[discia] GCSE Maths › Number › Calculation Problems

Calculation Problems

discia.org 10 questions · 29 marks
Name Date
  1. Either paper 2 marks

    Zainab buys some sweets for £1.00.

    She pays the exact amount with four coins.

    List the coins she uses.

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    50p, 20p, 20p, 10p
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  2. Either paper 3 marks

    Priya goes to a gift shop.

    She buys five photo frames costing £2.10 each and three candles costing £1.65 each.

    She pays with a £20 note.

    Work out how much change Priya should get.

    Show answer
    \(\text{£}4.55\)
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  3. Either paper 3 marks

    A group of five friends go to an Italian cafe.

    They each buy one pasta dish, costing £10.75.

    They also buy eight orange juices costing £1.50 each.

    They share the total cost equally between them.

    Work out how much each friend pays.

    Show answer
    \(\text{£}13.15\)
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  4. Either paper 3 marks

    A machine prints 86 leaflets every minute.

    The machine runs for 30 minutes.

    The leaflets are then packed into bundles. Each bundle holds 15 leaflets.

    Work out how many bundles are filled.

    Show answer
    \(172\ \text{bundles}\)
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  5. Either paper 3 marks

    Callum will pay income tax if he earns more than £15000 in a year.

    After 4 months Callum has earned a total of £4250.

    For the rest of the year he earns £1350 each month.

    Will Callum pay income tax?

    You must show your working.

    Show answer
    Yes, Callum earns £15050 in the year against the £15000 limit
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  6. Either paper 4 marks

    A football club sells 15,070 tickets for a match.

    Assume that each ticket costs £61.15.

    (a)

    Work out the total amount of money from ticket sales for this match.

    (b)

    In fact, the tickets do not all cost £61.15. Every ticket costs more than this.

    What does this mean about the total amount of money from ticket sales for this match? Tick one box.

    \(\square\) It is not possible to tell

    \(\square\) It is more than the answer to part (a)

    \(\square\) It is less than the answer to part (a)

    \(\square\) It is the same as the answer to part (a)

    (c)

    For a second match the club sells 19,564 tickets. It expects each ticket to cost £30.05 and works out an expected total on that basis.

    In fact, the tickets do not all cost £30.05. Some cost less than this and some cost more than this, but the mean price of a ticket is exactly this.

    What does this mean about the actual total from ticket sales for the second match? Tick one box.

    \(\square\) It is less than the expected total

    \(\square\) It is the same as the expected total

    \(\square\) It is not possible to tell

    \(\square\) It is more than the expected total

    Show answer
    (a) \(\text{£}921530.50\)
    (b) It is more than the answer to part (a)
    (c) It is the same as the expected total
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  7. Either paper 2 marks

    Here are two sets of numbers.

    Set A: \(28,\ 34,\ 65,\ 69\)

    Set B: \(32,\ 33,\ 62,\ 63\)

    One number from set A is swapped with one number from set B.

    The total of the numbers in each set is now the same.

    Which two numbers are swapped?

    Show answer
    \(65\) from set A and \(62\) from set B
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  8. Either paper 3 marks
    Here are three number cards.
    982
    In each part, write all three cards in the boxes of the calculation. Use each card once.
    (a)

    Use all three cards to make the answer to this calculation a multiple of 10.

    \((\square + \square) \times \square\)

    (b)

    Use all three cards to make the answer to this calculation a single-digit number.

    \(\square \times \square - \square\)

    (c)

    Use all three cards to make this a correct calculation.

    \(\square \times (\square - \square) = 54\)

    Show answer
    (a) \((2 + 8) \times 9\) (the two cards that are not on their own can swap places)
    (b) \(2 \times 8 - 9\) (the two multiplied cards can swap places)
    (c) \(9 \times (8 - 2) = 54\)
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  9. Either paper 2 marks

    School B has 19 tutor groups. Each tutor group has 16 students.

    School A has 76 tutor groups. Each tutor group has 24 students.

    Show that the number of students at School A divided by the number of students at School B is a whole number.

    Show answer
    School A has \(76 \times 24 = 1824\) students and School B has \(19 \times 16 = 304\) students; \(1824 \div 304 = 6\), a whole number.
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  10. Either paper 4 marks

    Zainab has 56 beads.

    25% of the beads are blue.

    Zainab gives 9 of the blue beads to a friend. She then buys 3 new blue beads.

    Find the percentage of her beads that are now blue. You must show your working.

    Show answer
    \(16\ \%\)
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discia.org Calculation Problems · sheet 1
Answers Calculation Problems · sheet 1
  1. 50p, 20p, 20p, 10p
  2. \(\text{£}4.55\)
  3. \(\text{£}13.15\)
  4. \(172\ \text{bundles}\)
  5. Yes, Callum earns £15050 in the year against the £15000 limit
  6. (a) \(\text{£}921530.50\)
    (b) It is more than the answer to part (a)
    (c) It is the same as the expected total
  7. \(65\) from set A and \(62\) from set B
  8. (a) \((2 + 8) \times 9\) (the two cards that are not on their own can swap places)
    (b) \(2 \times 8 - 9\) (the two multiplied cards can swap places)
    (c) \(9 \times (8 - 2) = 54\)
  9. School A has \(76 \times 24 = 1824\) students and School B has \(19 \times 16 = 304\) students; \(1824 \div 304 = 6\), a whole number.
  10. \(16\ \%\)
discia.org Calculation Problems · sheet 1