KS2 SATs-Style Maths Paper (Reasoning 6)
A sixth practice reasoning paper is built to the same format as the two official KS2 reasoning papers, Paper 2 and Paper 3: about 40 minutes, no calculator, worth 35 marks, and covering the whole of the Year 6 maths curriculum through worded and pictorial problems rather than bare calculations. Where the arithmetic paper tests whether a child can calculate, a reasoning paper tests whether they can work out WHAT to calculate: unpicking a multi-step word problem, reading a table, or converting a unit before the actual sum even starts. This practice paper draws on fractions, percentages, decimals, factors and primes, money and statistics, so a child who has already worked through the official papers gets fresh questions on a broad spread of Year 6 skills rather than repeats of ones they have seen before.
Before you start
Make sure you're comfortable with these topics first:
Method
- Note the marks printed next to each question before starting it: a question worth 1 mark wants a single answer, while a question worth 2 or more marks expects working to be shown, since a method mark is available even when the final answer is wrong.
- With around 40 minutes for the whole paper, do not let one hard question eat the time meant for three easier ones. If a question is not falling into place after a minute or so, put a small mark by it and move on, then return once every other question has been attempted.
- Use the size of the answer space as a clue: a large boxed area usually expects working to be shown, while a small box usually wants a single number or word.
- Turn the words into a calculation before writing anything down properly: decide what operation the problem needs, and for a multi-step problem, write down each step in order first.
- Convert units, simplify fractions and check decimal places BEFORE calculating, not after, since a mismatched unit or an unsimplified fraction is one of the most common ways a correct method still loses the final mark.
- For a question giving information in a table, read the whole table first, including its headings, so you know what each row and column means before hunting for one figure inside it.
- Estimate roughly the size of answer you expect before calculating properly, so an answer that is ten times too big, or a fraction where a whole number was expected, gets caught before the paper is handed in.
Worked example
Yusuf has 45 pounds saved. He spends two-fifths of it on a new football, then spends 20% of what is LEFT on a drink and a snack at the match. How much money does Yusuf have left?
- Identify the two separate reductions in order: first a fraction of the original 45 pounds is spent, then a percentage of what REMAINS is spent, not a percentage of the original amount. The order matters.
- Find the cost of the football: two-fifths of 45 pounds. Divide 45 by 5 to find one fifth, 45 / 5 = 9, then multiply by 2 to find two fifths, 9 x 2 = 18. The football costs 18 pounds.
- Find what is left after the football: 45 - 18 = 27 pounds.
- Find 20% of the new amount, 27 pounds, since the question asks for 20% of what is left, not 20% of the original 45 pounds. 20% is the same as 0.2, so 27 x 0.2 = 5.40 pounds.
- Subtract the drink and snack from the 27 pounds: 27 - 5.40 = 21.60 pounds.
- Check the answer makes sense: 21.60 pounds is less than the 27 pounds Yusuf had after buying the football, and the two amounts he spent, 18 pounds and 5.40 pounds, add up to 23.40 pounds, which is less than the original 45 pounds, so the answer is sensible.
Practice questions
Try each question, then tap to reveal the answer.
Q1A ribbon is 64 cm long. Priya cuts off three-quarters of it to use for a display. How long is the piece she cuts off?Show answer
Answer: 64 divided by 4 = 16, then 16 x 3 = 48 cm.
Q2A school library has 340 books. 20% of them are non-fiction. How many non-fiction books are there?Show answer
Answer: 10% of 340 is 34, so 20% is 34 x 2 = 68 non-fiction books.
Q3Which of these numbers is a prime number: 21, 29, 33 or 35? Explain how you know.Show answer
Answer: 29, because its only factors are 1 and itself. The others all have more factors: 21 = 3 x 7, 33 = 3 x 11, and 35 = 5 x 7.
Q4A stopwatch shows a runner's time as 6.847 seconds. Round this time to one decimal place.Show answer
Answer: 6.8 seconds, because the digit after the first decimal place is 4, so it rounds down.
Q5Six children collected this many stickers: 8, 15, 6, 20, 11 and 9. What is the range (the difference between the highest and lowest number) of stickers collected?Show answer
Answer: The highest is 20 and the lowest is 6, so the range is 20 - 6 = 14 stickers.
Q6A square patio has an area of 49 square metres. What is the length of one side of the patio?Show answer
Answer: 7 m, since 7 x 7 = 49.
Q7Mrs Ahmed buys shopping costing 34.65 pounds and pays with a 50 pound note. How much change does she get?Show answer
Answer: 50 - 34.65 = 15.35 pounds change.
Q8A car park has 120 spaces. On Saturday, 0.65 of the spaces were full. How many spaces were empty?Show answer
Answer: 0.65 x 120 = 78 spaces full, so 120 - 78 = 42 spaces were empty.
Exam-style questions
Written in the style of a KS1 and KS2 SATs exam paper, with a full mark scheme.
The table shows how far four friends cycled during a sponsored bike ride: Amara cycled 8.4 km, Ben cycled 6.75 km, Chloe cycled 9.2 km, and Dev cycled 7.65 km. Each rider is sponsored 2 pounds for every WHOLE kilometre they cycle, plus a flat 5 pounds just for taking part. How much sponsorship money did Chloe raise in total?
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
To work out 30% of 90, Freya calculates 90 divided by 30, and gets 3. She writes the answer as 3. Explain the mistake Freya has made, and give the correct answer.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
Free printable worksheet
Want more practice on paper? Download the ks2 sats-style maths paper (reasoning 6) worksheet pack - 8 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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