Question 1

Which of the following numbers is irrational?

Accepted Answer

√2

Question 2

A student claims that every number with a non-terminating decimal expansion is irrational. Which of the following best evaluates this claim?

Accepted Answer

The claim is incorrect because some rational numbers have non-terminating repeating decimals.

Question 3

Which of the following statements is TRUE about rational numbers?

Accepted Answer

They can always be written as a ratio of two integers with a nonzero denominator.

Question 4

Which of the following is NOT a property of the set of integers?

Accepted Answer

It is closed under division (except by zero).

Question 5

A medical dosage calculation requires the square root of 2. Which of the following best describes the value used in the calculation?

Accepted Answer

An irrational number, because it cannot be exactly written as a fraction.

Question 6

Which of the following numbers is both an integer and a rational number?

Accepted Answer

0

Question 7

A chemist measures a solution and records the value as 0.666... (with the 6 repeating). Which type of number is this?

Accepted Answer

Rational number

Question 8

Which of the following best explains why the decimal expansion of √2 is infinite and non-repeating?

Accepted Answer

Because √2 cannot be written as a ratio of two integers.

Question 9

A historian is analyzing ancient Greek mathematics. Which discovery about numbers did the Greeks make that is still relevant in calculus today?

Accepted Answer

They proved that √2 is irrational.

Question 10

Which of the following is the best approximation for √2 based on the table of x and x² values between 1 and 2?

Accepted Answer

Between 1.4 and 1.5

Question 11

Which of the following statements about the real number system is correct?

Accepted Answer

It includes both rational and irrational numbers.

Question 12

A student is asked to classify the number π. Which of the following is the correct classification?

Accepted Answer

Irrational number

Question 13

Which of the following is a correct statement about the operations on rational numbers?

Accepted Answer

The sum, difference, product, or quotient (except by zero) of two rational numbers is always a rational number.

Question 14

Which of the following numbers is NOT a rational number?

Accepted Answer

√2

Question 15

A real-world scenario: A carpenter needs to cut a piece of wood to a length of √2 meters. Which of the following is true about this measurement?

Accepted Answer

It is an irrational number and can only be approximated.

Question 16

Which of the following is an example of a number that is both an integer and a rational number?

Accepted Answer

-4

Question 17

Which of the following best describes the decimal representation of a rational number?

Accepted Answer

It is either terminating or repeating.

Question 18

A student writes 3 = 3/1. What concept does this illustrate?

Accepted Answer

All integers are rational numbers.

Numbers and Functions: Foundations for Calculus

Study Guide - Practice Questions