Question 1

Solve for $$x$$: $$|x^2$ + 4x - 2| - 4 = 0$$

Accepted Answer

$$x = -2 \pm \sqrt{6}$$ and $$x = -2 \pm \sqrt{2}$$

Question 2

Solve for $$x$$: $$4|x - 2| + 5 = -10$$

Accepted Answer

No real or complex solutions

Question 3

Which of the following best describes the solution set for $$3|x + 4| \u003c -5$$?

Accepted Answer

No solution

Question 4

Solve the inequality $$-x^2 - 5x - 6$$ \u003e 0$$.

Accepted Answer

$$-6 \u003c x \u003c -1$$

Question 5

Solve for $$x$$: $$2x^2 - 4x + 10 = 9 - x$

Accepted Answer

$$x = 1 \pm 2i$$

Question 6

Solve for $$x$$: $$(x + 2)(3x + 5) + 7 = 2x - 4$$

Accepted Answer

$$x = -2 \pm i$$

Question 7

Given $$z = 1 - 2i$$ and $$w = 3 + i$$, compute $$zw.$$

Accepted Answer

$$5 - 5i$$

Question 8

Given $$z = 1 - 2i$$ and $$w = 3 + i$$, compute $$2w(z - w) + z.$$

Accepted Answer

$$-11 - 13i$$

Question 9

Which of the following best describes the nature of the solutions to $$2x^2 - 4x + 10 = 9 - x$?

Accepted Answer

Two complex solutions

Question 10

A real-world application: The height $$h (in $$meters) of a ball thrown upward is given by $$h = -5t^2$ + 20t + 2. At $$what time(s) $$t$$ does the ball reach a height of $$12$$ meters?

Accepted Answer

$$t = 0.46 s $$and $$t = 4.54 s$$

Question 11

If $$|x| = 3$$, which of the following is true?

Accepted Answer

$$x = 3 or$$ $$x = -3$$

Question 12

Which of the following is the correct solution set for $$|x - 5| = -2$$?

Accepted Answer

No solution

Question 13

Which of the following is the correct factorization of $$-x^2 - 5x - 6$?

Accepted Answer

$$-(x + 2)(x + 3)$$

Question 14

If $$z = 1 - 2i$$ and $$w = 3 + i$$, what is the conjugate of $$zw$$?

Accepted Answer

$$5 + 5i$$

Question 15

Which of the following is the correct solution to $$(x + 2)(3x + 5) + 7 = 2x - 4$$?

Accepted Answer

$$x = -2 \pm i$$

Precalculus Study Guide: Absolute Value, Inequalities, Quadratics, and Complex Numbers

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