250+ SATs Questions Free To Download [With Answers]

April 17, 2024 | 14 min read

Emma Johnson

Here are hundreds of free SATs questions for you to use in the run up to the KS2 Maths SATs in May. Because we never just want to give you a load of links, we start with some useful background on the type and format of SATs questions to expect as well as some tips for using them and strategies for answering them.

If you just want the free download, you’ll find it here: Free resource pack of 100 arithmetic and 100 reasoning questions

Guided practice and support to answer SATs questions is at the heart of the one to one online maths lessons we teach every week. We have thousands of these questions on our tutoring platform so that pupils on the SATs revision programme can work through them step by step with their tutor, building confidence and expertise. Regular exposure to the types of questions pupils will be expected to tackle in May is one of the key ways to ensure children are as prepared as they can be for their SATs tests.

Try the one to one maths lessons for yourself in this free downloadable SATs intervention pack.

A Third Space Learning SATs revision lesson aligned with the SATs tests, including support prompts to help your pupils.

In this article, we take a look at why SATS questions are a useful tool for teachers in the run up to the KS2 SATS tests. We also take a deeper look at the three papers: the types of questions which have come up previously, and how we can best help children prepare for these. We analyse the different topic domains; what proportion of the papers we can expect to include questions from each of the content domains and, finally, we provide questions for you to use, covering each of the topic areas. We also provide links to a range of free resources for you to use to support children in their SATS preparation.

Why do teachers and tutors need SATs questions?

You probably already know the answer to this question but for those who don’t, let’s take a look at the benefits SATS style questions can provide as part of your SATs preparation:

Reinforcing content: Practising SATS style questions and working through past SATS papers helps to reinforce the National Curriculum concepts pupils have been taught. It also gives students the opportunity to apply their knowledge across different types of questions.
Familiarity with the format of the exam/questions: Many SATS questions follow a specific format. If students are exposed to these questions, then it helps them to prepare and also improve confidence in their ability to complete the tests.
Identifying gaps: Practice questions enable both the teacher and the students to see where there may be areas of weakness and where they may benefit from extra support or intervention.
Read more: SATs i nterventions
Assessing progress: Completing SATS questions provides teachers with a benchmark of where students are and enables progress to be tracked over time. This is useful for the teacher in understanding how the children are progressing and also for the pupils to see how they are improving.
Read more: Formative assessment
Building confidence: Children can feel very nervous as SATS are approaching. By practising questions which are a similar style to those they will be given, this helps to build confidence that the tests aren’t as intimidating as they initially thought.
Read more: Confidence in maths
Reducing anxiety around the test: By practising SATS questions, as part of the maths revision, students are more likely to feel confident in approaching the test, which in turn will mean they feel less stress when it comes to sitting the actual test.
Read more: Maths anxiety
Developing exam strategies: Through exposure to SATS style questions, children are able to learn strategies to solve them. When they get to the actual test, they will then be more confident in tackling the different questions they are given.
Read more: SATs strategies
Time management: By practising similar questions to the questions they will be given in the test, students can learn how to use their time wisely – understanding which questions to spend more time on and which questions to move on from more quickly.

200 arithmetic and reasoning questions for Year 6

Download 100 free arithmetic questions and 100 free reasoning questions for Year 6. Includes answers and mark scheme.

Download Free Now!

What you should know about the maths questions in the SATs papers

SATs questions are not only for Year 6!

SATS style questions don’t have to be saved for use only with year 6 pupils. Students also benefit from exposure to SATS style questions in the other year groups in Key Stage 2. By having this experience in other year groups, the style of questions they will meet in their SATS exam aren’t something new and different to anything they’ve experienced in previous years.

The tricky questions

Sometimes SATS questions can be designed to catch children out, or to highlight when a question hasn’t been read correctly. If students have plenty of opportunities to practise these questions, they then know what to look out for and are much less likely to be tripped up by the time they reach the actual SATS.

Format and structure of the maths SATs test

The maths SATS consist of three papers:

Paper 1: Arithmetic (30 minutes)

This paper is designed to assess students’ understanding in mathematical concepts through fixed response, fluency style questions.

