Question 1

Simplify the following expression and write your answer in standard form: $$rac{1 + 7i}{8 + 2i}$$

Accepted Answer

$$\frac{1 + 7i}{8 + 2i} = \frac{1 + 7i}{8 + 2i} \cdot \frac{8 - 2i}{8 - 2i} = \frac{22 + 54i}{68} = \frac{11}{34} + \frac{27}{34}i$$

Question 2

Solve the rational inequality and write the solution set in interval notation: $$\frac{x - 4}{x + 5} \leq 0$$

Accepted Answer

$$(-\infty, -5) \cup (-5, 4]$$

Question 3

Given the points $$A(2, 3)$$ and $$B(-4, 7)$$, what is the distance between them?

Accepted Answer

$$\sqrt{52}$$

Question 4

For the equation $$y = 2x + 3$$, complete the table of ordered pairs that are solutions of the equation for $$x = -2, 0, 2.$$

Accepted Answer

y-values: $$-1, 3, 7$$

Question 5

Which graph best represents the function $$f(x) = \sqrt{x + 6}$$?

Accepted Answer

Graph C

Question 6

Let $$f(x) = x^2$ + 11$$ and $$g(x) = x + 4. $$Find $$(f - g)(1).$$

Accepted Answer

$$(f - g)(1) = 7$$

Question 7

Determine whether the relation $$\{(0,3),(-2,6),(5,1),(0,8)\} is a $$function and if it is one-to-one.

Accepted Answer

It is not a function.

Question 8

Find the slope of the line passing through the points $$(-1, 3)$$ and $$(3, -2).$$

Accepted Answer

$$-\frac{5}{4}$$

Question 9

For the quadratic equation $$h(x) = x^2$ - 10x + 25$$, what are the coordinates of the vertex?

Accepted Answer

Question 10

Evaluate the exponential function $$g(x) = 3$$^{-x + 2}$$ at x = 1$.

Accepted Answer

$$g(1) = 3$$^{1}$$

Question 11

Solve the exponential equation $$(13)^{x + 5} = 2202$. What is the value of x$?

Accepted Answer

$$x = -1$$

Question 12

Convert the logarithmic equation $$y = \log_6$(216) to $$its exponential form.

Accepted Answer

$$6^y = 216$$

Question 13

Solve the logarithmic equation $$\log(5x) = 4. $$What is the value of $$x$$?

Accepted Answer

$$x = 200$$

Question 14

For the quadratic function $$f(x) = -3(x - 5)^2$ - 1$$, what is the vertex?

Accepted Answer

$$(5, -1)$$

Question 15

Which of the following is the correct center-radius form for a circle with center $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 25$$

Question 16

If $$f(x) = 2x^2$ + 4$$, what is the y-intercept?

Accepted Answer

$$4$$

Question 17

For the function $$g(x) = 4x^3$ - x$$, is it odd, even, or neither?

Accepted Answer

Odd

Question 18

Use synthetic division to determine if $$x = 2 is a $$zero of $$x^4 - 4$. What is f(2$$)$$?

Accepted Answer

$$f(2) = 12$$

Question 19

List all possible rational zeros for $$g(x) = x^3$ - 3x^2$ - 13x + 15$$ using the Rational Root Theorem.

Accepted Answer

$$\pm1, \pm3, \pm5, \pm15$$

Algebra Study Guide: Complex Numbers, Rational Inequalities, and Graphing

Study Guide - Practice Questions