Question 1

Which of the following numbers is irrational?

Accepted Answer

$$\sqrt{2}$$

Question 2

Which set includes all integers, rational numbers, and irrational numbers?

Accepted Answer

Real numbers

Question 3

Which of the following is the correct interval notation for $$2.5 \u003c x \leq 6$$?

Accepted Answer

$$(2.5, 6]$$

Question 4

If $$a \geq b$$, which statement is true?

Accepted Answer

$$a is $$greater than or equal to $$b$$

Question 5

Which of the following is a rational number?

Accepted Answer

$$0.555\ldots$$

Question 6

Simplify the expression $$x^4$$ $$(2y)^5$$ \div $$(x^3$$ $$y^2$$)$$.

Accepted Answer

$$32xy^3$$

Question 7

Which property states that $$ab + ac = a(b + c)$$?

Accepted Answer

Distributive property

Question 8

What is the union of the intervals $$(5,7)$$ and $$(9,\infty)$$?

Accepted Answer

$$(5,7) \cup (9,\infty)$$

Question 9

Which of the following is the correct simplification of $$\left( -\dfrac{2}{3} \$$right)^3$$?

Accepted Answer

$$-\dfrac{8}{27}$$

Question 10

If $$a^0$$ 
eq 0$$, what is the value of a^0$?

Accepted Answer

$$1$$

Question 11

Which of the following is NOT a whole number?

Accepted Answer

$$-2$$

Question 12

Given the interval $$(6, x)$$ where $$x \u003e 7$$, which of the following could represent the intersection with $$(5,7)$$?

Accepted Answer

$$(6,7)$$

Question 13

Which of the following is the correct exponent rule for multiplying powers with the same base?

Accepted Answer

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

Question 14

Which of the following is a real-world example of a set?

Accepted Answer

A collection of all students enrolled in a university

Question 15

If $$a \u003c 0$$, which statement is true?

Accepted Answer

$$a is $$negative

Question 16

Which of the following is a terminating decimal?

Accepted Answer

$$0.6$$

Question 17

Which of the following is the correct interval notation for $$x \u003e 2$$?

Accepted Answer

$$(2, \infty)$$

Question 18

If $$a \cdot b = 0$$, which property allows us to conclude that either $$a = 0 or$$ $$b = 0$$?

Accepted Answer

Zero product property

Question 19

Which of the following is the correct simplification of $$(-2)^3$$?

Accepted Answer

$$-8$$

Question 20

Which of the following is a repeating decimal?

Accepted Answer

$$0.555\ldots$$

Real Numbers, Inequalities, and Integer Exponents: Precalculus Study Notes

Study Guide - Practice Questions