Algebra and Functions Quizzes - Master Your Math Skills

Question 1

Solve the inequality: x + 5 > -3

Accepted Answer

x > -8

Answer

x > 8

Answer

x < -8

Answer

x < 8

Question 2

Factorise the expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 1)

Question 3

Which of the following is the domain of the function f(x) = 1 / (x - 2)?

Accepted Answer

{x | x ≠ 2}

Answer

{x | x > 2}

Answer

{x | x < 2}

Answer

All real numbers

Question 4

The graph of y = f(x) is increasing for x < 2 and decreasing for x > 2. At what value of x does the function have a critical point?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 5

Which of the following is equivalent to the inequality x < 5?

Accepted Answer

x - 5 < 0

Answer

5 - x > 0

Answer

x + 5 < 0

Answer

5 + x < 0

Question 6

Solve the system of equations: x + y = 5 and x - y = 1

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = -3, y = 8

Answer

x = -2, y = 7

Question 7

Identify the rational function from the following options:

Accepted Answer

f(x) = x/(x + 1)

Answer

f(x) = x^2 + 1

Answer

f(x) = e^x

Answer

f(x) = sin(x)

Question 8

Determine the equation of the line that has a slope of 2 and passes through the point (1, 3)

Accepted Answer

y = 2x + 1

Answer

y = 2x - 1

Answer

y = x + 2

Answer

y = x - 2

Question 9

Solve the system of equations: 2x + y = 5, x - y = 1

Accepted Answer

x = 2, y = 1

Answer

x = 1, y = 2

Answer

x = 3, y = 2

Answer

x = 2, y = 3

Question 10

Find the inverse of the function f(x) = 2x - 5:

Accepted Answer

f^-1(x) = (x + 5)/2

Answer

f^-1(x) = (x - 5)/2

Answer

f^-1(x) = 2x + 5

Answer

f^-1(x) = 2x - 5

Question 11

Determine the vertex of the parabola represented by the equation y = -x^2 + 4x + 3:

Accepted Answer

(2, 7)

Answer

(-2, 7)

Answer

(2, 3)

Answer

(-2, 3)

Question 12

Find the inverse of the function f(x) = 3x + 4

Accepted Answer

f^-1(x) = (x - 4)/3

Answer

f^-1(x) = 3x - 4

Answer

f^-1(x) = 1/(3x + 4)

Answer

f^-1(x) does not exist

Question 13

Determine the solution to the inequality: 2x + 1 > 5

Accepted Answer

x > 2

Answer

x < 2

Answer

x > 1

Answer

x < 1

Question 14

Which expression represents the sum of twice a number and 5?

Accepted Answer

2x + 5

Answer

5 + 2x

Answer

2(x + 5)

Answer

5(2 + x)

Question 15

What is the domain of the function: f(x) = 1/x?

Accepted Answer

All real numbers except 0

Answer

All real numbers

Answer

All positive real numbers

Answer

All negative real numbers

Question 16

Which of the following is a quadratic equation?

Accepted Answer

x^2 - 4x + 3 = 0

Answer

x + 2 = 5

Answer

x^3 - 2x + 1 = 0

Answer

2x - 5y = 10

Question 17

Factorise the expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

(x - 3)(x - 3)

Answer

(x + 9)(x - 1)

Question 18

Graph the function: f(x) = |x - 1|

Accepted Answer

A V-shaped graph with vertex at (1, 0).

Answer

A U-shaped graph with vertex at (1, 0).

Answer

A line with a slope of 1.

Answer

A parabola with vertex at (1, 0).

Question 19

Identify the linear equation among the given options:

Accepted Answer

y = 2x + 1

Answer

y^2 = 4x

Answer

y = sin(x)

Answer

y = 1/x

Question 20

Solve the equation: 3x - 5 = 10

Accepted Answer

x = 7

Answer

x = 3

Answer

x = 5

Answer

x = 9

Question 21

Calculate the gradient of the line defined by the equation y = -2x + 3:

Accepted Answer

-2

Answer

2

Answer

3

Answer

4

Question 22

Translate the following statement into an inequality: 'The difference of x and 5 is less than 12'.

Accepted Answer

x - 5 < 12

Answer

x - 5 > 12

Answer

5 - x > 12

Answer

5 - x < 12

Question 23

Find the equation of the line with a gradient of -1 and a y-intercept of 4.

Accepted Answer

y = -x + 4

Answer

y = x + 4

Answer

y = -x - 4

Answer

y = x - 4

Question 24

Determine the domain of the function f(x) = sqrt(9 - x^2).

