Why "13+ Maths" is not one exam - and what Foundation, Core, Additional and CASE actually mean once you know which route your child's target school uses.
Book a Free Consultation"13+ Maths" means two different exams, and which one your child sits depends on the target school's route, not the family. A Pre-Test school uses ISEB's online, adaptive Common Pre-Test: a Maths paper sat in Year 6 or 7, built from the National Curriculum up to Year 5, no calculator allowed. A Common Entrance school instead sets a Year 8 paper exam - Non-calculator, Calculator and Mental Arithmetic - plus an optional Additional paper. One route never includes the other.
Already know whether your child's target school uses the ISEB Pre-Test or Common Entrance for 13+ Maths? Our expert 13+ Maths tutors build every programme around the paper your child will actually sit, not a generic revision pack.
Book a Free Consultation Message us on WhatsAppMost 13+ families meet Maths twice, years apart, in two exams that share nothing but a name. The first is the ISEB Common Pre-Test, which ISEB's own Families Hub describes as being "taken by children in Year 6 for Year 7 entry (11+) or used as a precursor to Year 9 entry (13+)." Its Mathematics component, per ISEB's 2026-27 Common Pre-Tests Framework, "will assess a pupil's knowledge of mathematics topics from the National Curriculum Programme of Study up until the end of Year 5," delivered online and adaptively, with some questions testing arithmetic fluency and others multi-topic problem solving. ISEB is explicit that "textbooks, calculators, mobile devices, and other materials which might assist an applicant must not be accessible" during the test.
The second exam is entirely separate: ISEB's Common Entrance 13+ Maths paper, sat in Year 8, drawn from Key Stage 3 content rather than the Pre-Test's Year 5 ceiling. A school that uses the Pre-Test for its 13+ decision never also sets the Common Entrance Maths papers, and vice versa - so a family cannot assume their child's Pre-Test result says anything about how they will handle the very different Common Entrance paper years later. Verbal and non-verbal reasoning sit inside that same Pre-Test alongside Maths; our separate guides to 13+ verbal reasoning and 13+ non-verbal reasoning cover those components in full. The rest of this page is about the Common Entrance route - Foundation, Core, Additional and CASE - since that is where almost all of the genuine subject complexity sits.
ISEB's own Common Entrance Mathematics page sets out three levels: "At 13+, we offer the CE mathematics examination at three levels. These are Foundation (Non-Calculator and Calculator papers), Core (Non-Calculator and Calculator papers) and Additional. All candidates take either Foundation or Core papers, and some candidates who take Core may also take the Additional paper. All candidates are expected to sit the mental arithmetic test, no matter which level they are taking."
Which tier applies is not left to guesswork by the family. ISEB's CE/CASE Mathematics specification is direct about the default: "The expectation is that all candidates will take the Core Papers. An Additional Paper is available to offer challenge to the more able." Foundation is explicitly the exception, not a parallel track: it exists "for support in individual circumstances," used "by agreement with senior schools, or as practice and stepping-stones towards CE."
Here Maths genuinely differs from Science. On our separate page about 13+ Science, ISEB itself publishes two conflicting percentage thresholds - 35% in one document and 40% in another - for who should move from Core to Foundation. For Maths, we checked both the specification document and the live assessments page directly, and neither publishes any percentage-average threshold at all. The Foundation-versus-Core decision for Maths is made case by case, in agreement with the senior school - there is no published number to aim for or against, and a family should not assume one exists just because Science has one.
Foundation and Core each carry the same paper shape, just at different difficulty: two papers of 100 marks and 60 minutes each - one Non-calculator, one Calculator - confirmed in ISEB's specification as "Foundation Non-calculator 100, 60 minutes. Foundation Calculator 100, 60 minutes" and "Core Non-calculator 100, 60 minutes. Core Calculator 100, 60 minutes." Every candidate, Foundation or Core, also sits the same Mental Arithmetic Test: 40 marks in 10 minutes, and the specification notes explicitly that "the same mental arithmetic test is taken by both Foundation and Core candidates." The optional Additional Paper adds a further 100 marks in 60 minutes, calculator permitted, for Core candidates the school judges ready for it.
| Paper | Marks / time | Who sits it |
|---|---|---|
| Foundation Non-calculator | 100 marks, 60 minutes | Foundation candidates |
| Foundation Calculator | 100 marks, 60 minutes | Foundation candidates |
| Core Non-calculator | 100 marks, 60 minutes | Core candidates |
| Core Calculator | 100 marks, 60 minutes | Core candidates |
| Mental Arithmetic Test | 40 marks, 10 minutes | All candidates, both tiers |
| Additional Paper (optional) | 100 marks, 60 minutes | Some Core candidates |
Source: ISEB CE/CASE Mathematics specification, retrieved 8 September 2026.
