Decision Mathematics 2 Quizzes - Test Your Skills and Prepare for Exams

Question 1

Which of the following is outside the scope of the Decision Mathematics 2 unit?

Accepted Answer

Geometry

Answer

Matrices

Answer

Statistics

Answer

Algebra

Question 2

The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. If events A and B are independent, what is the probability of both events occurring?

Accepted Answer

0.24

Answer

0.1

Answer

0.2

Answer

0.4

Question 3

Which of the provided matrices is invertible?

Accepted Answer

[1 0]
[0 1]

Answer

[1 2]
[3 4]

Answer

[1 2]
[1 2]

Answer

[0 0]
[0 0]

Question 4

The equation of a line is given by y = 2x + 3. What is the slope of this line?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 5

Which of the following is a graphical representation of a quadratic function?

Accepted Answer

Parabola

Answer

Line

Answer

Circle

Answer

Hyperbola

Question 6

A game consists of rolling a fair six-sided die. If the number rolled is greater than 3, the player wins £1. Otherwise, the player loses £1. What is the expected value of the game?

Accepted Answer

£0.17

Answer

-£0.17

Answer

0

Answer

£1

Question 7

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

Accepted Answer

Mean of 0 and standard deviation of 1

Answer

Symmetric

Answer

Bell-shaped

Answer

Unimodal

Question 8

The objective function of a linear programming problem is to minimize z = 3x + 4y. Which of the following constraints would ensure that x and y are non-negative?

Accepted Answer

x ≥ 0 and y ≥ 0

Answer

x ≤ 0 and y ≤ 0

Answer

x ≥ 0 and y ≤ 0

Answer

x ≤ 0 and y ≥ 0

Question 9

Which of the following is a key skill developed in Decision Mathematics 2?

Accepted Answer

Problem-solving

Answer

Memory recall

Answer

Fact memorization

Answer

Rote learning

Question 10

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 11

Which of the following is NOT a benefit of using mathematics in real-world situations?

Accepted Answer

Guaranteed success

Answer

Improved decision-making

Answer

Enhanced problem-solving skills

Answer

Increased confidence

Question 12

What is a function?

Accepted Answer

A relation that assigns to each element of a set a unique element of another set

Answer

A set of ordered pairs

Answer

A straight line

Answer

A quantity that has both magnitude and direction

Question 13

Which of the following is the correct form of the objective function for a maximization problem?

Accepted Answer

Maximize Z = 3x + 5y (correct answer)

Answer

Minimize Z = 3x + 5y

Answer

Maximize Z - 3x + 5y

Answer

Minimize Z - 3x + 5y

Question 14

Which of the following distributions is symmetric about the mean?

Accepted Answer

Normal distribution (correct answer)

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Exponential distribution

Question 15

A matrix A has dimensions m x n and a matrix B has dimensions r x s. Which of the following operations is possible?

Accepted Answer

AB

Answer

A + B

Answer

A - B

Answer

BA

Question 16

A linear function is given by f(x) = 2x + 5. What is the gradient of this function?

Accepted Answer

2

Answer

5

Answer

7

Answer

10

Question 17

A survey found that 60% of students prefer mathematics. If there are 25 students in a class, how many students are likely to prefer mathematics?

Accepted Answer

15

Answer

10

Answer

20

Answer

25

Question 18

Which of the following is a vector?

Accepted Answer

(3, 5)

Answer

3 + 5i

Answer

3x + 5

Answer

x^2 + y^2

Question 19

A system of equations has infinitely many solutions. What can be concluded about the system?

Accepted Answer

The equations are consistent and dependent.

Answer

The equations are inconsistent.

Answer

The equations are consistent and independent.

Answer

The equations cannot be solved.

Question 20

A function f(x) is increasing on the interval (a, b). What is the sign of f'(x) on this interval?

Accepted Answer

Positive

Answer

Negative

Answer

Zero

Answer

Cannot be determined

Question 21

Which of the following is NOT a step in the decision-making process?

Accepted Answer

Ignore the outcome

Answer

Identify the problem

Answer

Analyze the data

Answer

Implement the solution

Question 22

A matrix can be used to represent a system of linear equations. What is the order of a matrix with 3 rows and 4 columns?

Accepted Answer

3 by 4

Answer

4 by 3

Answer

3 by 3

Answer

4 by 4

Question 23

In optimization problems, which function represents the quantity that needs to be maximized or minimized?

Accepted Answer

Objective function

Answer

Constraint function

Answer

Feasible region

Answer

Optimal solution

Question 24

Which algorithm is specifically designed for solving linear programming problems?

