Question 1

Which of the following sets contains all numbers with a repeating or terminating decimal representation?

Accepted Answer

$$\mathbb{Q}$$

Question 2

What is the interval notation for the set $$\{ x \mid -1 \leq x \u003c 4 \}$$?

Accepted Answer

$$[-1, 4)$$

Question 3

According to the Law of Trichotomy, for any two real numbers $$a$$ and $$b$$, which statement is always true?

Accepted Answer

Exactly one of $$a  b$$, or $$a = b is $$true.

Question 4

Simplify $$\frac{(4-2)(2 \cdot 4) - (4)^2$}{(4-2)^2$}.$$

Accepted Answer

$$2$$

Question 5

Which property of real numbers states that $$a + b = b + a$$ for all real numbers $$a$$ and $$b$$?

Accepted Answer

Commutativity

Question 6

What is the result of $$\frac{1}{4} + \frac{6}{7}$$ written in lowest terms?

Accepted Answer

$$\frac{25}{28}$$

Question 7

Which of the following is NOT a property of real number addition?

Accepted Answer

Distributivity

Question 8

What is the simplified value of $$2^{-3}$$?

Accepted Answer

$$\frac{1}{8}$$

Question 9

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

Accepted Answer

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

Question 10

Which interval notation represents all real numbers less than or equal to $$5$$?

Accepted Answer

$$(-\infty, 5]$$

Question 11

If $$ab = 0$$ for real numbers $$a$$ and $$b$$, what must be true?

Accepted Answer

Either $$a = 0 or$$ $$b = 0 (or $$both).

Question 12

Which of the following is the correct way to distribute negatives across addition?

Accepted Answer

$$-(a + b) = -a - b$$

Question 13

What is the result of $$\frac{5}{12} - \left( \frac{47}{30} - \frac{7}{3} \right)$$ written in lowest terms?

Accepted Answer

$$\frac{7}{20}$$

Question 14

Which property allows you to write $$ab + ac = a(b + c)$$?

Accepted Answer

Distributive Property

Question 15

What is the interval notation for the set $$\{ x \mid x \u003e 3 \}$$?

Accepted Answer

$$(3, \infty)$$

Question 16

Which of the following is the correct quotient rule for integer exponents?

Accepted Answer

$$\frac{a^n}{a^m} = a$$^{n-m}$$

Question 17

Which of the following is an irrational number?

Accepted Answer

$$\sqrt{2}$$

Question 18

What is the simplified value of $$\frac{\left(5 \cdot 3$$^{51}$$\right) / 4$$^{36}$$}{\left(5 \cdot 3$$^{49}$$\right) / 4$$^{34}$$}$$?

Accepted Answer

$$\frac{3^2$}{4^2$}$$

Question 19

Which property of fractions states that $$\frac{a}{b} = \frac{c}{d} if $$and only if $$ad = bc$$?

Accepted Answer

Fraction Equality

Fundamental Concepts of Algebra: Real Numbers, Intervals, and Operations

Study Guide - Practice Questions