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Free Year 7 Maths Test With Answers And Mark Scheme: Mixed Topic Questions
This year 7 maths test is suitable for the majority of year 7 students and contains questions on a wide variety of topics. The test includes both procedural questions and applied problems.
This test is designed to be taken at the end of year 7. If you’re looking for a test for the start of year 7, we recommend you download the free year 6 maths test instead as it will provide a much fairer assessment of what students know.
What topics are likely to be covered in Year 7 maths
Year 7 maths is likely to feel a little different to primary school maths. Students will be introduced to a number of new topics, as well as new vocabulary and methods for tackling problems. They will cover topics from across all of the 6 areas of maths: number, ratio and proportion, algebra, geometry, statistics and probability.
Although there is no set list of topics that students need to cover in Year 7, schools often choose to focus on number topics during Year 7. It is important that students develop their skills with mental and written calculations with whole numbers and decimals and working with fractions, percentages and ratios. They will need skills in these areas to be able to tackle problems across the curriculum as they progress through KS3.
Algebra and the use of algebraic notation is also a focus during Year 7 level maths. Again, it is important that students have a good foundation in algebra as they will build on this throughout their mathematical journey up to KS4 and beyond.
Other topics that are likely to be covered in Year 7 include:
- Place value
- Negative numbers
- Order of operations
- Area and perimeter of 2D shapes
- Angles
- Charts and graphs
- Averages
- Probability
Check out our comprehensive revision guides and maths worksheets for these topics here:
- Place value
- Negative numbers
- Order of operations (BIDMAS)
- Area and perimeter of 2D shapes
- Angles
- Types of graphs
- Averages (Mean, Median, Mode)
- Probability
Many Year 7 students find the transition to secondary school a challenge.
Some students may need focused support to plug gaps and grow in confidence.
You can give your target students a smoother transition from KS2 to KS3 with personalised one to one tuition from specialist tutors with Third Space Learning. Our lessons cover content from Year 5-7 and are designed by former teachers and pedagogy experts and are designed to encourage students towards independent practice.
Year 7 maths questions
Students in Year 7 will be challenged to answer a variety of questions. Some questions will be procedural and will focus on learning and practising new methods. Other questions will ask students to apply their knowledge to solve problems and work through functional skills tasks. At this stage, most problems will not be too complicated, with perhaps one or two steps.
Year 7 Maths Test
Download this FREE Year 7 Maths Test to check the progress of your students. Designed to be delivered at the end of the year with questions on a range of topics from across the KS3 curriculum. Includes answers and mark scheme.
About this Year 7 maths test
This Year 7 test contains 16 questions of increasing difficulty. The test begins with questions accessible to the vast majority of Year 7 students, with questions becoming progressively more challenging. The maths topics covered in the test are:
| Number | Ratio & proportion | Algebra | Geometry | Statistics | Probability |
| Money Place value Decimal addition and subtraction Percentage of amount Fraction of amount Negative numbers Square and prime numbers | Ratio Proportion | Equations Simplify expressions Formula Straight line graph | Read a scale Metric units Properties of a quadrilateral Area and perimeter Angles Rotation | Reading a table Pictogram Pie chart | Probability |
The total number of marks available for this test paper is 50.
How to use this Year 7 maths test
Our Year 7 maths test is designed to be taken as an end of year exam. The test is one hour long, allowing it to be sat within a lesson.
Students should be encouraged to show all of their working when completing the test, as in most maths practice papers. Students may use a calculator during the test.
Mark scheme and grade boundaries
Don’t forget to download our test, which is accompanied with a mark scheme. The recommended grade boundaries are:
| Mark | Old National Curriculum Level | New GCSE grade |
| 0-5 | 2 | – |
| 6-15 | 3 | – |
| 16-28 | 4 | 1 |
| 29-42 | 5 | 2 |
| 43-50 | 6 | 3 |
Year 7 maths test
Questions for our Year 7 maths test follow below. Download our FREE Year 7 maths test for an easy-to-print format, mark scheme and answers.
Thinking about marking already? You could consider using the mark scheme in our download and have students peer assess. You could also consider using whole class feedback to reduce your workload – we’ve included a free template in our blog!
Other recommended KS3 resources
- Articles on Year 7 Maths, Year 8 Maths and Year 9 Maths
- Year 8 maths test
- Year 9 maths test
- Fun maths problems for KS2 and KS3
- 30 problem solving maths questions
By the end of Year 7, students will have made a good start to the KS3 maths curriculum. They will have gained a basic understanding of many topics across the six main areas of maths; number, ratio and proportion, algebra, geometry, statistics and probability.
These may include:
• Number: fractions, decimals, percentages, place value, negative numbers, factors and multiples, rounding, order of operations
• Algebra: manipulating algebraic expressions, solving simple linear equations, using formulae, sequences, straight line graphs
• Ratio, proportion and rates of change: ratio, direct proportion, conversion rates
• Geometry and measures: area and perimeter, angles, properties of polygons, transformations, construction and loci
• Probability: basic probability, sample space diagrams, Venn diagrams
• Statistics: data collection, pie charts, scatter diagrams, averages
It is worth noting that different schools cover the curriculum in different orders and there is no set list of what a student should know by the end of Year 7.
You can find a full list of topics that students should cover by the end of KS3 here.
Year 7 maths lessons build on the maths done in primary school as well as introducing a number of new topics and new vocabulary.
You can prepare for Year 7 maths by ensuring you are confident with your number work, including knowing your times tables, being able to use mental and written methods for calculations and having an understanding of fractions. Some good resources to help you with this are:
• Revision guides and maths worksheets available on our website:
• Subscription sites that your school may use, for example Sumdog or ttrockstars
• CGP workbooks or other maths revision guides/workbooks
By the end of Year 7, most students will be working between GCSE grades 1 and 3. Different schools use different types of levels for Key stage 3 maths so it is best to check how your school assigns levels to your work.
Do you have students who need extra support in maths?
Every week Third Space Learning’s maths specialist tutors support thousands of students across hundreds of schools with weekly online 1-to-1 lessons and maths interventions designed to plug gaps and boost progress.
Since 2013 we’ve helped over 150,000 primary and secondary students become more confident, able mathematicians. Find out more about our GCSE Maths tuition or request a personalised quote for your school to speak to us about your school’s needs and how we can help.
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