Algebra Quizzes: Master Algebraic Expressions, Equations, and Inequalities

Question 1

A car rental company charges a base fee of $25 plus $0.30 for each kilometer driven. Write an equation that shows the total cost of renting the car, y, in terms of the number of kilometers driven, x.

Accepted Answer

y = 0.30x + 25

Answer

y = 0.30 + 25x

Answer

y = 25x + 0.30

Answer

y = 25 - 0.30x

Question 2

Solve the following system of equations:

x + y = 5
x^2 + y^2 = 13

Accepted Answer

(x, y) = (2, 3)

Answer

(x, y) = (3, 2)

Answer

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

Answer

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

Question 3

Quadratic equations have a squared variable term. Which of the following is a quadratic equation?

Accepted Answer

x squared plus 2x minus 3 equals 0

Answer

x plus 2 equals 3

Answer

y equals 3x plus 1

Answer

x is greater than 2

Question 4

Solving simultaneous equations involves finding values of variables that satisfy all equations. Solve the simultaneous equations: x plus y equals 5 and x minus y equals 1

Accepted Answer

x equals 3, y equals 2

Answer

x equals 2, y equals 3

Answer

x equals 1, y equals 4

Answer

x equals 4, y equals 1

Question 5

Which of the following is equivalent to (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 6

Which of the following is a valid equation to find the area of a triangle?

Accepted Answer

A = 1/2 * b * h

Answer

A = b * h

Answer

A = 2 * b * h

Answer

A = 1/4 * b * h

Question 7

Solve for x in the equation: 2x - 5 = 11

Accepted Answer

x = 8

Answer

x = 3

Answer

x = 16

Answer

x = 22

Question 8

Which of the following is a quadratic equation?

Accepted Answer

x^2 + 2x - 3 = 0

Answer

x + 2 = 0

Answer

y = 3x - 1

Answer

log(x) = 5

Question 9

Solve the linear equation: 5x - 2 = 13

Accepted Answer

x = 4

Answer

x = 3

Answer

x = 5

Answer

x = 6

Question 10

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

Accepted Answer

2x^2 + x - 6

Answer

2x^2 - x - 6

Answer

2x^2 + 4x - 6

Answer

2x^2 - 4x - 6

Question 11

Find the equation of the line that passes through the points (1, 3) and (-2, 5).

Accepted Answer

y = -2x + 5

Answer

y = 2x + 1

Answer

y = -x + 4

Answer

y = x + 2

Question 12

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

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = 4, y = 1

Answer

x = 1, y = 4

Question 13

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 14

Graph the linear equation: y = -2x + 3

Accepted Answer

A line with a slope of -2 and a y-intercept of 3

Answer

A line with a slope of 2 and a y-intercept of 3

Answer

A line with a slope of -2 and a y-intercept of -3

Answer

A line with a slope of 2 and a y-intercept of -3

Question 15

Solve the inequality: x - 3 < 2

Accepted Answer

x < 5

Answer

x > 5

Answer

x < -5

Answer

x > -5

Question 16

Which of the following is the equation of a circle with center (2, 3) and radius 5?

Accepted Answer

(x - 2)² + (y - 3)² = 25

Answer

(x + 2)² + (y - 3)² = 5

Answer

(x - 2)² + (y + 3)² = 5

Answer

(x + 2)² + (y + 3)² = 25

Question 17

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

Accepted Answer

2x + 7y

Answer

2x + 3y

Answer

4x + 7y

Answer

4x + 3y

Question 18

Graph the linear 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, 2) with a gradient of 1.

Answer

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

Answer

A circle with a radius of 1 centered at (0, 1).

Question 19

Which of the following is an inequality?

