Preparing for the 13 Plus Common Entrance (CE) Maths Exam can be a crucial step in securing a place at a top UK independent school. This guide walks you through what to expect, how to prepare, and which resources can support your child’s success in the Maths part of the admissions test.
What Is the 13 Plus Exam?
The 13+ Common Entrance Exam is a pre-GCSE assessment taken by students applying to independent schools for entry into Year 9. The exam is offered at multiple difficulty levels—Level 1 (Foundation), Level 2 (Core), and Level 3 (Additional)—with most candidates sitting Level 2.
While the exam assesses a wide range of subjects, Maths, English, and Science are considered core. It is worth thinking of the CE as a holistic exam with students also being tested in as many as five other subjects such as modern foreign languages, classics, geography, religious studies and history.
Who Takes the Exam?
Almost all students applying to independent schools in the UK take the 13+ CE exam. Gaining a good set of results will serve to confirm a school place, with many students being offered a place at their choice of school already, conditional on achieving positive results in 13 Plus exams. These assessments take place mostly in June of Year 8, with some schools offering a November session.
Understanding the 13 Plus Maths Exam
Exam Format
The ISEB (Independent Schools Examinations Board) is the main provider of the 13+ Maths exam. The exam is offered at three levels:
- Foundation (Level 1)
- Core (Level 2)
- Additional (Level 3) – for the most advanced candidates
Each candidate will sit:
- A Non-Calculator paper (60 minutes)
- A Calculator paper (60 minutes)
- A Mental arithmetic test (10 minutes)
Schools may create their own papers but generally base them on ISEB specifications.
Grading and What Counts as a Good Score for 13 Plus Maths
There’s no official pass mark, as each school sets its own benchmark. However:
- 60% or above is usually considered competitive
- 70%+ across subjects is highly competitive
Schools often look at performance across all subjects. So lower scores in English, for example, might pass if scores in Maths and Science exceed the school’s own average.
Key Topics Covered in the 13+ Maths Exam
The assessment is set up to test pupils’ ability across a wide range of factors and skills. They should be able to use numbers with confidence, make links with multiplication, division and fractions, and apply decimals, percentages and ratios. The test will involve solving a wide range of issues, with complex numerical properties of numbers; problems will involve solving written and mental methods of calculation with efficiency. Students must employ the language of algebra accurately and show excellent knowledge of geometry, with the skills to classify shapes; fluency in written methods is crucial, long multiplication and division. Mathematical knowledge should be able to be applied across subjects, including science and geography.
The above summary vastly simplifies the technicalities which the ISEB curriculum prescribes, and the true depth of knowledge to be acquired is helpfully broken down and detailed on the ISEB website. These documents define the knowledge and understanding that students should possess before sitting the 13+ assessments, as well as providing examples of what will be examined.
Students are expected to demonstrate mastery in six core areas:
1. Number
- Mixed operations, including squares, cubes, and brackets
- Inverse operations and relationships between them
- Powers and roots, including negatives
2. Algebra
- Changing quantities by percentages
- Estimation and word problems
- Substitution in expressions and formulae
3. Measurement
- Converting metric units (e.g., mm to cm, g to kg)
- Speed, distance, and time calculations
4. Geometry
- Geometric terminology and classification
- Properties of 2D shapes up to decagons
5. Probability
- Expressing probabilities as simplified fractions
6. Statistics
- Calculating mean, median, mode, and range
The exam requires fluency in both mental and written methods, application of maths to real-world scenarios, and cross-subject links (e.g., maths in science).
Comparison with National Curriculum (KS3)
The content closely mirrors Key Stage 3 standards in the National Curriculum. Students and parents can use both the ISEB syllabus and the KS3 Maths programme of study as a guide to what you need to know.
How to Prepare for the 13+ Maths Exam
Top Preparation Tips
- Identify Weak Areas: Use practice papers to find topics needing more revision.
- Gamify Your Practice: Make revision fun with mental arithmetic challenges involving family or friends.
- Teach!: An ability to explain something demonstrates wide knowledge: tell a sibling or friend how to do something tricky, simplifying and going over it multiple times.
- Stretch Yourself: Try more advanced papers even if you’re not due to sit it.
- Open Book Practice: When using past papers, you should initially sit them with text or schoolbooks open. You can therefore create model or ideal answers, acquiring knowledge before moving on to timed conditions.
- Timed Conditions: Practising in timed exam conditions is absolutely crucial.
- Use Mark Schemes: Understand common mistakes by marking your own papers.
- Show Your Working: In the exam itself, there is a strong emphasis on showing working in both the calculator and non-calculator papers, so be sure to practise this. Marks are awarded for working out—not just the final answer.
- Tackle Difficult Questions: Don’t skip the tougher questions at the end of the paper; effort and method matter. Students should not assume they cannot do these and perseverance – and demonstration of foundational knowledge – will be rewarded.
Recommended Resources
1. Past Papers
- Start with the schools you're applying to; many provide example or previous papers on their website.
- Use reputable sources for ISEB-style past papers, but ensure they’re post-2021 to reflect the latest format.
- ISEB past papers can also be purchased directly through their official site.
2. Books and Online Platforms
In addition to the plethora of free material available online, many publishers provide resources for 13+ Mathematics which will contain topic based resources, tips, guidance and a host of relevant shorter questions with which to test yourself.
Look for up-to-date study guides that offer:
- Topic-based revision
- Step-by-step strategies
- Practice exercises and past-paper-style questions
Some publishers include:
Tutors for 13+ Common Entrance Maths
Keystone Tutors provide specialist Maths tutors who are experts at providing the sort of structured support that ensures students are best prepared for 13+ Maths entrance. We have over a decade of experience providing tuition to families who wish to send their children to some of the leading UK independent and boarding schools at 13+. View our 13+ Common Entrance tutors or book a free consultation.