Number and Quantity: Master the Fundamentals of Numbers

Question 1

Identify the number that is NOT a rational number:

Accepted Answer

√2

Answer

0.5

Answer

-3/5

Question 2

Simplify the radical expression by rationalizing the denominator: (2 / (√3 - 1))

Accepted Answer

(2√3 + 2) / 2

Answer

(2√3 - 2) / 2

Answer

2√3

Question 3

Express the imaginary unit $i$ in terms of the trigonometric functions sine and cosine.

Accepted Answer

$i = cos(θ) + isin(θ)$

Answer

$i = sin(θ) + cos(θ)$

Answer

$i = sin(θ) - cos(θ)$

Answer

$i = -sin(θ) + cos(θ)$

Question 4

Express the radical expression √(8) in its equivalent exponential form.

Accepted Answer

8^(1/2)

Answer

8^2

Answer

2^3

Answer

1/8

Question 5

Simplify the polynomial (x - 2)(x + 3):

Accepted Answer

x^2 + 5x - 6

Answer

x^2 + x - 6

Answer

x^2 - x - 6

Answer

x^2 - 5x - 6

Question 6

Which of the following is an irrational number?

Accepted Answer

sqrt(2)

Answer

0.25

Answer

1/3

Answer

-5

Question 7

Given that the sum of two numbers is 10 and one number is x, determine the value of the other number:

Accepted Answer

10 - x

Answer

x - 10

Answer

2x

Answer

10x

Question 8

Solve the problem: The sum of two real numbers is 10, and their difference is 4. Determine the numbers.

Accepted Answer

7 and 3

Answer

6 and 4

Answer

8 and 2

Answer

5 and 5

Question 9

Determine the slope of the line passing through points (2, 3) and (4, 7):

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 10

Calculate the result of (3 + 2i) + (5 - i):

Accepted Answer

8 + i

Answer

8 - i

Answer

10 + i

Answer

10 - i

Question 11

Which of the following is a prime number?

Accepted Answer

17

Answer

12

Answer

24

Answer

33

Question 12

Determine the degree of the polynomial x^3 - 2x^2 + 5x - 1:

Accepted Answer

3

Answer

2

Answer

4

Answer

5

Question 13

Determine the slope of the line represented by the equation y = 2x - 5:

Accepted Answer

2

Answer

-5

Answer

5

Answer

-2

Question 14

Which of the following is a prime number?

Accepted Answer

17

Answer

9

Answer

15

Answer

20

Question 15

Which characteristic is NOT associated with quadratic functions?

Accepted Answer

Degree of 3

Answer

A vertex point

Answer

A parabolic graph

Answer

Two x-intercepts

Question 16

Solve for x: (x - 3)^2 = 16

Accepted Answer

x = ±4

Answer

x = ±2

Answer

x = ±6

Answer

x = ±8

Question 17

What is the prime factorization of 100?

Accepted Answer

2 x 2 x 5 x 5

Answer

2 x 5 x 10

Answer

4 x 5 x 5

Answer

5 x 5 x 5 x 2

Question 18

Which of the following is the factored form of x^2 - 9?

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 9)

Answer

(x - 3)^2

Answer

x^2 - 9

Question 19

Which of the following numbers is rational?

Accepted Answer

1/3

Answer

√2

Answer

π

Answer

e

Question 20

Factor the polynomial x⁴ - 16:

Accepted Answer

(x² + 4)(x² - 4)

Answer

(x + 4)(x - 4)(x² + 4)

Answer

(x² - 4)²

Answer

(x + 4)(x - 4)(x² + 2)(x² - 2)

Question 21

Identify the zero of the polynomial f(x) = x³ - 2x² - 5x + 6.

Accepted Answer

x = 3

Answer

x = 1

Answer

x = 2

Answer

x = -2

Question 22

In cryptography, why are large prime numbers preferred for encryption?

Accepted Answer

They are harder to factorize.

Answer

They are more common.

Answer

They are easier to generate.

Answer

They have special mathematical properties.

Question 23

Simplify the expression (2x + 3)(x - 5)

Accepted Answer

2x^2 - 7x - 15

Answer

2x^2 - 10x + 3

Answer

2x^2 + x - 15

Answer

x^2 - 10x + 3

Question 24

Which of the following is a prime number?

Accepted Answer

19

Answer

10

Answer

15

Answer

21

Question 25

On the complex plane, the point representing the complex number -3 + 4i is located where?

