Algebra Quizzes: Master Algebraic Expressions, Equations, and Inequalities

Question 1

Identify the equation that represents a parabola opening downwards with its vertex at (-2, 3).

Accepted Answer

y = -(x - 2)² + 3

Answer

y = (x + 2)² - 3

Answer

y = -x² + 4x + 3

Answer

y = -2x² + 3

Question 2

In the algebraic expression 2x + 3y - 5, what is the value of the coefficient 3?

Accepted Answer

3

Answer

2

Answer

-5

Answer

y

Question 3

Which of the following represents the inequality 'x is greater than or equal to 5'?

Accepted Answer

x ≥ 5

Answer

x > 5

Answer

x < 5

Answer

x ≤ 5

Question 4

Find the gradient of the line represented by the equation: y = -2x + 5

Accepted Answer

-2

Answer

2

Answer

5

Answer

-5

Question 5

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

Accepted Answer

y = 2x + 3

Answer

y = 2x + 1

Answer

y = x + 3

Answer

y = x + 5

Question 6

Find the solution to the system of equations: y = x + 2 and y = 2x

Accepted Answer

(1, 3)

Answer

(0, 2)

Answer

(2, 4)

Answer

No solution

Question 7

Which of the following is the solution to the inequality x - 3 > 5?

Accepted Answer

x > 2

Answer

x < 2

Answer

x < -2

Answer

x > -2

Question 8

Factorise the algebraic expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 9)

Answer

(x - 3)^2

Answer

(x + 3)^2

Question 9

Identify an algebraic expression.

Accepted Answer

x + 2

Answer

x = 5

Answer

x > 5

Answer

x is a number greater than 5

Question 10

Simplify 3(x + 2).

Accepted Answer

3x + 6

Answer

x + 6

Answer

2x + 6

Answer

3x + 2

Question 11

Solve the equation: 2(x - 3) = 10

Accepted Answer

x = 8

Answer

x = 5

Answer

x = 2

Answer

x = 1

Question 12

The volume of a cone is given by the expression (1/3)πr^2h. What is the height of a cone with a volume of 12π?

Accepted Answer

6

Answer

3

Answer

9

Answer

12

Question 13

Which of the following is an example of a non-linear equation?

Accepted Answer

y = x^2

Answer

x + y = 5

Answer

3x - 6 = 0

Answer

2y + 3 = 7

Question 14

Which graphical representation corresponds to the inequality: x < 2?

Accepted Answer

A shaded region to the left of x = 2

Answer

A line at x = 2 with an open circle

Answer

A line at x = 2 with a closed circle

Answer

A shaded region to the right of x = 2

Question 15

Factorize the mathematical expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

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

Answer

Cannot be factorised

Question 16

Determine the equation for the line that passes through points (2, 3) and (5, 7).

Accepted Answer

y = 2x + 1

Answer

y = x + 1

Answer

y = x - 1

Answer

y = -2x + 1

Question 17

Select the expression that represents an algebraic expression:

Accepted Answer

x + 5

Answer

x = 5

Answer

The value of x is 5

Answer

x is larger than 5

Question 18

Solve the equation: 2x - 7 = 15

Accepted Answer

x = 11

Answer

x = 6

Answer

x = 16

Answer

x = 22

Question 19

Expand the brackets in the expression: 2(x - 3)

Accepted Answer

2x - 6

Answer

2x - 3

Answer

x - 6

Answer

x - 3

Question 20

Which of the following is a quadratic equation?

Accepted Answer

x^2 + 3x + 2 = 0

Answer

x + 2 = 5

Answer

x = 10

Answer

x > 5

Question 21

Factorise the expression x² - 4x + 4

Accepted Answer

(x - 2)²

Answer

(x + 2)²

Answer

(x - 4)(x + 1)

Answer

(x + 4)(x - 1)

Question 22

Solve the equation: x(x + 2) = 0

Accepted Answer

x = 0, x = -2

Answer

x = 2, x = -2

Answer

x = 0

Answer

x = -2

Question 23

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

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = -3, y = -2

Answer

x = -2, y = -3

Question 24

Factorise the expression: x^2 - 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x - 4)^2

Answer

(x + 2)^2

Answer

Cannot be factorised

Question 25

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

Accepted Answer

x^2 - 5x + 6

Answer

x^2 + 5x - 6

Answer

x^2 - x - 6

Answer

x^2 + x - 6

Question 26

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

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = 3, y = -2

Answer

x = 2, y = -3

Question 27

Identify the algebraic expression from the given options:

Accepted Answer

2x + 3

Answer

x equals 5

Answer

2 is greater than x

Answer

The sum of two numbers

Question 28

Simplify the expression: (x plus y) cubed

Accepted Answer

x cubed plus 3x squared y plus 3xy squared plus y cubed

Answer

x cubed plus y cubed

Answer

x cubed plus 3x squared y plus y cubed

Answer

x cubed minus 3x squared y plus 3xy squared minus y cubed

Question 29

Factorise the quadratic expression: x² - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 3)²

Answer

(x + 3)²

Answer

(x + 1)(x - 9)

Question 30

Which equation is a quadratic equation?

