Question 1

Which of the following is the correct definition of the imaginary unit $$i$$?

Accepted Answer

$$i = \sqrt{-1}$$

Question 2

Simplify the expression $$(-5 + i) - (-11 - 6i)$$ and write your answer in standard form $$a + bi.$$

Accepted Answer

$$6 + 7i$$

Question 3

Multiply $$(4i)(3 - 5i)$$ and write your answer in standard form $$a + bi.$$

Accepted Answer

$$20 + 12i$$

Question 4

Divide $$\frac{4i}{3 - 9i}$$ and write your answer in standard form $$a + bi.$$

Accepted Answer

$$-\frac{4}{30} + \frac{12i}{30}$$

Question 5

What is the principal square root of $$-49$$?

Accepted Answer

$$7i$$

Question 6

Solve the quadratic equation $$x^2 = 8x - 15$ by factoring.

Accepted Answer

$$x = 3 or$$ $$x = 5$$

Question 7

Which of the following best describes the solutions to $$ax^2 + bx + c = 0$ if b^2$ - 4ac \u003c 0$$?

Accepted Answer

No real solution; two imaginary solutions

Question 8

Solve $$4(x - 5)^2$ = 28$$ using the square root property.

Accepted Answer

$$x = 5 \pm \sqrt{7}$$

Question 9

Given the quadratic equation $$x^2 - 6x + 10 = 0$, what is the discriminant and what does it tell you about the solutions?

Accepted Answer

Discriminant is $$-4$$, so there are two complex solutions

Question 10

A rectangular park is 6 miles long and 2 miles wide. How long is the diagonal route across the park? Express your answer in simplest radical form.

Accepted Answer

$$2\sqrt{3}$$ miles

Question 11

Solve the equation $$\sqrt{x + 1} = x - 1$$ and check for extraneous solutions.

Accepted Answer

$$x = 2$$ only

Question 12

Solve the absolute value equation $$|2x - 3| = 11.$$

Accepted Answer

$$x = 7 or$$ $$x = -4$$

Question 13

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 14

Solve the equation $$x^{2/3} = 27$.

Accepted Answer

$$x = 27$$ only

Question 15

If $$|3x + 5| \u003c 10$$, what is the solution set for $$x$$?

Accepted Answer

$$-5 \u003c 3x + 5 \u003c 10$$ which simplifies to $$-5 \u003c x \u003c \frac{5}{3}$$

Question 16

Which of the following best describes the solutions to $$ax^2 + bx + c = 0$ if b^2$ - 4ac = 0$$?

Accepted Answer

One repeated real solution

Question 17

Solve the equation $$x^2 + 6x + 13 = 0$ using the quadratic formula.

Accepted Answer

$$x = -3 \pm 2i$$

Question 18

A student needs an average of at least 90% to earn an A. Their first four exam scores are 86%, 88%, 92%, and 84%. If the final exam counts as two grades, what is the minimum score they must earn on the final to get an A?

Accepted Answer

95%

Question 19

Which of the following is a correct application of the Pythagorean Theorem for a right triangle with legs of length 5 and 12?

Accepted Answer

$$c = \sqrt{5^2$ + 12^2$}$$

Question 20

Solve the radical equation $$\sqrt{2x + 19} = -8$$ and check for extraneous solutions.

Accepted Answer

No real solution

Precalculus Study Notes: Complex Numbers, Quadratic Equations, and Inequalities

Guida di studio - Domande di pratica

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