Every topic tested, real worked questions from named school papers, and how GL Assessment differs from a school-set test
Book a Free ConsultationThe Year 7 maths entrance exam — the test most families call the "11+", sat in Year 6 for a September Year 7 place — covers seven core topic areas: number and arithmetic, fractions/decimals/percentages, ratio and proportion, algebra, geometry, data handling, and multi-step word problems. How those topics are tested varies sharply by school: GL Assessment sets a 50-question multiple-choice paper used by most state grammar schools, while independent senior schools such as Dulwich College, The Perse School and Mount House School write and mark their own written papers entirely in-house. This guide sets out exactly what is tested, shows real worked sample questions from published school specimen papers, and explains which route your target school actually uses.
Every Year 7 maths entrance paper we reviewed — whether set by GL Assessment or written in-house by an individual school — draws from the same underlying pool of Key Stage 2 maths content, organised into seven recurring topic groups. The weighting differs between test providers, but the topic list itself is remarkably consistent across GL Assessment's standardised papers and the school-set papers published by Dulwich College, The Perse School and Mount House School.
Number and arithmetic is the largest single topic group in almost every paper: place value up to millions, the four operations with whole numbers, instant recall of multiplication tables to 12×12, order of operations, rounding, factors, multiples and prime numbers, and negative number arithmetic. Fractions, decimals and percentages come next in weighting — simplifying and comparing fractions, converting between the three forms, and calculating a percentage of an amount or a percentage increase or decrease. Ratio and proportion covers simplifying ratios, dividing an amount in a given ratio, and direct proportion problems (a recipe or a unit-price question, for example). Algebra at Year 7 entrance level means continuing sequences, solving one- and two-step equations, substitution, and "function machine" style questions where an invented operation must be applied. Geometry covers 2D shape properties, area and perimeter (including compound shapes), angle facts, coordinates in all four quadrants, and simple transformations such as reflection and rotation. Data handling and statistics covers mean, median, mode and range, and reading bar charts, pie charts and tables. Finally, multi-step word problems — often the highest-value questions on a paper — combine two or more of the above topics into a single real-world scenario, such as a money, time or speed-distance-time calculation.
| Topic Area | GL Assessment (multiple choice) | School-Set Papers (written) |
|---|---|---|
| Number & arithmetic | Highest-frequency topic across the paper | Core opening questions; e.g. Dulwich's "2017 + 597" |
| Fractions, decimals, % | Regular, single-answer format | Often scaffolded; e.g. Mount House's 56% of 80 |
| Ratio & proportion | Included, moderate frequency | Real-world framing; e.g. Perse's hamster-food question |
| Algebra & sequences | Sequences and simple equations | Invented-operation style; e.g. Dulwich's "x ♠ y" question |
| Geometry & coordinates | Shape properties, area, angles | Adds transformations; e.g. Dulwich's 180° rotation question |
| Data handling | Charts and tables, single-answer | Pie charts and surveys; written interpretation required |
| Word problems | Money, time, speed-distance-time | Multi-step; e.g. Mount House's giraffe feeding-time question |
For a priority-rated revision checklist that breaks each of these seven areas down further into individual sub-skills, see our companion 11+ maths topics checklist. That page focuses on what to revise and in what order; this guide focuses on how the topics actually appear on real papers, with worked examples below.
Structure is the single biggest variable between different Year 7 entrance routes, and it matters more to preparation than the topic list itself, because a child who has only ever practised multiple choice will lose easy marks on a written paper by not showing method, and vice versa. GL Assessment, which sets tests for over 80% of grammar schools in England, uses a strictly multiple-choice format: a typical GL 11+ maths paper runs 50 questions in 50 minutes, with four or five answer options per question and no partial credit for working shown. Scores are reported as an age-standardised score so that a child born in August is compared fairly against a child born the previous September, not against raw marks alone.
Independent senior schools that write their own Year 7 entrance papers take a different approach entirely. Dulwich College's published Year 7 Entrance and Scholarship Mathematics Specimen Paper F runs for one hour, contains 26 questions worth 100 marks in total, does not permit a calculator, and requires full written working for every answer — there is no multiple choice anywhere on the paper. The Perse School's Year 7 (11+) sample maths paper allows 45 minutes for 17 written-response questions covering arithmetic, fractions, ratio, algebra, geometry and data interpretation. Mount House School's Year 7 entry sample paper similarly runs 45 minutes across 23 questions of varying mark values, again entirely written response. Manchester Grammar School publishes real past arithmetic papers (with full mark schemes) going back to 2014, and its own admissions material confirms it does not test verbal or non-verbal reasoning at all — maths and English carry the whole assessment.