Accepted Answer

Simplex method

Answer

Newton's method

Answer

Lagrange multipliers

Answer

Gradient descent

Question 25

In a PERT network, which term refers to the earliest possible time at which an event can occur?

Accepted Answer

Earliest event time

Answer

Latest event time

Answer

Slack time

Answer

Critical path

Question 26

In inventory management, what does the term 'storage capacity' refer to?

Accepted Answer

Maximum amount of inventory that can be stored

Answer

Amount of inventory currently in stock

Answer

Minimum amount of inventory required

Answer

Average inventory level

Question 27

Which property is NOT characteristic of a convex set?

Accepted Answer

The set may be unbounded.

Answer

The line segment connecting any two points in the set lies entirely within the set.

Answer

The set can be expressed as the intersection of a finite number of half-spaces.

Answer

The set is closed.

Question 28

What is the dual problem associated with a linear programming problem?

Accepted Answer

A linear programming problem with the same constraints but a different objective function

Answer

A linear programming problem with the same objective function and constraints

Answer

A linear programming problem with the same objective function but different constraints

Answer

A linear programming problem with a different objective function and different constraints

Question 29

Which of the following is NOT a crucial step in the decision-making process?

Accepted Answer

Implementing the decision without evaluating its effectiveness

Answer

Analyzing the information and generating alternative solutions

Answer

Identifying the problem and gathering relevant information

Question 30

Which of the following is an advantage of using a decision matrix?

Accepted Answer

It provides a clear and visual representation of the alternatives and their consequences

Answer

It guarantees the best decision will be made

Answer

It eliminates the need for subjective judgment

Question 31

Which of the following is a potential bias in decision-making?

Accepted Answer

Confirmation bias

Answer

Randomness

Answer

Objectivity

Answer

Linearity

Question 32

Which of the following is a key characteristic of a well-informed decision?

Accepted Answer

It is based on relevant and accurate information

Answer

It is always the most popular decision

Answer

It benefits only the decision-maker

Answer

It is made quickly and without hesitation

Question 33

Which of the following is a convex set?

Accepted Answer

The set of all points in the plane that are at most 1 unit from the origin.

Answer

The set of all points in the plane that lie on the line y = x.

Answer

The set of all points in the plane that are at least 1 unit from the origin.

Question 34

Which of the following is a valid equality for the set of all points in the plane that lie on the line y = x?

Accepted Answer

y - x = 0

Answer

y = 2x

Answer

y + x = 0

Question 35

Which of the following is a valid inequality for the set of all points in the plane that lie inside the triangle with vertices (0, 0), (1, 0), and (0, 1)?

Accepted Answer

y <= 1 - x

Answer

y <= x

Answer

y >= 1 - x

Answer

y >= x

Question 36

Which of the following is a valid inequality for the set of all points in the plane that lie outside the circle x^2 + y^2 <= 1?

Accepted Answer

x^2 + y^2 > 1

Answer

x^2 + y^2 < 1

Answer

y - x > 1

Answer

x^2 - y^2 > 1

Question 37

Which of the following is a valid inequality for the set of all points in the plane that lie on or below the line y = x?

Accepted Answer

y <= x

Answer

y > x

Answer

y >= x

Answer

y < x

Question 38

A distinctive characteristic of a linear programming problem is:

Accepted Answer

Linear objective function and linear constraints

Answer

Non-linear objective function and non-linear constraints

Answer

Linear objective function and non-linear constraints

Answer

Non-linear objective function and linear constraints

Question 39

A sensitivity analysis is primarily conducted to determine:

Accepted Answer

How changes in input variables affect the optimal solution

Answer

The expected value of the best decision

Answer

The exact probability of making the correct decision

Question 40

Simulated annealing is an example of a:

Accepted Answer

Heuristic technique for optimization

Answer

Exact algorithm for optimization

Answer

Dynamic programming technique

Answer

Deterministic optimization technique

Question 41

An application of Markov chains is:

Accepted Answer

Modeling the behavior of queuing systems

Answer

Solving partial differential equations

Answer

Finding the shortest path in a graph

Question 42

Game theory models are used to analyze:

Accepted Answer

Strategic interactions between decision-makers

Answer

Continuous processes and their derivatives

Answer

Random events and their probabilities

Answer

Large data sets and their patterns

Question 43

What is a major advantage of using regression analysis?

Accepted Answer

It enables us to make predictions about continuous outcome variables.

Answer

It can be used to establish causal relationships.

Answer

It is particularly suitable for small sample sizes.

Question 44

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

Accepted Answer

Range

Answer

Mode

Answer

Mean

Answer

Median

Question 45

Differentiate between a population and a sample in statistics.

