Question 1

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

Accepted Answer

$$8$$

Question 2

Solve the equation $$v^2 = 16$ by taking square roots.

Accepted Answer

$$v = 4 or$$ $$v = -4$$

Question 3

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

Accepted Answer

$$25$$

Question 4

Given the quadratic equation $$2x^2 + 5x - 3 = 0$, what is the discriminant and what does it indicate about the solutions?

Accepted Answer

$$\Delta = 49$$; two real solutions

Question 5

Solve the equation $$x^2 + 6x - 91 = 0$ by completing the square.

Accepted Answer

$$x = 7 or$$ $$x = -13$$

Question 6

Which of the following equations has no real solution?

Accepted Answer

$$r^2 + 10 = -4$

Question 7

Find the value of $$c$$ that completes the square for $$z^2 - 24z + c$.

Accepted Answer

$$144$$

Question 8

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

Accepted Answer

$$x = 15 or$$ $$x = -4$$

Question 9

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

Accepted Answer

$$\Delta = -252$$; two imaginary solutions

Question 10

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

Accepted Answer

$$p = 3.5 or$$ $$p = -5$$

Question 11

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

Accepted Answer

$$5/4$$

Question 12

If $$a^2 + 2a + c$ is a perfect square trinomial, what is the value of c$?

Accepted Answer

$$1$$

Question 13

Solve $$n^2 + 14n - 72 = 0$ by completing the square.

Accepted Answer

$$n = 4 or$$ $$n = -18$$

Question 14

Which equation has no real solution when solved with the quadratic formula?

Accepted Answer

$$4a^2 + 2a + 5 = 0$

Question 15

What are the solutions to $$x^2 - 20x + 36 = 0$ by completing the square?

Accepted Answer

$$x = 18 or$$ $$x = 2$$

Question 16

Simplify $$\sqrt{16/4}.$$

Accepted Answer

$$2$$

Question 17

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

Accepted Answer

$$p = 4 or$$ $$p = -10$$

Question 18

Which of the following is the correct simplification of $$6 	imes \sqrt{8}$$?

Accepted Answer

$$12 \sqrt{2}$$

Question 19

If the discriminant $$\Delta of a $$quadratic equation is negative, what does this indicate about the solutions?

Accepted Answer

There are two imaginary solutions.

Question 20

Which of the following is the correct simplification of $$2 	imes \sqrt{3}$$?

Accepted Answer

$$2 \sqrt{3}$$

Algebra 1 Unit 9 Review – Quadratics and Simplification Guidance

Study Guide - Practice Questions