A third route exists for some independent schools: the ISEB Common Pre-Test, a computer-adaptive assessment taken on a laptop or tablet rather than a fixed paper, where each child's exact question set is generated individually and age-standardised in real time. There is no traditional "past paper" for this route at all — preparation instead uses ISEB's official Walkthrough tool and practice question banks. Before choosing any preparation material, confirm directly on your target school's own admissions page which of these three routes it actually uses; the difference between a 50-minute multiple-choice paper and a one-hour written paper worth 100 marks changes almost everything about how a child should practise.
Reading about topic lists only goes so far — seeing the actual question style used by real schools is far more useful for calibrating a child's preparation. Below are worked examples drawn from published specimen and sample papers, with full working shown.
Example 1 — Ratio and proportion (The Perse School, Year 7 sample paper). "Hamster food costs 70p for 40 grams. What is the cost of 100g of hamster food?" Working: 40g costs 70p, so 1g costs 70 ÷ 40 = 1.75p. 100g therefore costs 1.75 × 100 = 175p, i.e. £1.75. This is a classic unitary-method proportion question — the same technique (find the value of "one unit", then scale up) answers the large majority of ratio and proportion questions across every Year 7 entrance paper we reviewed.
Example 2 — Algebra / invented operation (Dulwich College, Year 7 Entrance Specimen Paper F). "The instruction x ♠ y means double x and add y. Work out the value of 14 ♠ 55." Working: double 14 is 28; add 55 gives 28 + 55 = 83. This "invented operation" or function-machine style question tests whether a child can follow a defined rule precisely rather than testing memorised algebra facts — it appears in some form on the large majority of independent-school written papers because it cannot be answered by rote-learned formulas.
Example 3 — Fractions with scaffolding (Mount House School, Year 7 entry sample paper). "Calculate 56% of 80", with the paper prompting an intermediate step: "50% of 80 = ___". Working: 50% of 80 = 40; 6% of 80 = 4.8; 56% of 80 = 40 + 4.8 = 44.8. The scaffolded intermediate step is a deliberate feature of several school-set papers aimed at younger Year 6 candidates — it rewards a child who can break a percentage into 50%, 10% and smaller "building block" percentages rather than requiring a single memorised percentage method.
Example 4 — Negative numbers in context (The Perse School, Year 7 sample paper). "On Christmas Day the temperature in Lisbon was −5°C. On New Year's Day the temperature was 3 degrees lower. What was the temperature on New Year's Day?" Working: 3 degrees lower than −5 is −5 − 3 = −8°C. Negative-number word problems set in a temperature or money context appear on the majority of school-set written papers and on GL Assessment's number topic, precisely because they test whether a child understands the number line rather than just arithmetic procedure.
Preparing for a Year 7 Maths Entrance Exam?
Our specialist tutors match preparation to the exact format your target school uses — GL Assessment multiple choice, a written school-set paper like Dulwich's or Perse's, or the ISEB Common Pre-Test — and track error patterns by topic so revision time goes where it is actually needed.
Rated 4.8/5 on Trustpilot. Families we have supported have secured places at grammar and independent schools across the country.
Book a Free Consultation Message us on WhatsAppKnowing which route a school actually uses is the single most useful piece of information a family can have before starting preparation, because it determines whether a child should practise timed multiple choice or full written method. Most state grammar schools — including consortium areas such as Kent, Buckinghamshire and the Consortium of Selective Schools in Essex (CSSE) — use GL Assessment's standardised multiple-choice papers, and GL Assessment itself confirms it sets tests for over 80% of grammar schools in England. A smaller but significant group of independent senior schools writes and marks its own Year 7 entrance papers entirely in-house: Dulwich College, The Perse School, Mount House School and Manchester Grammar School all publish specimen or genuine past maths papers on their own admissions websites rather than using GL or CEM material, and each sets its own mark scheme, time limit and pass mark. CEM (the Centre for Evaluation and Monitoring, run by Durham University) is a fourth historic route, though it stopped administering paper-based 11+ tests altogether in late 2022, with the roughly 28 local authority areas that used it moving to GL Assessment or bespoke local papers — a fact that trips up many parents who search for "CEM past papers" and cannot find any, because CEM had a deliberate policy of never releasing them publicly even while it still operated.
