Question 1

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

Accepted Answer

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

Question 2

A rational expression is undefined for which value of $$x in $$the expression $$\frac{2x + 1}{x^2$ - 9}$$?

Accepted Answer

$$ x = 3 $$ and $$ x = -3 $$

Question 3

Simplify the following expression: $$\frac{3x^2$}{6x}$$ for $$x 
eq 0.$$

Accepted Answer

$$ \frac{x}{2} $$

Question 4

Which of the following is the solution set for the equation $$x^2 + 4x + 4 = 0$?

Accepted Answer

$$ x = -2, x = -2 $$

Question 5

Given the function $$f(x) = 2x - 5$$, what is $$f(3)$$?

Accepted Answer

$$ 1 $$

Question 6

Which of the following is the correct simplification of $$\sqrt{50}$$?

Accepted Answer

$$ 5\sqrt{2} $$

Question 7

If $$x = 2 + 3i$$ and $$y = 1 - 2i$$, what is $$x + y$$?

Accepted Answer

$$ 3 + i $$

Question 8

Which of the following is the solution to the equation $$2x - 7 = 3x + 5$$?

Accepted Answer

$$ x = -12 $$

Question 9

A chemist needs to mix a 10% saline solution with a 30% saline solution to obtain 100 mL of a 25% saline solution. How many mL of the 30% solution should be used?

Accepted Answer

$$ 75 $$

Question 10

Which of the following is the correct solution to the system of equations: $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$ x = 3, y = 2 $$

Question 11

Which of the following is the correct way to express $$\frac{1}{\sqrt{3}}$$ with a rationalized denominator?

Accepted Answer

$$ \frac{\sqrt{3}}{3} $$

Question 12

If $$f(x) = x^2$ - 4x + 7$$, what is the value of $$f(-2)$$?

Accepted Answer

$$ 19 $$

Question 13

Which of the following is the solution to the inequality $$2x - 3 \u003e 7$$?

Accepted Answer

$$ x \u003e 5 $$

Question 14

A projectile is launched from the ground and its height $$h in $$meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 19.6t. At $$what time does it reach its maximum height?

Accepted Answer

$$ t = 2 $$

Question 15

Which of the following is the correct solution for $$x in $$the equation $$\frac{2}{x} = 8$$?

Accepted Answer

Question 16

Which of the following is the correct value of the discriminant for the quadratic equation $$x^2 - 6x + 9 = 0$?

Accepted Answer

$$ 0 $$

Question 17

If $$x$$ and $$y$$ are complex numbers such that $$x = 4 + 2i$$ and $$y = 1 - 3i$$, what is $$x \cdot y$$?

Accepted Answer

$$ 10 - 10i $$

Question 18

Which of the following best describes the graph of the equation $$y = 2x + 3$$?

Accepted Answer

A straight line with slope $$2$$ and $$y-$$intercept $$3$$

Question 19

Which of the following is the correct solution to the equation $$x^2 = 16$?

Accepted Answer

$$ x = 4, x = -4 $$

Question 20

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

$$ 18$$ thousand dollars at $$x = 2$$ thousand units

Intermediate Algebra (College Algebra) – Course Syllabus and Study Guide

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