Question 1

Which property of real numbers is illustrated by the equation $$a + b = b + a$$?

Accepted Answer

Commutative Property

Question 2

Evaluate the expression $$13 - \frac{20}{5 	imes 2}$$ using the correct order of operations.

Accepted Answer

$$9$$

Question 3

Which of the following is NOT a real number?

Accepted Answer

$$\sqrt{-1}$$

Question 4

Simplify the expression $$\left( \frac{x^3$ y^5$}{x^4$ y^2$} \$$right)^2$$.

Accepted Answer

$$\frac{x$$^{-2}$$ y^6$}{1}$$

Question 5

Which of the following is equivalent to $$\sqrt[3]{16}$$?

Accepted Answer

$$16^{1/3}$$

Question 6

A medical researcher needs to dilute a solution so that the concentration is reduced by a factor of $$\sqrt{2}. If $$the original concentration is $$C$$, what is the new concentration?

Accepted Answer

$$\frac{C}{\sqrt{2}}$$

Question 7

Which expression is NOT simplified because it contains a radical in the denominator?

Accepted Answer

$$\frac{1}{\sqrt{5}}$$

Question 8

Convert $$32^{7/5} to $$radical form.

Accepted Answer

$$\sqrt[5]{32^7$}$$

Question 9

Simplify $$\$$left(27x^{2/3}$$\right) \$$left(3x^{5/6}$$\right).$$

Accepted Answer

$$81x^{3/2}$$

Question 10

Which of the following is the correct factorization of $$x^2 - 49$?

Accepted Answer

$$(x - 7)(x + 7)$$

Question 11

A chemical reaction produces a compound whose mass is modeled by $$m = 5x^2$ + 6x - 7. $$Which method would you use to factor this trinomial?

Accepted Answer

Trinomial factoring

Question 12

Which of the following is the greatest common factor (GCF) of $$35x^5$$ - $$14x^4 + 7x$?

Accepted Answer

$$7x$$

Question 13

Simplify $$\frac{x^2$ - 3x + 2}{x^2$ - x - 2}.$$

Accepted Answer

$$\frac{x - 1}{x + 1}$$

Question 14

Find the domain of $$g(x) = \frac{3}{(x + 1)(x - 5)}.$$

Accepted Answer

All real numbers except $$x = -1$$ and $$x = 5$$

Question 15

Which property is used in the equation $$a(b + c) = ab + ac$$?

Accepted Answer

Distributive Property

Question 16

A biologist is studying population growth modeled by $$P = 2$$^{t}$$, where t$ is time in years. What is P$ after t = 3$ years?

Accepted Answer

$$8$$

Question 17

Simplify $$\frac{2x^2$ - 3x + 2}{x^2$ - x - 2} \div \frac{x^2$ - 3x + 2}{x^2$ - x - 2}.$$

Accepted Answer

$$2$$

Question 18

Which of the following is the correct factorization for $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 19

Which of the following expressions is equivalent to $$a^{p/q}$$?

Accepted Answer

$$\sqrt[q]{a^p}$$

Question 20

A pharmaceutical company needs to rationalize the denominator in the expression $$\frac{1}{\sqrt{2}}. $$What is the simplified form?

Accepted Answer

$$\frac{\sqrt{2}}{2}$$

Fundamental Concepts of Algebra: Study Guide

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