DSAT Advanced Math 2 — Questions and Answers
Question 1: Which of the following is equivalent to (x² - 9) / (x - 3) for x ≠ 3?
- x - 3
- x + 3 (Correct answer)
- x² + 3
- x - 9
Correct answer: x + 3
Factor the numerator as (x-3)(x+3), then cancel (x-3) to get x+3.
Question 2: If f(x) = 3x² - 2x + 1, what is f(-2)?
- 9
- 13
- 17 (Correct answer)
- 21
Correct answer: 17
f(-2) = 3(4) - 2(-2) + 1 = 12 + 4 + 1 = 17.
Question 3: The function g(x) = x² - 6x + 8 has zeros at x = 2 and x = 4. What is the vertex of g(x)?
- (3, -1) (Correct answer)
- (3, 1)
- (4, 0)
- (2, 0)
Correct answer: (3, -1)
The vertex x-coordinate is the midpoint of the zeros: (2+4)/2 = 3, and g(3) = 9 - 18 + 8 = -1.
Question 4: Which expression is equivalent to (2x³y²)(3xy⁴)?
- 5x⁴y⁶
- 6x⁴y⁶ (Correct answer)
- 6x³y⁸
- 5x³y⁶
Correct answer: 6x⁴y⁶
Multiply coefficients (2×3=6) and add exponents: x^(3+1)=x⁴ and y^(2+4)=y⁶, giving 6x⁴y⁶.
Question 5: If 2^(x+1) = 32, what is the value of x?
- 3
- 4 (Correct answer)
- 5
- 6
Correct answer: 4
32 = 2⁵, so 2^(x+1) = 2⁵ means x+1 = 5, giving x = 4.
Question 6: What are the solutions to 2x² + x - 6 = 0?
- x = 3/2 and x = -2
- x = -3/2 and x = 2 (Correct answer)
- x = 3 and x = -2
- x = -3 and x = 2
Correct answer: x = -3/2 and x = 2
Factor as (2x - 3)(x + 2) = 0, giving x = 3/2 or x = -2; wait — actually (2x+3)(x-2)=0 gives x=-3/2 or x=2.
Question 7: If h(x) = √(4x - 8), what is the domain of h?
- x > 2
- x ≥ 2 (Correct answer)
- x ≥ 4
- x > 0
Correct answer: x ≥ 2
The radicand must be non-negative: 4x - 8 ≥ 0 → x ≥ 2.
DSAT Advanced Math 2
Which of the following is equivalent to (x² - 9) / (x - 3) for x ≠ 3?