Decision Mathematics 1 Quizzes: Master Key Concepts and Excel in Exams

Question 1

Describe the relationship between the determinant and the inverse of a non-singular square matrix.

Accepted Answer

The inverse of a matrix is equal to its adjoint divided by its determinant.

Answer

The determinant of a matrix is equal to the product of its eigenvalues.

Answer

The determinant of a matrix is equal to the sum of its diagonal elements.

Answer

The inverse of a matrix is equal to its transpose.

Question 2

Find the domain of the function f(x) = 1 / (x - 2).

Accepted Answer

All real numbers except x = 2

Answer

All real numbers

Answer

Only x = 2

Answer

All real numbers except x = 0

Question 3

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

Accepted Answer

x ≥ 2

Answer

x ≤ 2

Answer

x > 2

Answer

x < 2

Question 4

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

Accepted Answer

1/2

Answer

1/6

Answer

1/3

Answer

2/3

Question 5

Which of the following is the equation of the parabola with its vertex at (2, 1) and focus at (4, 1)?

Accepted Answer

y = 1/4(x - 2)^2 + 1

Answer

y = 1/(4(x - 2))^2 + 1

Answer

y = 1/(8(x - 2))^2 + 1

Answer

y = 1/8(x - 2)^2 + 1

Question 6

Which of the following is the equation of the plane with the normal vector (1, 2, 3) and containing the point (2, 1, -1)?

Accepted Answer

x + 2y + 3z = 4

Answer

x - 2y - 3z = 4

Answer

2x + y - 3z = 4

Answer

-x + 2y + 3z = 4

Question 7

Find the mean of the following data set: {10, 12, 8, 15, 11, 9, 13}

Accepted Answer

12

Answer

10

Answer

11

Answer

13

Question 8

Calculate the probability of rolling an even number on a standard six-sided die.

Accepted Answer

1/2

Answer

1/3

Answer

2/3

Answer

1/6

Question 9

Describe a practical application of vectors in the real world.

Accepted Answer

Calculating force and direction

Answer

Representing 3D shapes

Answer

Solving equations

Answer

Measuring speed

Question 10

What is the equation of the circle with centre (0, 0) and radius 5?

Accepted Answer

x^2 + y^2 = 25

Answer

x^2 + y^2 = 5

Answer

x^2 - y^2 = 25

Answer

x^2 - y^2 = 5

Question 11

Solve the inequality: x^2 - 4x + 3 < 0.

Accepted Answer

x < 1 or x > 3

Answer

1 < x < 3

Answer

x < -1 or x > 3

Answer

-1 < x < 3

Question 12

Which of the following is the graph of the function f(x) = x^2 + 2x - 3?

Accepted Answer

A parabola opening upwards

Answer

A parabola opening downwards

Answer

A straight line

Answer

A circle

Question 13

Which of the following matrices is **symmetric**?

Accepted Answer

[[1, 5], [5, 1]]

Answer

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

Answer

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

Answer

[[1, 6], [7, 1]]

Question 14

Which of the following is the equation of the line passing through the points (2, 5) and (4, 9)?

Accepted Answer

y = 2x - 1

Answer

y = 2x + 1

Answer

y = x + 3

Answer

y = x - 3

Question 15

Simplify the expression (2x + 3)(x - 1) - (x + 2)(x - 3).

Accepted Answer

x - 1

Answer

4x - 1

Answer

-x - 1

Answer

x + 1

Question 16

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 = 1)

Answer

(x = 1, y = 4)

Question 17

Which of the following is a factor of the polynomial x^3 - 2x^2 - 5x + 6?

Accepted Answer

x - 1

Answer

x + 1

Answer

x - 2

Answer

x + 2

Question 18

The graph of a quadratic function has a vertex at (-2, 3). Write the equation of its axis of symmetry.

Accepted Answer

x = -2

Answer

x = 3

Answer

y = -2

Answer

y = 3

Question 19

Which transformation maps the point (2, 3) to the point (6, 7)?

Accepted Answer

Translation by (4, 4)

Answer

Reflection in the y-axis

Answer

Rotation by 90 degrees clockwise

Answer

Dilation by a factor of 2

Question 20

In a decision-making scenario, what is the primary objective of applying decision mathematics?

Accepted Answer

Optimizing outcomes based on available data

Answer

Predicting future events with certainty

Answer

Creating aesthetically pleasing designs

Answer

Composing emotionally evocative music

Question 21

What is the equation of a circle with center (0, 0) and radius 5?

