Algebraic Expressions and Equations: Master Algebra with Online Quizzes

Question 1

Factorise the expression x^2 - 4:

Accepted Answer

(x + 2)(x - 2)

Answer

(x - 2)^2

Answer

(x - 4)(x + 1)

Answer

(x + 4)(x - 1)

Question 2

Which of the following is the solution to the linear inequality: 3x - 5 < 10?

Accepted Answer

x < 5

Answer

x > 5

Answer

x < -5

Answer

x > -5

Question 3

Simplify the expression: (x + y)(x - y)

Accepted Answer

x^2 - y^2

Answer

x + y

Answer

x - y

Answer

x^2 + y^2

Question 4

Expand the expression: (2x + 3y)^2

Accepted Answer

4x^2 + 12xy + 9y^2

Answer

4x^2 + 9y^2

Answer

2x^2 + 6xy + 3y^2

Answer

4x^2 - 12xy + 9y^2

Question 5

Which of the following expressions is equivalent to (x + y)^3?

Accepted Answer

x^3 + 3x^2y + 3xy^2 + y^3

Answer

x^3 + y^3

Answer

x^3 - 3x^2y + 3xy^2 - y^3

Answer

x^3 - y^3

Question 6

Solve the equation: 2x + 5 = 13

Accepted Answer

x = 6

Answer

x = 4

Answer

x = 8

Answer

x = 10

Question 7

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

Accepted Answer

x = 2, 3

Answer

x = -2, -3

Answer

x = 1, 6

Answer

x = -1, -6

Question 8

Which of the following is a polynomial with degree 3?

Accepted Answer

x^3 - 2x + 1

Answer

2x

Answer

3x^2 + 5x - 1

Answer

1 / x

Question 9

Identify the number of terms in the expression: 3x^2 + 5x - 1 + 7x^3 - 2

Accepted Answer

5

Answer

2

Answer

3

Answer

4

Question 10

Solve the equation 2x + 5 = 13:

Accepted Answer

x = 4

Answer

x = 3

Answer

x = 5

Answer

x = 6

Question 11

Solve the simultaneous equations:
x + y = 5
x - y = 1

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = 5, y = 0

Answer

No solution exists

Question 12

Factor the following expression: **2x^2 - 5x + 3**

Accepted Answer

(x - 1)(2x - 3)

Answer

(x + 1)(2x - 3)

Answer

(x - 3)(2x + 1)

Answer

(x + 3)(2x - 1)

Question 13

Which of the following is the equation of a circle with center at **(0, 0)** and radius **5**?

Accepted Answer

x^2 + y^2 = 25

Answer

x^2 + y^2 = 10

Answer

x^2 + y^2 = 50

Answer

x^2 + y^2 = 100

Question 14

Solve the inequality x - 3 < 7:

Accepted Answer

x < 10

Answer

x > 10

Answer

x < 4

Question 15

Find the value of x when x^2 = 25, and justify your answer.

Accepted Answer

5, -5

Answer

-5

Answer

5

Question 16

Which of the following expressions is equivalent to 3x + 5?

Accepted Answer

5 + 3x

Answer

5 - 3x

Answer

x + 3 + 5

Answer

x - 5 + 3

Question 17

Which of the following is the quadratic equation corresponding to the parabola with vertex (2, -3)?

Accepted Answer

y = (x - 2)^2 - 3

Answer

y = (x + 3)^2 - 2

Answer

y = (x + 2)^2 - 3

Answer

y = (x - 3)^2 - 2

Question 18

Factorise the expression: x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)²

Answer

x(x - 9)

Answer

(x + 3)²

Question 19

Solve the inequality: x - 2 > 5

Accepted Answer

x > 7

Answer

x > 3

Answer

x < 7

Answer

x < 3

Question 20

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

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = 1, y = 4

Answer

x = 4, y = 1

Question 21

Which of the following is a rational expression?

Accepted Answer

x/(x-2)

Answer

x²/(x-2)

Answer

x/(x²+2)

Answer

(x-2)/x

Question 22

Simplify the following expression: 2x(x + 3) - (x - 2)

Accepted Answer

2x^2 + 6x - x + 2

Answer

x^2 + 7x + 2

Answer

x^2 + 6x - x + 2

Answer

2x^2 + 7x + 2

Question 23

Expand and simplify: (x - 2)(2x + 3)

Accepted Answer

2x^2 - x - 6

Answer

x^2 - 4x + 6

Answer

2x^2 - 4x + 6

Answer

x^2 - x - 6

Question 24

Factorize the following expression: x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x + 2)^2

Answer

(x - 2)(x - 2)

Answer

(x - 2)^2

Question 25

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

Accepted Answer

2 or 3

Answer

-2 or -3

Answer

1 or 4

Answer

-1 or -4

Question 26

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

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = 1, y = 4

Answer

x = 4, y = 1

Question 27

Solve the following inequality for x: 2x - 5 > 7

Accepted Answer

x > 6

Answer

x > -6

Answer

x < 6

Answer

x < -6

Question 28

Which of the following is NOT an operation that can be performed on algebraic expressions?

