Number Systems: Master the Properties and Operations of Real Numbers

Question 1

In the number sequence 2, 4, 8, 16, ___, 64, what number comes next?

Accepted Answer

32

Answer

24

Answer

48

Question 2

Which number below is a rational number?

Accepted Answer

0.75

Answer

√2

Answer

π

Answer

√-1

Question 3

A prime number is a positive integer greater than 1 that is divisible only by 1 and itself. Which of the following is a prime number?

Accepted Answer

13

Answer

8

Answer

15

Answer

20

Question 4

The square root of a number is a number that, when multiplied by itself, gives the original number. Which of the following is equivalent to √16?

Accepted Answer

4

Answer

-4

Answer

8

Answer

16

Question 5

Determine if the statement: 'All prime numbers are odd' is true or false

Accepted Answer

True

Answer

False

Question 6

Which of the following is a surd?

Accepted Answer

√2

Answer

2

Answer

1/2

Answer

0.5

Question 7

Which number is a perfect square?

Accepted Answer

25

Answer

10

Answer

30

Question 8

Find the volume of a cube with an edge length of 4 centimeters.

Accepted Answer

64 cubic centimeters

Answer

16 cubic centimeters

Answer

32 cubic centimeters

Question 9

Which property is NOT applicable to integers?

Accepted Answer

They are not closed under division.

Answer

They are closed under addition and subtraction.

Answer

They form an ordered set.

Answer

They encompass both positive and negative numbers.

Question 10

A savings account starts with $500. Each month, $100 is added. Write the equation in slope-intercept form (y = mx + b) that represents the balance in the account over time.

Accepted Answer

y = 100x + 500

Answer

y = 500x + 100

Answer

y = x + 500

Answer

y = 500 - 100x

Question 11

A train travels 240 kilometers in 3 hours. What is its average speed in kilometers per hour (km/hr) and meters per second (m/s)?

Accepted Answer

80 km/hr, 22.22 m/s

Answer

120 km/hr, 33.33 m/s

Answer

60 km/hr, 16.67 m/s

Question 12

Which of the following is a rational number?

Accepted Answer

1/2

Answer

√3

Answer

π

Answer

e

Question 13

Which of these numbers is a rational number?

Accepted Answer

-1.5

Answer

e

Answer

π

Answer

√3

Question 14

Which of the following numbers is a rational number?

Accepted Answer

-3/4

Answer

√2

Answer

π

Answer

e

Question 15

Factor the following algebraic expression: 12x² + 16x

Accepted Answer

4x(3x + 4)

Answer

x(12x + 16)

Answer

4x²(3x + 4)

Answer

2x(6x + 8)

Question 16

Which of the following is not a property of real numbers?

Accepted Answer

They are discontinuous.

Answer

They can represent negative values.

Answer

They are ordered.

Answer

They are dense.

Question 17

Find the prime factorization of 72:

Accepted Answer

2^3 x 3^2

Answer

2 x 3 x 6 x 6

Answer

3 x 4 x 6

Answer

2 x 2 x 2 x 3 x 3

Question 18

Which of the following is a rational number?

Accepted Answer

-1/4

Answer

e

Answer

√2

Answer

π

Question 19

Which of the following is equivalent to 10^3?

Accepted Answer

1,000

Answer

100

Answer

10

Answer

1

Question 20

Identify the mixed number:

Accepted Answer

2 1/3

Answer

5.2

Answer

-2

Answer

1/3

Question 21

Which of the following is NOT a property of integers?

Accepted Answer

They are infinitely divisible.

Answer

They can be positive, negative, or zero.

Answer

They are ordered.

Answer

They are closed under addition and subtraction.

Question 22

Find the prime factorization of 72.

Accepted Answer

2³ x 3²

Answer

3 x 4 x 6

Answer

2 x 3 x 12

Answer

2² x 9 x 2

Question 23

Which of the following is a rational number?

Accepted Answer

-3/4

Answer

0.1010010001...

Answer

√2

Answer

π

Question 24

Simplify the expression: (3⁻²)³

Accepted Answer

1/27

Answer

9

Answer

27

Answer

-9

Question 25

Convert 0.75 to a fraction.

Accepted Answer

3/4

Answer

1/2

Answer

2/3

Answer

1/4

Question 26

Which arithmetic operation is NOT closed for integers?

Accepted Answer

Division

Answer

Subtraction

Answer

Multiplication

Answer

Addition

Question 27

Which of these numbers is rational?

Accepted Answer

0.75

Answer

π

Answer

√2

Answer

e

Question 28

What is the prime factorization of 36?

Accepted Answer

2² × 3²

Answer

6 × 6

Answer

4 × 9

Answer

2 × 3 × 6

Question 29

What is the greatest common factor (GCF) of 18 and 24?

Accepted Answer

6

Answer

8

Answer

12

Answer

2

Question 30

Which of the following is an irrational number?

Accepted Answer

√5

Answer

0.5

Answer

10/3

Answer

-3

Question 31

What is the prime factorization of the number 36?

Accepted Answer

2² × 3²

Answer

6 × 6

Answer

3 × 12

Answer

2 × 3 × 5

Question 32

Which of the following numbers is divisible by both 2 and 3?

Accepted Answer

12

Answer

15

Answer

21

Answer

7

Question 33

What is the value of (-3)²?

