Question 1

Subtract and simplify: $$ (7 - 6i) - (6 + 8i) $$

Accepted Answer

$$ 1 - 14i $$

Question 2

Multiply: $$ \sqrt{-16} \cdot \sqrt{-36} $$

Accepted Answer

$$ 24 $$

Question 3

Which of the following is the correct graph for the solution set $$ -3 \leq x \leq 5 $$? (Assume the number line is from $$-10 to$$ $$10.)$$

Accepted Answer

A line segment from $$-3 to$$ $$5$$ with closed circles at both ends.

Question 4

Given the function $$ f(x) = x^2$ - 4 $$, which of the following describes its graph?

Accepted Answer

A parabola opening upwards with vertex at $$(0, -4).$$

Question 5

Which of the following is the solution to $$ 2x + 5 \u003e 9 $$?

Accepted Answer

$$ x \u003e 2 $$

Question 6

If $$ f(x) = 3x - 2 $$, what is $$ f$$^{-1}$$(x) $$, the inverse function?

Accepted Answer

$$ f$$^{-1}$$(x) = \frac{x+2}{3} $$

Question 7

Solve for $$x$$: $$ |2x - 3| = 7 $$

Accepted Answer

$$ x = 5  or$$ $$ x = -2 $$

Question 8

Which of the following is the solution set for $$ x^2$ - 9 \u003c 0 $$?

Accepted Answer

$$ -3 \u003c x \u003c 3 $$

Question 9

A chemist mixes two solutions, one with a concentration of $$30\%$$ and another with $$50\%. If $$she wants $$100 mL of a$$ $$40\%$$ solution, how much of each should she use?

Accepted Answer

$$50 mL of $$each solution

Question 10

Which of the following is the correct simplification of $$ (2 + 3i)(4 - i) $$?

Accepted Answer

$$ 11 + 10i $$

Question 11

If $$ f(x) = |x - 2| $$, which of the following is true about its graph?

Accepted Answer

It is a V-shaped graph with vertex at $$(2, 0).$$

Question 12

Solve for $$x$$: $$ \sqrt{x+5} = 4 $$

Accepted Answer

$$ x = 11 $$

Question 13

Which of the following is the solution to $$ 3(x - 2) \leq 9 $$?

Accepted Answer

$$ x \leq 5 $$

Question 14

If $$ f(x) = x^2$ + 2x + 1 $$, what is the vertex of the parabola?

Accepted Answer

$$( -1, 0 )$$

Question 15

Which of the following is the correct solution set for $$ |x| \geq 3 $$?

Accepted Answer

$$ x \leq -3  or$$ $$ x \geq 3 $$

College Algebra Practice Exam Guidance

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