Decision Mathematics 1: Master Algebra, Functions, and More

Question 1

Find the point where the lines 2x - 3y = 6 and 3x + 5y = 15 intersect.

Accepted Answer

(3, 2)

Answer

(1, 0)

Answer

(5, -1)

Answer

(0, -2)

Question 2

A car travels east at 20 m/s, while a truck travels north at 30 m/s. Determine the car's velocity relative to the truck.

Accepted Answer

36 m/s

Answer

0 m/s

Answer

10 m/s

Answer

50 m/s

Question 3

In computer graphics, matrices are used for various transformation operations. Which of the following operations can be represented using a translation matrix?

Accepted Answer

Moving an object in a straight line

Answer

Enlarging or shrinking an object

Answer

Turning an object around a fixed point

Answer

Flipping an object over a line

Question 4

How can matrices be used to encrypt and decrypt messages? Describe a simple encryption algorithm using matrices.

Accepted Answer

To encrypt, multiply the message matrix by an encryption key matrix. To decrypt, multiply the encrypted matrix by the inverse of the encryption key matrix.

Answer

Matrices cannot be used for encryption.

Answer

To encrypt, subtract the key matrix from the message matrix. To decrypt, add the key matrix to the encrypted message.

Answer

Matrix encryption is limited to encrypting numeric messages only.

Question 5

Determine the slope of a line that is perpendicular to a line with a slope of -2.

Accepted Answer

-0.5

Answer

0.5

Answer

2

Answer

-2

Question 6

Calculate the determinant of the matrix [[2, 3], [4, 5]]

Accepted Answer

10

Answer

-2

Answer

2

Answer

-10

Question 7

Determine the mean of the following data set: 5, 7, 9, 11, 13

Accepted Answer

9

Answer

7

Answer

11

Answer

13

Question 8

Which of the following is NOT a characteristic of a normal distribution?

Accepted Answer

Kurtosis

Answer

Bell-shaped

Answer

Symmetrical

Answer

Unimodal

Question 9

What is the probability of rolling a 6 on a fair six-sided dice?

Accepted Answer

1/6

Answer

1/3

Answer

1/4

Answer

1/5

Question 10

Determine the expected value of a fair coin toss.

Accepted Answer

0.5

Answer

0

Answer

1

Answer

2

Question 11

Calculate the median of the following data set: {2, 4, 5, 7, 9}

Accepted Answer

5

Answer

4

Answer

6

Answer

7

Question 12

Find the domain of the function f(x) = sqrt(x - 2).

Accepted Answer

[2, ∞)

Answer

[-2, ∞)

Answer

(-∞, 2]

Answer

(-∞, ∞)

Question 13

Determine the equation of the line with a slope of -3 and a y-intercept of 5.

Accepted Answer

y = 5 - 3x

Answer

y = -5 + 3x

Answer

y = 5x - 3

Answer

y = -5x - 3

Question 14

Which of the following is the formula to calculate the mean of a dataset?

Accepted Answer

Sum of all data values divided by the number of values

Answer

Average of the highest and lowest values

Answer

Sum of all squared values divided by the number of values

Answer

Product of all values

Question 15

If the probability of event A occurring is 0.4 and the probability of event B occurring is 0.6, what is the probability of both A and B occurring?

Accepted Answer

0.24

Answer

0.1

Answer

0.8

Answer

1

Question 16

Calculate the derivative of the function f(x) = e^x.

Accepted Answer

e^x

Answer

xe^x

Answer

e^(x^2)

Answer

0

Question 17

What is the domain of the function f(x) = √(x + 2)?

Accepted Answer

x ≥ -2

Answer

x ≥ 0

Answer

x ≤ -2

Answer

All real numbers

Question 18

A dataset has a mean of 10 and a standard deviation of 2. After standardising the data, what will be the mean and standard deviation of the new data?

Accepted Answer

Mean: 0, Standard deviation: 1

Answer

Mean: 10, Standard deviation: 2

Answer

Mean: 0, Standard deviation: 2

Answer

Mean: 10, Standard deviation: 1

Question 19

Which of the following algebraic expressions represents the statement 'The sum of two numbers is 15'?

Accepted Answer

x + y = 15

Answer

x + 15 = y

Answer

15 - x = y

Answer

x - y = 15

Question 20

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

Accepted Answer

4/3

Answer

-4/3

Answer

3/4

Answer

-3/4

Question 21

Which of the following is NOT a property of a linear function?

Accepted Answer

Y-intercept does not need to equal zero

Answer

Constant rate of change

Answer

Straight line graph

Answer

Domain of all real numbers

Question 22

Which of the following is the equation of the line passing through the points (1, 2) and (3, 8)?

Accepted Answer

y = 2x + 1

Answer

y = 2x

Answer

y = x + 1

Answer

y = 3x - 1

Question 23

Which of the following is the inverse of the function f(x) = x^3?

Accepted Answer

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

Answer

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

Answer

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

Answer

f^-1(x) does not exist

Question 24

What is the domain of the function f(x) = sqrt(x - 2)?

