Topic 1 Mid-Chapter Review

• whole numbers

• irrational numbers

• integers

• rational numbers

Answer explanation

Repeating decimals are always rational!

Irrational numbers are non-terminating AND non-repeating.

To which set of real numbers does the number -12 belong?

• whole numbers

• irrational numbers

• integers

• rational numbers

Answer explanation

Repeating decimals are always rational!

Irrational numbers are non-terminating AND non-repeating.

To which set of real numbers does the number 2π belong?

• whole numbers

• irrational numbers

• integers

• rational numbers

Answer explanation

Repeating decimals are always rational!

Irrational numbers are non-terminating AND non-repeating.

Which of the following must be an irrational number?

• the sum of two irrational numbers

• the product of two irrational numbers

• the sum of a rational and an irrational number

• the product of a rational number and an irrational number

Which numbers in Set A = {–7, –4, 2, 14, 21, 34, 42} are elements of both Set B and Set C, shown below?

Set B = {odd numbers}

Set C = {multiples of 7}

• -7, 21

• -7, 14, 21, 42

• 21

• 21, 42

Order the numbers from least to greatest.

• 2.8

• 2π

• x = 1

• x = 7

• x = 11

• x = 5

• no solution

• infinitely many solutions

• two solutions

• one solution

Which of the equations shown have infinitely many solutions?
Select all that apply.

• 3x – 1 = 3x + 1

• 3(x – 1) = 3x – 3

• 2x + 2 = 2(x + 1)

• 3(x – 2) = 2(x – 3)

• 2x – 1 = 1 – 2x

Tonya’s dog-walking service charges a flat rate of $30 per month, plus $2 per mile that each dog is walked. Beth does not charge a monthly fee for her dog-walking service, but she charges $6 per mile that each dog is walked.

Choose the equation that can be used to find the number of miles m for which Tonya and Beth would charge the same amount.

• 30 + 2m = 6m

• 30 = 2m + 6m

• 30 + 6m = 2m

• 30 + m = 8m