ACT Math: Algebra 1 — Questions and Answers
Question 1: If 3x + 7 = 22, what is the value of x?
- 3
- 5 (Correct answer)
- 7
- 9
Correct answer: 5
Subtract 7 from both sides to get 3x = 15, then divide by 3 to find x = 5.
Question 2: Which expression is equivalent to 2(x + 3) − 4x?
- −2x + 6 (Correct answer)
- 2x + 6
- −2x + 3
- 6x + 6
Correct answer: −2x + 6
Distribute to get 2x + 6 − 4x, then combine like terms to get −2x + 6.
Question 3: What are the solutions to x² − 5x + 6 = 0?
- x = 1 and x = 6
- x = 2 and x = 3 (Correct answer)
- x = −2 and x = −3
- x = −1 and x = 6
Correct answer: x = 2 and x = 3
Factor as (x − 2)(x − 3) = 0, giving x = 2 or x = 3.
Question 4: If 4x − 2y = 10 and x = 3, what is the value of y?
- 1 (Correct answer)
- 2
- 3
- 4
Correct answer: 1
Substitute x = 3 to get 12 − 2y = 10, then solve to find y = 1.
Question 5: What is the slope of the line passing through the points (2, 3) and (6, 11)?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
Slope = (y₂ − y₁)/(x₂ − x₁) = (11 − 3)/(6 − 2) = 8/4 = 2.
Question 6: Which values of x satisfy |2x − 4| = 6?
- x = 1 or x = 5
- x = −1 or x = 5 (Correct answer)
- x = −5 or x = 1
- x = 5 or x = −5
Correct answer: x = −1 or x = 5
Set 2x − 4 = 6 (giving x = 5) and 2x − 4 = −6 (giving x = −1).
Question 7: If f(x) = 3x² − 2x + 1, what is the value of f(2)?
- 7
- 9 (Correct answer)
- 11
- 13
Correct answer: 9
f(2) = 3(4) − 2(2) + 1 = 12 − 4 + 1 = 9.
ACT Math: Algebra 1
If 3x + 7 = 22, what is the value of x?