Year 6 SATS Reasoning Practice Paper

Test Information and Setup

This is the cover page of your KS2 Mathematics reasoning paper. You'll need to fill in your personal details like name, date of birth, and school information before starting.

The test code M00070 A helps identify this specific paper. Make sure you write clearly in all the boxes so your test can be processed properly.

Quick Tip: Take a moment to fill in all your details carefully before the test begins - rushing this bit could cause problems later!

Blank Page

This page is intentionally left blank for the test layout. You shouldn't write anything here during your exam.

The page numbering shows this is page 2 of 24, so you've got plenty of questions ahead. Don't worry though - you'll work through them step by step.

Remember: Only write on pages that have actual questions on them!

Test Instructions

Here are the key rules you need to follow during your 40-minute test. No calculators allowed, so you'll be doing all calculations by hand or in your head.

You can use the space around each question for working out, which is really helpful for complex problems. Some questions have a special "Show your method" box where you can earn marks just for showing how you worked something out.

If you get stuck on a question, skip it and come back later. This stops you wasting precious time on one tricky problem when you could be earning marks on easier ones.

Smart Strategy: Always check the marks available for each question - it tells you how much time and effort to spend on it!

Question 1: Reflection

Time to show your geometry skills with this triangle reflection question. You need to draw the mirror image of the triangle across the given mirror line.

Use your ruler to measure carefully and make sure each point of the reflected triangle is the same distance from the mirror line as the original. Think of it like the triangle is looking in a mirror.

Top Tip: Count grid squares to help you place each corner of the reflected triangle in exactly the right spot!

Question 2: Money Problem

This word problem tests your mental maths with money. Amir spent 50p total (£2.00 - £1.50 change = £0.50) on two pieces of fruit.

Look at the prices: banana (12p), plum (23p), apple (32p), pear (38p). You need to find two fruits that add up to 50p exactly.

Try different combinations: 12p + 38p = 50p, so Amir bought a banana and a pear. Always double-check your addition!

Money Maths: Work backwards from the change given - it's often quicker than trying every combination!

Questions 3 & 4: Graphs and Sequences

The bar graph shows Layla's basketball points across games. She scored 25 points total after 4 games, and you can see she got 8 + 6 + 4 = 18 points in the first three games, so Game 4 must be 7 points.

For the number sequence, work out the pattern: -11 to 7 is +18, then 7 to 19 is +12. The sequence goes up by 6 each time: -11, -5, 1, 7, 13, 19.

Pattern Spotting: Always check your sequence by seeing if the differences between numbers stay the same!

Questions 5 & 6: Missing Numbers

The multiplication problem needs you to work out what digits make the calculation correct. Try different numbers systematically until 6 × 5 × something gives you the right answer.

For Olivia's mystery number, use the clues step by step: greater than 236, less than 245, has 3 in tens place 23_, and is even. The only number that fits all these clues is 238.

Detective Work: Cross out impossible answers as you go through each clue - it makes the final choice obvious!

Questions 7 & 8: Multiplication and Rounding

The envelope problem is straightforward multiplication: 40 boxes × 25 envelopes = 1,000 envelopes total. Break it down if needed: 40 × 20 = 800, plus 40 × 5 = 200.

For the rounding questions, think about which numbers would round to give these answers. For example, numbers from 3,500 to 4,499 would round to 4,000 when rounded to the nearest thousand.

Rounding Rules: Remember that 5 always rounds up, and check the digit immediately after your rounding position!

Question 9: Division with Decimals

These division calculations all give decimal answers. Work them out: 4÷10 = 0.4, 40÷10 = 4, 4÷100 = 0.04, 40÷100 = 0.4.

You can see that 4÷10 and 40÷100 both equal 0.4, so that's your answer. Division by 10 moves the decimal point one place left, division by 100 moves it two places left.

Decimal Trick: Dividing by 10, 100, 1000 just moves the decimal point - no long division needed!

Questions 10 & 11: Prime Numbers and Ratios

Prime numbers only divide by 1 and themselves. From the list, the primes are 17, 19, and 23. The pair with a difference of 2 are 17 and 19.

For the ratio table, work out how many children per adult in each row. The 4-5 year olds have 24 children with 8 adults, giving 3 children per adult $24÷8=3$.

Prime Memory: The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23 - worth memorising these!