Algebraic Expressions: Master the Basics of Algebra

Question 1

Solve the equation 2x + 5 = 15:

Accepted Answer

x = 10

Answer

x = 5

Answer

x = 15

Answer

x = 20

Question 2

Factorize the expression x^3 - 8:

Accepted Answer

(x - 2)(x^2 + 2x + 4)

Answer

(x + 2)(x^2 - 2x + 4)

Answer

(x - 2)^3

Answer

(x + 2)^3

Question 3

Simplify the expression: (2x^2y)^3

Accepted Answer

8x^6y^3

Answer

8x^5y^2

Answer

8x^4y^3

Answer

8x^3y^4

Question 4

Which of the following is a quadratic equation?

Accepted Answer

x^2 - 4x + 4 = 0

Answer

x + 2 = 5

Answer

x^3 - 2x^2 + x - 1 = 0

Answer

2x - 3y = 6

Question 5

Expand and simplify the expression: (3x - 5)(x + 2)

Accepted Answer

3x^2 + 11x - 10

Answer

3x^2 + x - 10

Answer

6x^2 + 11x - 10

Answer

3x^2 + 10

Question 6

Which of the following is 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 -2 and a y-intercept of -1

Answer

A parabola with a vertex at (0, -1)

Answer

A circle with a radius of 1 and a center at (0, -1)

Question 7

Factorise the expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

(x - 3)^2

Answer

(x + 9)(x - 1)

Question 8

Factorise the expression: x^3 - 8

Accepted Answer

(x + 2)(x^2 - 2x + 4)

Answer

(x - 2)^3

Answer

(x - 2)(x^2 + 2x + 4)

Answer

(x + 2)(x^2 - 4)

Question 9

Factorise the expression: x^4 - 16

Accepted Answer

(x^2 + 4)(x^2 - 4)

Answer

(x + 4)(x^2 - 4)(x - 4)

Answer

(x - 4)(x^2 + 4)(x + 4)

Answer

(x + 4)(x^3 - 4x^2 + 16x - 64)

Question 10

Solve the inequality: x^2 - 4 > 0

Accepted Answer

x < -2 or x > 2

Answer

x > -2 and x < 2

Answer

x < -2 and x > 2

Answer

x > -2 or x < 2

Question 11

If a rectangle has a length of (x + 3) cm and a width of (x - 2) cm, what is its perimeter?

Accepted Answer

4x + 2 cm

Answer

2x + 1 cm

Answer

4x - 2 cm

Answer

2x - 1 cm

Question 12

Which of the following is a quadratic equation?

Accepted Answer

x^2 - 4x + 4 = 0

Answer

x + 2 = 5

Answer

x^3 - 2x^2 + x - 1 = 0

Answer

x^(1/2) - 2 = 0

Question 13

Factorize the expression: x^2 - 4x + 4

Accepted Answer

(x - 2)^2

Answer

(x + 2)^2

Answer

(x - 4)^2

Answer

(x + 4)^2

Question 14

Solve the equation: 2x + 5 = 13

Accepted Answer

x = 4

Answer

x = 3

Answer

x = 5

Answer

x = 6

Question 15

Expand the expression: (x + 2)^3

Accepted Answer

x^3 + 6x^2 + 12x + 8

Answer

x^3 + 3x^2 + 3x + 1

Answer

x^3 + 8x^2 + 12x + 16

Answer

x^3 + 6x^2 + 8x + 4

Question 16

Factorize the expression: x^2 + 6x + 8

Accepted Answer

(x + 2)(x + 4)

Answer

(x - 2)(x - 4)

Answer

(x + 8)(x - 1)

Answer

(x - 8)(x + 1)

Question 17

Solve the system of equations:
2x + 3y = 11
x - y = 1

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = 4, y = 3

Answer

x = 3, y = 4

Question 18

Factorise 12x^2 - 3xy - 20y^2:

Accepted Answer

(3x - 5y)(4x + 4y)

Answer

(4x - 5y)(3x + 4y)

Answer

(3x + 5y)(4x - 4y)

Answer

(4x + 5y)(3x - 4y)

Question 19

Solve for x: 2(x + 3) - 5 = 9:

Accepted Answer

x = 4

Answer

x = -4

Answer

x = 2

Answer

x = -2

Question 20

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

Accepted Answer

-2x + 3y

Answer

5x - 3y

Answer

5x + 3y

Answer

-5x + 3y

Question 21

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

Accepted Answer

x² - x - 6

Answer

x² + x - 6

Answer

x² + x + 6

Question 22

Factorise completely: 6x² - 9xy

Accepted Answer

3x(2x - 3y)

Answer

3(2x² - 3xy)

Answer

x(6x - 9y)

Answer

3x(2x + 3y)

Question 23

Solve the equation: 2x + 5 = 11

Accepted Answer

x = 3

Answer

x = -3

Answer

x = 8

Question 24

Solve the equation: x² - 5x + 6 = 0

Accepted Answer

x = 2, x = 3

Answer

x = -2, x = -3

Answer

x = 1, x = 6

Question 25

The perimeter of a rectangle is given by the expression 2(l + w), where l is the length and w is the width. If the perimeter of a rectangle is 20 cm and the length is 6 cm, what is the width?

Accepted Answer

7 cm

Answer

14 cm

Answer

8 cm

Answer

4 cm

Question 26

Which of the following is NOT equivalent to the expression 4x + 2?

Accepted Answer

2x + 2

Answer

4(x + 1/2)

Answer

x + x + x + x + 2

Answer

2(2x + 1)

Question 27

A taxi company charges a £3 boarding fee and £1.50 per mile.  Which expression represents the total cost (C) of a journey of 'm' miles?

Accepted Answer

C = 3 + 1.5m

Answer

C = 4.5m

Answer

C = 3m + 1.5

Answer

C = 1.5(m + 3)

Question 28

The area of a square is given by the expression s², where s is the length of a side. If the area of a square is 49 cm², what is the perimeter of the square?

Accepted Answer

28 cm

Answer

98 cm

Answer

14 cm

Answer

196 cm

Question 29

Simplify: (3x²y³) / (xy²)

Accepted Answer

3xy

Answer

3x²y

Answer

3x²y³

Answer

3x/y