Accepted Answer

x ≤ -3 or x ≥ 3

Answer

x < -3 or x > 3

Answer

x ≥ -3 and x ≤ 3

Answer

x > -3 and x < 3

Question 25

Solve the quadratic equation by factorising: x^2 - 7x + 12 = 0.

Accepted Answer

x = 3 or x = 4

Answer

x = -3 or x = -4

Answer

x = 2 or x = 6

Answer

x = -2 or x = -6

Question 26

Which of the following is the graph of the inequality: y > x^2 - 1

Accepted Answer

Quadratic curve above y = x^2 - 1

Answer

Quadratic curve below y = x^2 - 1

Answer

Linear line above y = x^2 - 1

Answer

Linear line below y = x^2 - 1

Question 27

Which of the following is a rational function?

Accepted Answer

j(x) = x/(x + 1)

Answer

f(x) = x^2 + 2x - 3

Answer

g(x) = sin(x)

Answer

h(x) = sqrt(x)

Question 28

Which of the following is the range of the function: g(x) = |x + 2|?

Accepted Answer

y ≥ 0

Answer

y ≤ 0

Answer

y < 0

Answer

y > 2

Question 29

To ensure the accuracy of your solutions, which method should you use when solving equations and inequalities?

Accepted Answer

Substitute the solution back into the original problem

Answer

Use a graphing calculator to check the solution

Answer

Apply the quadratic formula to verify the solution

Question 30

Identify the function represented by the following equation: y = 3x² - 2x + 1

Accepted Answer

Quadratic function

Answer

Trigonometric function

Answer

Linear function

Answer

Exponential function

Question 31

Identify the statement that is NOT a property of a linear function:

Accepted Answer

The graph is a parabola

Answer

The y-intercept is the value of f(0)

Answer

The graph is a straight line

Answer

The slope is constant

Question 32

Factor the quadratic expression: x² - 5x + 6

Accepted Answer

(x - 2)(x - 3)

Answer

(x - 2)(x + 3)

Answer

(x + 2)(x - 3)

Answer

(x + 2)(x + 3)

Question 33

Find the equation of the line that passes through the points (2, 3) and (4, 7)

Accepted Answer

y = 2x + 1

Answer

y = x - 1

Answer

y = -2x + 7

Answer

y = x + 5

Question 34

Identify the rational function from the given options:

Accepted Answer

f(x) = (x² + 2)/(x - 1)

Answer

f(x) = e^x

Answer

f(x) = sin(x)

Answer

f(x) = √x

Question 35

Simplify the expression: 2x(x - 3)

Accepted Answer

2x^2 - 6x

Answer

x^2 - 3

Answer

x^2 - 6x + 9

Answer

2x^2 + 6x

Question 36

Which inequality represents the statement "x is less than or equal to 5"?

Accepted Answer

x ≤ 5

Answer

x > 5

Answer

x ≥ 5

Answer

x < 5

Question 37

Which function has a positive y-intercept?

Accepted Answer

f(x) = 2x + 3

Answer

k(x) = -2x

Answer

g(x) = -x + 2

Answer

h(x) = x - 5

Question 38

Solve the quadratic equation: x^2 - 5x + 6 = 0

Accepted Answer

x = 2 or x = 3

Answer

x = 1 or x = 6

Answer

x = -2 or x = -3

Answer

x = -1 or x = -6

Question 39

What is the domain of the function f(x) = 1/(x - 2)?

Accepted Answer

All real numbers except x = 2

Answer

x ≥ 2

Answer

All real numbers

Answer

x ≤ 2

Question 40

Which of the following is an inequality that represents the statement 'x is less than or equal to 5'?

Accepted Answer

x ≤ 5

Answer

x ≥ 5

Answer

x > 5

Answer

x < 5

Question 41

Which of the following is a quadratic function?

Accepted Answer

f(x) = x^2 + 2x - 3

Answer

f(x) = 3x - 2

Answer

f(x) = x + 2

Question 42

Find the domain of the function f(x) = 1/(x - 2):

Accepted Answer

All real numbers except 2

Answer

All negative real numbers

Answer

All real numbers

Answer

All positive real numbers

Question 43

Which of the following is the inverse of the function f(x) = 2x + 1?