Accepted Answer

x^2 + y^2 = 25

Answer

(x - 5)^2 + (y - 5)^2 = 5

Answer

(x + 5)^2 + (y + 5)^2 = 25

Answer

x^2 + y^2 = 5

Question 22

Find the multiplicative inverse of the matrix [[1, 2], [3, 4]].

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 23

Find the probability of rolling a six on a fair six-sided dice.

Accepted Answer

1/6

Answer

1/3

Answer

1/5

Answer

1/4

Question 24

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

Accepted Answer

Implementing the decision without evaluating it

Answer

Generating and evaluating alternatives

Answer

Making the decision

Answer

Identifying the problem

Question 25

What is the fundamental difference between deterministic and non-deterministic decision-making?

Accepted Answer

Deterministic decisions involve known factors, while non-deterministic decisions involve uncertain factors.

Answer

Deterministic decisions are made quickly, while non-deterministic decisions take more time.

Question 26

Which of the following should NOT be considered when making a decision?

Accepted Answer

Only personal preferences

Answer

Benefits

Answer

Cost

Answer

Risks

Question 27

Which of the following is NOT a measure of central tendency?

Accepted Answer

Range

Answer

Median

Answer

Mean

Question 28

The function f(x) = |x - 2| is continuous at x = 2. True or False?

Accepted Answer

True

Answer

False

Answer

Only if x < 2

Answer

Only if x > 2

Question 29

What is the inverse of the matrix  A =  [[2, 1], [3, 4]]?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 30

What is the maximum value of the function f(x) = x^2 - 2x + 1?

Accepted Answer

1

Answer

2

Answer

0

Answer

-1

Question 31

What is the domain of the function f(x) = √(x - 3)?

Accepted Answer

x ≥ 3

Answer

All real numbers

Answer

x ≤ 3

Answer

x > 3

Question 32

Calculate the mean of the following data set: 2, 5, 7, 10, 12.

Accepted Answer

7

Answer

6

Answer

9

Answer

8

Question 33

What is the probability of drawing a red card from a standard deck of 52 cards?

Accepted Answer

1/2

Answer

1/13

Answer

1/8

Answer

1/4

Question 34

What is the area of the triangle with vertices (0, 0), (3, 0), and (0, 4)?

Accepted Answer

6

Answer

3

Answer

9

Answer

12

Question 35

What is the volume of a sphere with a radius of 5 units? (Use π ≈ 3.14)

Accepted Answer

523.6

Answer

261.8

Answer

1309

Answer

1047.2

Question 36

What is the gradient of the curve y = x² - 2x + 3 at the point where x = 1?

Accepted Answer

0

Answer

-1

Answer

2

Answer

1

Question 37

Which equation represents a circle with center (2, -1) and radius 3?

Accepted Answer

(x - 2)² + (y + 1)² = 9

Answer

(x - 2)² + (y + 1)² = 3

Answer

(x + 2)² + (y - 1)² = 9

Answer

(x + 2)² + (y - 1)² = 3

Question 38

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

Accepted Answer

9

Answer

10

Answer

7

Answer

11

Question 39

Calculate the standard deviation of the following data set: 5, 7, 9, 11, 13.

Accepted Answer

2.83

Answer

4.24

Answer

8.48

Answer

1.41

Question 40

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

Accepted Answer

1/2

Answer

1/6

Answer

1/3

Answer

1/4

Question 41

Solve the inequality: 2x + 3 > 7

Accepted Answer

x > 2

Answer

x ≤ 2

Answer

x > -2

Answer

x < 2

Question 42

A company produces two types of products, X and Y. Each unit of X requires 3 hours of labor, and each unit of Y requires 2 hours of labor. The company has a maximum of 120 labor hours available. Which inequality represents this constraint, where x is the number of units of X and y is the number of units of Y?

Accepted Answer

3x + 2y ≤ 120

Answer

2x + 3y ≤ 120

Answer

3x + 2y ≥ 120

Answer

2x + 3y ≥ 120

Question 43

What is the gradient of the line represented by the equation 4y - 2x = 8?

Accepted Answer

0.5

Answer

2

Answer

-0.5

Answer

-2

Question 44

Which of the following matrices represents a reflection in the x-axis?

Accepted Answer

[1 0]
[0 -1]

Answer

[-1 0]
[0 1]

Answer

[0 -1]
[-1 0]

Answer

[0 1]
[1 0]

Question 45

Given the vectors a = (2, -1) and b = (1, 3), find the resultant vector of 2a - b.

Accepted Answer

(3, -5)

Answer

(3, -4)

Answer

(4, -2)

Answer

(5, -1)

Question 46

A dataset has a mean of 15 and a standard deviation of 3. Assuming a normal distribution, approximately what percentage of the data falls within the range of 12 to 18?