Accepted Answer

9

Answer

-9

Answer

6

Question 34

Which of the following is equivalent to -5 + 2?

Accepted Answer

-3

Answer

10

Answer

-7

Answer

7

Question 35

What is the least common denominator (LCD) of 1/2 and 1/4?

Accepted Answer

4

Answer

2

Answer

16

Answer

8

Question 36

Which of the following statements about irrational numbers is true?

Accepted Answer

They cannot be expressed as a fraction of two integers.

Answer

They are rational numbers that have been rounded.

Answer

They are always positive.

Question 37

Which of the following is NOT a property of real numbers?

Accepted Answer

They are discrete.

Answer

They can be plotted on a number line.

Answer

They can be ordered from least to greatest.

Answer

They include fractions and decimals.

Question 38

What is the prime factorization of 36?

Accepted Answer

2 x 2 x 3 x 3

Answer

6 x 6

Answer

2 x 18

Answer

3 x 12

Question 39

Which of the following is a rational number?

Accepted Answer

-3/4

Answer

e (Euler's number)

Answer

sqrt(2) (Square root of 2)

Answer

pi (Pi)

Question 40

What is the greatest common factor (GCF) of 12 and 18?

Accepted Answer

6

Answer

2

Answer

3

Answer

12

Question 41

What is the absolute value of -12?

Accepted Answer

12

Answer

-12

Answer

0

Answer

24

Question 42

Which of the following numbers is divisible by 5 without a remainder?

Accepted Answer

1,025

Answer

1,027

Answer

1,022

Answer

1,023

Question 43

Find the prime factorization of 120.

Accepted Answer

2^3 * 3 * 5

Answer

2 * 3 * 5 * 10

Answer

2^2 * 3^2 * 5

Question 44

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

Accepted Answer

√2

Answer

-3

Answer

0.5

Answer

100

Question 45

Simplify the following expression using exponent rules: (3^-2) * (3^4)

Accepted Answer

3^2

Answer

3^6

Answer

3^-2

Question 46

Which of the following statements accurately describes the set of rational numbers?

Accepted Answer

It is closed under addition, subtraction, multiplication, and division (excluding division by zero).

Answer

It is not ordered.

Answer

It contains all integers and irrational numbers.

Question 47

Simplify the fraction -6/12. Which of the following is equivalent?

Accepted Answer

-1/2

Answer

-2/3

Answer

1/2

Answer

2/3

Question 48

Find the greatest common factor (GCF) of 18 and 24.

Accepted Answer

6

Answer

8

Answer

12

Answer

3

Question 49

Which of the following numbers is an integer that is greater than -5 and less than 5?

Accepted Answer

0

Answer

√10

Answer

-6

Answer

5.5

Question 50

What is the absolute value of -15?

Accepted Answer

15

Answer

30

Answer

-15

Answer

0

Question 51

Which of the following represents a mixed number?

Accepted Answer

3 1/2

Answer

-5

Answer

0.5

Answer

10%

Question 52

Which of these numbers is a prime number? A prime number is a whole number greater than 1 that has only two factors: 1 and itself.

Accepted Answer

17

Answer

24

Answer

36

Answer

12

Question 53

What are the prime factors of 60? Remember, prime factors are only divisible by 1 and themselves.

Accepted Answer

2 x 2 x 3 x 5

Answer

2 x 30

Answer

5 x 6 x 2

Answer

2 x 3 x 10

Question 54

Which of these numbers is a rational number? A rational number can be written as a fraction.

Accepted Answer

0.5

Answer

√9

Answer

π

Answer

√2

Question 55

What is the least common multiple (LCM) of 12 and 18? The LCM is the smallest number that is a multiple of both 12 and 18.

Accepted Answer

36

Answer

72

Answer

24

Answer

6

Question 56

Which of these numbers is divisible by 3?  A number is divisible by 3 if the sum of its digits is divisible by 3.

Accepted Answer

123

Answer

121

Answer

127

Answer

125

Question 57

What is the greatest common factor (GCD) of 24 and 36? The GCD is the largest number that divides both 24 and 36 without leaving a remainder.

Accepted Answer

12

Answer

6

Answer

36

Answer

8

Question 58

Which of these numbers is an integer? Integers are whole numbers, including zero, and their opposites.

Accepted Answer

-5

Answer

√3

Answer

1/2

Question 59

What is the absolute value of -8? The absolute value of a number is its distance from zero on the number line.

Accepted Answer

8

Answer

16

Answer

0

Answer

-8

Question 60

A baker has 36 cupcakes and wants to arrange them in equal rows. Which of these is NOT a possible number of cupcakes in each row?

Accepted Answer

11

Answer

6

Answer

9

Answer

12

Question 61

Which of these numbers is an irrational number? An irrational number cannot be written as a fraction and its decimal representation goes on forever without repeating.

Accepted Answer

√7

Answer

-4

Answer

0.75

Answer

1/3

Question 62

Which of the following is the smallest rational number?

Accepted Answer

-1/2

Answer

-0.75

Answer

0

Answer

-1.5

Question 63

Find the prime factorization of 42.

Accepted Answer

2 x 3 x 7

Answer

2 x 7 x 12

Answer

3 x 14

Answer

6 x 7

Question 64

Which of the following is an irrational number?

Accepted Answer

π

Answer

4/5

Answer

-7

Answer

0.5