Problem Solving Quizzes for Year 11 Mathematics in the UK

Question 1

How can modifying your problem-solving approach and strategies affect the outcome?

Accepted Answer

Adapting strategies can enhance both effectiveness and efficiency, leading to more accurate and timely solutions.

Answer

Modifying strategies has no impact on problem-solving effectiveness or efficiency.

Answer

Adjusting strategies can improve effectiveness but may reduce efficiency.

Answer

Efficiency is maximized by always using the same problem-solving approach.

Question 2

How does using knowledge you already have help you solve problems more effectively?

Accepted Answer

It helps you understand new information and choose the best ways to solve problems.

Answer

It means you don't have to think about different ways to solve a problem.

Answer

It guarantees you will always find the right answer.

Question 3

Heuristics are strategies used to solve problems. Explain how heuristics work and provide real-world examples of how they are used.

Accepted Answer

Heuristics involve making educated guesses or simplifications to help solve problems, but their accuracy is not always guaranteed.

Answer

Heuristics always guarantee the best possible solution to a problem.

Answer

Heuristics are only useful for solving abstract mathematical problems.

Answer

Heuristics are computer programs that automatically solve problems without human intervention.

Question 4

In problem-solving, why is effective communication crucial?

Accepted Answer

A. It helps everyone involved understand the problem and its possible solutions.

Answer

B. It only involves speaking, so writing and documentation are not needed.

Answer

C. It slows down problem-solving by adding distractions and complications.

Question 5

Which of the following is NOT a step in the problem-solving process defined by George Polya?

Accepted Answer

Guessing and checking

Answer

Understanding the problem

Answer

Devising a plan

Answer

Carrying out the plan

Question 6

What is the initial stage in solving a logical problem, as suggested by George Polya?

Accepted Answer

Identifying the goal

Answer

Gathering information

Answer

Making a plan

Answer

Implementing the plan

Question 7

Which of the following is NOT an advantage of using a systematic approach to problem-solving, as described by George Polya?

Accepted Answer

Improves creativity

Answer

Reduces errors

Answer

Increases efficiency

Answer

Enhances clarity

Question 8

Which of the following is NOT a characteristic of a good problem solver, as described by George Polya?

Accepted Answer

Impulsiveness

Answer

Perseverance

Answer

Open-mindedness

Answer

Curiosity

Question 9

Which of the following is NOT a step in the problem-solving process?

Accepted Answer

Write a short story

Answer

Define the problem

Answer

Explore possible solutions

Answer

Draw a diagram

Question 10

What is typically the first step in solving a geometry problem?

Accepted Answer

Draw a diagram

Answer

Write an equation

Answer

Guess and check

Answer

Use a calculator

Question 11

What is the key difference between inductive and deductive reasoning?

Accepted Answer

Inductive reasoning moves from specific to general, while deductive reasoning moves from general to specific.

Answer

Deductive reasoning moves from specific to general, while inductive reasoning moves from general to specific.

Answer

Inductive reasoning is based on evidence, while deductive reasoning is based on logic.

Answer

Deductive reasoning is based on evidence, while inductive reasoning is based on logic.

Question 12

Which of the following is a linear equation?

Accepted Answer

y = 2x + 3

Answer

y = x² + 2x - 1

Answer

y = sin(x)

Answer

y = e^x

Question 13

Which of the following is not a strategy for solving mathematical problems?

Accepted Answer

Memorization

Answer

Reasoning

Answer

Trial and improvement

Answer

Logic

Question 14

Which of the following logical connectives represents 'and'?

Accepted Answer

∧

Answer

∨

Answer

⇒

Answer

⇔

Question 15

Which of the following is a characteristic of a valid deductive argument?

Accepted Answer

The conclusion follows logically from the premises.

Answer

The premises are true in all cases.

Answer

The conclusion is more probable than the premises.

Answer

The argument is persuasive.

Question 16

Which of the following is not a heuristic for solving mathematical problems?

