Question 1

Which of the following numbers is NOT a real number?

Accepted Answer

$$\sqrt{-1}$$

Question 2

What is the value of $$\sqrt{180} in $$simplest radical form?

Accepted Answer

$$6\sqrt{5}$$

Question 3

Simplify the expression $$\frac{2^5$ \cdot 2^3$}{2^4$}.$$

Accepted Answer

$$2^4$$

Question 4

Which property is illustrated by the equation $$a + (b + c) = (a + b) + c$$?

Accepted Answer

Associative Property of Addition

Question 5

If $$\log_{10}(x) = 2$$, what is the value of $$x$$?

Accepted Answer

$$100$$

Question 6

What is the sum of the arithmetic sequence $$7, 10, 13, 16, 19$$?

Accepted Answer

$$60$$

Question 7

Which of the following is the correct product rule for exponents?

Accepted Answer

$$a^m \cdot a^n = a$$^{m+n}$$

Question 8

A sample decays according to the formula $$y = y_0$ \cdot (\frac{1}{2})^t. If$$ $$y_0 = 80$ and t = 3$, what is y$?

Accepted Answer

$$20$$

Question 9

Which of the following is the correct quotient rule for logarithms?

Accepted Answer

$$\log_b(\frac{x}{y}) = \log_b(x) - \log_b(y)$$

Question 10

If the ratio of students in Group A to Group B is $$5:3$$ and there are $$120$$ students in total, how many students are in Group A?

Accepted Answer

$$60$$

Question 11

Which of the following is the correct way to express $$0.00042 in $$scientific notation?

Accepted Answer

$$4.2 	imes 10$$^{-3}$$

Question 12

What is the least common multiple (LCM) of $$6$$ and $$8$$?

Accepted Answer

$$24$$

Question 13

Simplify $$\frac{3}{4} \div \frac{2}{5}.$$

Accepted Answer

$$\frac{15}{8}$$

Question 14

Which of the following is an example of an improper fraction?

Accepted Answer

$$\frac{7}{4}$$

Question 15

If $$a = 2$$, $$b = 3$$, and $$c = 4$$, what is the value of $$a^b + c^a$$?

Accepted Answer

$$2^3$$ + $$4^2 = 8 + 16 = 24$

Question 16

Which of the following is the correct change of base formula for logarithms?

Accepted Answer

$$\log_b(a) = \frac{\log_c(a)}{\log_c(b)}$$

Question 17

What is the 9th term of the arithmetic sequence $$3, 7, 11, 15, \ldots$$?

Accepted Answer

$$35$$

Question 18

Which of the following is the correct way to multiply decimals: $$2.5 	imes 0.05$$?

Accepted Answer

$$0.125$$

Question 19

If $$x^3 = 27$, what is the value of x$?

Accepted Answer

$$3$$

Question 20

Which of the following is the correct way to simplify $$\sqrt{50}$$?

Accepted Answer

$$2\sqrt{5}$$

Fundamental Concepts of Algebra: Numbers, Fractions, Exponents, Radicals, Logarithms, Ratios, and Sequences

Study Guide - Practice Questions