Question 1

Which of the following numbers is NOT a rational number?

Accepted Answer

$$\sqrt{2}$$

Question 2

Which interval notation represents all real numbers $$x$$ such that $$-2 \u003c x \u003c 5$$?

Accepted Answer

$$(-2,5)$$

Question 3

If $$x is a $$real number such that $$x \geq 3$$, which of the following is the correct interval notation?

Accepted Answer

$$[3, \infty)$$

Question 4

Which set contains all numbers that can be written as fractions of integers?

Accepted Answer

Rational numbers

Question 5

What is the absolute value of $$-13$$?

Accepted Answer

$$13$$

Question 6

Which of the following is the correct set-builder notation for the interval $$(-\infty, 6)$$?

Accepted Answer

$$\{x \mid x \u003c 6\}$$

Question 7

Which of the following is the union of the intervals $$[-5,2)$$ and $$(8,\infty)$$?

Accepted Answer

$$[-5,2) \cup (8,\infty)$$

Question 8

If $$a = -10$$ and $$b = 7$$, what is the distance between $$a$$ and $$b on $$the number line?

Accepted Answer

$$|a-b| = |-10-7| = 17$$

Question 9

Which of the following is an example of a closed interval?

Accepted Answer

$$[2,6]$$

Question 10

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

Accepted Answer

Distributive property

Question 11

Which of the following is the correct interval notation for all real numbers except $$-3$$?

Accepted Answer

$$(-\infty, -3) \cup (-3, \infty)$$

Question 12

Which of the following is the intersection of the intervals $$[-10,0]$$ and $$[-2,6]$$?

Accepted Answer

$$[-2,0]$$

Question 13

If $$x is a $$real number such that $$x \u003e 4$$, which of the following is the correct set-builder notation?

Accepted Answer

$$\{x \mid x \u003e 4\}$$

Question 14

Which of the following is the correct interval notation for all real numbers $$x$$ such that $$x \leq 6$$?

Accepted Answer

$$(-\infty,6]$$

Question 15

Which of the following is an irrational number?

Accepted Answer

$$\sqrt{2}$$

Question 16

What is the value of $$|-2| + |4|$$?

Accepted Answer

$$6$$

Question 17

Which of the following is the correct interval notation for all real numbers $$x$$ such that $$x is $$strictly greater than $$8$$?

Accepted Answer

$$(8, \infty)$$

Question 18

Which of the following is the correct set-builder notation for the interval $$[a, b)$$?

Accepted Answer

$$\{x \mid a \leq x \u003c b\}$$

Question 19

If $$x is a $$real number such that $$-25 \u003c x \u003c 6$$, which of the following is the correct interval notation?

Accepted Answer

$$(-25,6)$$

Precalculus Study Guide: Real Numbers, Intervals, Absolute Value, and Exponents

Study Guide - Practice Questions