ACCUPLACER Test Questions With Complete
Solutions
Course
ACCUPLACER
1. Arithmetic (Fractions)
Question: What is the result of: 3/4 + 2/3?
Solution:
Find the common denominator (LCM of 4 and 3 is 12):
3/4 = 9/12
2/3 = 8/12
Add the fractions:
9/12 + 8/12 = 17/12 = 1 5/12
Answer: 1 5/12
2. Arithmetic (Percents)
Question: 20% of what number is 36?
Solution:
Let x be the unknown number:
0.20x = 36
x = 36 ÷ 0.20 = 180
Answer: 180
3. Quantitative Reasoning (Algebraic Expressions)
Question: Simplify: 3(x - 2) + 4(2x + 1)
Solution:
Distribute:
= 3x - 6 + 8x + 4
Combine like terms:
= 11x - 2
Answer: 11x - 2
4. Quantitative Reasoning (Solving Equations)
Question: Solve for x: 2x + 5 = 3x - 7
Solution:
Subtract 2x from both sides:
5=x-7
Add 7 to both sides:
x = 12
Answer: 12
,5. Advanced Algebra (Exponents)
Question: Simplify: (2x³)²
Solution:
Apply exponent rules:
= 2² × x⁶ = 4x⁶
Answer: 4x⁶
6. Advanced Algebra (Inequalities)
Question: Solve: 5 - 2x < 1
Solution:
Subtract 5 from both sides:
-2x < -4
Divide by -2 (reverse the inequality):
x>2
Answer: x > 2
7. Reading Comprehension (Inference)
Passage: "Despite their size, blue whales feed almost exclusively on krill—tiny shrimp-like
animals found in all the world's oceans."
Question: What can be inferred from this sentence?
A. Blue whales eat many kinds of fish
B. Blue whales rely on small prey for survival
C. Krill are endangered
D. All whales eat krill
Solution:
The passage suggests that blue whales depend on krill.
Answer: B
8. Reading Comprehension (Main Idea)
Passage: "With the rapid growth of cities, urban planners must consider sustainable development
to minimize environmental impact."
Question: What is the main idea?
A. Cities should stop growing
B. Urban planners ignore the environment
C. Sustainable development is crucial in growing cities
D. Environmental damage is irreversible
Solution:
,The sentence focuses on the importance of sustainability in urban planning.
Answer: C
9. Writing (Sentence Structure)
Question: Which of the following is a complete sentence?
A. Running through the park.
B. After the rain stopped.
C. The children played in the puddles.
D. Because the sun came out.
Solution:
Only C is a complete sentence with subject and verb.
Answer: C
10. Writing (Grammar and Usage)
Question: Choose the correct sentence:
A. Its going to rain today.
B. It’s going to rain today.
C. Its’ going to rain today.
D. Its going too rain today.
Solution:
"It’s" is the correct contraction for "it is."
Answer: B
11. Arithmetic (Decimals)
Question: What is 5.7 × 0.4?
Solution:
Multiply:
5.7 × 0.4 = 2.28
Answer: 2.28
12. Arithmetic (Order of Operations)
Question: What is the result of: 6 + 2 × (5 – 3)²?
Solution:
Step 1: Parentheses → (5 – 3) = 2
Step 2: Exponent → 2² = 4
Step 3: Multiply → 2 × 4 = 8
Step 4: Add → 6 + 8 = 14
Answer: 14
, 13. Quantitative Reasoning (Solving for a Variable)
Question: Solve for y: 3y – 4 = 2y + 5
Solution:
Subtract 2y: y – 4 = 5
Add 4: y = 9
Answer: 9
14. Quantitative Reasoning (Rational Expressions)
Question: Simplify: (x² – 9)/(x + 3)
Solution:
Factor numerator: (x – 3)(x + 3)
Cancel (x + 3):
Result = x – 3
Answer: x – 3
15. Advanced Algebra (Radicals)
Question: Simplify: √(49x²)
Solution:
= √49 × √x² = 7x
Answer: 7x
16. Advanced Algebra (Quadratic Equations)
Question: Solve: x² – 4x – 5 = 0
Solution:
Factor: (x – 5)(x + 1) = 0
x = 5 or x = –1
Answer: 5, –1
17. Reading Comprehension (Vocabulary in Context)
Passage: "The manager was commended for her exemplary leadership during the crisis."
Question: What does exemplary most nearly mean?
