Algebra Quizzes: Master Equations, Expressions, and Inequalities

Question 1

Find the value of x in the equation: 2x - 5 = 15

Accepted Answer

x = 10

Answer

x = 5

Answer

x = 15

Answer

x = 20

Question 2

In a basket of fruits, let's represent the number of apples as 'x' and the number of oranges as 'y'. Write a simple math expression that shows the total number of fruits in the basket.

Accepted Answer

x + y

Answer

x - y

Answer

x * y

Answer

x / y

Question 3

A rectangular garden measures 5 meters more in length than in width. If its perimeter is 30 meters, what is the width of the garden?

Accepted Answer

10 meters

Answer

5 meters

Answer

15 meters

Question 4

Simplify the expression: 3x + 2x - x

Accepted Answer

2x

Answer

4x

Answer

5x

Answer

6x

Question 5

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

Accepted Answer

x ≥ 5

Answer

x < 5

Answer

x > 5

Answer

x ≤ 5

Question 6

Which of the following is equivalent to the expression: 3(2x - 1)?

Accepted Answer

6x - 3

Answer

6x + 3

Answer

5x - 3

Answer

5x + 3

Question 7

Which of the following is an example of a quadratic equation?

Accepted Answer

x^2 = 9

Answer

x + 2 = 5

Answer

x - 3 = 0

Answer

2x + 1 > 0

Question 8

Factor the expression: x² - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x - 2)(x - 2)

Answer

(x + 4)(x - 4)

Answer

Cannot be factored

Question 9

Which term is not part of the algebraic expression 3x + 2y - 5?

Accepted Answer

y

Answer

3x

Answer

2y

Answer

5

Question 10

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

Accepted Answer

3x + 6

Answer

x + 6

Answer

x - 6

Answer

3x - 6

Question 11

The perimeter of a rectangle is 24 cm. If its length is 8 cm, what is its width?

Accepted Answer

6 cm

Answer

4 cm

Answer

8 cm

Answer

16 cm

Question 12

Factorise the expression: x² - 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x - 4)(x + 4)

Answer

(x - 1)(x - 1)

Answer

(x + 2)(x + 2)

Question 13

Simplify the expression 2x + 3x - x

Accepted Answer

4x

Answer

0

Answer

x

Answer

6x

Question 14

Solve the equation: 2(x - 5) = 10

Accepted Answer

x = 7

Answer

x = 3

Answer

x = 10

Answer

x = 15

Question 15

Which of these is the solution to the inequality x + 3 < 7?

Accepted Answer

x < 4

Answer

x > 4

Answer

x < 10

Answer

x > 10

Question 16

Which of these graphs represents the equation y = 2x + 1?

Accepted Answer

A straight line passing through (0, 1) with a slope of 2

Answer

A straight line passing through (0, 2) with a slope of 1

Answer

A parabola opening upwards with vertex at (0, 1)

Answer

A circle with center (0, 1) and radius 2

Question 17

Which of these is a linear equation?

Accepted Answer

y = 2x + 3

Answer

y = x^2 + 2x + 1

Answer

y = 1/x

Answer

y = sin(x)

Question 18

What is the value of x in the equation: In the equation 2x - 5 = 15, isolate the variable x on one side of the equation.

Accepted Answer

10

Answer

5

Answer

-10

Answer

-5

Question 19

Simplify the expression: To simplify the expression (2x + 3)(x - 5), use the FOIL method.

Accepted Answer

2x^2 - 7x - 15

Answer

2x^2 - 10x + 3

Answer

x^2 - 10x + 3

Answer

x^2 - 7x - 15

Question 20

Factorise the expression: To factorise the expression x^2 - 9, find two numbers that multiply to -9 and add to 0.

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x - 3)

Answer

(x + 9)(x - 9)

Answer

(x + 3)(x + 3)

Question 21

What is the gradient of the line y = 2x + 1? The gradient of a line is the ratio of the change in y to the change in x.

Accepted Answer

2

Answer

1

Answer

-1

Answer

-2

Question 22

Which of the following is an example of an algebraic expression?

Accepted Answer

5x + 2

Answer

x equals 5

Answer

x is greater than 5

Answer

5 plus 2

Question 23

Simplify the expression: 2x plus 3x minus x

Accepted Answer

4x

Answer

2x

Answer

x

Answer

0

Question 24

Use the distributive property to expand: 3 multiplied by (x plus 2)

Accepted Answer

3x plus 6

Answer

x plus 6

Answer

3x plus 2

Answer

3x plus 8

Question 25

Which of the following represents an algebraic expression?

Accepted Answer

5 + x

Answer

x = 5

Answer

x > 5

Answer

Five apples

Question 26

Find the value of x that makes the inequality true: x - 3 > 5

Accepted Answer

x = 8

Answer

x = 2

Answer

x = 10

Answer

x = 12

Question 27

Which of the following is a variable?

Accepted Answer

x

Answer

5

Answer

ten

Answer

London

Question 28

Which of the following describes the graph of the equation: y = 2x + 1?

Accepted Answer

A straight line with a slope of 2 and a y-intercept of 1

Answer

A straight line with a slope of 1 and a y-intercept of 2

Answer

A parabola with a vertex at (0, 1)

Answer

A circle with a radius of 1

Question 29

What are the solutions to the quadratic equation: x^2 - 5x + 6 = 0?

Accepted Answer

x = 2, x = 3

Answer

x = -2, x = -3

Answer

x = 4, x = 5

Answer

There are no real solutions

Question 30

An inequality compares two values. Which of the following is NOT an inequality?

Accepted Answer

x = 7

Answer

x > 5

Answer

x < 10

Answer

x ≠ 3

Question 31

Expanding brackets means multiplying a number outside the brackets by each term inside the brackets. Which of the following is equivalent to the expression 5(x + 2)?