Paper 2: Reasoning (40 minutes)
Paper 3: Reasoning (40 minutes)

These 2 papers evaluate students’ reasoning and problem solving skills. Questions on this paper vary in style, with some involving more complex problem solving scenarios.

Whilst the arithmetic paper predominantly contains 1 mark questions, with minimal need to show workings out, the reasoning papers contain far more 2 mark questions and even a 3 mark question, where marks can be gained from showing workings out or explaining reasoning. It is important for children to have exposure to this type of question to ensure they know how to answer, in order to achieve as many marks as possible.

How to achieve a high score on questions in SATs

The two most content-heavy content domains in the year 6 SATS papers are calculations and fractions, decimals and percentages (FDP). These two areas account for 58% of the total mark. With 51% being the pass mark, it is clear how important it is that children are as secure as they can be in these 2 areas.

Of the three papers, the arithmetic paper is the easiest to prepare children for, due to the straightforward nature of the questions, compared to the reasoning papers. If children can achieve a score of at least 30 out of 40 in the arithmetic paper, they only need a further 26 marks across both reasoning papers, to be considered as having achieved the expected standard.

Examples of SATs maths questions

As part of their SATS preparation, Children need to build their confidence in solving multi step word problems, such as this one. It’s important to practise these multi-step questions, to avoid losing marks by not completing everything that is being asked.

SATs maths question example 1

Paper 2, qu.17 (2023)

Some questions can have a much higher level of cognitive demand than you would expect from the number of points awarded. It’s good to ensure children see this type of question in advance and to think about whether leaving it until the end would potentially mean answering more straight forward questions in the allocated time. It’s important children understand that spending a long time on one question can potentially impact on their final score, if they run out of time to complete easier/quicker questions.

SATs maths question example 2

Paper 2, qu.24 (2023)

The content of the maths questions in SATS has previously involved some quite obscure questions, which have no relevance to the children taking the test, however in recent years, questions have followed themes which children are better able to relate to.

SATs maths question example 3

Paper 2, qu. 4 (2023)

It is worth taking the time to look at previous questions, which have not been so relatable to children, to ensure they are prepared to tackle this type of question.

Strategies for solving SATS questions effectively

For children to have the best possible chance of scoring well in the maths SATS, it is important to equip them with the skills to do this. Working through practice papers and past SATS test papers, is useful for helping them to prepare. Providing students with a bank of strategies is also beneficial For example:

Making sure the question has been understood: Read the question carefully and make sure the they fully understand what is being asked, before attempting to solve it.

Underlining the key information: Focus on the key points within word problems. A lot of information in this type of question isn’t relevant for solving it. Children need to learn to underline the information that they will need.

Showing workings out: Children need to be taught the importance of showing workings out. Marks can be lost by children calculating answers in their heads. If they show their workings out, but make a mistake with the final answer, they can still earn marks. If they calculate in their head and make a mistake, they won’t receive any marks.

Managing time carefully: Make sure students are aware of the time they should spend on each question and when it would be more appropriate to put a star next to a question and move on. It is better to miss a question out and attempt it again at the end, than spend time on a question and fail to complete the rest of them.

How to improve mental maths skills for SATS

Although mental maths is no longer assessed as part of the maths SATS, strong mental maths skills are still essential. Knowledge of the times tables is vital to success in many areas of the maths curriculum. Other mental maths skills children need to develop include estimation skills, and speed and accuracy.

To improve these skills, little and often is the key. Students should be given the opportunity to practise daily through a variety of resources, including: online maths games, in-person maths games, worksheets and flashcards.

Mark schemes and available marks in maths for SATs questions

Understanding how marks are awarded in the KS2 maths SATs is useful for both teachers and students. The arithmetic paper is predominantly one mark questions, so marks are only awarded for the correct answer, not for showing the correct working out. The only questions which students can pick up two marks for, on this paper, are long division and long multiplication. For these questions, it’s essential that students show their workings out, as they can pick up one mark for an incorrect answer, if they show that they have used the correct calculation to attempt to solve it.

