Number and Quantity: Master the Basics of Real Numbers and Operations

Question 1

Express (a^3b^-2)^-1 in terms of a and b

Accepted Answer

a^-3b^2

Answer

a^3b^2

Answer

a^-3b^-2

Answer

a^3b^-3

Question 2

If the perimeter of a rectangle is 24 cm and the length is 8 cm, what is the width?

Accepted Answer

6 cm

Answer

4 cm

Answer

8 cm

Answer

12 cm

Question 3

Which of the following is equivalent to x^(-2)?

Accepted Answer

1/x^2

Answer

x^2

Answer

-x^2

Answer

1/x^-2

Question 4

Which of the following is not a rational number?

Accepted Answer

π

Answer

1/2

Answer

0.5

Answer

-3/4

Question 5

When multiplying two rational numbers, a and b, what can you conclude about the result, ab?

Accepted Answer

ab is always rational

Answer

ab is always a whole number

Answer

ab is always a negative number

Question 6

Given real numbers a, b, and c, where a > b and b > c, which of the following is true?

Accepted Answer

a > c

Answer

a < c

Answer

a = c

Question 7

Classify the following numbers: √2 and π. Which statement is correct?

Accepted Answer

√2 is an algebraic irrational number, and π is a transcendental number.

Answer

Both √2 and π are algebraic numbers.

Answer

Both √2 and π are rational numbers.

Answer

Both √2 and π are transcendental numbers.

Question 8

Which number has the largest absolute value?

Accepted Answer

-7.5

Answer

-6

Answer

5.2

Answer

0

Question 9

Classify the number 1.414 as either rational or irrational.

Accepted Answer

Irrational

Answer

Rational

Question 10

Simplify the expression: 2(x minus 3) plus 3(x plus 2)

Accepted Answer

5x minus 3

Answer

2x minus 9

Answer

5x plus 3

Question 11

A square has a perimeter of 24 inches. How long is each side of the square?

Accepted Answer

6 inches

Answer

4 inches

Answer

8 inches

Question 12

State two properties that characterize rational numbers.

Accepted Answer

Expressible as fractions or decimals

Answer

Irrational and non-terminating

Answer

Finite and non-repeating

Answer

Positive and negative

Question 13

Which of the following numbers is a rational number?

Accepted Answer

0.5

Answer

√2 (square root of 2)

Answer

e

Answer

π (pi)

Question 14

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

Accepted Answer

Commutative property of subtraction

Answer

Associative property of addition

Answer

Identity property of multiplication

Answer

Distributive property of multiplication over addition

Question 15

Which of the following expressions is equivalent to 3^-2?

Accepted Answer

1/9

Answer

9/3

Answer

9/-3

Answer

3/9

Question 16

Simplify the expression: (3x^2y)^3

Accepted Answer

27x^6y^3

Answer

3x^5y^2

Answer

9x^6y^3

Answer

81x^8y^9

Question 17

Which of the following is a rational number?

Accepted Answer

-2/3

Answer

√2

Answer

e

Answer

π

Question 18

Which of these is **not** a property of real numbers?

Accepted Answer

They are not ordered.

Answer

They are closed under addition and multiplication.

Answer

They can be positive, negative, or zero.

Question 19

What is the simplified form of (-3)²?

Accepted Answer

9

Answer

3

Answer

-9

Question 20

Which of these numbers is the largest: 0.5, -0.25, 0.75, -0.125?

Accepted Answer

0.75

Answer

-0.125

Answer

0.5

Answer

-0.25

Question 21

What is the solution to the equation 2x - 5 = 11?

Accepted Answer

8

Answer

10

Answer

6

Answer

12

Question 22

Which of the following represents the solution set of the inequality x > 3?

Accepted Answer

{x | x > 3}

Answer

{x | x ≥ 3}

Answer

{x | x < 3}

Question 23

What is the value of 12 - |-4|?

Accepted Answer

8

Answer

-8

Answer

16

Answer

4

Question 24

What is the simplified form of (3√5)²?

Accepted Answer

45

Answer

75

Answer

25

Answer

60

Question 25

Simplify the expression: (2x²y)³(x³y⁴)

Accepted Answer

8x⁸y¹⁰

Answer

6x⁸y¹⁰

Answer

10x⁸y¹⁰

Answer

12x⁸y¹⁰

Question 26

What are the solutions to the equation x² - 5x + 6 = 0?