Accepted Answer

Division by zero

Answer

Subtraction

Answer

Multiplication

Answer

Addition

Question 29

What is the coefficient of x^2 in the expression 2x^2 - 3x + 5?

Accepted Answer

2

Answer

-3

Answer

5

Answer

1

Question 30

Which of the following is the most appropriate expression to represent the area of a rectangle with length (x + 2) and width (x - 1)?

Accepted Answer

(x + 2)(x - 1)

Answer

x(x + 2) - 1

Answer

(x - 1) + (x + 2)

Answer

2x - 1

Question 31

Simplify the expression: 3x + 2y - 5x + 4y

Accepted Answer

x + 6y

Answer

-x + 6y

Answer

x - 6y

Answer

2x + 6y

Question 32

Expand the brackets: (2x - 3)(x + 4)

Accepted Answer

2x^2 + 5x - 12

Answer

2x^2 + x - 12

Answer

2x^2 + 7x - 12

Answer

2x^2 + 7x + 12

Question 33

Factorise the expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x + 3)

Answer

(x + 9)(x - 9)

Answer

(x - 9)(x + 9)

Question 34

Solve the equation: 2x + 5 = 13

Accepted Answer

4

Answer

2

Answer

6

Answer

8

Question 35

Solve the inequality: x - 3 < 7

Accepted Answer

x < 10

Answer

x > 4

Answer

x < 4

Answer

x > 10

Question 36

Solve the simultaneous equations:
    x + y = 5
    x - y = 1

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = -2, y = -3

Answer

x = -3, y = -2

Question 37

Determine the discriminant of the quadratic equation: 2x^2 + 3x - 5 = 0

Accepted Answer

29

Answer

49

Answer

19

Answer

39

Question 38

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

Accepted Answer

x = 2, x = 3

Answer

x = -2, x = -3

Answer

x = 1, x = -6

Answer

x = 1, x = 6

Question 39

Find the vertex of the parabola: y = x^2 - 4x + 3

Accepted Answer

(2, -1)

Answer

(2, 1)

Answer

(1, -2)

Answer

(1, 2)

Question 40

Sketch the graph of the function: f(x) = -x^2 + 2x + 1

Accepted Answer

A parabola opening downwards

Answer

A straight line with a negative gradient

Answer

A straight line with a positive gradient

Answer

A parabola opening upwards

Question 41

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

Accepted Answer

2x^2 - 7x - 15

Answer

2x^2 - 10x - 15

Answer

x^2 - 7x - 15

Answer

x^2 - 10x - 15

Question 42

Factorise the expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

(x + 9)(x - 1)

Question 43

Solve the equation: 2x + 5 = 11

Accepted Answer

3

Answer

4

Answer

5

Answer

2

Question 44

Which of the following is the solution set of the inequality 2x - 3 < 5?

Accepted Answer

x < 4

Answer

x < 1

Answer

x > 4

Question 45

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

Accepted Answer

x = 3, y = 2

Answer

x = 1, y = 4

Answer

x = 4, y = 1

Answer

x = 2, y = 3

Question 46

Which of the following is the equation of the line passing through the points (2, 3) and (5, 7)?

Accepted Answer

y = x + 1

Answer

y = 2x + 1

Answer

y = x - 1

Answer

y = 2x - 1

Question 47

What is the discriminant of the quadratic equation x^2 + 2x + 5 = 0?

Accepted Answer

-16

Answer

4

Answer

-4

Answer

16

Question 48

Which of the following is the solution set of the quadratic equation x^2 - 4x + 4 = 0?

Accepted Answer

{2}

Answer

{} (empty set)

Answer

{0}

Answer

{4}

Question 49

What is the vertex of the parabola y = x^2 - 2x + 1?

Accepted Answer

(1, 0)

Answer

(-1, 0)

Answer

(2, 1)

Answer

(0, 1)

Question 50

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

Accepted Answer

[2, infinity)

Answer

(2, infinity)

Answer

(-infinity, 2]