A useful diagnostic: if your target school's admissions page names "GL Assessment" or refers to a "familiarisation booklet" issued by a local authority, expect a multiple-choice paper on a fixed date shared with other schools in that consortium. If instead the school's own admissions page hosts a downloadable "specimen paper" or "past paper" with its own school crest, expect a written paper marked entirely by that school's own maths department, on that school's own bespoke timetable. Our companion resource, Year 7 entrance exam past papers by school and board, lists exactly which schools and boards publish free official material, and is a useful next step once you know which route applies to your target school.
Even though CEM stopped setting paper-based 11+ tests in late 2022, the distinction between "GL-style" and "CEM-style" maths questions still shapes a great deal of practice material sold online, so it is worth understanding for families comparing resources. GL Assessment maths questions are typically presented as a clean, standalone calculation or short word problem with four or five multiple-choice answer options, and the maths paper is usually timetabled separately from the verbal and non-verbal reasoning papers. CEM's historic approach mixed maths questions in among English comprehension and vocabulary questions within the same timed section, moved at a noticeably faster pace per question, and sometimes embedded a maths question inside a longer written passage rather than presenting it in isolation. Because the areas that used CEM have now moved to GL Assessment or to bespoke local papers, "CEM-style" practice material bought today is, at best, a stylistic approximation rather than a current test format — always confirm your target local authority's current test provider directly rather than assuming the format your older sibling sat still applies.
Effective preparation starts with confirming the exact format your target school uses, then building a topic-by-topic plan around that format rather than working through generic practice books in order. A sensible timeline for most families runs from Year 5 through the autumn of Year 6, when most tests are actually sat.
12-18 months before the test (Year 5): Sit one full paper, untimed, with no prior revision, purely as a diagnostic baseline. This tells you which of the seven core topic areas — number, fractions, ratio, algebra, geometry, data handling, word problems — are genuinely weak rather than assumed weak, and it should shape everything that follows rather than a generic revision order.
9-12 months before: Work through topic-sorted questions rather than full timed papers, closing specific gaps identified in the diagnostic. If your target school uses GL Assessment, practise exclusively in multiple-choice format from this point; if it sets its own written paper, insist on full written working for every answer, since marks are awarded for method as well as the final answer on papers like Dulwich's.
6-9 months before: Introduce single timed sections — for example, one 20-minute block of arithmetic questions — rather than whole papers, to build working speed without the added fatigue of a full sitting. Both GL Assessment and school-set papers reward speed under pressure: GL's 50 questions in 50 minutes allows roughly one minute per question, and Dulwich's written paper allows an average of just over two minutes per question across its 26 questions, factoring in the time needed to show full working.
3-6 months before: Move to full timed mock sittings under exam-hall conditions, roughly one every two to three weeks, using papers that match your target school's actual format as closely as possible.
Final 4-8 weeks: Use papers matched exactly to the target school or board's real format and, where available, genuine past or specimen papers from that specific school rather than generic practice material. Keep an error log by topic and error type — careless slip, timing pressure, or genuine knowledge gap — rather than tracking only a raw score, since a percentage alone does not tell you what to fix next.
"Passing" means different things depending on the route. On GL Assessment tests, results are reported as an age-standardised score, with 100 representing the national average for a child's exact age in months. Most competitive grammar schools set an effective qualifying mark somewhere around 110-115 across the combined papers, and the most heavily oversubscribed schools in London and the South East effectively expect 120 or higher once the full applicant pool is ranked — though schools rarely publish a single fixed "pass mark" in advance, since the actual cut-off moves with that year's cohort and the number of places available. On school-set written papers such as Dulwich College's, Mount House's or The Perse School's, there is no standardised score at all: the admissions team ranks candidates by raw marks across maths, English and, where the school sets one, a reasoning or reasoning-adjacent paper, combined with the current school's report and, at many schools, a short interview. This means the realistic "score needed" genuinely changes from year to year, and a mark that secured an offer in one admissions cycle is not a reliable benchmark for the next.
