11+ maths topics: every topic explained with practice strategies

11+ maths topics span the full primary syllabus and beyond — and maths is tested by almost every grammar school and selective independent school in England. The gap between what children learn in school and what the exam actually tests is often widest here. In Trafford, Paper 2 covers Maths only with no NVR component, making maths performance proportionally more important than in other CEM areas — see the Trafford 11+ maths — Paper 2 is maths only guide for how this affects preparation. This guide lists every topic on the 11 plus maths syllabus, explains what is expected at exam standard, where children most commonly lose marks, and how to structure 11+ maths practice from start to exam day.

How 11+ maths differs from school maths

The Year 6 National Curriculum sets expectations for the average child. Grammar schools are selecting from the top 10–25% of the academic ability range — so the exam is deliberately pitched above curriculum level in two important ways.

Depth. Topics that are introduced in Year 6 — ratio, algebra, percentages — are tested at a level of complexity and in combinations that go beyond what most children encounter in class. A child who "knows" fractions at school level may still struggle with a question that requires converting between fractions, decimals and percentages in a multi-step problem.

Speed. GL Maths papers typically require children to answer 50 questions in 50 minutes — one question per minute. In Kent, children complete 50 maths questions in 50 minutes as part of the Kent Test maths paper. This demands fluency, not just understanding. A child who can work out 7 × 8 by counting on their fingers will run out of time long before a child for whom times tables are instant recall.

Understanding both of these differences shapes the entire preparation approach.

The complete 11+ maths topic list

Every topic below appears in GL-style 11+ maths papers. = core KS2 level. Three or four filled dots and an Extended tag = tested above typical Year 6 teaching — prioritise these in preparation.

Topic deep dives

Number and arithmetic

Place value, rounding and estimation

Place value questions in the 11+ go well beyond reading a number correctly. Children must understand how digits shift when multiplying or dividing by powers of 10, round to significant figures as well as decimal places, and use estimation sensibly to check answers in multi-step problems.

A typical exam question might ask: "What is 3.672 rounded to one decimal place?" — straightforward. A harder version: "A number rounded to the nearest hundred is 2,400. What is the largest whole number it could be?" — this requires understanding the upper boundary of a rounding range.

What children find hard: upper and lower bounds ("what is the largest/smallest number that rounds to X?") and applying rounding sensibly within a larger problem.

Multiplication and division

Times table fluency to 12 × 12 is the foundation on which everything else in 11+ maths is built. Children who cannot recall these instantly will not complete a 50-question paper in 50 minutes. Beyond tables, children need to be comfortable with long multiplication, short and long division, and division of decimals.

The exam regularly presents multiplication and division in unfamiliar forms — "find the missing number in □ × 7 = 336" or "a school orders 144 pencils and distributes them equally among 12 classes." Neither question is conceptually difficult, but it requires applying known facts flexibly.

What children find hard: long division with remainders expressed as decimals, and division involving larger numbers where a secure mental model of the process is needed.

Factors, multiples, primes and BODMAS

Factors and multiples questions are reliable marks for well-prepared children — they reward straightforward knowledge. Children should know how to find all factors of a number systematically, identify prime numbers up to 100, find highest common factors (HCF) and lowest common multiples (LCM), and recognise square numbers and cube numbers on sight.

BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) is the order of operations rule. It appears explicitly in some questions and implicitly in many others. A child who adds before multiplying will get consistent errors across a large category of questions.

What children find hard: finding HCF and LCM efficiently for larger numbers, and applying BODMAS correctly in expressions with multiple operations.

Fractions, decimals and percentages

This is the topic area that causes the most difficulty in 11+ maths — and the most marks lost by children who are otherwise well prepared. The reason is that FDP (fractions, decimals, percentages) appears both as a standalone topic and embedded in word problems across geometry, data, and ratio.

Fractions

Children need to be completely fluent with equivalent fractions, simplifying by finding the HCF, and converting between improper fractions and mixed numbers. Adding and subtracting fractions with different denominators requires finding a common denominator — a procedure that needs to be automatic.

Multiplying fractions (numerator × numerator, denominator × denominator) and dividing fractions (multiply by the reciprocal) go beyond the standard Year 6 curriculum but appear in most 11+ papers. Many children have not been taught these in school — making them one of the highest-impact topics to cover in preparation.

What children find hard: adding fractions with unrelated denominators (e.g. 3/7 + 2/5 requires finding a common denominator of 35), and fractions of amounts involving non-unit fractions ("find 3/8 of 240").