Accepted Answer

3 units left and 4 units up

Answer

3 units right and 4 units down

Answer

4 units left and 3 units up

Answer

4 units right and 3 units down

Question 26

What is the degree of the polynomial p(x) = x³ + 2x² - x + 5?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 27

What type of number can be expressed as a fraction (a/b), where 'a' and 'b' are whole numbers and 'b' is not zero?

Accepted Answer

Rational Number

Answer

Irrational Number

Answer

Imaginary Number

Answer

Complex Number

Question 28

Which of the following is equivalent to √(-16)?

Accepted Answer

-4i

Answer

4

Answer

-4

Answer

4i

Question 29

What is the least common multiple (LCM) of 6 and 15?

Accepted Answer

30

Answer

3

Answer

9

Answer

60

Question 30

Which of the following is a rational number?

Accepted Answer

-1/4

Answer

π

Answer

√2

Answer

e

Question 31

What is the value of (3^2)^3?

Accepted Answer

729

Answer

9

Answer

27

Answer

2187

Question 32

Which property of complex numbers is illustrated by the operation: (2 + 3i) * (4 - 5i)?

Accepted Answer

Closure under multiplication

Answer

Closure under subtraction

Answer

The imaginary unit i is a real number

Answer

Complex numbers cannot be graphed on the coordinate plane

Question 33

Which property of addition is illustrated in the equation (a + b) + c = a + (b + c)?

Accepted Answer

Associative Property

Answer

Commutative Property

Answer

Distributive Property

Answer

Identity Property

Question 34

Solve the equation 3x + 5 = 17:

Accepted Answer

4

Answer

2

Answer

6

Answer

8

Question 35

Determine whether the following statement is true or false: Every even number is composite.

Accepted Answer

True

Answer

False

Question 36

Which of the following is a quadratic equation?

Accepted Answer

x² - 5x + 6 = 0

Answer

x + 2 = 0

Answer

x³ - 2x² + 1 = 0

Answer

x²y + y = 0

Question 37

Which of the following is the equation of the circle with center (-2, 3) and radius 4?

Accepted Answer

(x + 2)² + (y - 3)² = 16

Answer

(x - 2)² + (y + 3)² = 16

Answer

x² + y² + 2x - 3y = 16

Answer

x² + y² - 2x + 3y = 16

Question 38

Calculate the result of multiplying the complex numbers (2 + 3i) and (4 - 5i):

Accepted Answer

26 - 11i

Answer

22 + 11i

Answer

-22 - 11i

Answer

-26 + 11i

Question 39

Determine a factor of the polynomial expression x^2 - 9:

Accepted Answer

(x - 3)

Answer

x

Answer

(x^2 + 3)

Answer

(x + 9)

Question 40

Simplify the radical expression √(128) into its most basic radical form:

Accepted Answer

8√2

Answer

2√16

Answer

4√8

Answer

16√2

Question 41

Classify the number 0.5:

Accepted Answer

Rational

Answer

Irrational

Answer

Transcendental

Answer

Imaginary

Question 42

Which of the following is NOT considered an integer?

Accepted Answer

π

Answer

-5

Answer

0

Question 43

Represent the set of all real numbers greater than -3 using set notation:

Accepted Answer

{x | x > -3}

Answer

{x | x ≤ -3}

Answer

{x | x ≥ -3}

Answer

{x | x < -3}

Question 44

Identify the complex number represented by the point (3, 4) in the complex plane.

Accepted Answer

3 + 4i

Answer

4 + 3i

Answer

4 - 3i

Answer

3 - 4i

Question 45

Find all the real solutions of the equation x² - 5x + 6 = 0.

Accepted Answer

2, 3

Answer

1, 6

Answer

-2, -3

Answer

5, -1

Question 46

Which of the following is a rational number?

Accepted Answer

0.125

Answer

√2

Answer

π

Question 47

Evaluate the expression (0.25)^-3

Accepted Answer

64

Answer

1

Answer

16

Answer

4

Question 48

Which of the following represents a complex number?

Accepted Answer

a + bi

Answer

a

Answer

√a

Answer

a/b

Question 49

Which of the following expressions is a factor of x² - 9?

Accepted Answer

(x - 3)(x + 3)

Answer

(x + 3)²

Answer

(x - 2)(x - 4)

Answer

x - 9

Question 50

Which of the following is NOT a complex number?

Accepted Answer

π

Answer

3 + 2i

Answer

-5 + 0i

Answer

√-1

Question 51

Which of the following is a repeating decimal?

Accepted Answer

0.333...

Answer

√2

Answer

π

Answer

√7