Accepted Answer

Linear search

Answer

Means-ends analysis

Answer

Working backwards

Answer

Guessing and checking

Question 17

Which of the following is NOT a recognized problem-solving strategy?

Accepted Answer

Guessing blindly

Answer

Reasoning logically

Answer

Using analogy

Answer

Applying formulas

Question 18

What is the first crucial step in the problem-solving process?

Accepted Answer

Grasping the problem's essence

Answer

Conjecturing a solution

Answer

Attempting to solve it using a specific method

Answer

Checking if the solution is correct

Question 19

What is the key difference between inductive and deductive reasoning?

Accepted Answer

Inductive reasoning infers general principles from specific observations, while deductive reasoning derives specific conclusions from general principles.

Answer

Inductive reasoning is subjective, while deductive reasoning is objective.

Answer

Inductive reasoning uses evidence, while deductive reasoning relies on assumptions.

Answer

Inductive reasoning is always true, while deductive reasoning can be false.

Question 20

When rolling a fair, six-sided die, what is the probability of obtaining a 6?

Accepted Answer

1/6

Answer

1/3

Answer

1/4

Answer

1/5

Question 21

Translate the following statement into an algebraic expression: "The sum of two numbers is 10".

Accepted Answer

x + y = 10

Answer

2x + y = 10

Answer

x - y = 10

Answer

x / y = 10

Question 22

Which of the following is NOT a valid problem-solving strategy?

Accepted Answer

Factoring

Answer

Guess and check

Answer

Trial and improvement

Answer

Making a table

Question 23

A farmer has 12 sheep and 6 goats. He wants to put them into pens of equal size, with each pen containing only sheep or only goats. What is the greatest number of animals that can be in each pen?

Accepted Answer

3

Answer

2

Answer

4

Answer

6

Question 24

A cone has a radius of 5 cm and a height of 12 cm. What is the cone's volume?

Accepted Answer

200π cm³

Answer

100π cm³

Answer

300π cm³

Answer

400π cm³

Question 25

How does understanding the role of emotions in problem-solving enhance your problem-solving skills?

Accepted Answer

It helps you recognize and manage emotions that can hinder logical thinking and problem-solving.

Answer

It allows you to completely suppress negative emotions, ensuring objectivity and clear thinking during problem-solving.

Answer

It enables you to focus solely on positive emotions, which can boost motivation and creativity during problem-solving.

Question 26

A car travels 120 miles using 6 gallons of petrol. Calculate the car's miles per gallon.

Accepted Answer

20

Answer

18

Answer

22

Answer

24

Question 27

Which of the following strategies is essential for effective problem-solving in this unit?

Accepted Answer

Employing logical reasoning and analytical thinking

Answer

Mindlessly attempting different solutions

Answer

Memorizing mathematical formulas without understanding

Answer

Relying solely on guesswork

Question 28

A farmer has 12 sheep and 18 cows. If he sells half of his sheep and a third of his cows, how many animals will he have remaining?

Accepted Answer

21

Answer

24

Answer

18

Answer

15

Question 29

Which of the following traits is NOT characteristic of effective problem-solvers?

Accepted Answer

Acting impulsively without considering consequences

Answer

Persistence in the face of challenges

Answer

Adaptability to changing situations

Answer

Willingness to consider different perspectives

Question 30

In the problem-solving process, which step is crucial for defining the problem accurately?

Accepted Answer

Defining the problem

Answer

Implementing the solution

Answer

Checking the solution

Answer

Brainstorming solutions

Question 31

What is a 'wicked problem'? Explain the challenges involved in solving such problems and provide real-world examples.

Accepted Answer

Complex problems with interconnected factors and no clear solution

Answer

Well-defined problems with a single, clear solution

Answer

Problems that can be solved using a step-by-step process

Answer

Problems that are not relevant to real-world situations

Question 32

When solving problems, it's important to consider ethical implications. How can we navigate these considerations responsibly?

Accepted Answer

Seek guidance from experts or relevant authorities to address ethical concerns.

Answer

Ignore ethical considerations, focusing solely on finding the most efficient solution.