Decimals

Decimal questions in the 11+ typically involve ordering decimals, rounding to given decimal places, and multiplying or dividing decimals by whole numbers or by other decimals. The most common error is misaligning decimal points in addition and subtraction, or miscounting decimal places after multiplication.

What children find hard: multiplying two decimals together (0.3 × 0.4 = 0.12, not 1.2), and dividing a decimal by a decimal (0.8 ÷ 0.02 = 40).

Percentages and ratio

These methods cover the FDP and ratio question types that appear most often in 11+ papers — and where the most marks are lost when children know the maths in isolation but not the procedure.

Geometry and shape

Angles

Angle questions in the 11+ go beyond simply measuring with a protractor. Children must know that angles in a triangle sum to 180°, angles on a straight line sum to 180°, angles at a point sum to 360°, and angles in a quadrilateral sum to 360°. These facts must be applied, often in combination, to find missing angles in complex diagrams.

Questions frequently involve parallel lines and the properties of alternate, corresponding, and co-interior angles — topics that many children have not encountered in Year 6 but that appear with some regularity in 11+ papers.

What children find hard: multi-step angle problems where two or three angle facts must be applied in sequence to reach the answer, and identifying which angle type applies in a given diagram.

Area and perimeter

Area questions in the 11+ frequently involve compound shapes — an L-shape, for example, or a rectangle with a triangular section removed. Children must decompose the compound shape into simpler parts, calculate the area of each, and then add or subtract.

The area of a triangle (½ × base × height) is essential knowledge. The area of a parallelogram (base × height, where height is the perpendicular height, not the slant side) is tested in some papers.

Circle questions — circumference = π × d, area = π × r² — appear in higher-difficulty 11+ papers. Children do not need to know π to many decimal places but must understand how to substitute radius and diameter correctly into the formulae.

What children find hard: compound area questions where the shape must be split or where a shape is subtracted from a larger one, and confusing radius with diameter in circle formulae.

Coordinates and transformations

Coordinates questions involve plotting and reading points in all four quadrants, and sometimes finding midpoints or identifying shapes from their vertices. Transformation questions ask children to reflect, rotate, translate, or enlarge shapes — and to describe transformations precisely.

What children find hard: reflections across lines other than the x- and y-axes (e.g. y = x), and rotations around a point that is not the origin.

Algebra and sequences

Algebra is the topic area where preparation makes the most dramatic difference. Most Year 6 children have had limited algebra teaching, so a child who has worked through 11+ algebra content systematically in preparation has a significant advantage over one who has not.

Sequences

Sequence questions ask children to identify the rule and find the next term, or to identify a specific term (e.g. the 20th term) using the nth term formula. Linear sequences (where consecutive terms differ by a constant amount) are the most common. Quadratic sequences (where the differences between terms themselves increase or decrease by a constant amount) appear in some papers.

What children find hard: finding the nth term formula — "the rule is add 4 each time, so the nth term is 4n + something — but how do I find the something?" The method: find 4n for n = 1 (which is 4), compare to the actual first term, and the adjustment is the difference.

Equations and expressions

Simple equations — "find the value of x if 3x + 7 = 22" — appear in most 11+ papers. The method is to isolate x by reversing operations in the correct order (subtract 7 from both sides, then divide both sides by 3). Children who have not been taught formal algebraic manipulation may try to guess-and-check, which is slower and unreliable for harder questions.

Substitution questions provide values for variables and ask children to evaluate an expression — "if a = 3 and b = 5, find 2a² − b." These require careful application of BODMAS as well as the substituted values.

What children find hard: equations where the variable appears on both sides ("5x + 3 = 2x + 12"), and expressions involving squared variables where BODMAS must be applied carefully.

Data, statistics and measures

Mean, median, mode and range

These four averages are tested regularly and usually in combination. Questions ask children to find the mean of a list of numbers, identify the median (middle value when ordered), find the mode (most frequent), and calculate the range. Harder questions ask children to work backwards — "the mean of five numbers is 12; four of the numbers are 8, 11, 14, 16 — what is the fifth?"

What children find hard: finding the median when there is an even number of values (the median is the mean of the two middle values), and reverse mean problems.

Probability

Probability questions ask children to express likelihood as a fraction, decimal, or percentage between 0 and 1. Simple questions involve single events ("what is the probability of rolling a 4 on a fair die?"). Harder questions involve combined events or require children to use the rule that all probabilities for mutually exclusive outcomes sum to 1.

What children find hard: combined events ("what is the probability of rolling a 4 and tossing a head?") which require multiplying individual probabilities.