The reasoning papers have a combination of 1, 2 and 3 mark questions. In the higher mark questions, pupils can usually pick up a mark for the correct calculation, but incorrect answer. With this in mind, it is important children are aware of this and are taught to always show their workings out, even if they feel it is something they can calculate in their heads.

Content domain coverage of the SATs questions

When preparing students for SATS, it is also useful to be aware of the content domain coverage table at the start of the mark scheme. This table lists which year group and which objectives each question is focusing on. Having an understanding of the content coverage is helpful for ensuring appropriate time is given to ensuring confidence in some of the key areas, such as the four operations and fractions, decimals and percentages.

How to prepare for the SATs questions in the Arithmetic papers

In recent years, the arithmetic papers have covered a very similar structure, with calculation and fractions, decimals and percentages being the focus of a high proportion of the paper each year. Only a few questions in each paper are outside these areas:

KS2-arithmetic-paper-questions-by-domain

Questions in this paper are straightforward, fluency questions. The structure of these questions is generally similar each year, with positioning the answer box at the start of the question, being a style of question which appears a lot. It’s important that children are exposed to questions where the answer is at both the beginning and end of the question.

Paper 1, Question 2 (2023)

It is also common to see similar questions throughout the paper, but with increasing levels of difficulty. For example, with the fractions and percentages questions here:

Children also need to be prepared for questions being presented in more than one way. For example, with this question, children who haven’t experienced a question presented this way before, may not recognise it as a question that would be easier to solve a fraction of an amount question, rather than a multiplying fraction question.

Strong arithemtic skills are key for helping students to develop speed fluency an automaticity in the arithmetic paper. There are a number of things teachers can do, to help children develop these skills:

Regular practice: Set aside a dedicated time each day to focus on these basic skills. Also regular exposure to practice tests
Begin with basic facts: Ensure students are secure in the basic arithmetic facts, such as addition, subtraction and times tables facts. Games (both in person and online) are great for helping children to learn these basic facts.
Mental maths strategies: Teach children mental maths strategies. This will help develop both speed and fluency for the arithemetic paper.
Practise with timed tasks: Time children completing short arithmetic tasks. Children work to improve their times.
Online resources: Online games are a great way to motivate children to practise skills, such as times tables facts.
Simulate test conditions: If children are exposed to test style conditions in advance of sitting the actual SATS, this helps familiarise the children and reduce anxiety for the actual maths test.

Understanding the mark scheme for SATs arithmetic questions

The mark scheme for the arithmetic maths paper in the Key Stage 2 SATS is very straight forward. The majority of the questions are worth one mark, with only the longer questions, such as long multiplication and long division calculations being given 2 marks. So, for most Year 6 arithmetic questions, the mark is simply one mark for getting the answer correct, whilst with the longer questions, children automatically receive two marks if the answer is correct, but can also receive one mark, if the answer is incorrect, but they have used the correct calculation.

Free SATs arithmetic questions:

How to prepare for the SATs questions in the Reasoning papers

The reasoning papers contain a wider variety of questions than the arithmetic paper. There are a mix of question types, including single-step, multi-step, explanation questions and sequencing/ordering questions. These are a combination of one, two and three mark questions and assess the children’s understanding more deeply than the arithmetic paper.

High levels of fluency are beneficial for the reasoning paper, with some questions designed to highlight students who have higher levels of fluency. For example, with this question, children with high levels of fluency could very quickly spot this question could be solved without any calculations needed. Whilst other children spent a long time trying to work out the calculations, to solve it:

Paper 3, Qu. 13 (2023)

The reasoning papers generally increase in difficulty as the paper progresses, with more content from year 6 appearing later in the paper. There can be a few surprises thrown in, early on, but generally the first half of each paper is easier than the second half.

Multi-step word problems are commonly introduced later in the paper. These are the longer two mark and occasional three mark questions.

Paper 3, Qu.16 (2023)

Children also need to be aware, with the reasoning papers, that there can be questions which take a considerable length of time to complete. These higher cognitive demand questions can hold students up from completing the rest of the paper. It is helpful to train children to be aware of these and encourage them to mark the question and move on to the rest of the paper.

