Problem Solving Strategies in Mathematics for Year 10

Question 1

Which problem-solving strategy involves starting with an estimate and refining it until you reach a solution?

Accepted Answer

Trial and Improvement

Answer

Heuristics

Answer

Solving Simpler Problems

Answer

Using Diagrams and Models

Question 2

Which problem-solving strategy is not introduced in this unit?

Accepted Answer

Rote memorization

Answer

Heuristics

Answer

Guess and check

Answer

Working backwards

Question 3

Which strategy involves making an initial estimation and then refining it until a satisfactory answer is found?

Accepted Answer

Trial and improvement

Answer

Working backwards

Answer

Using diagrams and models

Answer

Solving simpler problems

Question 4

Which of the following is a heuristic that involves using everyday knowledge and intuition to guide problem-solving?

Accepted Answer

Analogy

Answer

Means-ends analysis

Answer

Working backwards

Answer

Algorithm

Question 5

Which strategy involves starting from the desired result and working backwards to determine the steps needed to achieve it?

Accepted Answer

Working backwards

Answer

Using diagrams and models

Answer

Trial and improvement

Answer

Guess and check

Question 6

Visual representations can help solve problems. Which strategy emphasizes the use of diagrams and models?

Accepted Answer

Using diagrams and models

Answer

Heuristics

Answer

Guess and check

Answer

Solving simpler problems

Question 7

When solving a problem, it is a good idea to:

Accepted Answer

Consider using multiple strategies

Answer

Only use one strategy

Answer

Start with the most complex strategy

Answer

Choose the strategy you are most familiar with

Question 8

Which of the following is not considered a problem-solving strategy?

Accepted Answer

Rote memorization

Answer

Heuristics

Answer

Trial and improvement

Answer

Working backwards

Question 9

Which strategy involves making an initial guess and then refining it based on feedback?

Accepted Answer

Guess and check

Answer

Working backwards

Answer

Solving simpler problems

Answer

Using diagrams and models

Question 10

Which strategy involves starting with the desired outcome and working backward through the steps?

Accepted Answer

Working backwards

Answer

Solving simpler problems

Answer

Using diagrams and models

Answer

Heuristics

Question 11

Which strategy involves creating a visual representation of the problem to aid in solving it?

Accepted Answer

Using diagrams and models

Answer

Trial and improvement

Answer

Heuristics

Answer

Working backwards

Question 12

Which strategy is particularly useful for solving problems that involve a series of logical steps?

Accepted Answer

Working backwards

Answer

Heuristics

Answer

Solving simpler problems

Answer

Using diagrams and models

Question 13

Which of the following is NOT a problem-solving strategy taught in this unit?

Accepted Answer

Using a calculator

Answer

Heuristics

Answer

Trial and error

Answer

Guess and check

Question 14

Sarah wants to buy a new phone that costs £500. She has saved £150 so far. Which of the following equations represents the amount of money she still needs to save?

Accepted Answer

500 - 150 = x

Answer

150 - 500 = x

Answer

500 + 150 = x

Answer

150 x 500 = x

Question 15

What is the first step in the 'guess and check' strategy?

Accepted Answer

Make an initial guess

Answer

Check your guess

Answer

Refine your guess

Answer

Give up

Question 16

Which of the following is an example of working backwards?

Accepted Answer

Starting with the answer and working backwards to find the question

Answer

Trying different values until you find one that works

Answer

Drawing a diagram to represent the problem

Answer

Breaking the problem down into smaller parts

Question 17

Which of the following is **not** introduced as a problem-solving strategy in this unit?

Accepted Answer

Algebraic manipulation

Answer

Heuristics

Answer

Guess and check

Answer

Systematic trial and error

Question 18

The 'working backwards' strategy is most appropriate when you:

Accepted Answer

Know the final result and need to determine the steps to achieve it.

Answer

Have multiple variables and need to isolate a specific value.

Answer

Have a complex equation and need to simplify it.

Answer

Need to find a pattern in a sequence of numbers.

Question 19

Which of the following best describes a heuristic?

Accepted Answer

An educated guess that can be checked and refined.

Answer

Breaking down a problem into smaller parts.

Answer

Using a visual representation to aid in problem-solving.

Answer

Applying a standard mathematical formula to find a solution.

Question 20

A key advantage of using diagrams and models in problem-solving is that they:

Accepted Answer

Help visualize the problem and relationships within it.

Answer

Allow for easier simplification of complex equations.

Answer

Provide a guaranteed step-by-step solution to the problem.

Answer

Eliminate the need for any mathematical calculations.

Question 21

When implementing the 'guess and check' strategy, it is essential to:

Accepted Answer

Systematically check each guess and eliminate incorrect options.

Answer

Make random guesses without any logical basis.

Answer

Guess only once and hope for the correct answer.