Answer

Consider ethical considerations only in sensitive or controversial situations.

Answer

Apply a universal set of ethical principles to easily identify and resolve ethical considerations.

Question 33

When selecting a problem-solving strategy, what should be the primary consideration?

Accepted Answer

The nature and specific requirements of the problem

Answer

The amount of time available to solve the problem

Answer

The resources and tools at your disposal

Answer

Your personal strengths and weaknesses as a problem solver

Question 34

Calculate the area of a circle with a radius of 5 cm.

Accepted Answer

25π cm²

Answer

50π cm²

Answer

75π cm²

Answer

100π cm²

Question 35

Which of the following is NOT a factor of 12?

Accepted Answer

5

Answer

2

Answer

3

Answer

4

Question 36

To effectively solve complex real-world problems that don't have clear solutions, which change to your problem-solving approach would be most helpful?

Accepted Answer

Clearly define the problem

Accepted Answer

Break the problem into smaller parts

Answer

Guess and check possible solutions

Question 37

In problem-solving, heuristics are best described as:

Accepted Answer

Approximate methods that aim to find good solutions quickly

Answer

Exact methods that guarantee the optimal solution

Answer

Strict rules that must always be followed in a specific order

Question 38

To tackle a complex problem, which strategy involves breaking it down into smaller, easier parts?

Accepted Answer

Decomposition

Answer

Brainstorming

Answer

Analogy

Answer

Guess and check

Question 39

How do logical fallacies and cognitive biases affect problem-solving?

Accepted Answer

They can hinder problem-solving if not recognized.

Answer

They are not relevant to problem-solving.

Answer

They can improve problem-solving if used correctly.

Answer

They only affect complex mathematical problems.

Question 40

In collaborative problem-solving, which situation highlights the benefits of open communication and teamwork?

Accepted Answer

A group actively listens, shares diverse perspectives, and respectfully debates ideas, leading to a comprehensive solution.

Answer

A team leader dominates the discussion, preventing input from other members.

Answer

Group members work alone, avoiding idea exchange or seeking input.

Answer

The group struggles to reach a consensus due to poor communication and lack of respect for different viewpoints.

Question 41

When solving a complex problem, it is most effective to:

Accepted Answer

Break it into smaller, manageable steps

Answer

Memorize formulas and apply them blindly

Answer

Ignore the problem until it solves itself

Answer

Guess and check randomly

Question 42

Which of the following is a type of heuristic used in problem solving?

Accepted Answer

Means-ends analysis

Answer

Pythagorean theorem

Answer

Quadratic formula

Answer

Integration by substitution

Question 43

What is the initial step when using means-ends analysis to solve a problem?

Accepted Answer

Defining the current state and the goal

Answer

Evaluating the effectiveness of potential solutions

Answer

Implementing the chosen solution

Answer

Generating all possible solutions

Question 44

When applying a divide-and-conquer strategy, what is the first step?

Accepted Answer

Breaking the problem into smaller, independent subproblems

Answer

Solving the subproblems simultaneously

Answer

Combining the solutions of the subproblems

Answer

Checking the validity of the final solution

Question 45

Which of the following is an advantage of using flowcharts for problem-solving?

Accepted Answer

Providing a clear visual representation of the problem-solving process?

Answer

Guaranteeing a solution to any problem

Answer

Eliminating the need for logical thinking

Question 46

What is the primary purpose of using a decision table?

Accepted Answer

To illustrate the relationship between conditions and corresponding actions

Answer

To store data in a tabular format

Answer

To solve complex mathematical equations

Question 47

Which strategy can be most effective in overcoming problem-solving fixations?

Accepted Answer

Challenging assumptions and exploring alternative perspectives

Answer

Memorizing more problem-solving formulas

Answer

Ignoring the problem and waiting for inspiration

Question 48

Which of the following is a characteristic of effective problem solvers?

