Algebra Basics for Business: Master Variables, Expressions, and Equations

Question 1

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

Accepted Answer

3x^2 - x + 2

Answer

3x^2 + x - 2

Answer

3x^2 - 5x + 2

Answer

3x^2 + 5x + 2

Question 2

Which of the following is a polynomial?

Accepted Answer

x^2 + 3x + 2

Answer

x + 2

Answer

1 / x

Answer

sin(x)

Question 3

Factorize the following expression: x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x - 2)(x - 2)

Answer

(x + 4)(x - 1)

Answer

Cannot be factorized

Question 4

Which algebraic expression is invalid?

Accepted Answer

2x / x

Answer

2x + 3

Answer

x^2 - 5x + 6

Answer

(x + y)^2

Question 5

Solve the equation: 2x + 5 = 13

Accepted Answer

x = 4

Answer

x = -4

Answer

x = 6

Answer

x = -6

Question 6

Which graph represents the inequality x + 2y < 6?

Accepted Answer

Shaded area below the line x + 2y = 6

Answer

Line with a slope of -2

Answer

Line with a slope of 2

Answer

Shaded area above the line x + 2y = 6

Question 7

Which among the following is a quadratic equation?

Accepted Answer

x^2 - 4x + 3 = 0

Answer

2x + 5 = 0

Answer

y = 3x

Answer

√x = 5

Question 8

Factorise the expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 9)^2

Answer

(x + 9)^2

Answer

Cannot be factorised

Question 9

Solve the following equation for x: 3x - 5 = 10

Accepted Answer

x = 7

Answer

x = 5

Answer

x = -5

Answer

x = -7

Question 10

Which of the following is an inequality?

Accepted Answer

x - y > 0

Answer

x + y = 5

Answer

x * y = 10

Answer

x / y = 2

Question 11

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

Accepted Answer

y = 2x - 1

Answer

y = -2x - 1

Answer

y = 2x + 1

Answer

y = -2x + 1

Question 12

Find the vertex of the parabola given by the equation y = x^2 - 4x + 3

Accepted Answer

(2, -1)

Answer

(2, -5)

Answer

(-2, -1)

Answer

(-2, -5)

Question 13

Which of the following is the domain of the function f(x) = sqrt(x - 3)?

Accepted Answer

[3, ∞)

Answer

(3, ∞)

Answer

[-∞, 3]

Answer

(-∞, 3)

Question 14

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

Accepted Answer

2x + 5

Answer

12

Answer

x = 5

Answer

y > 0

Question 15

Which inequality represents the statement 'The sum of x and 5 is greater than 10'?

Accepted Answer

x + 5 > 10

Answer

10 > x + 5

Answer

x + 5 < 10

Question 16

What does the graph of the inequality y ≤ 2x + 1 look like?

Accepted Answer

A solid line y = 2x + 1 with the shaded area below the line.

Answer

A solid line y = 2x + 1 with the shaded area above the line.

Answer

A dashed line y = 2x + 1.

Answer

A solid line y = 2x + 1.

Question 17

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

Accepted Answer

2x + 5

Answer

The perimeter of a rectangle

Answer

6 > 3

Answer

y = 5

Question 18

Solve the equation: x + 10 = 15

Accepted Answer

5

Answer

10

Answer

25

Answer

15

Question 19

Which of the following is the solution to the inequality: 2x - 5 < 1?

Accepted Answer

x < 3

Answer

x < -3

Answer

x > -3

Answer

x > 3

Question 20

A business sells products for £x each. The total revenue generated from selling y products is given by the expression: R = xy. What is the revenue generated from selling 10 products at £5 each?

Accepted Answer

£50

Answer

£10

Answer

£100

Answer

£55

Question 21

The formula for circumference of a circle is C = 2πr, where r is the radius. What is the circumference of a circle with a radius of 10 cm?

Accepted Answer

20π cm

Answer

10π cm

Answer

40π cm

Answer

π cm

Question 22

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

Accepted Answer

4/3

Answer

3/1

Answer

-4/3

Answer

1/3

Question 23

The equation of a line is y = 2x + 1. What is the y-intercept of this line?

Accepted Answer

1

Answer

0

Answer

2