Accepted Answer

x ≥ 2

Answer

x ≤ 2

Answer

x ∈ all real numbers

Answer

x ∈ natural numbers

Question 25

Which concept is NOT covered in Decision Mathematics 1?

Accepted Answer

Trigonometry

Answer

Algebra

Answer

Statistics

Answer

Functions

Question 26

The graph of the function f(x) = x^2 + 2x - 3 is a:

Accepted Answer

Parabola

Answer

Straight line

Answer

Circle

Answer

Ellipse

Question 27

Which of the following matrices is the identity matrix?

Accepted Answer

[1, 0; 0, 1]

Answer

[0, 1; 1, 0]

Answer

[1, 0; 0, 0]

Answer

[0, 0; 1, 1]

Question 28

The dot product of the vectors [1, 2, 3] and [4, 5, 6] is:

Accepted Answer

21

Answer

32

Answer

43

Answer

54

Question 29

Which of the following is a technique used in decision-making to analyze the potential risks and rewards of different options?

Accepted Answer

Risk analysis

Answer

Venn diagrams

Answer

Linear programming

Answer

Scatter plots

Question 30

The derivative of the function f(x) = e^x is:

Accepted Answer

e^x

Answer

-e^x

Answer

x*e^x

Answer

1/e^x

Question 31

Which of the following is NOT a characteristic of a linear function?

Accepted Answer

Exponential growth

Answer

Constant rate of change

Answer

Straight-line graph

Answer

Passes through the origin

Question 32

What is the probability of rolling a 6 on a standard six-sided die?

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 33

Which of the following is the equation of a vector with magnitude 5 and direction 30° from the positive x-axis?

Accepted Answer

5[cos(30°)i + sin(30°)j]

Answer

5[cos(60°)i + sin(60°)j]

Answer

5[cos(45°)i + sin(45°)j]

Answer

5[cos(90°)i + sin(90°)j]

Question 34

What is the domain of the function f(x) = 1/(x-2)?

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

All positive real numbers

Answer

All non-negative real numbers

Question 35

Which of the following is 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) = 1 - 2x

Answer

f^-1(x) = 2 - x

Question 36

Which of the following equations represents a linear function?

Accepted Answer

y = mx + c

Answer

y = ax^2 + bx + c

Answer

y = e^x

Answer

y = sin(x)

Question 37

Which of the following matrices is the identity matrix?

Accepted Answer

[1, 0; 0, 1]

Answer

[0, 1; 1, 0]

Answer

[1, 1; 1, 1]

Answer

[0, 0; 0, 0]

Question 38

What is the determinant of the matrix [2, -1; 3, 4]?

Accepted Answer

8

Answer

5

Answer

11

Answer

14

Question 39

What is the magnitude of the vector (3, 4)?

Accepted Answer

7

Answer

5

Answer

9

Answer

11

Question 40

Which of the following probability distributions is used to model the number of defects in a sample of products?

Accepted Answer

Poisson distribution

Answer

Binomial distribution

Answer

Normal distribution

Answer

Chi-square distribution

Question 41

Sampling error refers to:

Accepted Answer

The possible difference between a sample statistic and the true population parameter it represents

Answer

The size difference between a sample and its corresponding population

Answer

Errors caused by using incorrect statistical methods

Answer

Biases introduced by inaccurate data collection or measurement

Question 42

When using a linear regression model to predict house prices based on square footage, which limitations should be considered?

Accepted Answer

The model assumes a linear relationship between square footage and house price.

Accepted Answer

The model does not account for the age of the house.

Answer

The model can accurately predict the price of any house.

Question 43

Which logical fallacy is present in the argument: 'Most car accidents involve speeding. Therefore, speeding is the only cause of car accidents'?

Accepted Answer

False cause

Answer

Appeal to ignorance

Answer

Hasty generalization

Question 44

Find the domain and range of the linear function f(x) = 3 - 2x.

Accepted Answer

Domain: (-∞, ∞), Range: (-∞, ∞)

Answer

Domain: [0, ∞), Range: [0, 3]

Answer

Domain: (-3, ∞), Range: (-∞, ∞)

Answer

Domain: (-∞, ∞), Range: [3, ∞)

Question 45

Two distinct plant species are being examined, and their average heights are thought to be different. Which statistical method is most suitable for testing this hypothesis?

Accepted Answer

Independent t-test

Answer

Pearson's correlation coefficient

Answer

Chi-square test

Question 46

Which of the following is **not** a type of function?

Accepted Answer

Vector

Answer

Quadratic

Answer

Exponential

Answer

Linear

Question 47

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

Accepted Answer

y = 2x - 1

Answer

y = -2x + 1

Answer

y = x - 2

Answer

y = -x + 2

Question 48

Which of the following is **not** a measure of central tendency?

Accepted Answer

Range

Answer

Mean

Answer

Mode

Answer

Median

Question 49

Which of the following is a quadratic equation?

Accepted Answer

x^2 - 5x + 6 = 0

Answer

x + 5 = 0

Answer

y = 2x^3 + x

Answer

2x - 1 = 3

Question 50

Which of the following is a statistical distribution?

Accepted Answer

Normal distribution

Answer

Quadratic distribution

Answer

Trigonometric distribution

Answer

Polynomial distribution