ACT Math Practice Test Pool 3 Flashcards

If 3x - 7 = 2x + 5, what is the value of x?

Answer: x = 12

Subtract 2x from both sides: x - 7 = 5. Add 7 to both sides: x = 12.

A rectangle has a perimeter of 54 cm. If the length is twice the width, what is the area of the rectangle?

Answer: 162 cm²

Let width = w, length = 2w. Perimeter: 2(w + 2w) = 54 → 6w = 54 → w = 9. Length = 18. Area = 9 × 18 = 162 cm².

What is the slope of a line that passes through (−3, 4) and (5, −2)?

Answer: -3/4

Slope = (y₂ − y₁)/(x₂ − x₁) = (−2 − 4)/(5 − (−3)) = −6/8 = −3/4.

Which of the following is equivalent to (x² − 9)/(x − 3) for x ≠ 3?

Answer: x + 3

Factor the numerator: x² − 9 = (x − 3)(x + 3). Cancel (x − 3): result is x + 3.

A car travels 240 miles in 4 hours. At this rate, how far will it travel in 7 hours?

Answer: 420 miles

Rate = 240 ÷ 4 = 60 mph. Distance in 7 hours = 60 × 7 = 420 miles.

If sin θ = 5/13 and θ is in the first quadrant, what is cos θ?

Answer: 12/13

Using the Pythagorean identity: cos²θ = 1 − sin²θ = 1 − 25/169 = 144/169. cos θ = 12/13 (positive in Q1).