Question 1

Which of the following is the simplified form of $$\sqrt{72}$$?

Accepted Answer

$$6\sqrt{2}$$

Question 2

What is the solution set for the equation $$x^2 - 9 = 0$?

Accepted Answer

$$x = 3,\ x = -3$$

Question 3

Given the quadratic equation $$x^2 + 6x + 9 = 0$, what are the roots?

Accepted Answer

$$x = -3$$

Question 4

Which of the following is the correct application of the quadratic formula to solve $$2x^2 - 4x - 6 = 0$?

Accepted Answer

$$x = \frac{4 \pm \sqrt{(-4)^2$ - 4 \cdot 2 \cdot (-6)}}{2 \cdot 2}$$

Question 5

If the discriminant $$b^2 - 4ac$ of a quadratic equation is negative, what type of solutions does the equation have?

Accepted Answer

Two imaginary solutions

Question 6

Simplify $$\sqrt{50} + 2\sqrt{8}.$$

Accepted Answer

$$7\sqrt{2}$$

Question 7

Which of the following is the standard form of a complex number?

Accepted Answer

$$a + bi$$

Question 8

What is the product $$\sqrt{3} \cdot \sqrt{12}$$?

Accepted Answer

$$6$$

Question 9

Solve for $$x$$: $$x^2 = -16$

Accepted Answer

$$x = 4i,\ x = -4i$$

Question 10

Which of the following best describes the graph of $$y = x^2$ + 4x + 4$$?

Accepted Answer

A parabola opening upwards with vertex at $$(-2, 0)$$

Question 11

Which method is most appropriate for solving $$x^2 - 8 = 0$?

Accepted Answer

Taking square roots

Question 12

Given $$x^2 + 2x - 15 = 0$, what are the solutions?

Accepted Answer

$$x = 3,\ x = -5$$

Question 13

Which of the following is a correct step in completing the square for $$x^2 + 6x + 5 = 0$?

Accepted Answer

Add $$9 to $$both sides to complete the square

Question 14

If $$i is $$the imaginary unit, what is $$i^4$$?

Accepted Answer

$$1$$

Question 15

A rectangular garden has an area of $$48$$ square meters and a length $$4$$ meters longer than its width. What is the width?

Accepted Answer

$$6$$ meters

Question 16

Which of the following is the correct factorization of $$x^2 - 2x - 15$?

Accepted Answer

$$(x - 5)(x + 3)$$

Question 17

What is the sum $$(3 + 2i) + (4 - 5i)$$?

Accepted Answer

$$7 - 3i$$

Question 18

Which of the following is true about the solutions to $$x^2 + 4 = 0$?

Accepted Answer

The solutions are imaginary

Question 19

If the discriminant of a quadratic equation is zero, what can you conclude about its solutions?

Accepted Answer

There is one real solution

Question 20

Which of the following is the correct solution to $$x^2 + 2x + 2 = 0$ using the quadratic formula?

Accepted Answer

$$x = -1 \pm i$$

Unit 1b Study Guide

Study Guide - Practice Questions