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Chapter 8: Strategies and problem solving

Combinations

  • You might need to find strategies for counting the total number of possible combinations

  • One way of finding combinations is to make a systematic list

  • Here are al the possible three-digit numbers that can be made from the number cards shown on the right

Counting with calculation

  • Sometimes it’s impossible to write down every possible combination

  • You can count combinations by multiplying the numbers of choices for each opion

  • Here is a four-character password for a website

  • The total number of possible passwords is 26x20x26x2=27040

Problem solving

  • Work out how many choices there are for each dial

    • Dial 1-letter = 26 choices

    • Dial 2-digit from 0 to 9=10 choices

    • Dial 3-digit from 0 to 9 = 10 choices

  • The numbers of choices for each fia; has changed sometimes so 26 choices would increase to 25 if a letter was used

Factors and Primes

  • You have to use a whole number of building blocks in each row, so the length of each row has to be a multiple of the length of one block

  • The answer will be the lowest common multiple

  • Top tip

    • If you are not sure how to start draw a sketch and this might help you see that the lengths are multiples of the numbers

Fractions

  • There are lots of steps in this question so makes sure you keep track of your working and write it down clearly

  • Top tip

    • Write words with each calculations to explain what you are doing

Recurring decimals

  • Start by writing x = the amount if you work out 1000x and 10x you can keep all your working in whole numbers

  • Top tip

    • If a question says ‘show that’ or ‘prove that’ you have to show every step of your working clearly and neatly

      • If a question says ‘shows that’ or ‘prove that’ you have to show every step of your working clearly and neatly

Chapter 8: Strategies and problem solving

Combinations

  • You might need to find strategies for counting the total number of possible combinations

  • One way of finding combinations is to make a systematic list

  • Here are al the possible three-digit numbers that can be made from the number cards shown on the right

Counting with calculation

  • Sometimes it’s impossible to write down every possible combination

  • You can count combinations by multiplying the numbers of choices for each opion

  • Here is a four-character password for a website

  • The total number of possible passwords is 26x20x26x2=27040

Problem solving

  • Work out how many choices there are for each dial

    • Dial 1-letter = 26 choices

    • Dial 2-digit from 0 to 9=10 choices

    • Dial 3-digit from 0 to 9 = 10 choices

  • The numbers of choices for each fia; has changed sometimes so 26 choices would increase to 25 if a letter was used

Factors and Primes

  • You have to use a whole number of building blocks in each row, so the length of each row has to be a multiple of the length of one block

  • The answer will be the lowest common multiple

  • Top tip

    • If you are not sure how to start draw a sketch and this might help you see that the lengths are multiples of the numbers

Fractions

  • There are lots of steps in this question so makes sure you keep track of your working and write it down clearly

  • Top tip

    • Write words with each calculations to explain what you are doing

Recurring decimals

  • Start by writing x = the amount if you work out 1000x and 10x you can keep all your working in whole numbers

  • Top tip

    • If a question says ‘show that’ or ‘prove that’ you have to show every step of your working clearly and neatly

      • If a question says ‘shows that’ or ‘prove that’ you have to show every step of your working clearly and neatly

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