Accepted Answer

5x + 10

Answer

x + 10

Answer

5x - 10

Answer

5x + 2

Question 32

Algebra has certain properties that make it easier to solve expressions. Which of the following is NOT a property of algebra?

Accepted Answer

Randomness property

Answer

Commutative property

Answer

Distributive property

Answer

Associative property

Question 33

Solve for x: 2x + 5 = 13

Accepted Answer

x = 4

Answer

x = 3

Answer

x = 5

Answer

x = 6

Question 34

Which of the following is equivalent to the inequality 2x - 5 < 10?

Accepted Answer

x < 7.5

Answer

x > 7.5

Answer

x < 2.5

Answer

x > 2.5

Question 35

Translate the phrase 'twice a number minus 3' into an algebraic expression.

Accepted Answer

2n - 3

Answer

3 - 2n

Answer

2n + 3

Answer

3 + 2n

Question 36

Which of the following is the graph of the equation y = 2x + 1?

Accepted Answer

A straight line with a slope of 2

Answer

A parabola with a vertex at (0, 1)

Answer

A circle with a radius of 1

Answer

A hyperbola with asymptotes y = 2x

Question 37

Which of the following is an algebraic expression?

Accepted Answer

2x + 5

Answer

x = 10

Answer

The sum of two numbers is 15

Answer

The product of a number and 7 is greater than 20

Question 38

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

Accepted Answer

11x - 6

Answer

8x - 1

Answer

8x + 1

Answer

11x + 6

Question 39

Solve the equation: x + 7 = 15

Accepted Answer

x = 8

Answer

x = 22

Answer

x = 1

Answer

x = -8

Question 40

Translate the phrase 'The difference between twice a number and 5' into an algebraic expression.

Accepted Answer

2n - 5

Answer

5 - 2n

Answer

2n + 5

Answer

5 + 2n

Question 41

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

Accepted Answer

x^2 - x - 6

Answer

x^2 + x - 6

Answer

x^2 - 5x - 6

Answer

x^2 + 5x - 6

Question 42

Factorise the expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

(x - 3)^2

Answer

(x + 3)^2

Question 43

Which of the following is an algebraic expression that shows the sum of x and 5?

Accepted Answer

x + 5

Answer

x = 5

Answer

x < 5

Answer

x > 5

Question 44

What is the value of x in the equation: x - 5 = 7?

Accepted Answer

12

Answer

5

Answer

10

Answer

15

Question 45

Which of the following is an inequality that represents the statement "The number y is less than 5"?

Accepted Answer

y < 5

Answer

y = 5

Answer

y > 5

Answer

y + 5 = 10

Question 46

Which of the following represents the area of a triangle?

Accepted Answer

bh/2

Answer

bh

Answer

l + w

Answer

lw

Question 47

Solve for y: 3y - 5 ≤ 10

Accepted Answer

y ≤ 5

Answer

y ≥ 5

Answer

y < 5

Answer

y > 5

Question 48

Solve the inequality: 2x - 5 > 7

Accepted Answer

x > 6

Answer

x > 1

Answer

x < 1

Answer

x < 6

Question 49

Which of the following is NOT a variable?

Accepted Answer

10

Answer

x

Answer

y

Answer

a

Question 50

Evaluate the expression: 3x²y when x = 2 and y = -1

Accepted Answer

-6

Answer

6

Answer

12

Answer

-12

Question 51

Solve the equation: 2x - 5 = 7

Accepted Answer

x = 6

Answer

x = 2

Answer

x = 12

Answer

x = -2

Question 52

Which of the following is equivalent to the expression 2(x + 3)?

Accepted Answer

2x + 6

Answer

2x - 6

Answer

x + 6

Answer

x - 6

Question 53

Which of the following is the graph of the equation y = 2x + 1?

Accepted Answer

A straight line passing through (0, 1) with a gradient of 2

Answer

A straight line passing through (1, 0) with a gradient of 2

Answer

A parabola opening upwards with a vertex at (0, 1)

Answer

A parabola opening downwards with a vertex at (1, 0)

Question 54

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

Accepted Answer

x - 6

Answer

5x - 3

Answer

-x - 3

Answer

-5x + 3

Question 55

Solve the equation: x + 5 = 12

Accepted Answer

x = 7

Answer

x = 5

Answer

x = 17

Answer

x = 12

Question 56

Graph the inequality: x - 2 > 5 on a number line.

Accepted Answer

A shaded region to the right of x = 7

Answer

A line at x = 7

Answer

A line at x = -3

Answer

A shaded region to the left of x = 7

Question 57

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

Accepted Answer

y = 2x + 1

Answer

y = x^2 + 2

Answer

y = 5

Answer

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

Question 58

Find the gradient of the line represented by the equation y = 3x - 2.

Accepted Answer

3

Answer

-2

Answer

2

Answer

-3

Question 59

Expand the brackets in the expression: (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 60

Which of the following is an algebraic expression?

Accepted Answer

A number added to a variable

Answer

A statement that two expressions are equal

Answer

A statement that one expression is greater than another

Answer

A value that does not change

Question 61

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

Accepted Answer

x ≥ 5

Answer

x ≤ 5

Answer

x = 5

Answer

x > 5

Question 62

Which of the following is a variable?

Accepted Answer

x

Answer

5

Answer

y + 3

Answer

Twenty-five

Question 63

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

Accepted Answer

8

Answer

12

Answer

5

Answer

15

Question 64

Which inequality represents 'x is greater than 5'?

Accepted Answer

x > 5

Answer

5 > x

Answer

x < 5

Answer

5 < x