PSAT/NMSQT PSAT/NMSQT Advanced Math 2

Question 1

Which of the following is a factor of x² + 7x + 12?

Accepted Answer

(x + 3)

Answer

x² + 7x + 12 factors as (x + 3)(x + 4), so (x + 3) is a factor.

Question 2

If 2^x = 32, what is the value of x?

Accepted Answer

5

Answer

Since 32 = 2⁵, we have 2^x = 2⁵, so x = 5.

Question 3

What is the sum of the solutions to 3x² − 12x + 9 = 0?

Accepted Answer

4

Answer

By Vieta's formulas, the sum of the roots equals −(−12)/3 = 4; you can also factor: 3(x − 1)(x − 3) = 0, so roots are 1 and 3, sum = 4.

Question 4

Which value of x satisfies the equation √(x + 5) = 4?

Accepted Answer

11

Answer

Square both sides: x + 5 = 16, so x = 11.

Question 5

If f(x) = x² and g(x) = x − 3, what is f(g(x))?

Accepted Answer

x² − 6x + 9

Answer

f(g(x)) = f(x − 3) = (x − 3)² = x² − 6x + 9.

PSAT/NMSQT Practice Test