Accepted Answer

x² - 5x + 6 = 0

Answer

x + 2 = 5

Answer

x³ + 2x - 1 = 0

Answer

y = 2x + 3

Question 31

Solve the equation: 3(x - 2) + 5 = 16

Accepted Answer

7

Answer

10

Answer

4

Answer

8

Question 32

Which of the following is a quadratic equation?

Accepted Answer

x² - 3x + 2 = 0

Answer

x + 3 = 5

Answer

2x³ - 5x = 7

Question 33

Which of the following is an algebraic expression?

Accepted Answer

2x + 5

Answer

The sum of any two numbers

Answer

5 > 2

Answer

x = 5

Question 34

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

Accepted Answer

x - 5 > 0

Answer

x - 5 < 0

Answer

x + 5 < 0

Answer

x + 5 > 0

Question 35

Factorise the expression: x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x - 2)^2

Answer

(x + 2)^2

Answer

(x - 4)(x + 4)

Question 36

Which of the following is the equation of a straight line with a gradient of 2 and a y-intercept of -1?

Accepted Answer

y = 2x - 1

Answer

y = -2x - 1

Answer

y = x - 2

Answer

y = x + 2

Question 37

Simplify the expression: (2x + 3)(x - 1)

Accepted Answer

2x^2 + x - 3

Answer

2x^2 - x - 3

Answer

2x^2 + 2x + 3

Answer

2x^2 - x + 3

Question 38

Which of the following is equivalent to the inequality x > 3?

Accepted Answer

x - 3 > 0

Answer

3 - x < 0

Answer

x - 3 < 0

Answer

3 - x > 0

Question 39

Factorise the expression: x^2 - 25

Accepted Answer

(x + 5)(x - 5)

Answer

(x + 25)(x - 25)

Answer

(x - 5)^2

Answer

(x + 5)^2

Question 40

Solve the inequality: 2x + 1 > 5

Accepted Answer

x > 2

Answer

x < 2

Answer

x > 1

Question 41

Solve the system of equations: 2x + y = 7, x - y = 1

Accepted Answer

x = 2, y = 3

Answer

x = 3, y = 2

Answer

x = 2, y = -3

Answer

x = -2, y = 3

Question 42

The perimeter of a rectangle is calculated using the formula '2(l + w)', where 'l' represents the length and 'w' represents the width. What is the perimeter of a rectangle with a length of 8cm and a width of 5cm?

Accepted Answer

26cm

Answer

18cm

Answer

13cm

Answer

40cm

Question 43

Solve the equation 3x - 7 = 14 for the value of 'x'.

Accepted Answer

x = 7

Answer

x = 3

Answer

x = 21

Answer

x = -7

Question 44

A taxi company charges a base fare of £2.50 and an additional £1.80 per mile travelled. Which equation correctly represents the total cost 'C' of a ride that covers 'm' miles?

Accepted Answer

C = 1.80m + 2.50

Answer

C = 2.50m + 1.80

Answer

C = 4.30m

Answer

C = (1.80 + 2.50)m

Question 45

Solve the inequality 2x + 5 < 11 for the value of 'x'.

Accepted Answer

x < 3

Answer

x ≥ 3

Answer

x ≤ 3

Answer

x > 3

Question 46

Factorise the expression 6x² - 12xy completely.

Accepted Answer

6x(x - 2y)

Answer

x(6x - 12y)

Answer

6(x² - 2xy)

Answer

3x(2x - 4y)

Question 47

The area of a square is calculated using the expression 's²', where 's' represents the length of a side. If the area of a square is 49cm², what is the length of one side?

Accepted Answer

7cm

Answer

14cm

Answer

24.5cm

Answer

98cm

Question 48

Which of the following is an example of an equation?

Accepted Answer

2x + 5 = 11

Answer

4x² - 9

Answer

x < 3

Answer

2x + 5

Question 49

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

Accepted Answer

-2x + 6y

Answer

-2x - 2y

Answer

8x + 6y

Answer

8x - 2y

Question 50

Which of these values for *x* satisfies the inequality 3x + 2 > 11?

Accepted Answer

x = 4

Answer

x = 3

Answer

x = -1

Answer

x = 2

Question 51

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

Accepted Answer

x² + x - 6

Answer

x² + 5x - 6

Answer

x² - 5x - 6

Answer

x² - 6

Question 52

Factor the expression completely: x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 9)(x - 1)

Answer

(x - 9)(x + 1)

Answer

(x + 9)(x - 1)

Question 53

What is the slope of the line represented by the equation y = 2x + 5?

Accepted Answer

2

Answer

-5

Answer

5

Answer

-2

Question 54

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

Accepted Answer

x = 2, y = 1

Answer

x = 1, y = 2

Answer

x = 3, y = -1

Answer

x = -1, y = 3

Question 55

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

Accepted Answer

2x² - x - 6

Answer

2x² + x - 6

Answer

2x² + 5x - 6

Answer

2x² - 5x - 6

Question 56

Factorise the expression: x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x - 2)^2

Answer

Cannot be factorised

Answer

(x + 2)^2

Question 57

Solve the inequality: 2x - 5 < 11

Accepted Answer

x < 8

Answer

x > 8

Answer

x > 6

Answer

x < 6

Question 58

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