PSAT/NMSQT Algebra & Functions 3

Question 1

If 2(x - 4) = 3x + 1, what is the value of x?

Accepted Answer

-9

Answer

Expanding gives 2x - 8 = 3x + 1, so -9 = x.

Question 2

What is the value of the expression (x^3 · x^4) when written as a single power of x?

Accepted Answer

x^7

Answer

When multiplying powers with the same base, add the exponents: 3 + 4 = 7.

Question 3

If g(x) = 5 - x and g(a) = 2, what is the value of a?

Accepted Answer

3

Answer

Set 5 - a = 2, so a = 3.

Question 4

Which of the following is a factor of x^2 - 9?

Accepted Answer

x - 3

Answer

x^2 - 9 is a difference of squares factoring to (x - 3)(x + 3).

Question 5

The cost C of renting a bike is C = 5 + 2h, where h is hours. What does the 2 represent?

Accepted Answer

Cost per hour

Answer

The coefficient 2 multiplies hours, so it is the cost added per hour.

PSAT/NMSQT Practice Test