KS2 SATs-Style Maths Paper (Reasoning 5)
The fifth practice reasoning paper follows the same format as the official Key Stage 2 Paper 2 and Paper 3, for extra practice once the earlier reasoning papers feel secure. Its questions are weighted towards ratio and direct proportion, converting between units of measurement, and multi-step problems involving money and scaling, using different numbers, units and contexts from the ratio and conversion questions in the second practice paper.
Before you start
Make sure you're comfortable with these topics first:
Method
- For a direct proportion problem, where one amount scales up or down in step with another, such as a recipe, find the value for ONE unit first by dividing, then multiply that unit value by whatever amount the question asks for.
- For a ratio problem, work out the total number of equal parts by adding the numbers in the ratio, divide the total amount by that number of parts to find the value of one part, then multiply by however many parts each share needs.
- For unit conversion, know the key facts: 1000 grams in a kilogram, 1000 millilitres in a litre, 10 millimetres in a centimetre, 100 centimetres in a metre, and roughly 5 miles for every 8 kilometres.
- Decide whether you are converting to a SMALLER unit (multiply) or a LARGER unit (divide), since going from kilograms to grams needs more of the smaller unit, and going from grams to kilograms needs fewer of the larger unit.
- For a multi-step money problem, list what needs to be paid for as separate lines before calculating, work out each line, then add or subtract them in the order the question describes.
- Draw a bar model for a ratio or proportion problem when the numbers feel hard to hold in your head: it turns the parts of the ratio into a picture you can divide and label.
- Show every step of your working, since reasoning papers usually give a method mark for a correct approach and a separate mark for the final answer.
- Check the answer is the right SIZE for the context: a scaled-up recipe should need MORE of each ingredient, not less, and a distance in metres should usually be a much bigger number than the same distance in kilometres.
Worked example
A recipe for 4 people uses 300 grams of flour. How much flour is needed for 10 people?
- Find the amount for ONE person by dividing the amount for 4 people by 4: 300 divided by 4 = 75 grams per person.
- Multiply the amount for one person by the number of people needed: 75 x 10 = 750.
- Write the answer with its unit: 750 grams of flour are needed for 10 people.
- Check the answer makes sense: 10 people is more than 4 people, so the amount of flour needed should be bigger than 300 grams, and 750 grams is bigger, so the answer is reasonable.
- Check by another route: 10 people is two and a half times as many as 4 people, since 10 divided by 4 = 2.5, and 300 x 2.5 = 750, which matches.
Practice questions
Try each question, then tap to reveal the answer.
Q1A recipe for 6 people uses 180 grams of butter. How much butter is needed for 9 people?Show answer
Answer: 270 grams, because 180 divided by 6 = 30 grams per person, and 30 x 9 = 270.
Q2Paint is mixed in the ratio 2 parts blue to 5 parts white to make 700 ml of paint. How much blue paint is used?Show answer
Answer: 200 ml, because there are 7 equal parts in total (2 + 5), 700 divided by 7 = 100 ml for one part, and 2 parts of blue is 2 x 100 = 200 ml.
Q3Convert 2.5 kilograms into grams.Show answer
Answer: 2500 g, because there are 1000 grams in a kilogram, so 2.5 x 1000 = 2500.
Q4Convert 850 millimetres into centimetres.Show answer
Answer: 85 cm, because there are 10 millimetres in a centimetre, so 850 divided by 10 = 85.
Q5A cinema ticket costs 7.50 pounds for an adult and 4.25 pounds for a child. A family buys 2 adult tickets and 3 child tickets. What is the total cost?Show answer
Answer: 27.75 pounds, because 2 adult tickets cost 2 x 7.50 = 15.00 pounds, 3 child tickets cost 3 x 4.25 = 12.75 pounds, and 15.00 + 12.75 = 27.75 pounds.
Q6A car journey is roughly 40 miles. Roughly how many kilometres is that, using 5 miles is about 8 kilometres?Show answer
Answer: About 64 km, because 40 miles is 8 lots of 5 miles, and each 5 miles is about 8 km, so 8 x 8 = 64 km.
Q7Explain why finding the value of ONE part or ONE unit first is a reliable method for both ratio and direct proportion problems.Show answer
Answer: Because once you know what a single part or a single unit is worth, you can multiply it by any number of parts or units the question asks for, which works whether the amounts are being scaled up or down.
Q8A model car is built at a scale of 1 to 20. The real car is 4 metres long. How long is the model, in centimetres?Show answer
Answer: 20 cm, because the real car is 4 metres, which is 400 cm, and at a scale of 1 to 20 the model is 400 divided by 20 = 20 cm long.
Exam-style questions
Written in the style of a KS1 and KS2 SATs exam paper, with a full mark scheme.
A youth club mixes squash in the ratio 1 part cordial to 6 parts water to make 3.5 litres of drink. (a) How many equal parts are there in total? (b) How much cordial is needed, in millilitres?
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A school trip costs 12.50 pounds per pupil for entry, plus a coach hire of 180 pounds shared equally between however many pupils go. If 30 pupils go on the trip, work out the total cost per pupil, showing your working.
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Free printable worksheet
Want more practice on paper? Download the ks2 sats-style maths paper (reasoning 5) worksheet pack - 9 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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