Question 1

Which of the following is the correct simplification of the expression $$\frac{x^2$ - 9}{x^2$ - 6x + 9}$$?

Accepted Answer

$$\frac{(x+3)(x-3)}{(x-3)^2$}$$

Question 2

A chemist needs to dilute a solution by mixing 100 mL of a 60% acid solution with water to obtain a 40% acid solution. How much water should be added?

Accepted Answer

$$50 mL$$

Question 3

Simplify the following radical expression: $$\sqrt{27} \cdot \sqrt{3}$$

Accepted Answer

$$9$$

Question 4

Which of the following is the correct result of dividing $$\frac{2x^2$y}{4xy^2$}$$?

Accepted Answer

$$\frac{x}{2y}$$

Question 5

A car travels 120 miles at a speed of 60 mph. How long does the trip take?

Accepted Answer

$$2$$ hours

Question 6

Given the linear equation $$3x - 2y = 6$$, what is the slope of the line?

Accepted Answer

Question 7

What is the result of $$\frac{\sqrt{3} \cdot \sqrt{15}}{\sqrt{5}}$$?

Accepted Answer

$$\sqrt{9}$$

Question 8

If $$z = 2 + 3i$$ and $$w = 1 - i$$, what is $$z + w$$?

Accepted Answer

$$3 + 2i$$

Question 9

Which of the following is the complex conjugate of $$4 - 2i$$?

Accepted Answer

$$4 + 2i$$

Question 10

A loan of $$\1$$,000$$ is taken at an annual interest rate of 8$$\%$. What is the interest earned after one year?

Accepted Answer

$$\80$

Question 11

Simplify the expression $$\frac{(2x^2$y^3)^2$}{4x^3$y}.$$

Accepted Answer

$$x y^5$

Question 12

Which of the following is the correct solution to the equation $$2(x-3) = 4x + 6$$?

Accepted Answer

$$x = -6$$

Question 13

What is the result of multiplying $$\sqrt{5} \cdot \sqrt{20}$$?

Accepted Answer

$$10$$

Question 14

If $$a = 2 + i$$ and $$b = 3 - 2i$$, what is $$a \cdot b$$?

Accepted Answer

$$8 - i$$

Question 15

Which of the following is the correct simplification of $$\frac{2x^2$ - 8}{4x}$$?

Accepted Answer

$$\frac{x-2}{2}$$

Question 16

A train travels at 80 mph for 2.5 hours. What is the total distance covered?

Accepted Answer

$$200$$ miles

Question 17

What is the result of dividing $$\frac{6 + 2i}{2 - i}$$? (Express in the form $$a + bi)$$

Accepted Answer

$$2 + 2i$$

Question 18

Which of the following is the correct simplification of $$\frac{\sqrt{18}}{\sqrt{2}}$$?

Accepted Answer

$$\sqrt{9}$$

Question 19

If $$x = 2$$ and $$y = -1$$, what is the value of $$x^2 + 2xy$$ + $$y^2$$?

Accepted Answer

$$1$$

Precalculus Study Notes: Rational Expressions, Radicals, Linear Equations, and Complex Numbers

Study Guide - Practice Questions

Study Guide - Flashcards