Developing the skills needed to answer SATS reasoning questions

The reasoning papers cover a broader range of topics than the arithmetic paper. For pupils to successfully complete the reasoning papers, they need to have a solid understanding of the key concepts. The weighting is still more towards calculations and fractions decimals and percentages, but to score well, children do also need to be confident in other maths curriculum areas.

Skills pupils need to be successful in the reasoning papers include:

Problem solving: The ability to understand and analyse a problem and apply mathematical concepts to real life situations.
Reasoning: Be able to make logical connections between different pieces of information.
Mathematical operations: Confident in the four operations and be able to apply this in various contexts.
Mathematical vocabulary: Knowledge of key mathematical terms which could be used in the papers.
Time management: Children need the skills to complete the test within the allocated time and the understanding of when to attempt a question and when it would be better to move on.

Understanding the mark scheme for reasoning questions

The mark scheme for the reasoning paper goes into considerably more detail than the mark scheme for the arithmetic paper. It is important to be aware of the mark scheme when marking any questions from KS2 SATS papers, as marks can be scored in on these papers, even if the answer is incorrect. If children show they have understood the method, but have made an error in the calculation, they are able to score one mark in a two mark question. It’s important children learn to always show their calculations, to ensure they pick up as many marks as possible

Free SATs reasoning questions:

SATs questions by maths topic and content domain

When preparing for the SATS tests, it’s helpful to know which topics to prioritise. The papers generally follow a similar format each year, with certain areas (such as calculation and fractions, decimals and percentages) having a much higher weighting than areas such as ratio and proportion or statistics.

For a more in depth analysis of the SATS papers look at this article on the top 20 Year 6 maths revision topics.

Below we have included 22 exemplar SATs arithmetic and SATs reasoning questions – with answers of course – arranged by topic. As in the real life SATs we’ve roughly weighted the number of questions per topic.

Don’t miss the links at the end of this article for lots more free SATs questions, SATs revision resources and SATs intervention support.

Calculations SATS questions

The four operations are guaranteed to come up throughout all three papers. The highest percentage of the SATS exam is focused on this domain. Therefore, it is important children are secure and confident in all four written methods and applying this knowledge to a range of one-step and multi-step word problems.

Calculations SATs questions – arithmetic

SATs arithmetic question 1

3,362,879 + 36,279 =

Answer: 3,599,158 (1 mark)

3,362,879 + 36,279 = 3,599,158

SATs arithmetic question 2

3,978 ÷ 26 =

Answer: 153 (1 mark)

3,978 ÷ 26 = 153

Calculations SATS questions – reasoning

SATs reasoning question 1

A house sold for £485,999. 5 years later, it sold for 123,899 more. How much did it sell for 5 years later?

Answer: £609,898 (1 mark)

485,999 + 123,899 = £609,898

SATs reasoning question 2

There were 9,725 passengers on a cruise ship. At the next port a further 487 passengers got on, but 276 passengers got off. How many are on the cruise ship now?

Answer: 9,936 (2 marks)

9,725 + 487 = 10,212

10,212 – 276 = 9,936

SATs reasoning question 3

Circle the two numbers which have a difference of 326:

423 , 716, 832, 749, 581

Answer: 423 and 749 (1 mark)

423, 716, 832, 749 , 581

SATs reasoning question 4

Mr Smith spent £28,749 on a new car. He then spent £7,389 on a caravan. He now has £6,752 left in his bank account. How much did he have to start with?

Answer: £42,890 (2 marks)

£28,749 + £7,389 + £6,752 = £42,890

More calculations questions: Year 6 addition and subtraction questions for SATs

Fractions, Decimals and Percentages SATs questions

Fractions, decimals and percentages are an area which children need a secure understanding. Usually, there are a large number of questions in the KS2 SATs from this content domain.

If children are secure in the four operations and fractions, decimals and percentages, it may be possible to gain enough marks to reach the expected standard — Even if other areas are weak.