A. Minor
B. Perfect
C. Faulty
D. Outstanding
Solutions
Course
ACCUPLACER
1. Arithmetic (Fractions)
Question: What is the result of: 3/4 + 2/3?
Solution:
Find the common denominator (LCM of 4 and 3 is 12):
3/4 = 9/12
2/3 = 8/12
Add the fractions:
9/12 + 8/12 = 17/12 = 1 5/12
Answer: 1 5/12
2. Arithmetic (Percents)
Question: 20% of what number is 36?
Solution:
Let x be the unknown number:
0.20x = 36
x = 36 ÷ 0.20 = 180
Answer: 180
3. Quantitative Reasoning (Algebraic Expressions)
Question: Simplify: 3(x - 2) + 4(2x + 1)
Solution:
Distribute:
= 3x - 6 + 8x + 4
Combine like terms:
= 11x - 2
Answer: 11x - 2
4. Quantitative Reasoning (Solving Equations)
Question: Solve for x: 2x + 5 = 3x - 7
Solution:
Subtract 2x from both sides:
5=x-7
Add 7 to both sides:
x = 12
Answer: 12
,5. Advanced Algebra (Exponents)
Question: Simplify: (2x³)²
Solution:
Apply exponent rules:
= 2² × x⁶ = 4x⁶
Answer: 4x⁶
6. Advanced Algebra (Inequalities)
Question: Solve: 5 - 2x < 1
Solution:
Subtract 5 from both sides:
-2x < -4
Divide by -2 (reverse the inequality):
x>2
Answer: x > 2
7. Reading Comprehension (Inference)
Passage: "Despite their size, blue whales feed almost exclusively on krill—tiny shrimp-like
animals found in all the world's oceans."
Question: What can be inferred from this sentence?
A. Blue whales eat many kinds of fish
B. Blue whales rely on small prey for survival
C. Krill are endangered
D. All whales eat krill
Solution:
The passage suggests that blue whales depend on krill.
Answer: B
8. Reading Comprehension (Main Idea)
Passage: "With the rapid growth of cities, urban planners must consider sustainable development
to minimize environmental impact."
Question: What is the main idea?
A. Cities should stop growing
B. Urban planners ignore the environment
C. Sustainable development is crucial in growing cities
D. Environmental damage is irreversible
Solution:
,The sentence focuses on the importance of sustainability in urban planning.
Answer: C
9. Writing (Sentence Structure)
Question: Which of the following is a complete sentence?
A. Running through the park.
B. After the rain stopped.
C. The children played in the puddles.
D. Because the sun came out.
Solution:
Only C is a complete sentence with subject and verb.
Answer: C
10. Writing (Grammar and Usage)
Question: Choose the correct sentence:
A. Its going to rain today.
B. It’s going to rain today.
C. Its’ going to rain today.
D. Its going too rain today.
Solution:
"It’s" is the correct contraction for "it is."
Answer: B
11. Arithmetic (Decimals)
Question: What is 5.7 × 0.4?
Solution:
Multiply:
5.7 × 0.4 = 2.28
Answer: 2.28
12. Arithmetic (Order of Operations)
Question: What is the result of: 6 + 2 × (5 – 3)²?
Solution:
Step 1: Parentheses → (5 – 3) = 2
Step 2: Exponent → 2² = 4
Step 3: Multiply → 2 × 4 = 8
Step 4: Add → 6 + 8 = 14
Answer: 14
, 13. Quantitative Reasoning (Solving for a Variable)
Question: Solve for y: 3y – 4 = 2y + 5
Solution:
Subtract 2y: y – 4 = 5
Add 4: y = 9
Answer: 9
14. Quantitative Reasoning (Rational Expressions)
Question: Simplify: (x² – 9)/(x + 3)
Solution:
Factor numerator: (x – 3)(x + 3)
Cancel (x + 3):
Result = x – 3
Answer: x – 3
15. Advanced Algebra (Radicals)
Question: Simplify: √(49x²)
Solution:
= √49 × √x² = 7x
Answer: 7x
16. Advanced Algebra (Quadratic Equations)
Question: Solve: x² – 4x – 5 = 0
Solution:
Factor: (x – 5)(x + 1) = 0
x = 5 or x = –1
Answer: 5, –1
17. Reading Comprehension (Vocabulary in Context)
Passage: "The manager was commended for her exemplary leadership during the crisis."
Question: What does exemplary most nearly mean?
A. Minor
B. Perfect
C. Faulty
D. Outstanding