Only a simple scientific calculator is permitted on the Calculator paper - the specification is specific that "calculators with more advanced features, such as graph plotting and solving equations, are not permitted."
Timing follows a fixed pattern every session. ISEB's published exam timetable sets the Autumn 2026 session as: "TUESDAY 3 NOVEMBER 2026: Mathematics Foundation or Core Non-calculator (1 hour). WEDNESDAY 4 NOVEMBER 2026: Mathematics Foundation or Core Calculator (1 hour) and Mathematics Mental Arithmetic Test (10 minutes). THURSDAY 5 NOVEMBER 2026: Mathematics Additional (1 hour)." The Spring 2027 session repeats the identical Tuesday-Wednesday-Thursday order on 26, 27 and 28 January 2027, and Summer 2027 repeats it again on 8, 9 and 10 June 2027 - the Calculator paper and Mental Arithmetic Test always fall together on the same middle day, whichever of the three sessions a target school schedules.
Whichever tier and session your child faces - Foundation or Core, November, January or the Summer round - our 13+ Maths tutors plan backward from the actual papers your child will sit, not a generic timetable.
Book a Free Consultation Message us on WhatsAppEvery paper above - Foundation, Core and Additional alike - is set against a single specification, printed with the header "SPECIFICATION SEPTEMBER 2020" on every page and published by ISEB under a filename identifying it as version 7.1. The specification itself dates the syllabus more precisely still: it is "a revision of the syllabus released in 2014 for 13+ and CASE," with 11+ content explicitly unchanged, and applies "for teaching from September 2021 onwards" and "for examinations from November 2022 onwards" - three different dates doing three different jobs, not one date restated three ways.
The most useful thing on this syllabus is what it excludes. Trigonometry is never examined at 13+ Maths, at either level: the specification states against the relevant National Curriculum descriptor that "Core: Pythagoras' Theorem will not be examined, trigonometry will not be examined. Additional: Pythagoras' Theorem may be examined, trigonometry will not be examined." A pupil revising trigonometric ratios for 13+ Maths is preparing for content that will not appear on any paper, at any tier.
The 2021 revision removed several other topics outright. ISEB's own specification comparison is explicit: "Bearings - Map scale drawings will not be examined... Constructions - Accurate drawing will not be examined... Drawing of pie charts - Candidates will not be expected to draw pie charts but will still be expected to interpret them." Significant figures were removed at Core and Foundation in the same revision, though the specification confirms they remain examinable "from the Additional Level."
The same revision changed how the papers are answered, not just what they cover. It introduced "a new-style Mental Arithmetic paper with written questions rather than aural" in place of the old spoken format, alongside "questions with less scaffolding" and an explicit expectation of "greater quality of thought and working, rather than quantity of questions." A pupil practising only from an older past paper is working from a different exam shape as well as a wider syllabus.
A Core candidate and an Additional candidate are not sitting "the same exam, harder." Entire topics exist only on the Additional paper, which matters for deciding where extra tutoring time actually pays off. ISEB's specification lists quadratic equations, simultaneous equations, algebraic proof, rearranging formulae, explicit nth-term sequences, standard form with positive indices, significant figures, enlargement by a fractional scale factor, and average speed for multi-part journeys as Additional-only content.
Some topics sit in between rather than being clean inclusions or exclusions. HCF and LCM may be tested explicitly at Additional level, where Core only requires them implicitly, inside other calculations rather than as a named question. Solving inequalities, by contrast, is not examined at either Core or Additional level - it does not become available even to the most able candidates.
None of the competitor pages we reviewed for this exam name a single one of these inclusions or exclusions. A family relying on a generic "13+ Maths papers" guide has no way of knowing that trigonometry, bearings, constructions and drawn pie charts are all off the syllabus, or that quadratic equations only appear once a child is entered for Additional.
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Additional-only topics like quadratics and simultaneous equations need real teaching time, not last-minute cramming. Our 13+ Maths tutors map every session against the exact papers your child's tier requires.
Book a Free Consultation Message us on WhatsAppNo - CASE, the 13+ scholarship route, is a different paper structure again, not a harder Core paper. ISEB's specification describes it as "based on the Core/Additional sections of the 13+ mathematics specification" but sat as "one paper, divided into two sections. In Section A, candidates are expected to answer all the questions. Section B is more demanding and candidates will be told to attempt as many questions as they can."