Accepted Answer

x = 2 or x = 3

Answer

x = 0 or x = 5

Answer

x = 1 or x = 4

Answer

x = -2 or x = -3

Question 27

Which of the following is an example of a complex number?

Accepted Answer

3 + 2i

Answer

-7

Answer

5

Answer

0.5

Question 28

What is the conjugate of the complex number 4 - 3i?

Accepted Answer

4 + 3i

Answer

4 - 3i

Answer

-4 + 3i

Answer

-4 - 3i

Question 29

What is the square root of 64?

Accepted Answer

8

Answer

32

Answer

64

Answer

16

Question 30

Which of the following is an irrational number?

Accepted Answer

√2

Answer

0.5

Answer

√9

Answer

3/4

Question 31

Simplify the expression: (2x³)²

Accepted Answer

4x⁶

Answer

4x⁵

Answer

2x⁶

Answer

4x⁹

Question 32

What is 5⁻² equivalent to?

Accepted Answer

1/25

Answer

25

Answer

-25

Answer

-10

Question 33

Which of the following numbers is not a perfect square?

Accepted Answer

250

Answer

144

Answer

169

Answer

196

Question 34

Simplify the expression: √27 + √12

Accepted Answer

5√3

Answer

9√3

Answer

3√3

Answer

√39

Question 35

Which of the following is a rational number?

Accepted Answer

2/3

Answer

√2

Answer

e

Answer

π

Question 36

What is the value of 2^3?

Accepted Answer

8

Answer

16

Answer

64

Answer

4

Question 37

Simplify the expression: (x^2 * x^3) / x

Accepted Answer

x^4

Answer

x^5

Answer

x^2

Question 38

Find the square root of 144.

Accepted Answer

12

Answer

8

Answer

24

Answer

18

Question 39

Which of the following is the largest number?

Accepted Answer

10^3

Answer

10^-2

Answer

10^2

Answer

10^-1

Question 40

Convert the rational number -3/4 to a decimal.

Accepted Answer

-0.75

Answer

1.25

Answer

-0.5

Answer

0.75

Question 41

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

Accepted Answer

The product of two positive numbers is negative.

Answer

The sum of any two real numbers is a real number.

Answer

The real numbers are a closed set under addition.

Answer

The real numbers are an ordered set.

Question 42

Simplify the expression: √(16 * 9)

Accepted Answer

12

Answer

8

Answer

36

Answer

24

Question 43

Which of the following rational numbers is equivalent to 0.125?

Accepted Answer

1/8

Answer

1/16

Answer

1/32

Answer

1/4

Question 44

Evaluate the expression: 2^4 - 3^2

Accepted Answer

7

Answer

5

Answer

9

Answer

11

Question 45

Which of the following is an irrational number?

Accepted Answer

√2

Answer

3/4

Answer

-16

Answer

2.5

Question 46

Simplify: (2⁷ * 2³) / 2⁸

Accepted Answer

4

Answer

8

Answer

16

Answer

2

Question 47

What is the value of 8 raised to the power of 2/3?

Accepted Answer

4

Answer

2

Answer

16

Answer

8

Question 48

The area of a square is 50 square units. Which of the following is closest to the length of one side of the square?

Accepted Answer

7.1

Answer

7

Answer

5

Answer

10

Question 49

Express 0.00045 in scientific notation.

Accepted Answer

4.5 x 10⁻⁴

Answer

0.45 x 10⁻³

Answer

45 x 10⁻⁵

Answer

4.5 x 10⁴

Question 50

Which of the following is equivalent to √72?

Accepted Answer

6√2

Answer

9√2

Answer

2√18

Answer

36

Question 51

If x = 4 and y = -3, what is the value of (x² - y²) / (x + y)?

Accepted Answer

7

Answer

1

Answer

-7

Answer

-1

Question 52

The population of a town is 2.5 x 10⁵.  What is this number expressed in standard notation?

Accepted Answer

250,000

Answer

25,000

Answer

2,500,000

Answer

0.000025

Question 53

Which number line represents the solution to the inequality: -2x + 5 < 1?

Accepted Answer

[Image of a number line with an open circle on 2 and an arrow pointing to the right]

Answer

[Image of a number line with a closed circle on 2 and an arrow pointing to the right]

Answer

[Image of a number line with an open circle on 2 and an arrow pointing to the left]

Question 54

A rectangle has a length of (3√5) meters and a width of (2√10) meters. What is the area of the rectangle in square meters?

Accepted Answer

30√2

Answer

60

Answer

15√2

Answer

6√15