Question 1

Which of the following is the correct slope-intercept form of a linear equation?

Accepted Answer

$$y = mx + b$$

Question 2

A chemist is mixing two solutions. The total volume is 12 liters, and the first solution is 3 times the volume of the second. Which equation models this situation if $$x is $$the volume of the second solution?

Accepted Answer

$$3x + x = 12$$

Question 3

Solve for $$x$$: $$\dfrac{2}{3}x - \dfrac{1}{4} = \dfrac{5}{6}$$

Accepted Answer

$$x = 4$$

Question 4

Which of the following equations is an identity?

Accepted Answer

$$2(x + 1) = 2x + 2$$

Question 5

Simplify $$\sqrt{-200}.$$

Accepted Answer

$$10i\sqrt{2}$$

Question 6

What is the sum of $$(3 + 4i)$$ and $$(1 - 5i)$$?

Accepted Answer

$$4 - i$$

Question 7

Find the absolute value of $$3 + 4i.$$

Accepted Answer

$$5$$

Question 8

Solve the quadratic equation by factoring: $$x^2 - 4x - 15 = 0$.

Accepted Answer

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

Question 9

A ball is thrown upward from a height of 20 meters with an initial velocity of 10 m/s. Its height after $$t$$ seconds is given by $$h(t) = -5t^2$ + 10t + 20. $$After how many seconds does the ball hit the ground?

Accepted Answer

$$t = 4.53$$

Question 10

Solve for $$x$$ using the quadratic formula: $$2x^2 + x - 3 = 0$.

Accepted Answer

Question 11

Solve for $$x$$: $$\sqrt{x + 5} = x - 1$$

Accepted Answer

$$x = 2, x = -2 ($$but only $$x = 2 is $$valid)

Question 12

Solve for $$x$$: $$|2x - 5| = 7$$

Accepted Answer

$$x = 6, x = -1$$

Question 13

Which of the following is the solution to the inequality $$3x - 7 \u003c 8$$?

Accepted Answer

$$x \u003c 5$$

Question 14

Solve the compound inequality: $$2 \u003c 3x + 1 \u003c 8$$

Accepted Answer

$$\dfrac{1}{3} \u003c x \u003c \dfrac{7}{3}$$

Question 15

Solve for $$x$$: $$x^{2/3} = 4$

Accepted Answer

$$x = 8, x = -8$$

Question 16

A medical researcher is studying the growth of bacteria, which doubles every hour. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 500 \cdot 2^t$$

Question 17

Which of the following is the correct form for a complex number?

Accepted Answer

$$a + bi$$

Question 18

Solve for $$y$$: $$\dfrac{y}{y-1} \u003e 2$$

Accepted Answer

$$y  2$$

Question 19

Which of the following best describes a contradiction?

Accepted Answer

An equation that is never true for any value of the variable.

Question 20

A quadratic equation $$ax^2 + bx + c = 0$ has no real solutions if:

Accepted Answer

$$b^2 - 4ac$$ \u003c 0$$

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

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