# 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!

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

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)

= –*x*² + 5*x* + 4*x* – 20

= –*x*² + 9*x* – 20

Don’t let (B) fool you—the question asks for the coefficient of *x*, not *x*^{2}, so the correct answer is (D).

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.

Answer 4

**B: **Find the volume of each box and then subtract.

Box 1: *V = x*(*x +* 1)(*x* – 1) *= x*(*x*^{ 2} *– 1*) *= x*^{ 3} *– x*

Box 2: Substitute 2*x* for *x* in the volume you already found:

(2*x*)^{3} – 2*x* = 2^{3}*x*^{ 3} – 2*x* = 8*x*^{ 3} – 2*x*

Difference: (8*x*^{ 3} – 2*x*) – (*x*^{ 3} – *x*) = 8*x*^{ 3} – *x*^{ 3} – 2*x* + *x* = 7*x*^{ 3} – *x*, (B).

Answer 5

**B**

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