Answer

Repeat the same guess multiple times.

Question 22

The 'working backwards' strategy involves:

Accepted Answer

Starting from the desired result and working back to the initial conditions.

Answer

Starting from the initial conditions and working towards the desired result.

Answer

Guessing a solution and then checking it.

Answer

Using a diagram to represent the problem.

Question 23

Which heuristic suggests breaking a problem into smaller, more manageable parts?

Accepted Answer

Means-ends analysis

Answer

Working backwards

Answer

Analogy

Answer

Trial and improvement

Question 24

What is problem-solving, and what are the key steps involved in solving problems effectively?

Accepted Answer

Problem-solving is finding a solution to a challenge. It involves breaking the problem into smaller parts, coming up with and testing possible solutions, and choosing the best one.

Answer

Problem-solving is only for people who are good at math and science.

Answer

Problem-solving is just about trying different solutions until you find one that works.

Answer

You don't need to know anything about a problem to solve it.

Question 25

In a two-step word problem, what is the first step typically used for?

Accepted Answer

Understanding the problem and identifying the information given

Answer

Solving the problem

Answer

Checking the solution

Answer

Drawing a diagram

Question 26

Which of the following is a good approach to use when trying to solve a complex problem?

Accepted Answer

Break it down into smaller, more manageable steps

Answer

Guess and hope for the best

Answer

Ignore the problem until it goes away

Answer

Ask someone else to solve it for you

Question 27

When using the 'Guess and Check' strategy, what is the most important thing to remember?

Accepted Answer

To check all possible solutions systematically

Answer

To guess a solution that is close to the correct answer

Answer

To use technology to find the exact answer

Answer

To give up if you can't find the correct answer right away

Question 28

In a multi-step problem, what is the purpose of writing an equation?

Accepted Answer

To represent the mathematical relationship between the given information and what is being asked

Answer

To guess the solution

Answer

To check the solution

Answer

To simplify the problem

Question 29

When drawing a diagram to solve a problem, what is the most important thing to consider?

Accepted Answer

Accuracy and clarity

Answer

Artistic value

Answer

Size of the diagram

Answer

Colour scheme

Question 30

What is the first step when solving a problem using logical reasoning?

Accepted Answer

Identify the given information and what is being asked

Answer

Draw a diagram

Answer

Guess and check

Answer

Write an equation

Question 31

A train travels 240 miles in 4 hours. Calculate the average speed of the train in miles per hour.

Accepted Answer

60 mph

Answer

40 mph

Answer

80 mph

Answer

100 mph

Question 32

Which problem-solving strategy involves making educated guesses and checking the results?

Accepted Answer

Trial-and-error

Answer

Creating a visual representation

Answer

Reasoning backward

Answer

Applying algebraic equations

Question 33

A rectangular garden measures 10 meters in length and 5 meters in width. Calculate the perimeter of the garden in meters.

Accepted Answer

30m

Answer

15m

Answer

25m

Answer

50m

Question 34

Which of the following is NOT a factor of the number 12?

Accepted Answer

5

Answer

1

Answer

2

Answer

3

Question 35

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

Accepted Answer

Means-ends analysis

Answer

Working backward

Answer

Visualizing the problem

Answer

Using a formula

Question 36

A car travels 250 miles on 10 gallons of petrol. Calculate the car's fuel efficiency in miles per gallon.

Accepted Answer

25 mpg

Answer

15 mpg

Answer

35 mpg

Answer

45 mpg

Question 37

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

Accepted Answer

Linear programming

Answer

Means-end analysis

Answer

Trial and improvement

Question 38

Which of the following is NOT a problem-solving strategy used to find solutions to mathematical problems?

Accepted Answer

Memorize Mathematical Formulas

Answer

Guess and Check

Answer

Create a Diagram or Model

Answer

Work Backwards

Question 39

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

Accepted Answer

Memorizing formulas without understanding their application

Answer

Guess and check

Answer

Draw a diagram

Answer

Solve a simpler problem

Question 40

Which of the following is the first step in the guess and check strategy?

Accepted Answer

Making an initial guess at the solution

Answer

Checking if the guess is correct

Answer

Adjusting the guess based on the results of the check

Answer

Repeating steps 1-3 until the solution is found

Question 41

How does perseverance contribute to effective problem-solving?

Accepted Answer

It helps individuals persist in finding solutions despite challenges

Answer

It encourages individuals to give up easily if the solution is not immediately apparent

Answer

It promotes seeking assistance from others without attempting to solve the problem independently

Answer

It leads to a focus on finding a quick solution rather than the optimal solution

Question 42

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

Accepted Answer

Ignore the problem

Answer

Guess and Check

Answer

Draw a diagram

Answer

Use logical reasoning

Question 43

Which strategy is most suitable for solving a problem involving large amounts of data?

