Free ACT Math Question and Answers 3

Question 1

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

Accepted Answer

x = 7 and x = −2

Answer

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

Question 2

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

Accepted Answer

282.6 m³

Answer

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

Question 3

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?

Accepted Answer

39

Answer

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.

Question 4

What is the value of log₂(64)?

Accepted Answer

6

Answer

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

Question 5

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

Accepted Answer

x-intercept = 4, y-intercept = −3

Answer

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

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Free ACT Math Question and Answers 3