Accepted Answer

x > 3

Answer

x = 5

Answer

x - 2 = 0

Answer

x + y = 10

Question 20

Solve the inequality: x - 4 < 10

Accepted Answer

x < 6

Answer

x > 6

Answer

x < 14

Answer

x > 14

Question 21

Rearrange the formula: A = P(1 + r)^t into the form P =

Accepted Answer

P = A/(1 + r)^t

Answer

P = A(1 + r)^t

Answer

P = A(1 - r)^t

Answer

P = A/(1 - r)^t

Question 22

Which of the following is a quadratic equation?

Accepted Answer

x^2 - 3x + 2 = 0

Answer

2x + 5 = 0

Answer

y = mx + c

Answer

sin(x) = 0.5

Question 23

Solve for x: 2x - 5 = 11

Accepted Answer

x = 8

Answer

x = 3

Answer

x = -3

Answer

x = 16

Question 24

Graph the linear equation y = 2x + 1.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 25

Which of the following is the equation of the line that passes through the points (2, 3) and (-1, 5)?

Accepted Answer

y = -x + 5

Answer

y = x + 1

Answer

y = -x + 1

Answer

y = x - 5

Question 26

Which of the following does NOT represent an algebraic expression?

Accepted Answer

x = 5

Answer

x^2 - 4

Answer

5 - x

Answer

2x + 3

Question 27

Which inequality is represented by the graph below?

[Image of a number line with an open circle at -2 and a shaded region to the right.]

Accepted Answer

x > -2

Answer

x ≥ -2

Answer

x < -2

Answer

x ≤ -2

Question 28

Determine the slope of the line represented by the equation y = 2x - 1

Accepted Answer

2

Answer

4

Answer

1

Answer

3

Question 29

Graph the linear inequality: y > 2x - 1

Accepted Answer

The solution is the region above the line y = 2x - 1.

Answer

The solution is the region below the line y = 2x - 1.

Answer

The solution is the region on the line y = 2x - 1.

Question 30

Which of these is an inequality?

Accepted Answer

x > 5

Answer

x = 5

Answer

x + 5 = 10

Answer

2x + 5

Question 31

Solve the inequality: 2x - 5 < 10

Accepted Answer

x < 7.5

Answer

x < 2.5

Answer

x > 7.5

Answer

x > 2.5

Question 32

Which of these is a quadratic equation?

Accepted Answer

x^2 + 2x - 3 = 0

Answer

y = 2x + 1

Answer

x + 2 = 3

Answer

2x - 5 < 10

Question 33

Factor the expression: x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x - 2)^2

Answer

x(x - 4)

Answer

(x + 2)^2

Question 34

Simplify the algebraic expression: 4a + 2b - a + 3b.

Accepted Answer

3a + 5b

Answer

3a + b

Answer

5a - b

Answer

5a + 5b

Question 35

Solve the linear equation: 2x - 7 = 15.

Accepted Answer

x = 11

Answer

x = 8

Answer

x = -4

Answer

x = 4

Question 36

The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. If the perimeter of a rectangle is 20 centimeters and its width is 4 centimeters, what is its length?

Accepted Answer

6 centimeters

Answer

12 centimeters

Answer

8 centimeters

Answer

5 centimeters

Question 37

Identify the slope of the line represented by the equation y = -2x + 3.

Accepted Answer

-2

Answer

3

Answer

2

Answer

-3

Question 38

Which value of x satisfies the equation x² - 9 = 0?

Accepted Answer

x = 3

Answer

x = -9

Answer

x = 6

Answer

x = 0

Question 39

A taxi company charges a base fare of £5 plus £1.50 per mile. Which equation represents the total cost (C) of a ride in terms of the number of miles (m)?

