Question 1

Which of the following points is located in Quadrant II of the Cartesian coordinate system?

Accepted Answer

$$(-5, 3)$$

Question 2

Given the function $$y = x^3$ - 2$$, what is the $$y-$$intercept of its graph?

Accepted Answer

$$(0, -2)$$

Question 3

Solve the linear equation: $$2 - (7x + 5) = 13 - 3x$$

Accepted Answer

$$x = -4$$

Question 4

Solve the rational equation: $$\dfrac{x+1}{4} = 1 + \dfrac{2-x}{3}$$

Accepted Answer

$$x = 2$$

Question 5

Which of the following best describes an identity equation?

Accepted Answer

An equation that is always true for all real numbers.

Question 6

Solve and classify the equation: $$x^2 = 9$

Accepted Answer

Conditional equation

Question 7

A number is such that $$0.8n + n = 252. $$What is the value of $$n$$?

Accepted Answer

$$n = 140$$

Question 8

Nick earned a $$10,000 bonus and wants to invest in two stocks: one at 6$$\%$$ and one at 11$$\%$$ annual interest. If he wants to earn 800$ in interest in the first year, how much should he invest at 6$$\%$?

Accepted Answer

$$4,000$$

Question 9

Given the formula for the area of a trapezoid $$A = \dfrac{1}{2}h(a+b)$$, solve for $$b in $$terms of $$A$$, $$h$$, and $$a.$$

Accepted Answer

$$b = \dfrac{2A}{h} - a$$

Question 10

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

Accepted Answer

$$i^2 = -1$

Question 11

Find the product: $$(3 - 4i)(3 + 4i)$$

Accepted Answer

$$25$$

Question 12

What is the complex conjugate of $$a + bi$$?

Accepted Answer

$$a - bi$$

Question 13

Divide the complex numbers: $$\dfrac{4 + 7i}{5 + i}$$

Accepted Answer

$$\dfrac{27}{26} + \dfrac{31}{26}i$$

Question 14

Which of the following equations is inconsistent?

Accepted Answer

$$0 = 10$$

Question 15

If the area of a rectangle is $$40$$ and its length is $$2w - 6$$, what is the width $$w$$?

Accepted Answer

$$w = 10$$

Question 16

Which of the following is a real-world application of a rational equation?

Accepted Answer

Calculating how much to invest in two accounts with different interest rates to reach a target interest.

Question 17

Solve for $$x$$: $$\dfrac{2}{x-2} = \dfrac{x}{x-2} - 2$$

Accepted Answer

$$x = 2 ($$extraneous solution)

Question 18

Which of the following is the correct result of $$(8 - 4i)(-3 + 9i)$$?

Accepted Answer

$$12 + 84i$$

Question 19

If $$A = \dfrac{1}{4}fm$$, solve for $$f in $$terms of $$A$$ and $$m.$$

Accepted Answer

$$f = \dfrac{4A}{m}$$

Question 20

Which of the following statements about the $$x-$$intercept of a graph is correct?

Accepted Answer

It is the point where $$y = 0.$$

College Algebra Study Notes: Coordinate Systems, Equations, and Complex Numbers

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