Question 1

What is the result of the following complex number operation: $$ (3 - 4i)(-2 + 4i) $$?

Accepted Answer

$$ 10 + 20i $$

Question 2

Solve the quadratic equation $$ 6x^2$ - x = 5 .$$

Accepted Answer

$$ x = 1, x = -\frac{5}{6} $$

Question 3

Which of the following is the solution set for $$ 9x^2$ - 16 = 0 $$?

Accepted Answer

$$ x = \pm \frac{4}{3} $$

Question 4

A car rental company offers two plans: Unlimited Mileage for $$40, or 24 $$plus $0.20 per mile. For what number of miles do the two plans cost the same?

Accepted Answer

$$ 80 $$ miles

Question 5

Solve for $$x$$: $$2|x - 3| - 6 = 10$$

Accepted Answer

$$ x = 11, x = -5 $$

Question 6

Which of the following best describes the graph of $$y^2 = -2x + 6$?

Accepted Answer

It is not a function because some $$x$$ values map to two $$y$$ values.

Question 7

Given $$f(x) = -2x^2$ + x - 1$$, what is $$f(x + \Delta x) - f(x)$$ simplified?

Accepted Answer

$$ -4x\Delta x - 2(\Delta x)^2$ + \Delta x $$

Question 8

Find the slope of the line passing through the points $$(-3, 5)$$ and $$(1, 9). $$

Accepted Answer

$$ 1 $$

Question 9

Solve the inequality: $$-11 \u003c 2x - 1 \u003c -5$$

Accepted Answer

$$ -5 \u003c x \u003c -2 $$

Question 10

Which of the following is the correct solution to $$x^2$$ + \sqrt{3x + 7} = 1$$?

Accepted Answer

$$ x = -1, x = -2 $$

Question 11

If $$f(x) = 3x - 5$$ and $$g(x) = x^2$, what is f(g(x$$))$$?

Accepted Answer

$$ 3x^2$ - 5 $$

Question 12

What is the $$x-$$intercept of the line $$3x + 2y - 4 = 0$$?

Accepted Answer

$$ (\frac{4}{3}, 0) $$

Question 13

Which of the following is the correct solution to $$8x^4 - 24 = 0$?

Accepted Answer

$$ x = \pm 3$$^{1/4}$$ $$

Question 14

Given the function $$f(x) = -2x^2$ + x - 1$$, what is the difference quotient $$\frac{f(x+\Delta x) - f(x)}{\Delta x}$$?

Accepted Answer

$$ -4x - 2\Delta x + 1 $$

Question 15

Solve for $$x$$: $$x^2 - 5x - 14 = 0$

Accepted Answer

$$ x = -2, x = 7 $$

Question 16

Which of the following is the correct solution to $$12x^2 - 25x = 0$?

Accepted Answer

$$ x = 0, x = \frac{25}{12} $$

Question 17

A gym offers two payment options: No Tag for $$5x$$ dollars, or Tag for $$(5 - 5 	imes 0.3)x + 30. $$For what minimum number of uses $$x$$ does the Tag option become cheaper?

Accepted Answer

$$ x \u003e 20 $$

Question 18

Solve the inequality $$3 - \frac{3}{4}x \u003e 9.$$

Accepted Answer

$$ x \u003c -8 $$

Question 19

Which of the following is the correct solution to $$k^3$$ + $$x^2 = 4x + 4$ for x$?

Accepted Answer

$$ x = -1, x = \frac{2}{3} $$

College Algebra Exam 1 Review – Step-by-Step Study Guidance

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