ACT Math: Algebra 2

Question 1

What is the y-intercept of the line 3x − 4y = 12?

Accepted Answer

−3

Answer

Set x = 0 and solve: −4y = 12, so y = −3.

Question 2

Simplify: (3x²y)(4xy³)

Accepted Answer

12x³y⁴

Answer

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?

Accepted Answer

7

Answer

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?

Accepted Answer

x > 7

Answer

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?

Accepted Answer

Exactly one real solution

Answer

The discriminant b² − 4ac = 36 − 36 = 0, which means exactly one real (repeated) solution: x = 3.

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