Accepted Answer

C = 1.5m + 5

Answer

C = 5m + 1.5

Answer

C = 5m

Answer

C = 6.5m

Question 40

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

Accepted Answer

x + 6y

Answer

-x + 4y

Answer

x + 4y

Answer

-x + 6y

Question 41

Solve for x: 2x + 5 = 11

Accepted Answer

x = 3

Answer

x = 5

Answer

x = 4

Answer

x = 2

Question 42

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

Accepted Answer

2

Answer

1

Answer

-2

Answer

-3

Question 43

A rectangular garden has a perimeter of 20 cm. If the length of the garden is 7 cm, calculate its width

Accepted Answer

6.5 cm

Answer

7 cm

Answer

5.5 cm

Answer

10 cm

Question 44

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

Accepted Answer

x² - x - 6

Answer

x² - 5x - 6

Answer

x² + 5x - 6

Answer

x² + x - 6

Question 45

Factor the following expression: x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x - 3)

Answer

(x - 9)(x - 9)

Answer

(x + 3)(x + 3)

Question 46

Solve the following system of linear equations using any method: 2x + y = 7 and x - y = 2

Accepted Answer

x = 3, y = 1

Answer

x = 4, y = -1

Answer

x = 1, y = 5

Answer

x = 2, y = 3

Question 47

Which value of x satisfies the inequality: 3x - 2 > 7?

Accepted Answer

x > 3

Answer

x = 3

Answer

x < 3

Answer

x > -3

Question 48

A phone call costs £0.50 for the first minute and £0.20 for each additional minute. Write an algebraic equation that represents the total cost (C) of a phone call lasting (t) minutes.

Accepted Answer

C = 0.50 + 0.20(t - 1)

Answer

C = 0.50 - 0.20(t - 1)

Answer

C = 0.20 + 0.50(t - 1)

Answer

C = 0.50 + 0.20t

Question 49

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

Accepted Answer

-2x + 5y

Answer

5xy

Answer

6xy

Answer

2x - y

Question 50

Solve for x: 3(x - 2) = 12

Accepted Answer

6

Answer

2

Answer

4

Answer

8

Question 51

Find the value of x that satisfies the inequality: 2x - 5 < 11

Accepted Answer

x < 8

Answer

x < 3

Answer

x > 3

Answer

x > 8

Question 52

Expand the brackets: (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 53

Factorise the expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)^2

Answer

(x + 3)^2

Answer

(x + 9)(x - 9)

Question 54

Solve the equation: x^2 + 4x - 5 = 0

Accepted Answer

x = 1 or x = -5

Answer

x = 3 or x = -3

Answer

x = 2 or x = -2

Answer

x = 4 or x = -4

Question 55

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

Accepted Answer

y = 2x + 1

Answer

y = x + 3

Answer

y = 2x - 1

Question 56

Graph the inequality: y ≤ 2x + 1

Accepted Answer

A shaded region below the line y = 2x + 1

Answer

A shaded region to the left of the line y = 2x + 1

Answer

A shaded region above the line y = 2x + 1

Question 57

Which of the following is NOT a property of an algebraic expression?

Accepted Answer

It can be simplified to a single number

Answer

It contains variables

Answer

It can involve operations such as addition and multiplication

Answer

It can be evaluated for a given value of the variables

Question 58

What is the degree of the polynomial: 3x^2 - 2x + 1?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 59

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

Accepted Answer

5x - 12

Answer

3x + 6

Answer

x^2 - 9

Question 60

Solve for x: 3x + 5 = 17

Accepted Answer

4

Answer

7

Answer

5

Answer

6

Question 61

Which of the following is equivalent to 2x - y = 5?

Accepted Answer

y = 2x - 5

Answer

x = 2y + 5

Answer

y = 5 - 2x

Question 62

Factorise the expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x + 9)

Answer

(x + 9)(x - 9)

Answer

Cannot be factorised

Question 63

Expand the brackets: (2x + 3)(x - 1)

Accepted Answer

2x^2 - 2x + 3x - 3

Answer

4x^2 - 6x + 3

Answer

x^2 - 2x + 3

Answer

2x^2 + 4x - 3

Question 64

Which of the following is the equation of the line passing through the points (2, 3) and (-1, 1)?

Accepted Answer

y = 2x + 1

Answer

y = 2x - 1

Answer

y = x + 3

Answer

y = -x + 5