[discia] GCSE Maths › Number › Calculation Problems › Practise
  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.

    Show answer
    50p, 20p, 20p, 10p

    The fewest coins that make £1.00 are £1 (1 coin), which is not four coins.

    So a coin has to be swapped for smaller coins until there are four coins.

    50p + 20p + 20p + 10p = £1.00, and that is four coins.

    The coins are 50p, 20p, 20p, 10p.

    • B1coins that add up to £1.00, shown as 50p + 20p + 20p + 10p
    • B1exactly four coins: 50p, 20p, 20p, 10p
  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
    \(\text{£}4.55\)

    The photo frames: \(5 \times £2.10 = £10.50\)

    The candles: \(3 \times £1.65 = £4.95\)

    Total cost: \(£10.50 + £4.95 = £15.45\)

    Change from £20: \(£20 - £15.45 = £4.55\)

    • M1cost of the photo frames \(£10.50\) and of the candles \(£4.95\)
    • M1total cost \(£15.45\)
    • A1change \(£4.55\)
  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
    \(\text{£}13.15\)

    The pasta dishes: \(5 \times £10.75 = £53.75\)

    The orange juices: \(8 \times £1.50 = £12.00\)

    Total cost: \(£53.75 + £12.00 = £65.75\)

    Shared between 5 friends: \(£65.75 \div 5 = £13.15\)

    • M1cost of the pasta dishes \(£53.75\) and of the orange juices \(£12.00\)
    • M1total cost \(£65.75\)
    • A1each pays \(£13.15\)
  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
    \(172\ \text{bundles}\)

    First work out how many leaflets the machine makes altogether:

    \(86 \times 30 = 2580\)

    Then share them out, 15 to a bundle:

    \(2580 \div 15 = 172\)

    • M12580 leaflets made altogether
    • M12580 divided by 15
    • A1172 bundles
  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

    A year has 12 months, so the months still to come are \(12 - 4 = 8\).

    Pay for those months: \(8 \times 1350 = 10800\)

    Add the amount already earned: \(4250 + 10800 = 15050\)

    The yearly total of £15050 is greater than the £15000 limit, so Callum will pay income tax.

    Answer: Yes

    • M1remaining months \(8\), so \(8 \times 1350 = 10800\)
    • M1yearly total \(4250 + 10800 = 15050\)
    • A1Yes, \(15050\) is greater than \(15000\)
  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

    Split the price into pounds and pence:

    \(15070 \times 61 = 919270\)

    \(15070 \times 0.15 = 2260.50\)

    Total takings: \(919270 + 2260.50 = 921530.50\)

    The total is £921530.50.

    Every ticket brings in more than the assumed price, so the total is more than the answer to part (a).

    It is more than the answer to part (a).

    The tickets that cost less lose exactly what the tickets that cost more gain, since the mean price is the assumed price. The actual total equals the expected total.

    It is the same as the expected total.

    • (a) M1splits the price: \(919270\) for the pounds and \(2260.50\) for the pence
    • (a) A1total \(£921530.50\)
  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

    Total of set A: \(196\)

    Total of set B: \(190\)

    The totals differ by \(6\). A swap moves the same amount out of one set as into the other, so each total must move by half of this: \(6 \div 2 = 3\).

    Set A has the larger total, so the number taken from set A must be \(3\) more than the number taken from set B.

    The pair with that difference is \(65\) from set A and \(62\) from set B.

    Check: set A becomes \(193\) and set B becomes \(193\).

    • M1totals \(196\) and \(190\), difference \(6\), half the difference \(3\)
    • A1\(65\) from set A swapped with \(62\) from set B
  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) \(9 \times (8 - 2) = 54\)

    Try each card as the one that stands on its own.

    \((8 + 9) \times 2 = 34\)

    \((2 + 9) \times 8 = 88\)

    \((2 + 8) \times 9 = 90\)

    Only \(90\) is a multiple of 10, so the calculation is \((2 + 8) \times 9 = 90\).

    Try each card as the one that is subtracted.

    \(8 \times 9 - 2 = 70\)

    \(2 \times 9 - 8 = 10\)

    \(2 \times 8 - 9 = 7\)

    Only \(7\) is a single-digit number, so the calculation is \(2 \times 8 - 9 = 7\).

    Try each card as the one that stands on its own.

    \(2 \times (9 - 8) = 2\)

    \(8 \times (9 - 2) = 56\)

    \(9 \times (8 - 2) = 54\)

    Only \(9 \times (8 - 2)\) gives \(54\).

  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.

    Multiply the number of tutor groups by the students in each group, for each school.

    School A: \(76 \times 24 = 1824\)

    School B: \(19 \times 16 = 304\)

    Divide the number of students at School A by the number at School B:

    \(1824 \div 304 = 6\)

    This is a whole number, so the statement is shown.

    • M1both totals, \(1824\) students at School A and \(304\) students at School B
    • A1divide, \(1824 \div 304 = 6\), stated as a whole number
  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
    \(16\ \%\)

    Number of blue beads at the start: \(25\% \text{ of } 56 = 14\)

    After giving 9 away and buying 3: \(14 - 9 + 3 = 8\) blue beads

    New total: \(56 - 9 + 3 = 50\) beads

    Percentage that are blue: \(\frac{ 8 }{ 50 } \times 100 = 16\%\)

    • M1blue beads at the start, \(14\)
    • M1blue beads now, \(8\)
    • M1new total \(50\) beads
    • A1percentage \(16\%\)