PSAT Math Quiz: Exponents, Roots and Polynomials

Content Review:

PSAT Math: Exponents and Radicals
PSAT Math: Polynomials
PSAT Math: Rational Expressions and Equations

Test your PSAT readiness by taking this PSAT math quiz!

Question 1
Which of the following is equivalent to the expression:
(9⁴ x 3²) / 9⁵
A. 0
B. 1
C. 3
D. 9

Answer 1

B: Raising 9 to the 4th and 5th powers is very time-consuming without a calculator. Instead, start by using exponent rules to simplify expressions written in the same base. Then raise any remaining numbers to the resulting powers. The power of 9 is larger in the denominator, so subtract the exponents there. Then, simplify further if possible:
(9⁴ x 3²) / 9⁵ = (3²) / 9⁵⁻⁴ = 9/9 = 1

Question 2
What is the resulting coefficient of x after multiplying –x + 4 by x – 5 ?
A. -9
B. -1
C. 1
D. 9

Answer 2

D: Distribute each term in the first factor to each term in the second factor, paying careful attention to the signs.
(–x + 4)(x – 5)
= –x(x – 5) + 4(x – 5)
= –x² + 5x + 4x – 20
= –x² + 9x – 20
Don’t let (B) fool you—the question asks for the coefficient of x, not x², so the correct answer is (D).

Question 3
The power generated by a windmill is related to the velocity of the wind by the equation shown, where P is the power in watts and vis the wind velocity in miles per hour. What is the wind velocity when the windmill is generating 160 watts of power?

A. 20 mph
B. 32 mph
C. 64 mph
D. 89 mph

Answer 3

A: Substitute 160 for P and simplify using your calculator. Don’t try to enter the entire expression into the calculator all at one time—you’re likely to miss a parenthesis somewhere. Instead, divide 160 by 0.02 to get 8,000. Then, take the cube root of 8,000 using the cube root function or by raising it to the one-third power. The result is 20, so the wind velocity is 20 miles per hour. Choice (A) is correct.

Question 4

The length of Box 2 (y) shown above is twice the length of Box 1 (x). Which expression shows the difference in the volumes of the two boxes?

A. 2x ³ – 2x
B. 7x³ – x
C. 7x ³ – 2x
D. 8 x ³ – 2x

Answer 4

B: Find the volume of each box and then subtract.
Box 1: V = x(x + 1)(x – 1) = x(x² – 1) = x³ – x
Box 2: Substitute 2x for x in the volume you already found:
(2x)³ – 2x = 2³x³ – 2x = 8x³ – 2x
Difference: (8x³ – 2x) – (x³ – x) = 8x³ – x³ – 2x + x = 7x³ – x, (B).