Accepted Answer

A population is the entire group of individuals under study, while a sample is a subset of the population.

Answer

A population is always smaller than a sample.

Answer

A sample is always representative of the population.

Question 46

Which assumption is crucial for the Central Limit Theorem to hold?

Accepted Answer

The sample size should be sufficiently large.

Answer

The population must be normally distributed.

Answer

The data must be collected randomly.

Answer

The variable of interest must be continuous.

Question 47

What is the primary goal of hypothesis testing?

Accepted Answer

To determine whether there is sufficient evidence to reject or fail to reject a null hypothesis.

Answer

To prove a hypothesis is true.

Answer

To estimate the value of a population parameter.

Question 48

Which of the following is a characteristic of the chi-squared test?

Accepted Answer

It is used to test for associations between categorical variables.

Answer

It is highly sensitive to outliers.

Answer

It is a non-parametric test.

Question 49

What is the main purpose of constructing a confidence interval?

Accepted Answer

To estimate a population parameter with a specified level of confidence.

Answer

To test the significance of a difference between two groups.

Answer

To predict the value of an individual observation.

Question 50

A company surveys its 1000 customers and finds that 60% prefer Product A. How many customers prefer Product B?

Accepted Answer

400

Answer

800

Answer

600

Answer

200

Question 51

A matrix has 4 rows and 3 columns. What is the order of the matrix in row-column notation?

Accepted Answer

4 x 3

Answer

2 x 3

Answer

3 x 4

Answer

3 x 2

Question 52

What is the probability of rolling an even number on a standard six-sided die?

Accepted Answer

1 / 2

Answer

1 / 4

Answer

1 / 3

Answer

1 / 6

Question 53

What is the mean of the following data set: 12, 14, 16, 18, 20?

Accepted Answer

16

Answer

14

Answer

15

Answer

13

Question 54

Which of the following is an example of a linear programming problem?

Accepted Answer

Maximize z = 3x + 4y subject to x ≥ 0, y ≥ 0, x + y ≤ 5, 2x + y ≤ 6

Answer

Solve the system of equations: x + y = 5, x - y = 1

Answer

Find the maximum value of f(x) = x^2 + 2x

Question 55

What is the optimal solution to the following linear programming problem?
Maximize z = 2x + 3y subject to x ≥ 0, y ≥ 0, x + 2y ≤ 8, 3x + y ≤ 12

Accepted Answer

z = 18 when x = 6 and y = 0

Answer

z = 20 when x = 4 and y = 2

Answer

z = 26 when x = 6 and y = 1

Answer

z = 24 when x = 8 and y = 0

Question 56

Which of the following matrices is not invertible?

Accepted Answer

[[0, 1], [0, 0]]

Answer

[[1, 2], [3, 4]]

Answer

[[2, 1], [-1, 2]]

Question 57

What is the inverse of the matrix  [[2, 1], [3, 2]]?

Accepted Answer

[[2/5, -1/5], [-3/5, 2/5]]

Answer

[[1/5, -2/5], [-3/5, 1/5]]

Answer

[[2, -1], [-3, 2]]

Answer

[[1/2, -1/3], [-3/2, 1/3]]

Question 58

Which of the following is a vector in R^2?

Accepted Answer

[2, 3]

Answer

2x + 3y - z = 0

Answer

x^2 + y^2 - z^2 = 1

Answer

[[2, 3], [4, 5]]

Question 59

What is the dot product of the vectors [2, 3] and [1, 2]?

Accepted Answer

8

Answer

-1

Answer

12

Answer

5

Question 60

Which of the following is a probability distribution?

Accepted Answer

P(X = 1) = 0.2, P(X = 2) = 0.3, P(X = 3) = 0.5

Answer

P(X < 1) = 0.2, P(X > 2) = 0.3, P(X = 3) = 0.5

Answer

P(X = 1) = 0.2, P(X = 2) = 0.4, P(X = 3) = 0.6

Answer

P(X = 1, X = 2) = 0.2, P(X = 2, X = 3) = 0.3, P(X = 3, X = 1) = 0.5

Question 61

What is the expected value of the random variable X with probability distribution P(X = 1) = 0.2, P(X = 2) = 0.3, P(X = 3) = 0.5?

Accepted Answer

2.3

Answer

2.8

Answer

1.8

Answer

3.2

Question 62

Which of the following is a hypothesis test?

Accepted Answer

Test the hypothesis that the mean of a population is equal to 100

Answer

Predict the value of a future observation

Answer

Estimate the mean of a population

Question 63

What is the p-value for a hypothesis test with a test statistic of z = 2.576?

Accepted Answer

0.01

Answer

0.05

Answer

0.15

Answer

0.10