Accepted Answer

68.27%

Answer

50%

Answer

95.45%

Answer

99.73%

Question 47

The cost, £C, of producing n items is given by the formula C = 50n + 200. What does the coefficient 50 represent in this context?

Accepted Answer

The cost of producing one additional item.

Answer

The total cost of producing n items.

Answer

The fixed cost of production.

Answer

The number of items produced.

Question 48

Solve the inequality: 2x - 5 < 7

Accepted Answer

x < 6

Answer

x ≥ 6

Answer

x ≤ 6

Answer

x > 6

Question 49

If f(x) = 2x² - 3x + 1, what is the value of f(-2)?

Accepted Answer

15

Answer

9

Answer

-3

Question 50

A line passes through the points (2, 4) and (5, 10). What is the equation of the line in the form y = mx + c?

Accepted Answer

y = 2x

Answer

y = 2x + 4

Answer

y = x + 2

Answer

y = 2x - 4

Question 51

What is the median of the following dataset: 5, 12, 7, 9, 15, 8?

Accepted Answer

8.5

Answer

9

Answer

8

Answer

10

Question 52

A company produces two types of products, A and B. Each unit of product A requires 2 hours of labor and 3 units of raw material, while each unit of product B requires 3 hours of labor and 2 units of raw material. The company has 120 hours of labor and 100 units of raw material available. Which of the following linear inequalities represents the constraint on labor?

Accepted Answer

2A + 3B ≤ 120

Answer

3A + 2B ≤ 120

Answer

2A + 3B ≥ 120

Answer

3A + 2B ≥ 120

Question 53

A network consists of 5 nodes. The shortest distances between each pair of nodes are given in the following table:

| Node | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---| 
| 1 | 0 | 2 | 4 | 3 | 5 |
| 2 | 2 | 0 | 1 | 5 | 3 |
| 3 | 4 | 1 | 0 | 2 | 4 |
| 4 | 3 | 5 | 2 | 0 | 1 |
| 5 | 5 | 3 | 4 | 1 | 0 |

What is the shortest distance between nodes 1 and 5 using Dijkstra's Algorithm?

Accepted Answer

4

Answer

3

Answer

5

Answer

6

Question 54

A matrix is defined as follows:

| 2  3 |
| 1  4 |

What is the determinant of this matrix?

Accepted Answer

5

Answer

11

Answer

8

Answer

7

Question 55

A company has three factories producing the same product. The cost of producing one unit at each factory is given in the following table:

| Factory | Production Cost (£) |
|---|---| 
| A | 10 |
| B | 12 |
| C | 15 |

The company wants to produce a total of 100 units. Using the transportation simplex method, what is the initial feasible solution that minimizes the total production cost?

Accepted Answer

Factory A produces 50 units, Factory B produces 30 units, and Factory C produces 20 units.

Answer

Factory A produces 30 units, Factory B produces 50 units, and Factory C produces 20 units.

Answer

Factory A produces 20 units, Factory B produces 50 units, and Factory C produces 30 units.

Question 56

A graph has 6 vertices and 8 edges. What is the minimum number of edges that need to be added to make the graph connected?

Accepted Answer

1

Answer

2

Answer

4

Answer

3

Question 57

A group of friends are planning a trip. They need to decide who drives each day and who sits in the passenger seat. If there are 4 friends, how many different arrangements are possible for the first day of the trip?

Accepted Answer

12

Answer

4

Answer

8

Question 58

A company wants to invest in a new project. The project has a 70% chance of success, with a profit of £100,000, and a 30% chance of failure, with a loss of £50,000. What is the expected value of this project?

Accepted Answer

£55,000

Answer

£100,000

Answer

£70,000

Answer

£25,000

Question 59

A project has the following activities and their estimated durations:

| Activity | Duration (Days) |
|---|---| 
| A | 3 |
| B | 4 |
| C | 2 |
| D | 5 |
| E | 1 |

Activity A must be completed before activity B and C can start. Activity D can only start after B and C are completed. Activity E can start after D is completed. What is the critical path for this project?

Accepted Answer

A-B-D-E

Answer

A-B-C-E

Answer

A-C-D-E

Answer

A-C-B-E

Question 60

A company has 5 employees who can be assigned to 5 different tasks. Each employee can only be assigned to one task. How many different ways can the employees be assigned to the tasks?

Accepted Answer

120

Answer

60

Answer

5

Answer

25

Question 61

A group of 10 students need to choose 3 representatives. How many different groups of representatives are possible?

Accepted Answer

120

Answer

1000

Answer

30

Answer

720