Accepted Answer

Persistence and determination

Answer

Aversion to taking risks

Answer

Lack of creativity

Answer

Impulsivity

Question 49

A train leaves Station A at 10:00 AM and travels at a constant speed of 60 mph. Another train leaves Station B at 10:30 AM and travels at a constant speed of 75 mph. If the distance between Station A and Station B is 240 miles, at what time will the two trains meet?

Accepted Answer

11:36 AM

Answer

12:36 PM

Answer

12:06 PM

Answer

11:06 AM

Question 50

A circle has a radius of 5 centimeters. What is the area of the circle?

Accepted Answer

25π square centimeters

Answer

10π square centimeters

Answer

15π square centimeters

Answer

50π square centimeters

Question 51

A pyramid has a square base with sides of 10 centimeters. The height of the pyramid is 15 centimeters. What is the volume of the pyramid?

Accepted Answer

500 cubic centimeters

Answer

1000 cubic centimeters

Answer

250 cubic centimeters

Answer

750 cubic centimeters

Question 52

Which problem-solving strategy involves breaking down a complex problem into smaller, more manageable parts?

Accepted Answer

Divide and conquer

Answer

Ignoring the problem

Answer

Trial and error

Answer

Guessing and checking

Question 53

Which skill is essential for effective problem-solving?

Accepted Answer

Critical thinking

Answer

Memorization

Answer

Speed

Answer

Luck

Question 54

A train leaves London at 10:00 AM and travels at 80 miles per hour. Another train leaves Birmingham at 11:00 AM and travels at 100 miles per hour. If the distance between London and Birmingham is 120 miles, at what time will the two trains meet?

Accepted Answer

11:36 AM

Answer

12:00 PM

Answer

1:00 PM

Question 55

A company is offering a 15% discount on all its products. If a product originally costs £20, what will be its sale price?

Accepted Answer

£17

Answer

£15

Answer

£21

Answer

£19

Question 56

A bag contains 6 red balls, 4 blue balls, and 2 green balls. If a ball is drawn randomly from the bag, what is the probability of drawing a green ball?

Accepted Answer

1/6

Answer

1/3

Answer

1/4

Question 57

A rectangular garden is twice as long as it is wide. If the perimeter of the garden is 48 metres, what is the area of the garden?

Accepted Answer

128 square metres

Answer

96 square metres

Answer

192 square metres

Answer

64 square metres

Question 58

The sum of three consecutive even numbers is 102. What is the largest of the three numbers?

Accepted Answer

36

Answer

38

Answer

32

Answer

34

Question 59

The mean of five numbers is 12. If one number is removed, the mean of the remaining numbers becomes 10. What is the value of the removed number?

Accepted Answer

20

Answer

10

Answer

12

Answer

15

Question 60

A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is randomly selected from the bag, what is the probability that it is not blue?

Accepted Answer

7/10

Answer

1/2

Answer

2/5

Answer

3/10

Question 61

A farmer wants to divide his animals into equal groups with the largest possible number of animals in each group. He has 12 sheep, 8 cows, and 6 pigs. How many animals will be in each group?

Accepted Answer

2

Answer

6

Answer

12

Answer

4

Question 62

A train leaves London at 10:00 am and travels at a constant speed of 60 miles per hour. Another train leaves Birmingham at 11:00 am, travelling in the same direction at a constant speed of 80 miles per hour. If Birmingham is 120 miles from London, at what time will the second train overtake the first train?

Accepted Answer

1:00 pm

Answer

3:00 pm

Answer

2:00 pm

Answer

12:00 pm

Question 63

A rectangular garden is 10 metres long and 5 metres wide. A path of uniform width is to be built around the garden, increasing the total area to 100 square metres. What is the width of the path?

Accepted Answer

1 metre

Answer

2.5 metres

Answer

1.5 metres

Answer

2 metres

Question 64

A shop sells apples for £1.50 each and oranges for £0.75 each. Sarah buys 3 apples and 2 oranges. How much change does she receive if she pays with a £10 note?

Accepted Answer

£4.75

Answer

£6.25

Answer

£5.25

Answer

£3.75