PSAT/NMSQT PSAT/NMSQT Advanced Math 1 — Questions and Answers
Question 1: Which of the following is equivalent to (x² − 9)(x + 3)?
- x³ + 3x² − 9x − 27 (Correct answer)
- x³ − 3x² − 9x + 27
- x³ + 3x² + 9x − 27
- x³ − 27
Correct answer: x³ + 3x² − 9x − 27
Factor x² − 9 as (x − 3)(x + 3), then multiply (x − 3)(x + 3)(x + 3) = (x − 3)(x + 3)² to get x³ + 3x² − 9x − 27.
Question 2: If f(x) = 2x² − 5x + 1, what is f(−2)?
- 19 (Correct answer)
- −1
- 11
- −11
Correct answer: 19
Substituting −2: f(−2) = 2(4) − 5(−2) + 1 = 8 + 10 + 1 = 19.
Question 3: What are the solutions to x² − 5x + 6 = 0?
- x = 2 and x = 3 (Correct answer)
- x = −2 and x = −3
- x = 1 and x = 6
- x = −1 and x = −6
Correct answer: x = 2 and x = 3
Factor the quadratic as (x − 2)(x − 3) = 0, giving solutions x = 2 and x = 3.
Question 4: If g(x) = x³ − 4x, for which value of x does g(x) = 0?
- x = −2, 0, 2 (Correct answer)
- x = −4, 0, 4
- x = 0, 2
- x = −2, 2
Correct answer: x = −2, 0, 2
Factor as x(x² − 4) = x(x − 2)(x + 2) = 0, giving x = −2, 0, or 2.
Question 5: Which expression is equivalent to (3x²y)³?
- 27x⁶y³ (Correct answer)
- 9x⁶y³
- 27x⁵y³
- 9x⁵y
Correct answer: 27x⁶y³
Apply the power rule: 3³ = 27, (x²)³ = x⁶, y³ = y³, giving 27x⁶y³.
Question 6: If the function h(x) = ax² + bx + c has its vertex at (2, −3) and passes through (0, 5), what is the value of c?
- 5 (Correct answer)
- −3
- 2
- −5
Correct answer: 5
The y-intercept occurs when x = 0, so h(0) = c = 5.
PSAT/NMSQT PSAT/NMSQT Advanced Math 1
Which of the following is equivalent to (x² − 9)(x + 3)?