Time, money and measures

Time questions are consistently among the highest mark-scorers for well-prepared children — they reward straightforward knowledge — but also produce surprising errors. Converting between hours and minutes, calculating time differences that cross midnight, and working with 12-hour and 24-hour clock formats all trip up children who have not practised specifically.

Unit conversion — kilometres to metres, kilograms to grams, litres to millilitres — appears in most papers. Imperial to metric conversions (miles to km, pounds to kg, pints to litres) appear occasionally and require knowing standard approximations.

Word problems: the hardest marks to earn

Word problems are where the highest-ability children separate themselves — and where the most marks are dropped by children who know all the underlying maths but cannot apply it in context.

The topics children most commonly get wrong

Understanding where marks are lost is as important as knowing the syllabus. These are the ten topics that produce the most errors in 11+ maths, based on the types of questions that appear most frequently:

The maths facts every child must know by heart

There is a category of mathematical knowledge that is not "working out" — it is instant recall. Children who have to derive these facts during the exam lose time they cannot afford.

• Times tables — 1 through 12, instantly in any order. Not "let me work it out" — instant.
• Square numbers — 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
• Cube numbers — 1, 8, 27, 64, 125.
• Key FDP equivalents — ½ = 0.5 = 50%; ¼ = 0.25 = 25%; ¾ = 0.75 = 75%; ⅓ ≈ 33.3%; ⅕ = 20%; ⅛ = 12.5%; ¹⁄₁₀ = 10%.
• Prime numbers to 50 — 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
• Angle facts — triangle = 180°; quadrilateral = 360°; straight line = 180°; full turn = 360°.
• Area formulae — rectangle = l × w; triangle = ½ × b × h; circle = πr²; parallelogram = b × h.
• Speed, distance, time — D = S × T, rearranged as S = D ÷ T and T = D ÷ S.

Children should be tested on these regularly throughout preparation — not just in the context of longer questions, but as rapid-fire standalone drills. Two minutes of times table practice every morning compounds significantly over 12 months.

Preparation strategy: building 11+ maths from the ground up

Exam technique: how to approach the maths paper on the day

• Never leave a question blank. Most 11+ maths papers do not penalise wrong answers. A guess after eliminating one or two obviously wrong options is always better than a blank. In multiple choice, common wrong answers are built into the options — so eliminating the most predictable errors (adding instead of multiplying, confusing area with perimeter) often narrows five options to two.
• Write working for every multi-step question. Even in multiple-choice papers where working is not marked, writing each step down reduces errors significantly. Children who do mental arithmetic across three or four steps make far more mistakes than those who write intermediate results.
• Use estimation to check answers. Before circling an answer, check whether it is broadly the right order of magnitude. An answer of 4,500 for a question about a child's pocket money, or 0.003 for a question about a school's total budget, signals a calculation error. Estimation is a habit that must be practised deliberately.
• Manage time actively. One question per minute is the target pace for a 50-question paper. Children who are still on question 20 at the halfway point will not finish. Teach your child to skip questions that are taking too long — mark them clearly and return at the end. Two marks from the last section of the paper are worth exactly the same as two marks at the beginning.
• Beware the most common traps. Exam questions are written by people who know exactly which errors children make. The reversal of percentage change, the wrong use of radius vs diameter, adding fractions by adding denominators — these are not accidental. A child who has specifically practised not making these errors will consistently outscore one of equal raw ability who has not.

Recommended resources for 11+ maths preparation

• Bond 11+ Maths (age 10–11) is the most widely used and most well-calibrated resource. The questions are pitched at the right difficulty level and cover all syllabus topics. Complete the age 9–10 book first to build confidence before moving to the harder book.
• CGP 11+ Maths Practice Papers provide the most realistic full-paper practice for GL-format exams. Use these from Phase 3 onwards — they are not the right starting point for topic-by-topic learning but are excellent for timed practice and mock exam simulation.
• Schofield and Sims Mental Arithmetic is the best resource for building arithmetic speed and fluency. Books 4, 5, and 6 cover the right level for 11+ preparation. Five minutes of mental arithmetic daily from these books compounds significantly over 12 months.
• Bond Assessment Papers (Maths) are graded by age band and provide a large bank of mixed practice questions. Work through the 9–10 and then 10–11 age bands from Phase 2 onwards.
• CGP KS2 Maths SATs Revision is useful as a starting point for confirming curriculum-level knowledge before moving to 11+-specific material. It should not be relied upon as the main preparation resource because the difficulty level is below what the 11+ demands.
• Atom Learning offers adaptive online maths practice that targets gaps automatically. It is particularly useful for Phase 3 onwards, when identifying and drilling specific weak topics becomes the priority.