Q: Which of the following best describes the hierarchy of number sets?

$$\text{Natural} \subset \text{Whole} \subset \text{Integers} \subset \text{Rational} \subset \text{Real}$$

Question 1

Which of the following numbers is NOT a rational number?

Accepted Answer

$$\sqrt{3}$$

Question 2

Evaluate the expression $$2x^2 - 3y$ when x = 4$ and y = -2$.

Accepted Answer

$$26$$

Question 3

Which set(s) does the number $$0$$ belong to?

Accepted Answer

Whole, Integer, Rational, Real

Question 4

What is the absolute value of $$-12$$?

Accepted Answer

$$12$$

Question 5

Translate the phrase: 'Seven less than three times a number' into an algebraic expression.

Accepted Answer

$$3x - 7$$

Question 6

Which of the following is an example of an irrational number?

Accepted Answer

$$\sqrt{2}$$

Question 7

If $$x = -3$$ and $$y = 5$$, what is the value of $$|x| + y$$?

Accepted Answer

$$8$$

Question 8

Which of the following statements is TRUE?

Accepted Answer

All natural numbers are rational numbers.

Question 9

What is the opposite of $$-9$$?

Accepted Answer

$$9$$

Question 10

Which of the following decimals is a rational number?

Accepted Answer

$$0.121212\ldots$$

Question 11

A chemist measures a temperature drop of $$-7$$ degrees Celsius. What is the absolute value of this temperature change, and what does it represent?

Accepted Answer

$$7$$, the temperature changed by 7 degrees regardless of direction

Question 12

Which of the following numbers is NOT an integer?

Accepted Answer

$$\frac{3}{4}$$

Question 13

Translate the phrase: 'Half of a number increased by 8' into an algebraic expression.

Accepted Answer

$$\frac{x}{2} + 8$$

Question 14

Which of the following best describes the hierarchy of number sets?

Accepted Answer

$$	ext{Natural} \subset 	ext{Whole} \subset 	ext{Integers} \subset 	ext{Rational} \subset 	ext{Real}$$

Question 15

A patient’s heart rate is measured as $$|x|$$ beats per minute, where $$x is $$the difference from the normal rate. If $$x = -12$$, what is the patient’s heart rate difference from normal?

Accepted Answer

$$12$$ beats per minute

Question 16

Evaluate $$\frac{x+5}{6}$$ when $$x = 7.$$

Accepted Answer

$$3$$

Question 17

Which of the following numbers is both rational and irrational?

Accepted Answer

No number is both rational and irrational

Question 18

A company’s profit is represented by $$3x + 2$$, where $$x is $$the number of products sold. If the company sells 10 products, what is the profit?

Accepted Answer

$$32$$

Question 19

Which of the following is the correct algebraic expression for 'five more than twice a number'?

Accepted Answer

$$2x + 5$$

Question 20

If $$z = -2$$, what is the value of $$z^3$$?

Accepted Answer

$$-8$$

Algebraic Expressions and Sets of Numbers – Study Notes (Intermediate Algebra, Section 1.2)

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