Ratio and proportion: past paper questions

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• Question 14May/June 2026, paper 11Structured4 marks

  A bag contains 45 balls. The balls are red or green. The balls are in the ratio $\text{red balls}:\text{green balls}=2:3$.

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• Question 20Oct/Nov 2025, paper 11Structured2 marks

  Some students take a test. 75 of the students pass the test. This is $\frac{3}{5}$ of the students who take the test.

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• Question 5Oct/Nov 2024, paper 31Structured13 marks

  The scatter diagram shows the distance travelled and the cost for each of 12 taxi journeys. 'The scatter diagram shows positive correlation.' Is this statement true or false?

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• Question 9Oct/Nov 2023, paper 31Structured11 marksHas a diagram

  Pure gold costs $42 per gram. The fraction of pure gold in an object is measured in carats.

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• Question 14May/June 2026, paper 12Structured2 marks

  The total number of apples and oranges in a bowl is 20. The ratio $\text{apples}:\text{oranges}=7:3$. Work out the number of apples.

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• Question 22Oct/Nov 2025, paper 11Structured3 marks

  Chocolate cookies Makes 12 100 g flour 55 g butter 55 g sugar 20 g cocoa 1 egg Sunita makes 24 chocolate cookies. Work out how much flour she needs.

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• Question 6Oct/Nov 2024, paper 31Structured14 marks

  This is a recipe to make ice cream for 6 people. 270 ml cream 270 ml milk 100 g sugar 4 egg yolks Tom makes ice cream for 10 people. Work out how much milk he uses.

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• Question 7Oct/Nov 2023, paper 32Structured16 marksHas a diagram

  Elize, Lily and Marco start a business. Elize invests $5000. Lily invests $8000.

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• Question 5May/June 2026, paper 13Structured3 marks

  Sam takes 75 minutes to make a cake. The time taken to make the cake is in the ratio $\text{preparing}:\text{cooking}:\text{decorating}=6:10:9$. Work out the number of minutes Sam takes to decorate the cake.

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• Question 10Oct/Nov 2025, paper 12Structured1 mark

  A bag contains red balls and green balls. They are in the ratio red balls: green balls = 2:3. A ball is picked at random.

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• Question 1Oct/Nov 2024, paper 32Structured12 marks

  Onions cost $1.85 per kilogram and potatoes cost $2.34 per kilogram. Sophie buys 2.4 kg of onions and 4.5 kg of potatoes.

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• Question 3Oct/Nov 2023, paper 33Structured15 marks

  Aneel has 80 tea bags, $\frac{1}{2}\text{ kg}$ of sugar and 1 litre of milk. To make a cup of tea he uses: • 1 tea bag • 8 grams of sugar • 40 millilitres of milk. In the morning, Aneel makes 15 cups of tea.

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• Question 3May/June 2026, paper 31Structured1 mark

  Arya changes 250 pounds into dollars. The exchange rate is 1 pound = $1.26 . Calculate the amount that Arya receives. Arya changes 250 pounds into dollars. The exchange rate is 1 pound = $1.26 . Calculate the amount that Arya receives.

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• Question 5Oct/Nov 2024, paper 33Structured11 marksHas a diagram

  Kurt owns some toy cars of different colours. The pictogram shows the number of each colour. Write down the colour of toy car that Kurt owns most of.

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• Question 4Oct/Nov 2023, paper 33Structured13 marksHas a diagram

  A company makes glass using silica, soda, lime and magnesia. The table gives information about the proportions used.

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• Question 7May/June 2026, paper 32Structured2 marks

  Sian uses 2.7 litres of paint to cover $\frac{3}{5}$ of a wall. Work out the total amount of paint she uses to cover the whole wall.

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• Question 16Oct/Nov 2025, paper 13Structured3 marks

  Kai, Jo and Liz share some money in the ratio Kai : Jo : Liz = 4 : 7 : 13. Jo receives $1400. Find the total amount of money they share. Kai, Jo and Liz share some money in the ratio Kai : Jo : Liz = 4 : 7 : 13. Jo receives $1400. Find the total amount of money they share.

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• Question 6Oct/Nov 2024, paper 33Structured13 marksHas a diagram

  The diagram shows a plan of Zak’s garden. Find the perimeter of the garden.

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• Question 4May/June 2023, paper 12Structured3 marks

  Kai and Ava each have a piece of wood 57 cm long. Kai cuts his piece into 4 equal length parts. Find the length of one part.

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• Question 10Oct/Nov 2025, paper 31Structured2 marks

  Anna and Bruno share some money in the ratio Anna : Bruno = 3 : 7. Bruno receives $36 more than Anna. Calculate the total amount of money they share. Anna and Bruno share some money in the ratio Anna : Bruno = 3 : 7. Bruno receives $36 more than Anna.

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• Question 2May/June 2024, paper 31Structured15 marksHas a diagram

  Chen asks some people if they prefer a beach, cruise, lake or mountain holiday. The pie chart shows the results. Find the fraction of people who prefer a mountain holiday.

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• Question 14Oct/Nov 2025, paper 31Structured3 marks

  A bag contains red, yellow, blue and green cards. The table shows the probability of taking a red card and a yellow card. The probability of taking a blue card or a green card is in the ratio blue : green = 5 : 2 .

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• Question 3May/June 2024, paper 31Structured15 marksHas a diagram

  Here is part of the timetable for trains from Hinton to Jarmouth. All trains take the same time to travel from Hinton to Jarmouth. Complete the timetable.

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• Question 7May/June 2024, paper 32Structured14 marksHas a diagram

  The area of some land is in the ratio park : gardens : playground = 11 : 2 : 3. The park has an area of $4620{\text{ m}}^2$. Work out the area of the gardens and the area of the playground.

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• Question 3May/June 2023, paper 32Structured11 marks

  50 Australian dollars = 540 South African rands On the grid, draw a conversion graph between Australian dollars and South African rands.

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• Question 19May/June 2025, paper 11Structured5 marks

  A box contains 10 counters. The counters are either red or green. The ratio red counters : green counters = 1 : 4.

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• Question 2May/June 2024, paper 33Structured15 marks

  Here is part of the timetable for buses from the station to the city centre. All buses take the same time to travel from the station to the city centre.

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• Question 7May/June 2025, paper 13Structured3 marks

  70 students study one of French, Spanish and German. The ratio number who study French : number who study Spanish = 3 : 7. 15 students study French.

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• Question 14May/June 2025, paper 31Structured3 marksHas a diagram

  Tom needs $225\text{ g}$ of flour to make 10 cakes. A shop sells flour in $500\text{ g}$ bags. Work out the number of bags of flour Tom needs to make 70 cakes.

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• Question 8May/June 2025, paper 32Structured3 marks

  The exchange rate is $1 = 0.923 euros. Calculate the difference between 750 euros and $846. Give your answer in euros correct to 2 decimal places.

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