ACT Math: Algebra 2 — Questions and Answers
Question 1: What is the y-intercept of the line 3x − 4y = 12?
- −4
- −3 (Correct answer)
- 3
- 4
Correct answer: −3
Set x = 0 and solve: −4y = 12, so y = −3.
Question 2: Simplify: (3x²y)(4xy³)
- 7x²y⁴
- 12x³y⁴ (Correct answer)
- 12x²y⁴
- 7x³y³
Correct answer: 12x³y⁴
Multiply coefficients (3 × 4 = 12) and add exponents for matching bases (x²⁺¹ = x³, y¹⁺³ = y⁴).
Question 3: If a² − b² = 21 and a − b = 3, what is the value of a + b?
- 5
- 6
- 7 (Correct answer)
- 9
Correct answer: 7
Factor using difference of squares: (a − b)(a + b) = 21, so 3(a + b) = 21, giving a + b = 7.
Question 4: What is the solution set for the inequality 2x − 5 > 9?
- x > 2
- x > 4
- x > 7 (Correct answer)
- x > 14
Correct answer: x > 7
Add 5 to both sides to get 2x > 14, then divide by 2 to get x > 7.
Question 5: A quadratic equation has a = 1, b = −6, and c = 9. How many real solutions does it have?
- Zero real solutions
- Exactly one real solution (Correct answer)
- Exactly two real solutions
- Infinitely many solutions
Correct answer: Exactly one real solution
The discriminant b² − 4ac = 36 − 36 = 0, which means exactly one real (repeated) solution: x = 3.
Question 6: Which equation represents a line parallel to y = 2x + 5?
- y = −2x + 3
- y = 2x − 1 (Correct answer)
- y = ½x + 5
- y = −½x + 5
Correct answer: y = 2x − 1
Parallel lines have equal slopes; y = 2x − 1 has the same slope of 2 as the given line.
Question 7: If p(x) = x³ − 4x, what is the value of p(−2)?
- −8
- −4
- 0 (Correct answer)
- 8
Correct answer: 0
p(−2) = (−2)³ − 4(−2) = −8 + 8 = 0.
ACT Math: Algebra 2
What is the y-intercept of the line 3x − 4y = 12?