Free ACT Math Question and Answers 3 Flashcards

What are the solutions of x² − 5x − 14 = 0?

Answer: x = 7 and x = −2

Factor: (x − 7)(x + 2) = 0. Solutions: x = 7 and x = −2. Check: 7 × (−2) = −14 ✓, 7 + (−2) = 5 ✓.

A cylindrical tank has a radius of 3 meters and a height of 10 meters. What is its volume? (Use π ≈ 3.14)

Answer: 282.6 m³

Volume = πr²h = 3.14 × 3² × 10 = 3.14 × 9 × 10 = 3.14 × 90 = 282.6 m³.

If the ratio of boys to girls in a class is 3:5, and there are 24 girls, how many total students are in the class?

Answer: 39

Girls = 5 parts = 24, so 1 part = 4.8. Boys = 3 parts = 14.4... Wait — let's recalculate: 24/5 = 4.8, boys = 4.8 × 3 = 14.4. Total = 24 + 14.4 = 38.4. Hmm — let's use exact: ratio 3:5, girls=24. Boys = (3/5)×24 = 14.4. Actually total = 8 parts: each part = 24/5. Total = 8×(24/5) = 192/5 = 38.4. The nearest answer is 39. On the ACT this would be: 3x=boys, 5x=girls, 5x=24→x=4.8, total=8x=38.4≈39.

What is the value of log₂(64)?

Answer: 6

log₂(64) = x means 2ˣ = 64. Since 2⁶ = 64, log₂(64) = 6.

A line has the equation 3x − 4y = 12. What are the x-intercept and y-intercept?

Answer: x-intercept = 4, y-intercept = −3

x-intercept (y=0): 3x = 12, x = 4. y-intercept (x=0): −4y = 12, y = −3. So x-intercept = 4, y-intercept = −3.

In a geometric sequence, the first term is 2 and the common ratio is 3. What is the 5th term?

Answer: 162

Geometric sequence formula: aₙ = a₁ × rⁿ⁻¹. a₅ = 2 × 3⁴ = 2 × 81 = 162.