Question 1

Simplify the rational expression: 
$$
\frac{2x^2$ - 8}{4x}
$$

Accepted Answer

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

Question 2

Perform the indicated operation and simplify: 
$$
\frac{3x}{x^2$ - x} + \frac{2}{x}
$$

Accepted Answer

$$\frac{3x + 2(x-1)}{x(x-1)}$$

Question 3

Multiply and simplify: 
$$
\frac{2x + 4}{x^2$ - 4} 	imes \frac{x^2$ - 2x}{4x + 8}
$$

Accepted Answer

$$\frac{x-2}{2(x+2)}$$

Question 4

Simplify the radical expression, assuming all variables represent positive real numbers: 
$$
\sqrt{45x^6$y^3$$}
$

Accepted Answer

$$3x^3y$$\sqrt{5y}$$

Question 5

Multiply and then simplify if possible. Assume all variables represent positive real numbers: 
$$
\sqrt{7x} \cdot \sqrt{14x^3$}
$$

Accepted Answer

$$14x^2$$\sqrt{2}$$

Question 6

Solve the compound inequality: 
$$
-2 \u003c 4x - 6 \leq 10
$$

Accepted Answer

$$1 \u003c x \leq 4$$

Question 7

Solve the equation for $$x$$: 
$$
|3x - 4| + 6 = 13
$$

Accepted Answer

$$x = 3,\ x = -\frac{5}{3}$$

Question 8

Evaluate and simplify: 
$$
\sqrt{27} + 3\sqrt{12}
$$

Accepted Answer

$$3\sqrt{3} + 6\sqrt{3} = 9\sqrt{3}$$

Question 9

Which of the following is a real number? 
$$
\sqrt[3]{-27}
$$

Accepted Answer

Yes, the root is a real number because the index is odd.

Question 10

A ladder is leaning against a house. The base of the ladder is 8 feet from the house, and the top of the ladder is 15 feet above the ground. How long is the ladder? (Use the Pythagorean Theorem.)

Accepted Answer

$$\sqrt{8^2$ + 15^2$} = 17$$

Question 11

Given $$f(x) = x^2$ - 5x + 6$$, find $$f(3).$$

Accepted Answer

$$-6$$

Question 12

Sally can paint a room in 7 hours while Elaine takes 4 hours to paint the same room. How long would it take them to paint the room together?

Accepted Answer

$$\frac{28}{11}$$ hours

Question 13

Rewrite $$y = 3x + 1 in $$function notation.

Accepted Answer

$$f(x) = 3x + 1$$

Question 14

Which of the following is the correct solution for the system of equations?
$$
\begin{cases}
2x + 3y = 10 \
x - y = 1
\end{cases}
$$

Accepted Answer

$$x = 2,\ y = 1$$

Question 15

Solve for $$x$$: 
$$
5x - 4(x + 1) = 13
$$

Accepted Answer

$$x = 17$$

Question 16

If the cost $$C of $$manufacturing $$x$$ laptops at a principal plant is given by $$C(x) = 500x + 2000$$, what is the amount cost to manufacture 10 laptops?

Accepted Answer

$$7000$$

Question 17

Which of the following is the correct substitution for $$a, b, c in $$the quadratic formula $$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$ for the equation $$2x^2 + 5x - 3 = 0$?

Accepted Answer

$$a = 2,\ b = 5,\ c = -3$$

Question 18

Is $$\sqrt[4]{-16} a $$real number?

Accepted Answer

No, the root is not a real number because the index is even and the radicand is negative.

College Algebra Practice Exam Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards