PSAT/NMSQT PSAT/NMSQT Advanced Math 2 — Questions and Answers
Question 1: Which of the following is a factor of x² + 7x + 12?
- (x + 3) (Correct answer)
- (x − 3)
- (x + 6)
- (x − 4)
Correct answer: (x + 3)
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?
- 5 (Correct answer)
- 4
- 6
- 16
Correct answer: 5
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?
- 4 (Correct answer)
- 3
- −4
- 12
Correct answer: 4
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?
- 11 (Correct answer)
- 9
- 21
- 3
Correct answer: 11
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))?
- x² − 6x + 9 (Correct answer)
- x² − 3
- x² + 9
- x² − 9
Correct answer: x² − 6x + 9
f(g(x)) = f(x − 3) = (x − 3)² = x² − 6x + 9.
Question 6: For the equation y = −(x − 2)² + 5, what is the maximum value of y?
- 5 (Correct answer)
- 2
- −2
- −5
Correct answer: 5
The vertex form y = a(x − h)² + k shows the vertex at (h, k) = (2, 5); since a = −1 < 0, the parabola opens down and y = 5 is the maximum.
PSAT/NMSQT PSAT/NMSQT Advanced Math 2
Which of the following is a factor of x² + 7x + 12?