Fractions, Decimals and Percentages SATs questions – arithmetic

SATs arithmetic question 3

37.23 – 17.876 =

Answer: 19.354 (1 mark)

37.23 – 17.876 = 19.354

SATs arithmetic question 4

$\frac{3}{7}$ of 546

Answer: 234 (1 mark)

$\frac{1}{7}$ of 546 = 78

$\frac{3}{7}$ of 546 = 234

Fractions, Decimals and Percentages SATS questions – reasoning

SATs reasoning question 5

A factory makes 11,250 biscuits per hour. $\frac{4}{9}$ of the biscuits are chocolate. How many of the biscuits made each hour are not chocolate?

Answer: 6,250 biscuits (2 marks)

$\frac{5}{9}$ of 11,250 are not chocolate

$\frac{1}{9}$ of 11,250 = 1,250

$\frac{5}{9}$ of 11,250 = 6,250

SATs reasoning question 6

Chloe goes shopping and buys a pair of jeans for £48.35, a phone for £276.89 and a bag for £35.65. She now has £76.84 left. How much money did she have at the start of her shopping trip?

Answer: £437.73 (2 marks)

£48.35 + £276.89 + £35.65 + £76.84 = £437.73

SATs reasoning question 7

Max bought a hoodie in the sale. The original price was £42.60, but it was in the sale, with 25% off. How much did he pay for the hoodie?

Answer: £31.95 (2 marks)

25% of £42.60 = £10.65

£42.60 – £10.65 = £31.95

SATs reasoning question 8

Ahmed has a bag of sweets. He works out that $\frac{1}{8}$ are green $\frac{3}{8}$ are red, $\frac{2}{8}$ are yellow and $\frac{2}{8}$ are orange. He he has 21 red sweets, how many are in the bag altogether?

Answer: 56 sweets (2 marks)

$\frac{3}{8}$ = 21, so $\frac{1}{8}$ = 7

7 x 8 = 56

More questions: Year fractions questions for SATs (to come)

Number and Place Value SATS questions

Children need a secure understanding of place value for the SATS exam. Place value questions may appear less frequently than some other domains but it is the foundation for understanding many other mathematical concepts in the KS2 SATs exams.

On average, number and place value make up 12% of questions across the 3 papers.

Number and place value SATs questions – arithmetic

SATs arithmetic question 5

What is the value of the digit 7 in each of the numbers:

27.9

3.57

82.71

76.3

Answer: 7, 0, 07, 0.7, 70 (1 mark)

27.9 = 7

3.57 = 0.07 or $\frac{7}{100}$

82.71 = 0.7 or $\frac{7}{10}$

76.3 = 70

SATs arithmetic question 6

653 ÷ 100 =

Answer: 6.53 (1 mark)

653 ÷ 100 = 6.53

Number and place value SATS questions – reasoning

SATs reasoning question 9

How many times greater is the digit 6 in the number 4,365,281 than the digit 6 in 2,357,368?

Answer: 1000 times bigger (1 mark)

4,365,281 = 60,000

2,357,368 = 60

SATs reasoning question 10

What is the number exactly 2 less than 14 million?

Answer: 13,999,998 (1 mark)

More questions: Year 6 Place Value Questions for SATs

Measure SATS questions

Measure questions only appear in the two reasoning papers and make up an average of 13% of the total marks.

Measure SATS questions – reasoning

SATs reasoning question 11

The distance between 2 cities if 426km. What is the distance in meters?

Answer: 426,000m (1 mark)

SATs reasoning question 12

Year 6 are going on a school trip to a theme park. If the journey takes 1 hour and 25 minutes and they want to arrive by 9:45am. What time do they need to set off?

Answer: 8:20am (1 mark)

SATs reasoning question 12

A primary school is looking to put a fence round the school vegetable patch. The vegetable patch is a rectangle shape. The length of one side is 427cm and the length of the shorter side is 346cm. How many metres of fencing will he need?

Answer: 15.46m (2 marks)

427 + 346 = 773

77 x 2 = 1,546cm = 15.46m

Geometry SATs questions – properties of shape

Geometry SATs questions vary year to year. Some years include more geometry questions than others. It is important that pupils have a secure understanding of the geometry strands to help them in the reasoning papers.

