7
ANSWER: A) 3
Rationale: Parentheses: 2+1=3, multiply 3×3=9, 8-9=-1, +4=3. B) 19: 8-3=5×(3)=15+4=19 wrong. C) 11: 8-
(3×2)+1+4? No. D) 7: 8-(3×3)=-1+8? No.
18. Which decimal is equivalent to ⁷⁄₂₀?
A) 0.35
B) 0.7
C) 0.14
D) 0.28
Total questions: 156
Sections: Arithmetic (Q1–52), Quantitative Reasoning &
Algebra (Q53–104), Advanced Algebra & Functions (Q105–
156)
Arithmetic (Questions 1–52)
1. What is the value of 15 + 6 × 2?
A) 27
B) 42
C) 21
D) 33
ANSWER: A) 27
Rationale: Order of operations (PEMDAS): multiply first: 6×2=12, then add 15 → 27.
B) 42 is incorrect if you add first then multiply. C) 21 is incorrect (15+6=21, then ×2? No). D) 33 is
incorrect (15+18).
2. ¾ + ⅖ = ?
A) ⁷⁄₂₀
B) ²³⁄₂₀
C) ¹⁷⁄₂₀
D) ¹⁄₂₀
ANSWER: B) ²³⁄₂₀
Rationale: Common denominator 20: (15/20 + 8/20)=23/20.
A) 7/20 is sum of numerators without common denom. C) 17/20 is 15+2 over 20? No. D) 1/20 is
difference.
3. 0.08 × 0.5 = ?
A) 0.4
B) 0.04
C) 0.004
D) 0.0004
,ANSWER: B) 0.04
Rationale: 8×5=40, decimal places: 2+1=3 → 0.040 = 0.04.
A) 0.4 is 0.8×0.5. C) 0.004 is 4 decimal places wrong. D) 0.0004 is 4 decimal places wrong.
4. What is ⅝ as a decimal?
A) 0.625
B) 0.6
C) 0.63
D) 0.58
ANSWER: A) 0.625
Rationale: 5÷8=0.625. B) 0.6 is 3/5. C) 0.63 rounded but exact is 0.625. D) 0.58 is 58/100.
5. 7 - 2 × (3 + 1) = ?
A) 20
B) -1
C) 5
D) -9
ANSWER: B) -1
Rationale: Parentheses first: 3+1=4, multiply 2×4=8, subtract 7-8=-1.
A) 20 is 7-2=5×(4)=20 wrong order. C) 5 is 7-2=5 then +1? No. D) -9 is 7-16.
6. Which fraction is largest? ³⁄₄, ⁵⁄₈, ²⁄₃, ⁷⁄₁₂
A) ³⁄₄
B) ⁵⁄₈
C) ²⁄₃
D) ⁷⁄₁₂
ANSWER: A) ³⁄₄
Rationale: Convert to decimals: 0.75, 0.625, 0.666..., 0.583. Largest is 0.75.
B) 0.625 smaller. C) 0.667 smaller. D) 0.583 smallest.
7. 48 ÷ 0.6 = ?
A) 8
B) 80
C) 0.8
D) 800
ANSWER: B) 80
Rationale: 48 ÷ 0.6 = 48 ÷ (6/10) = 48 × (10/6) = 480/6 = 80.
A) 8 is 48÷6. C) 0.8 is 48×0.016. D) 800 is 48÷0.06.
8. What is 15% of 200?
A) 30
B) 15
C) 20
D) 25
,ANSWER: A) 30
Rationale: 0.15 × 200 = 30.
B) 15 is 7.5% of 200. C) 20 is 10%. D) 25 is 12.5%.
9. 5² + 3³ = ?
A) 34
B) 52
C) 25
D) 27
ANSWER: B) 52
Rationale: 5²=25, 3³=27, sum=52.
A) 34 is 25+9. C) 25 only. D) 27 only.
**10. A shirt costs $40. It is on sale for 25% off. What is the sale price?**
A) $10
B) $30
C) $20
D) $35
**ANSWER: B) $30**
Rationale: 25% of 40 = $10, subtract: $40-$10=$30.
A) $10 is discount. C) $20 is 50% off. D) $35 is 12.5% off.
11. ⁷⁄₈ - ¹⁄₄ = ?
A) ⁶⁄₈
B) ⁵⁄₈
C) ³⁄₄
D) ¹⁄₂
ANSWER: B) ⁵⁄₈
Rationale: 1/4=2/8, 7/8-2/8=5/8. A) 6/8=3/4 incorrect. C) 3/4=6/8. D) 1/2=4/8.
12. 0.75 × 0.2 = ?
A) 1.5
B) 0.15
C) 0.015
D) 0.0015
ANSWER: B) 0.15
Rationale: 75×2=150, decimal places 2+1=3 → 0.150=0.15.
A) 1.5 is 0.75×2. C) 0.015 is 3 decimal places? Actually 150 with 3 places=0.150, not 0.015. Wait
150→0.150=0.15, not 0.015. So C is wrong. D) 0.0015 is 4 places.
13. What is the average of 12, 15, 18, 21?
A) 15
B) 16.5
, C) 17
D) 18
ANSWER: B) 16.5
Rationale: Sum=66, divide by 4=16.5. A) 15 too low. C) 17 sum=68 no. D) 18 sum=72 no.
14. ⅖ ÷ ⅓ = ?
A) ²⁄₁₅
B) ⁶⁄₅
C) ⁵⁄₆
D) ¹⁄₅
ANSWER: B) ⁶⁄₅
Rationale: (2/5)×(3/1)=6/5. A) 2/15 is multiply instead of divide. C) 5/6 is reciprocal. D) 1/5 is 2/5 × 1/2
wrong.
15. 3.6 + 0.84 = ?
A) 4.44
B) 3.44
C) 4.4
D) 3.64
ANSWER: A) 4.44
Rationale: 3.60+0.84=4.44. B) 3.44 is subtract. C) 4.4 is rounding. D) 3.64 is wrong addition.
16. ⅓ of 60 is what percent of 40?
A) 20%
B) 50%
C) 25%
D) 30%
ANSWER: B) 50%
Rationale: 1/3 of 60=20, 20/40=0.5=50%. A) 20% is 8/40. C) 25% is 10/40. D) 30% is 12/40.
17. 8 - 3 × (2 + 1) + 4 = ?
A) 3
B) 19
C) 11
D) 7
ANSWER: A) 3
Rationale: Parentheses: 2+1=3, multiply 3×3=9, 8-9=-1, +4=3. B) 19: 8-3=5×(3)=15+4=19 wrong. C) 11: 8-
(3×2)+1+4? No. D) 7: 8-(3×3)=-1+8? No.
18. Which decimal is equivalent to ⁷⁄₂₀?
A) 0.35
B) 0.7
C) 0.14
D) 0.28
