Question 1

Which of the following is the correct simplification of $$\sqrt{15 - 5\sqrt{8}}$$?

Accepted Answer

$$\sqrt{5} - 2\sqrt{2}$$

Question 2

What is the sum of the complex numbers $$(4 + 6i) + (-2 - 3i)$$?

Accepted Answer

$$2 + 3i$$

Question 3

Multiply the complex numbers $$(4 + 6i)(-2 - 3i). $$What is the result?

Accepted Answer

Question 4

Divide the complex numbers $$\frac{15 - 20i}{6 + 8i}$$ and simplify your answer.

Accepted Answer

$$0.5 - 2i$$

Question 5

Which of the following is the standard form of a quadratic equation?

Accepted Answer

$$ax^2 + bx + c = 0$

Question 6

Solve the quadratic equation $$x^2 - 5x + 6 = 0$ using the zero-factor property.

Accepted Answer

$$x = 2, 3$$

Question 7

Using the quadratic formula, solve $$x^2 + 4x + 1 = 0$.

Accepted Answer

$$x = -2 \pm \sqrt{5}$$

Question 8

A rectangular garden has a length that is 2 yards more than twice the width. If the area is 70 square yards, what is the width?

Accepted Answer

$$5$$ yards

Question 9

A ball is dropped from a tall building. Its height is given by $$h = -16t^2$ + 160t + 400. $$How long will it take for the ball to hit the ground?

Accepted Answer

$$t = 10$$ seconds

Question 10

Solve the rational equation $$\frac{2}{x} + \frac{3}{x+1} = 1$$ for $$x.$$

Accepted Answer

$$x = 1, -2$$

Question 11

Solve the equation $$x = \sqrt{11 - x}$$ and check for extraneous solutions.

Accepted Answer

$$x = 4$$

Question 12

Which of the following intervals is the solution to the quadratic inequality $$x^2 - 2x - 3$$ \u003c 0$$?

Accepted Answer

$$(-3, 3)$$

Question 13

Solve the rational inequality $$\frac{2x}{x-3} \u003e 4.$$

Accepted Answer

$$(-\infty, -3) \cup (6, \infty)$$

Question 14

If $$i is $$the imaginary unit, what is $$i^{23}$$?

Accepted Answer

$$i$$

Question 15

Which of the following is the conjugate of the complex number $$3 - 4i$$?

Accepted Answer

$$3 + 4i$$

Question 16

Which of the following best describes the Zero-Factor Property?

Accepted Answer

If $$ab = 0$$, then $$a = 0 or$$ $$b = 0$$

Question 17

Which of the following is a solution to the equation $$x^2 = 25$?

Accepted Answer

$$x = 5$$ and $$x = -5$$

Question 18

If $$x^2 + 6x + 9 = 0$, what is the value of x$?

Accepted Answer

$$x = -3$$

Question 19

Which of the following is the correct solution set for the inequality $$x^2 - 4$$ \leq 0$$?

Accepted Answer

$$[-2, 2]$$

College Algebra Study Guide: Equations, Complex Numbers, and Inequalities

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