Free ACT Math Question and Answers 2 — Questions and Answers
Question 1: What is the value of |−15 + 8| − |−3|?
- 4 (Correct answer)
- 10
- −4
- 20
Correct answer: 4
|−15 + 8| = |−7| = 7. |−3| = 3. 7 − 3 = 4.
Question 2: If f(x) = 2x² − 3x + 1, what is f(−2)?
- 15 (Correct answer)
- 11
- −9
- 7
Correct answer: 15
f(−2) = 2(−2)² − 3(−2) + 1 = 2(4) + 6 + 1 = 8 + 6 + 1 = 15.
Question 3: A triangle has vertices at A(0,0), B(6,0), and C(3,4). What is its area?
- 12 square units (Correct answer)
- 24 square units
- 10 square units
- 18 square units
Correct answer: 12 square units
Base AB = 6 units (along x-axis). Height = 4 units (y-coordinate of C). Area = ½ × 6 × 4 = 12 square units.
Question 4: What is the solution set of |2x − 6| ≤ 4?
- 1 ≤ x ≤ 5 (Correct answer)
- x ≤ 1 or x ≥ 5
- −5 ≤ x ≤ 1
- x ≤ −1 or x ≥ 5
Correct answer: 1 ≤ x ≤ 5
|2x − 6| ≤ 4 → −4 ≤ 2x − 6 ≤ 4. Add 6: 2 ≤ 2x ≤ 10. Divide by 2: 1 ≤ x ≤ 5.
Question 5: A store marks up items by 40%, then offers a 20% sale discount. What is the net percent change from the original price?
- 12% increase (Correct answer)
- 20% increase
- 8% decrease
- No change
Correct answer: 12% increase
Markup: 1.40 × original. Discount: 0.80 × 1.40 × original = 1.12 × original. Net result: 12% increase over original price.
Question 6: In the standard (x,y) coordinate plane, what is the equation of a circle with center (−2, 3) and radius 5?
- (x + 2)² + (y − 3)² = 25 (Correct answer)
- (x − 2)² + (y + 3)² = 25
- (x + 2)² + (y − 3)² = 5
- (x − 2)² + (y − 3)² = 25
Correct answer: (x + 2)² + (y − 3)² = 25
Standard circle equation: (x − h)² + (y − k)² = r². Center (−2, 3) means h = −2, k = 3. Radius 5 means r² = 25. Equation: (x − (−2))² + (y − 3)² = 25 → (x + 2)² + (y − 3)² = 25.
Free ACT Math Question and Answers 2
What is the value of |−15 + 8| − |−3|?