Geometry SATS questions – reasoning

SATs reasoning question 13

Match the name of the 3D shape to the name of one of the shapes on its surface:

Square based pyramid	Circle
Hexagonal prism	Triangle
Cylinder	Rectangle

Answer: Square-based pyramid – Triangle, Hexagonal prism – Rectangle, Cylinder – Circle (1 mark)

SATs reasoning question 14

An isosceles triangle is labelled with the angles ‘A’, ‘B’ and ‘C’. Angle A measures 54°. What 2 possible sizes could angles B and C measure?

Answer: 54° and 72° or 63° and 63° (2 marks)

Ratio and proportion SATs questions

Ratio and proportion make up a small percentage of the reasoning papers and are often an area children can find quite difficult.

Before spending a lot of revision time on ratio and proportion, it can be a good idea to ensure pupils are confident in using the four operations and fractions, decimals and percentages. These curriculum areas are worth more marks in the SATs papers.

Ratio and proportion SATS questions – reasoning

SATs reasoning question 15

This is a recipe for making 25 chocolate chip cookies:

125g butter

150g sugar

200g plain flour

1 large egg

$\frac{1}{2}$ teaspoon bicarbonate of soda

How many grams of sugar are needed to make 15 cookies?

Answer: 90g sugar (2 marks)

5 cookies = 150 ÷ 5 = 30g

15 cookies = 30 x 3 = 90g

SATs reasoning question 16

Year 6 have been participating in a netball league. The team played 15 games over the season and the coach worked out that for every 2 wins they lost 1 game. How many more games did they win than lose over the season?

Answer: 5 games (1 mark)

15 games in total – 5 lots of 2 wins and 1 loss. In total they won 10 games and lost 5, therefore won 5 more games than they lost.

More questions: Year 6 ratio questions for SATs

Algebra SATs questions

Algebra is introduced to pupils in Year 6. For those close to the age related threshold, algebra can be tricky and require extra revision.

But with algebra making up a total of 9% of questions in the 2023 reasoning papers, revision for these pupils may be better spent on more frequent occurring strands.

Algebra SATS questions – reasoning

SATs reasoning question 17

I am thinking of a number. I multiply the number by 21 and add 3. The answer is 84. What was my number?

Answer: 4 (1 mark)

X x 21 + 3 = 87

21X = 84

X = 4

SATs reasoning question 18

Mrs Brown is roasting a chicken in the oven for lunch. She knows it takes 20 minutes to roast each kilogram of chicken. If Mrs Brown has a chicken weighing 2.5kg, how long does she have to roast the chicken for?

Answer: 50 minutes (1 mark)

2.5 x 20 minutes = 50

More questions: Year 6 algebra questions for SATs

Position and direction SATs questions

Position and direction accounts for the smallest proportion of the year 6 SATS, with an average of only 3% of questions taken from this content domain in the 2023 SATs papers.

Position and direction SATS questions – reasoning

SATs reasoning question 19

Sam is hunting for treasure using a coordinates grid. The treasure is hidden at (2, 4). Sam is stood at (7, 6). Describe how he can get to the treasure.

Answer: Move left 5 and down 2 (1 mark)

SATs reasoning question 20

Mason is facing East. He turns 270° clockwise. What direction is he facing now?

Answer: North (1 mark)

Statistics SATs questions

Statistics are another topic that appears less frequently in the SATS exams.

On average, the statistics questions account for approximately 4% of questions across the 2 reasoning papers.

Statistics SATS questions – reasoning

SATs reasoning question 21

6 children were comparing their test scores. They wanted to work out the average score the 6 of them had achieved. The scores were: 31, 24, 38, 27, 35 and 31. What was the average score?

Answer: 30 (1 mark)

31 + 24 + 38 + 27 + 35 + 25 = 180

180 ÷ 6 = 30

SATs reasoning question 22

In a survey of favourite foods, 30% of children chose burgers, 25% chose pizza, 35% chose ice cream and 10% chose cake. If 40 children chose pizza, how many chose burgers?

Answer: 48 children (1 mark)

40 children = 25%

160 children in total

10% = 16 children

30% = 16 x 3 = 48