One practical implication worth flagging: because school-set papers are marked in-house against that year's specific applicant pool, working accuracy and showing full method both matter more than they would on a multiple-choice paper, where an unexplained correct guess earns exactly the same mark as fully justified working. If your child is preparing for a written paper, build the habit of writing out every calculation step even when the answer seems obvious — several school mark schemes, including Manchester Grammar School's published arithmetic mark scheme, award method marks that a correct-answer-only response would miss entirely.
The Year 7 maths entrance exam (the 11+, sat in Year 6 for September Year 7 entry) tests seven core areas: number and arithmetic (place value, the four operations, factors and multiples), fractions, decimals and percentages, ratio and proportion, algebra (sequences, simple equations, function machines), geometry (angles, area, perimeter, coordinates, transformations), data handling and statistics, and multi-step word problems that combine several of these in one question. GL Assessment-style tests draw on the Key Stage 2 curriculum; school-set papers such as Dulwich College's and Mount House's add extension topics like speed calculations and negative numbers.
It depends entirely on who sets the paper. GL Assessment, used by over 80% of England's grammar schools, sets a 50-question, 50-minute multiple-choice paper with no working shown. Independent schools that write their own Year 7 entrance papers, such as Dulwich College and The Perse School, generally require full written working: Dulwich's specimen Paper F runs 26 questions over one hour worth 100 marks, with every answer requiring shown method, while Perse's sample paper allows 45 minutes for 17 written-response questions. Always check your target school's own admissions page — multiple-choice preparation habits transfer poorly to a written paper and vice versa.
For GL Assessment tests, scores are reported as age-standardised scores, and most competitive grammar schools set a qualifying mark around 110-115, with the most oversubscribed schools expecting 120 or higher — 100 represents the national average for a child's exact age in months. School-set written papers such as Dulwich's and Mount House's do not use standardised scores; instead the admissions team ranks candidates by raw marks across maths, English and, where set, reasoning, alongside a school report and sometimes an interview, so a good score varies year to year with the applicant pool.
No — there are three distinct routes. Most state grammar schools and many consortium areas, including Kent, Buckinghamshire and Essex's CSSE, use GL Assessment's standardised multiple-choice papers. A smaller number of independent senior schools write and mark their own Year 7 entrance papers entirely in-house — Dulwich College, The Perse School, Mount House School and Manchester Grammar School all publish their own specimen or past maths papers rather than using GL or CEM material. A third group of independent schools instead uses the ISEB Common Pre-Test, a computer-adaptive assessment with no fixed paper at all. Confirm which route your target school uses before choosing preparation material.
Across GL Assessment and the school-set papers we reviewed, seven topic groups recur consistently: number and arithmetic, fractions/decimals/percentages, ratio and proportion, algebra and sequences, geometry (shapes, angles, area, coordinates), data handling and statistics, and multi-step word problems. Number and arithmetic, fractions, and word problems appear in nearly every paper checked and deserve the most revision time; ratio, algebra and geometry appear regularly but slightly less densely; probability and 3D geometry appear in some papers but are rarely the majority of marks, so they are usually a lower priority once the core areas are secure.
Leading Tuition's specialist tutors build a topic-by-topic preparation plan matched to your target school's actual test format, whether that is a GL Assessment multiple-choice paper, a written school-set paper like Dulwich College's or The Perse School's, or the ISEB Common Pre-Test. We diagnose exactly which of the seven core topic areas need the most work using real past and specimen papers, track error patterns by topic rather than just a score, and time practice sessions to match the real exam's pacing. Rated 4.8/5 on Trustpilot. Book a free consultation at leadingtuition.co.uk/consultation or message us on WhatsApp.
For background on the exam beyond maths alone, see our guide to what the 11+ exam actually involves, and for current test dates across independent and grammar schools, see our 11+ exam dates timetable. You can also browse specific school guides and requirements in our full directory of 11+ school guides. Official free familiarisation material for GL Assessment tests is published directly by GL Assessment.
Our specialist tutors know exactly what GL Assessment and named independent schools test, and build a plan around your child's real gaps.
Rated 4.8/5 on Trustpilot — trusted by families preparing for grammar and independent school entry across the UK.
Book a Free Consultation Message us on WhatsApp