Accepted Answer

Organize the data

Answer

Guess and Check

Answer

Draw a diagram

Answer

Use trial and error

Question 44

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

Accepted Answer

Try to guess the answer without any method

Answer

Guess and check

Answer

Draw a diagram

Answer

Use a formula

Question 45

A group of students wants to raise £200 for charity. They decide to sell raffle tickets at £1 each. What is the minimum number of tickets they need to sell to reach their target?

Accepted Answer

200 tickets

Answer

250 tickets

Answer

300 tickets

Answer

350 tickets

Question 46

Which problem-solving strategy involves systematically testing out different possibilities to find a solution?

Accepted Answer

Guess and check

Answer

Working backwards

Answer

Drawing a diagram

Answer

Using a formula

Question 47

To solve the equation 'x + 5 = 12', which strategy could be used effectively?

Accepted Answer

Working backwards

Answer

Substitution

Answer

Elimination

Answer

Trial and error

Question 48

When solving a challenging problem, it is advisable to:

Accepted Answer

Break it down into smaller, more manageable steps

Answer

Focus solely on the most difficult aspect of the problem

Answer

Ignore any information that doesn't immediately seem relevant

Answer

Give up easily if a solution is not immediately apparent

Question 49

Which of the following is considered a primary benefit of using problem-solving strategies?

Accepted Answer

Enhanced problem-solving abilities

Answer

Reduced stress levels

Answer

Increased self-confidence

Answer

Enhanced creativity

Question 50

When solving mathematical problems, it is crucial to:

Accepted Answer

Verify the reasonableness of your answer

Answer

Give up quickly if you don't find a solution immediately

Answer

Memorize steps without comprehending the underlying concepts

Answer

Avoid using any shortcuts or tricks

Question 51

A farmer has 24 animals, consisting of cows and pigs. Each cow has 4 legs, and each pig has 2 legs. The farmer counts a total of 76 legs. How many cows does the farmer have?

Accepted Answer

8 cows

Answer

6 cows

Answer

10 cows

Answer

12 cows

Question 52

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

Accepted Answer

Memorize formulas

Answer

Guess and check

Answer

Draw a diagram

Answer

Work backwards

Question 53

Which problem-solving strategy is most effective for solving problems involving spatial relationships?

Accepted Answer

Draw a diagram

Answer

Make a table

Answer

Guess and check

Answer

Work backwards

Question 54

What is the initial step in the problem-solving process?

Accepted Answer

Understand the problem

Answer

Solve the problem

Answer

Plan a solution

Answer

Check the solution

Question 55

Which of the following is NOT an advantage of using problem-solving strategies?

Accepted Answer

They can guarantee a good grade on a math test

Answer

They can expedite problem-solving

Answer

They can simplify problem-solving

Answer

They can develop critical thinking skills

Question 56

Which strategy is most appropriate for solving a problem that involves a sequence of steps where a mistake in an earlier step can affect the outcome?

Accepted Answer

Backtracking

Answer

Trial and error

Answer

Guess and check

Answer

Substitution

Question 57

What is the initial step in solving a problem using the trial and error strategy?

Accepted Answer

Make an initial guess

Answer

Check the validity of your guess

Answer

Modify your guess

Answer

Repeat the process

Question 58

Which of the following is an advantage of using the substitution strategy?

Accepted Answer

Can simplify complex problems

Answer

Requires minimal computational effort

Answer

Guarantees a solution

Answer

Works for all types of problems

Question 59

When using the backtracking strategy, what action should be taken if a solution path leads to a dead end?

Accepted Answer

Try a different solution path

Answer

Restart the problem-solving process

Answer

Modify the original problem

Answer

Give up

Question 60

Which problem-solving strategy involves working backwards from the desired outcome?

Accepted Answer

Backward chaining

Answer

Forward chaining

Answer

Means-ends analysis

Answer

Analogy

Question 61

What is the purpose of using analogy in problem-solving?

Accepted Answer

To transfer knowledge from a familiar problem to a new problem

Answer

To generate multiple solutions

Answer

To simplify a complex problem

Answer

To evaluate the validity of a solution

Question 62

Which of the listed factors should NOT be considered when selecting a problem-solving strategy?

Accepted Answer

Personal preferences

Answer

Nature of the problem

Answer

Time available

Answer

Complexity of the problem

Question 63

A train covers a distance of 150 miles within 3 hours. Determine the average speed of the train.

Accepted Answer

50 miles per hour

Answer

45 miles per hour

Answer

55 miles per hour

Answer

60 miles per hour

Question 64

Which strategy is most appropriate for solving a problem involving a substantial amount of data?

Accepted Answer

Creating a table

Answer

Guessing and checking

Answer

Drawing a diagram

Answer

Solving a simplified version of the problem