ACT Math Practice Test Pool 3 — Questions and Answers
Question 1: If 3x - 7 = 2x + 5, what is the value of x?
- x = 12 (Correct answer)
- x = -12
- x = 2
- x = -2
Correct answer: x = 12
Subtract 2x from both sides: x - 7 = 5. Add 7 to both sides: x = 12.
Question 2: A rectangle has a perimeter of 54 cm. If the length is twice the width, what is the area of the rectangle?
- 162 cm² (Correct answer)
- 81 cm²
- 243 cm²
- 108 cm²
Correct answer: 162 cm²
Let width = w, length = 2w. Perimeter: 2(w + 2w) = 54 → 6w = 54 → w = 9. Length = 18. Area = 9 × 18 = 162 cm².
Question 3: What is the slope of a line that passes through (−3, 4) and (5, −2)?
- -3/4 (Correct answer)
- 3/4
- -4/3
- 4/3
Correct answer: -3/4
Slope = (y₂ − y₁)/(x₂ − x₁) = (−2 − 4)/(5 − (−3)) = −6/8 = −3/4.
Question 4: Which of the following is equivalent to (x² − 9)/(x − 3) for x ≠ 3?
- x + 3 (Correct answer)
- x − 3
- x² + 3
- x + 9
Correct answer: x + 3
Factor the numerator: x² − 9 = (x − 3)(x + 3). Cancel (x − 3): result is x + 3.
Question 5: A car travels 240 miles in 4 hours. At this rate, how far will it travel in 7 hours?
- 420 miles (Correct answer)
- 480 miles
- 380 miles
- 400 miles
Correct answer: 420 miles
Rate = 240 ÷ 4 = 60 mph. Distance in 7 hours = 60 × 7 = 420 miles.
Question 6: If sin θ = 5/13 and θ is in the first quadrant, what is cos θ?
- 12/13 (Correct answer)
- 5/12
- 13/12
- 8/13
Correct answer: 12/13
Using the Pythagorean identity: cos²θ = 1 − sin²θ = 1 − 25/169 = 144/169. cos θ = 12/13 (positive in Q1).
ACT Math Practice Test Pool 3
If 3x - 7 = 2x + 5, what is the value of x?