11+ maths: What's tested, key topics and worked examples

11+ maths is built on the Key Stage 2 national curriculum, but the question style is much closer to a problem-solving paper than a school maths test. Most questions are multi-step, the topics are blended, and many papers ban calculators. The content is largely material your child has seen in school, but the way it's tested catches a lot of children out.

This guide breaks down what's tested, where the difficulty jumps come, and how to plan a maths prep schedule that doesn't burn your child out before Year 6 even starts.

The content is drawn from the KS2 national curriculum programmes of study (DfE). The ISEB Common Pre-Test tends to focus on Year 5 maths content; some GL Assessment regional papers can stretch into early Year 6 material. The eight strands are:

Number and place value (rounding, negative numbers, Roman numerals, place value up to 10 million). Addition and subtraction (mental and column methods, multi-step problems). Multiplication and division (times tables to 12×12, long multiplication, short and long division, factors, multiples, primes). Fractions, decimals and percentages (equivalent fractions, mixed numbers, conversion between forms). Measurement (units, perimeter, area, volume, time, money). Geometry: properties of shape (angles, polygons, 2D and 3D shapes). Geometry: position and direction (reflection, translation, coordinates in all four quadrants). Statistics (tables, line graphs, pie charts, mean).

What your child won't see is anything from the Year 6 SATs that goes beyond what's in the KS2 programmes of study. Algebra is usually introduced only in its simplest form (finding the value of a single letter in a one-step equation).

The maths content is broadly the same across boards, but the format isn't.

GL Assessment (used by many grammar schools) uses a paper-based, multiple-choice test with answers shaded on a separate sheet. ISEB Common Pre-Test (independent schools) runs online, adaptive, with a 40-minute maths section (rough working on paper is allowed under the standard invigilation guidance). CSSE (also branded FSCE after the 2024 transition; Essex grammars) uses a paper-based test with both multiple-choice and free-response questions. The Kent Test uses a paper-based, multiple-choice maths paper. Cambridge Select Insight is online and non-adaptive, with the maths section running around 30 questions. Quest Admissions (independent schools) is online and adaptive, multiple-choice only.

The biggest practical difference between paper and adaptive online tests is that on an adaptive test, questions get harder if your child answers correctly. A child who finds the test getting harder isn't doing badly: That's the system working. The reverse is true for paper tests, where each child sees the same questions and the test gets harder as the paper progresses.

Past paper analysis from tutors and exam-prep publishers consistently flags four areas as the biggest mark-droppers:

Word problems with multiple steps. Children can do the maths but stop too early or skip a step. Fractions, decimals and percentages, especially questions that mix all three (e.g. converting between forms in the middle of a problem). Time and money calculations involving conversions (e.g. minutes to hours, pounds to pence). Reverse percentage problems (working out the original amount from a percentage change).

A child can be confident in each individual topic and still drop marks here, because the difficulty is in spotting that the question needs more than one operation.

Sarah has £24. She spends 1/3 of her money on a book, then 25% of what's left on a snack. How much money does she have now?

Step 1: Work out 1/3 of £24. That's £8. So she spends £8 on the book.

Step 2: Work out how much she has left. £24 − £8 = £16.

Step 3: Work out 25% of £16. 25% is 1/4, so 1/4 of £16 = £4. She spends £4 on a snack.

Step 4: Work out the final amount. £16 − £4 = £12.

Answer: £12.

The trap in this question is reading 25% as being of the original £24. The phrase "of what's left" is doing real work in the question, and children who skim past it get £18, which is wrong.

A jacket is in the sale at £42. It has been reduced by 30%. What was the original price?

Step 1: Work out what percentage of the original price £42 represents. The jacket has been reduced by 30%, so £42 is 70% of the original.

Step 2: Find 1% by dividing. £42 ÷ 70 = £0.60. So 1% of the original price is 60p.

Step 3: Find 100% by multiplying. £0.60 × 100 = £60.

Answer: £60.

The wrong instinct is to add 30% to £42 (which gives £54.60 and is incorrect). The reduction is a percentage of the original price, not the sale price, so you need to work backwards from the sale price.

A class records the number of pets per pupil:

0 pets: 5 pupils 1 pet: 12 pupils 2 pets: 6 pupils 3 pets: 2 pupils

What is the mean number of pets per pupil?

Step 1: Work out the total number of pets. (0 × 5) + (1 × 12) + (2 × 6) + (3 × 2) = 0 + 12 + 12 + 6 = 30.

Step 2: Work out the total number of pupils. 5 + 12 + 6 + 2 = 25.

Step 3: Divide. 30 ÷ 25 = 1.2.

Answer: 1.2 pets per pupil.

The common error is dividing by 4 (the number of categories) instead of by 25 (the total number of pupils). The mean is always total ÷ count, where count is the number of data points.

Most 11+ tests use standardised age scores, not raw marks. Your child's raw score is converted into a standardised score that adjusts for their age in months at the time of testing. This is to stop younger children in the year group being unfairly disadvantaged.

A standardised score of 100 is the average for that age group. Grammar schools each set their own qualifying threshold, often in the low-to-mid 100s, with more competitive schools sitting higher. There's no national pass mark, and each test centre or consortium publishes its own threshold (often after the test). Check your specific consortium's published criteria for the exact figure.

For independent schools, scores are usually combined across all four subjects and reported as a single figure. Schools weight the subjects differently and don't usually publish how they do so.

The most common mistake is starting too late and trying to cover everything at once. A more sustainable plan looks like this:

Months 6 to 4 before the test: Topic-by-topic coverage. Pick one strand (e.g. fractions, percentages, geometry) and work through it for one to two weeks. Use worksheet packs aligned to your test board. Don't time anything yet.

Months 4 to 2 before the test: Mixed-topic practice. Move to questions that blend strands together. This is where multi-step word problems become the main thing your child practises. Introduce timing in a relaxed way (a soft per-question limit).

Months 2 to 0: Full papers under exam conditions. Two to three full papers a week, marked together, with focused work on the topics that came out weakest in each. Stop new content in the final two weeks: Consolidation only.