- PSAT Math: Exponents and Radicals
- PSAT Math: Polynomials
- PSAT Math: Rational Expressions and Equations
Test your PSAT readiness by taking this PSAT math quiz!
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
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).
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.
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 2x for x in the volume you already found:
(2x)3 – 2x = 23x 3 – 2x = 8x 3 – 2x
Difference: (8x 3 – 2x) – (x 3 – x) = 8x 3 – x 3 – 2x + x = 7x 3 – x, (B).