Algebra for Business: Expressions, Equations, and More

Question 1

Determine the inverse function of f(x) = x^2 + 2x - 3.

Accepted Answer

f^-1(x) = x - 2 ± √(x^2 - 2x - 3)

Answer

f^-1(x) = x^2 - 2x + 3

Answer

f^-1(x) = -x^2 - 2x - 3

Answer

f^-1(x) = √(x - 2x - 3)

Question 2

Find the coordinates of the vertex of the parabolic function: y = x^2 - 4x + 3

Accepted Answer

(2, -1)

Answer

(1, -3)

Answer

(3, 0)

Answer

(0, 3)

Question 3

Factorize the quadratic expression: x^2 - 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x - 4)(x + 4)

Answer

(x^2 - 4)

Answer

(x - 2)(x - 2)

Question 4

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

Calculate the area of a rectangle with a length of **(x + 2)** cm and a width of **(x - 1)** cm.

Accepted Answer

x(x - 1) cm²

Answer

x² + cm²

Answer

x² - cm²

Answer

x(x + 2) cm²

Question 6

Which of the following statements is NOT a property of a quadratic function?

Accepted Answer

It always has two x-intercepts.

Answer

It has a U-shaped graph.

Answer

It has a maximum or minimum point.

Answer

It can be written in the form y = ax² + bx + c, where a ≠ 0.

Question 7

Which expression is equivalent to 2(x + 3) using the distributive property?

Accepted Answer

2x + 6

Answer

6x + 2

Answer

x + 6

Answer

2x - 6

Question 8

Factorise the following quadratic polynomial: x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 3)²

Answer

(x - 9)(x + 1)

Answer

(x - 3)²

Question 9

Find the solution to the simultaneous linear equations: 
2x + y = 10
x - y = 2

Accepted Answer

x = 4, y = 2

Answer

x = 0, y = 6

Answer

x = 2, y = 4

Answer

x = 6, y = 0

Question 10

Which of the following is the graph of the linear function: y = -x + 2?

Accepted Answer

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

Answer

Image of a circle

Answer

Image of a parabola

Question 11

Which of the following is a polynomial of degree 4?

Accepted Answer

x^4 - 2x^3 + x^2 + 5x - 1

Answer

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

Answer

2x - 1

Question 12

Factorise the polynomial: x^2 + 6x + 8

Accepted Answer

(x + 2)(x + 4)

Answer

(x + 8)(x - 1)

Answer

(x + 1)(x + 6)

Answer

(x - 2)(x - 4)

Question 13

Which of these functions is linear?

Accepted Answer

y = 3x + 5

Answer

y = x^2 + 2x

Answer

y = e^(x^2)

Answer

y = 1 / x

Question 14

What is the slope of the line defined by the equation y = -4x + 2?

Accepted Answer

-4

Answer

-2

Answer

4

Answer

2

Question 15

Which of these expressions is linear?

Accepted Answer

2x - 5

Answer

x^2 - 4

Answer

e^x

Answer

(x + 2)^2

Question 16

Find the discriminant of the quadratic equation: 3x^2 + 2x - 5 = 0

Accepted Answer

49

Answer

20

Answer

10

Answer

25

Question 17

Which of the following is an application of algebra in business?

Accepted Answer

Calculating profit margin

Answer

Writing marketing reports

Answer

Managing customer relationships

Answer

Conducting market research

Question 18

Which of the following is NOT a fundamental property of algebra?

Accepted Answer

It uses numeric values to represent operations.

Answer

It allows for generalization and abstraction.

Answer

It can be used to solve equations and inequalities.

Question 19

Simplify the following expression: 3(x - 2)

Accepted Answer

3x - 6

Answer

x - 6

Answer

6x - 3

Answer

3 - 6x

Question 20

Which of the following is NOT an inequality symbol?

Accepted Answer

=

Answer

<

Answer

>

Answer

≥

Question 21

Factorise the quadratic expression: x² - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x - 2)²

Answer

(x - 4)(x - 4)

Answer

(x + 2)²

Question 22

Which of the following graphs represents the linear function: y = 2x + 1?

Accepted 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

Question 23

Which of the following is a real-world application of algebra in business?

Accepted Answer

Calculating profit margins

Answer

Composing music

Answer

Predicting weather patterns

Answer

Designing bridges

Question 24

Which of the following is NOT a property of polynomials?

Accepted Answer

They can have imaginary roots.

Answer

They can be factorised into linear factors.

Answer

They can be expressed in the form ax^n + bx^(n-1) + ... + c, where a ≠ 0

Answer

They can have multiple roots.

Question 25

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

Accepted Answer

f(x) = x² - 2x + 1

Answer

f(x) = |x|

Answer

f(x) = sin(x)

Answer

f(x) = ln(x)

Question 26

A company's profit (P) is calculated as the difference between its revenue (R) and its costs (C). Which of the following algebraic expressions represents this relationship?

Accepted Answer

P = R - C

Answer

P = C - R

Answer

P = R / C

Answer

P = R + C

Question 27

Solve for x: 3x + 5 = 14

Accepted Answer

x = 3

Answer

x = -3

Answer

x = 9

Answer

x = 6

Question 28

A company sells widgets for £10 each. They have fixed costs of £500 and variable costs of £5 per widget. How many widgets must they sell to break even?

Accepted Answer

100

Answer

200

Answer

50

Question 29

Which of the following inequalities represents the statement 'The number of employees (n) must be at least 10'?

Accepted Answer

n ≥ 10

Answer

n ≤ 10

Answer

n > 10

Answer

n < 10

Question 30

Simplify the expression: 2x² + 3x - 5x² + 7x

Accepted Answer

-3x² + 10x

Answer

5x² + 10x

Answer

-3x² - 4x

Answer

7x² + 10x

Question 31

Factorise the expression: x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x + 1)

Answer

(x - 9)(x - 1)

Answer

(x - 9)(x + 1)

Question 32

Solve the following system of simultaneous equations: 2x + y = 7 and x - y = 1

Accepted Answer

x = 3, y = 1

Answer

x = 1, y = 5

Answer

x = 4, y = -1

Answer

x = 2, y = 3

Question 33

Find the roots of the quadratic equation: x² - 5x + 6 = 0

Accepted Answer

x = 2, x = 3

Answer

x = 1, x = 6

Answer

x = -1, x = -6

Answer

x = -2, x = -3

Question 34

Which of the following is the equation of a line with a slope of 2 and a y-intercept of 3?

Accepted Answer

y = 2x + 3

Answer

y = 3x + 2

Answer

y = -2x + 3

Answer

y = -3x + 2

Question 35

The graph of the quadratic function y = -x² + 4x - 3 intersects the y-axis at what point?

Accepted Answer

(0, -3)

Answer

(-3, 0)

Answer

(3, 0)

Answer

(0, 3)