KS2 SATs-Style Maths Paper (Reasoning 4)
The fourth practice reasoning paper follows the same 40-minute, mixed-question format as the official Key Stage 2 Paper 2 and Paper 3, for extra practice once those papers feel familiar. Its questions are weighted towards parts of the Year 6 curriculum that often feel newest to a child: using a function machine or a simple formula, describing and extending a number sequence, finding a missing number in a two-step equation, working with negative numbers and intervals that cross zero, and multi-step problems that combine a fraction or a percentage with another operation.
Before you start
Make sure you're comfortable with these topics first:
Method
- For a function machine or a simple formula, work out what happens to the input step by step in the order given, and apply the SAME steps in reverse, in the opposite order, to work backwards from an output.
- For a number sequence, work out the term-to-term rule first, what is added, subtracted or multiplied each time, by comparing two neighbouring terms, then apply that rule to extend the sequence or find a missing term.
- For an equation with a missing number, undo the operations one at a time in reverse order: if the equation multiplies then adds, undo the addition first, then the multiplication.
- For negative numbers, picture a number line. Moving right is adding, moving left is subtracting, and a journey that crosses zero covers the distance on both sides of zero added together.
- For a multi-step fraction or percentage problem, work out each step in order and label what each number means, since it is easy to lose track of what a fraction or percentage now refers to after the first step changes the total.
- Write down the rule or formula you are using in words before substituting numbers, since a method mark is often available for a correct approach even if the final number is wrong.
- Check a sequence answer by testing it against the rule with the term before and after it, and check a negative number answer by counting on a number line.
Worked example
A number sequence begins 4, 9, 14, 19. (a) Find the next two terms. (b) Find the 10th term, explaining your method.
- Compare neighbouring terms to find the rule: 9 - 4 = 5, 14 - 9 = 5, 19 - 14 = 5, so the rule is add 5 each time.
- Apply the rule twice more for the next two terms: 19 + 5 = 24, and 24 + 5 = 29.
- For the 10th term, notice the sequence starts at 4 and adds 5 each time, so after n terms you have added 5 a total of (n - 1) times to the first term.
- For the 10th term, that is 9 lots of 5 added to the first term: 4 + (9 x 5) = 4 + 45.
- Work out the sum: 4 + 45 = 49.
- Check by listing forward from the 4th term, 19: the 5th term is 24, the 6th is 29, the 7th is 34, the 8th is 39, the 9th is 44, and the 10th is 49, which matches.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A function machine multiplies the input by 3, then adds 2. What is the output when the input is 6?Show answer
Answer: 20, because 6 x 3 = 18, then 18 + 2 = 20.
Q2A function machine multiplies the input by 3, then adds 2. The output is 26. What was the input?Show answer
Answer: 8, because working backwards: 26 - 2 = 24, then 24 divided by 3 = 8.
Q3Find the missing number: 4n + 3 = 27.Show answer
Answer: n = 6, because 27 - 3 = 24, then 24 divided by 4 = 6.
Q4What is -8 + 15?Show answer
Answer: 7.
Q5The temperature is -4 degrees Celsius at midnight and rises by 9 degrees by midday. What is the midday temperature?Show answer
Answer: 5 degrees Celsius, because -4 + 9 = 5.
Q6A sequence begins 3, 7, 11, 15. What is the term-to-term rule, and what is the 6th term?Show answer
Answer: The rule is add 4 each time. The 5th term is 19 and the 6th term is 23.
Q7A shop reduces a 40 pound jacket by 25 percent, then takes a further 10 pounds off in a weekend sale. What is the final price?Show answer
Answer: 20 pounds, because 25 percent of 40 pounds is 10 pounds, leaving 30 pounds, and then a further 10 pounds off leaves 20 pounds.
Q8Explain why it is important to work out a multi-step problem in the correct order rather than any order you like.Show answer
Answer: Because each step often depends on the result of the one before it, such as a percentage being taken of a NEW total after a previous reduction, so doing the steps in a different order can use the wrong amount and give the wrong answer.
Exam-style questions
Written in the style of a KS1 and KS2 SATs exam paper, with a full mark scheme.
A function machine subtracts 5, then multiplies by 4. (a) What is the output when the input is 12? (b) The output is 48. What was the input? Show your method for both parts.
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A sequence of patterns is made from matchsticks. Pattern 1 uses 4 matchsticks, pattern 2 uses 7, and pattern 3 uses 10. (a) How many matchsticks does pattern 5 use? (b) Write a rule connecting the pattern number, n, to the number of matchsticks.
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Free printable worksheet
Want more practice on paper? Download the ks2 sats-style maths paper (reasoning 4) 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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