Question 1

Which of the following is the correct simplification of $$\sqrt{64}$$?

Accepted Answer

$$8$$

Question 2

A patient’s lab result shows $$v^2 = 16$. What are the possible values for v$?

Accepted Answer

$$4$$ and $$-4$$

Question 3

Given the quadratic equation $$x^2 + 6x - 91 = 0$, which method would be most efficient to solve for x$ and what are the solutions?

Accepted Answer

Completing the square; $$x = 7, -13$$

Question 4

What is the value of $$c$$ that completes the square for $$x^2 + 10x + c$?

Accepted Answer

$$25$$

Question 5

For the equation $$9n^2 - 6n + 8 = 0$, what is the discriminant and what does it indicate about the solutions?

Accepted Answer

$$-252$$; two imaginary solutions

Question 6

Solve $$x^2 = 0$ by taking square roots. What is the solution set?

Accepted Answer

$$\{0\}$$

Question 7

Which value of $$c$$ completes the square for $$z^2 - 24z + c$?

Accepted Answer

$$144$$

Question 8

A quadratic equation $$2x^2 + 5x - 3 = 0$ has a discriminant of 49$. What does this tell you about the solutions?

Accepted Answer

There are two real solutions.

Question 9

Solve $$4a^2 + 2a + 5 = 0$ using the quadratic formula. What is the nature of the solutions?

Accepted Answer

No solution (complex roots)

Question 10

If $$n^2 + 14n - 72 = 0$, what are the solutions for n$ after completing the square?

Accepted Answer

$$n = 4, -18$$

Question 11

Which of the following is the correct simplification of $$\sqrt{25/16}$$?

Accepted Answer

$$5/4$$

Question 12

Given $$x^2 - 20x + 36 = 0$, what are the solutions for x$?

Accepted Answer

$$x = 18, 2$$

Question 13

What is the value of $$c$$ that completes the square for $$a^2 + 2a + c$?

Accepted Answer

$$1$$

Question 14

Solve $$x^2 - 11x - 60 = 0$ using the quadratic formula. What are the solutions?

Accepted Answer

$$x = 15, -4$$

Question 15

A quadratic equation $$r^2 + 10 = -4$ is given. What is the solution set?

Accepted Answer

No solution

Question 16

Which of the following is the correct simplification of $$\sqrt{16/4}$$?

Accepted Answer

$$2$$

Question 17

Solve $$p^2 + 6p - 40 = 0$ using the quadratic formula. What are the solutions?

Accepted Answer

$$p = 4, -10$$

Question 18

What is the discriminant of $$2x^2 + 5x - 3 = 0$ and what does it indicate?

Accepted Answer

$$49$$; two real solutions

Question 19

Solve $$2p^2 + 3p - 35 = 0$ using the quadratic formula. What are the solutions?

Accepted Answer

$$p = \frac{7}{2}, -5$$

Question 20

Which of the following is the correct simplification of $$\sqrt{4/9}$$?

Accepted Answer

$$2/3$$

Algebra 1 Unit 9 Review – Quadratics and Simplification Guidance

Study Guide - Practice Questions