PSAT/NMSQT PSAT/NMSQT Advanced Math

Question 1

Which of the following is equivalent to (x² − 9)(x + 3)?

Accepted Answer

x³ + 3x² − 9x − 27

Answer

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)?

Accepted Answer

19

Answer

Substituting −2: f(−2) = 2(4) − 5(−2) + 1 = 8 + 10 + 1 = 19.

Question 3

What are the solutions to x² − 5x + 6 = 0?

Accepted Answer

x = 2 and x = 3

Answer

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?

Accepted Answer

x = −2, 0, 2

Answer

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?

Accepted Answer

27x⁶y³

Answer

Apply the power rule: 3³ = 27, (x²)³ = x⁶, y³ = y³, giving 27x⁶y³.

PSAT/NMSQT Practice Test