Accepted Answer

f^-1(x) = (x - 1)/2

Answer

f^-1(x) = 2x - 1

Answer

f^-1(x) = -2x - 1

Answer

f^-1(x) = (x + 1)/2

Question 44

Find the range of the function f(x) = |x - 1|:

Accepted Answer

[0, ∞)

Answer

(-∞, 0]

Answer

[1, ∞)

Answer

(-∞, 1]

Question 45

Simplify the expression 2(x + 3) - 4(x - 2).

Accepted Answer

-2x + 14

Answer

-2x - 2

Answer

6x - 14

Answer

-6x + 2

Question 46

Find the equation of the line passing through the points (2, 1) and (4, 5).

Accepted Answer

y = 2x - 3

Answer

y = x + 1

Answer

y = x - 1

Answer

y = -2x + 5

Question 47

Determine the domain of the function f(x) = √(x - 2).

Accepted Answer

x ≥ 2

Answer

x > 2

Answer

x ≤ 2

Answer

All real numbers

Question 48

Evaluate f(-1) for the function f(x) = x^2 + 2x - 3.

Accepted Answer

-4

Answer

0

Answer

4

Answer

-2

Question 49

The graph of the function y = x^2 + 1 is translated 2 units to the left. What is the equation of the new graph?

Accepted Answer

y = (x + 2)^2 + 1

Answer

y = x^2 - 1

Answer

y = (x - 2)^2 + 1

Answer

y = x^2 + 3

Question 50

Factorise the expression x^2 - 4x - 5.

Accepted Answer

(x - 5)(x + 1)

Answer

(x - 2)(x - 3)

Answer

(x + 2)(x - 3)

Answer

(x - 1)(x + 5)

Question 51

Find the roots of the quadratic equation x^2 - 6x + 8 = 0.

Accepted Answer

x = 2, x = 4

Answer

x = -2, x = -4

Answer

x = 1, x = 8

Answer

x = -1, x = -8

Question 52

Which of the following represents the graph of the inequality y > 2x - 1?

Accepted Answer

A shaded area above a line

Answer

A shaded area below a line

Answer

A solid line

Question 53

Determine the inverse of the function f(x) = 2x + 1.

Accepted Answer

f^-1(x) = (x - 1) / 2

Answer

f^-1(x) = -2x + 1

Answer

f^-1(x) = 1 / (2x + 1)

Answer

f^-1(x) = 2x - 1

Question 54

Factorise the expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)^2

Answer

x(x - 9)

Answer

(x + 9)(x - 1)

Question 55

Solve the system of equations: x + y = 5 and x - y = 1

Accepted Answer

x = 3, y = 2

Answer

x = 3, y = -2

Answer

x = 1, y = 4

Answer

x = 2, y = 3

Question 56

Determine the equation of the circle with centre (2, -3) and radius 5

Accepted Answer

(x - 2)^2 + (y + 3)^2 = 25

Answer

(x + 2)^2 + (y - 3)^2 = 5

Answer

(x - 3)^2 + (y + 2)^2 = 25

Answer

(x + 3)^2 + (y - 2)^2 = 5

Question 57

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

Accepted Answer

x = 3

Answer

x = 2

Answer

x = 8

Question 58

Which of the following is the graph of the function y = x^2 - 4?

Accepted Answer

A parabola that opens upwards, intersecting the y-axis at (0, -4)

Answer

A straight line with a positive slope

Answer

A parabola that opens downwards, intersecting the y-axis at (0, -4)

Question 59

Simplify the expression 3(2x + 5) - 4(x - 1)

Accepted Answer

2x + 19

Answer

6x + 11

Answer

2x + 11

Answer

6x + 19

Question 60

Find the value of x that satisfies the inequality 3x - 2 > 7.

Accepted Answer

x > 3

Answer

x > -3

Answer

x < -3

Answer

x < 3

Question 61

The inverse function of f(x) = 3x + 2 is:

Accepted Answer

f⁻¹(x) = (x - 2) / 3

Answer

f⁻¹(x) = 3x - 2

Answer

f⁻¹(x) = -3x - 2

Answer

f⁻¹(x) = (x + 2) / 3

Question 62

Simplify the expression: (2x + 3y)²

Accepted Answer

4x² + 12xy + 9y²

Answer

4x² + 6xy + 9y²

Answer

2x² + 6xy + 3y²

Answer

4x² + 9y²

Question 63

What is the solution to the inequality: 2x + 4 > 10

Accepted Answer

x > 3

Answer

x > -3

Answer

x < 3

Question 64

Find the equation of the line that passes through the points (2, 3) and (4, 7).

Accepted Answer

y = 2x - 1

Answer

y = x - 1

Answer

y = x + 1

Answer

y = -2x + 7