Reasoning Practice Paper
The Reasoning Practice Paper covers Papers 2 and 3 of the Key Stage 2 Maths SATs: two calculator-free tests, each 40 minutes long and worth 35 marks, sat after the Arithmetic paper (Paper 1).
Before you start
Make sure you're comfortable with these topics first:
Method
- Skim through the whole paper briefly before starting, so you know roughly how the marks are spread and are not caught out by a difficult question early on.
- Attempt the questions in order, but do not get stuck: if a question is taking too long, mark it to come back to and move on, since every question is worth the same effort of time regardless of its position.
- Read word problems carefully and underline the key numbers and exactly what is being asked, since reasoning papers often hide the actual calculation inside a longer sentence.
- Always show your method in the space provided, even for a question you can do in your head, since many questions award a method mark separately from the answer mark.
- Use a bar model, number line or quick sketch for word problems where the relationship between the numbers is not obvious, rather than guessing which operation to use.
- Manage your time using the marks available: with 35 marks in 40 minutes, aim to average a little over a minute per mark, spending less time on 1-mark questions to leave more time for the multi-mark questions later in the paper.
- In the last few minutes, check answers against the question again, not just the arithmetic, and make sure every answer box has something written in it, since a sensible guess can still earn marks on a multiple-choice or true-or-false question.
Worked example
A youth club has 96 members. Three eighths of the members are under 11 years old. Of the members who are 11 or older, a quarter play in the club football team. How many members play in the football team?
- Find the number of members under 11: 3/8 of 96. Divide 96 by 8 to find one eighth: 96 divided by 8 = 12.
- Multiply by 3 to find three eighths: 12 x 3 = 36 members are under 11.
- Find the number of members who are 11 or older by subtracting from the total: 96 - 36 = 60.
- Find a quarter of this remaining group: 60 divided by 4 = 15.
- So 15 members play in the football team.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1True or false: 0.6 is greater than 3/5. Explain your answer.Show answer
Answer: False - 3/5 is equal to 0.6, not less than it
Q2Circle the odd one out, giving a reason: 45, 60, 75, 90, 100Show answer
Answer: 100 - the other four numbers (45, 60, 75, 90) are all multiples of 15, but 100 is not
Q3Which calculation is equivalent to finding 3/4 of 48? A) 48 divided by 4 x 3 B) 48 x 4 divided by 3 C) 48 + 3 divided by 4 D) 48 divided by 3 x 4Show answer
Answer: A (48 divided by 4 x 3 = 36)
Q4A market trader sells oranges in bags of 6 for 2.40 pounds, or loose at 45p each. Chidi wants to buy 18 oranges. Work out the cheapest way for him to buy them, and how much he saves compared with the more expensive way.Show answer
Answer: Buying 3 bags (7.20 pounds) is cheaper than buying 18 loose (8.10 pounds); he saves 90p (0.90 pounds)
Q5A ferry departs at 09:35 and the crossing takes 1 hour 48 minutes. What time does the ferry arrive?Show answer
Answer: 11:23
Q6The mean age of 4 friends is 13. A fifth friend joins the group who is 23 years old. Work out the new mean age of all 5 friends.Show answer
Answer: 15
Q7A triangle has one angle of 90 degrees and another angle of 34 degrees. Work out the size of the third angle, and state what type of triangle it is (acute, right-angled or obtuse).Show answer
Answer: 56 degrees; it is a right-angled triangle, because one of its angles is 90 degrees
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A school office orders 15 boxes of paper. Each box contains 8 reams. The school already had 34 reams in the cupboard. Work out the total number of reams the school now has.
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Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
A gardener plants tulip bulbs in rows. Each row has 14 bulbs. She plants 9 complete rows, then has 5 bulbs left over that are not enough for another full row. Work out the total number of tulip bulbs she started with.
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Tick each line you got. Your score builds from the marks on the scheme.
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A cafe sells coffee for 2.80 pounds and tea for 1.95 pounds. On Saturday, the cafe sold 45 coffees and 32 teas. On Sunday, it sold 15 fewer coffees than on Saturday, but the same number of teas. Work out the total amount of money the cafe took from coffee and tea sales across both days.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Free printable worksheet
Want more practice on paper? Download the reasoning practice paper worksheet pack - 6 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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