Confirmed against the specification's own timing table, CASE Maths is worth 100 marks in a single 90-minute sitting - "Common Academic Scholarship: One paper 100, 90 minutes" - based, the document adds, "on the 13+ CE specification for the Additional Paper." A pupil preparing for CASE is therefore preparing Additional-level content, but sat continuously in one paper rather than split across the separate Non-calculator, Calculator and Additional papers a Common Entrance candidate sits on different days.
Whatever route your child's target school actually uses - Pre-Test, Common Entrance Foundation, Core with or without Additional, or CASE - the starting point is the same: confirm which one applies before assuming a generic "13+ Maths" resource covers it. Our wider 13+ tuition service sets out what each individual school requires, and our Maths tutoring page covers the subject beyond 13+, including the Key Stage 3 and GCSE Maths content that follows once Common Entrance is behind a pupil - our GCSE Maths page picks up from there.
Pre-Test or Common Entrance, Foundation or Core, standard papers or CASE - our 13+ Maths tutors will tell you honestly which route and tier fits your child, rather than defaulting to whichever pack is easiest to teach.
Book a Free Consultation Message us on WhatsAppIt depends entirely on which admissions route your child's target school uses. A Pre-Test school sets ISEB's Common Pre-Test Mathematics component: an online, adaptive, multiple-choice paper, usually sat in Year 6 or 7, built from the National Curriculum only up to the end of Year 5, with no calculator permitted. A Common Entrance school instead sets ISEB's paper-based 13+ Maths exam in Year 8, built from Key Stage 3 content: a non-calculator paper, a calculator paper, and a Mental Arithmetic test, with an optional Additional paper for the more able. A school using one route never sets the other.
ISEB's own specification states plainly: "The expectation is that all candidates will take the Core Papers. An Additional Paper is available to offer challenge to the more able." Foundation papers exist only "for support in individual circumstances," used by agreement with the senior school, or as practice and stepping-stones toward Common Entrance. Unlike ISEB's Science specification, which gives a percentage-average threshold for who should sit Foundation instead of Core, the Maths specification and ISEB's live assessments page both publish no percentage threshold at all - the decision is made case by case with the senior school, not against a published number.
Foundation and Core each split into two 60-minute, 100-mark papers - one Non-calculator, one Calculator - plus a single Mental Arithmetic Test worth 40 marks in 10 minutes, taken by every candidate regardless of tier. The optional Additional Paper is a further 100 marks in 60 minutes, calculator permitted. In the 2026-27 Common Entrance sessions, the Non-calculator paper falls on the Tuesday, the Calculator paper and Mental Arithmetic Test together on the Wednesday, and the Additional paper on the Thursday - the identical pattern repeating in Autumn 2026, Spring 2027 and Summer 2027. Only a simple scientific calculator is permitted; anything with graph-plotting or equation-solving features is not.
No, at either level. ISEB's own specification states it directly against the relevant National Curriculum descriptor: "Core: Pythagoras' Theorem will not be examined, trigonometry will not be examined. Additional: Pythagoras' Theorem may be examined, trigonometry will not be examined." So even a candidate sitting the harder Additional paper is never tested on trigonometric ratios - only Pythagoras' Theorem, and only at Additional level. A pupil revising trigonometry for 13+ Maths is preparing for content that will not appear on any paper.
ISEB's own comparison document lists bearings, ruler-and-compass constructions, and drawing pie charts as removed from Core and Foundation level in the 2021 revision, stating plainly: "Bearings - Map scale drawings will not be examined... Constructions - Accurate drawing will not be examined... Drawing of pie charts - Candidates will not be expected to draw pie charts but will still be expected to interpret them." Significant figures were also removed at Core and Foundation, though they remain examinable at Additional level. The same revision introduced a new written Mental Arithmetic paper in place of the previous aural format, and reduced scaffolding, with an explicit expectation of "greater quality of thought and working, rather than quantity of questions."
No - it is a different paper structure, not a harder Core paper. CASE, the 13+ scholarship route, is one 90-minute paper worth 100 marks, divided into two sections. ISEB's own specification describes it: "In Section A, candidates are expected to answer all the questions. Section B is more demanding and candidates will be told to attempt as many questions as they can." It is based on the Core and Additional sections of the 13+ specification, but sat as a single continuous paper rather than as separate Non-calculator, Calculator and Additional papers on different days.
Whether your child faces the ISEB Pre-Test, Common Entrance Foundation or Core, the Additional paper, or CASE, our expert 13+ Maths tutors build a plan around the exam your child will actually sit.
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