11 Plus Maths Questions and Answers: Free Worked Practice
11 Plus Maths Questions and Answers: Free Worked Practice
Key takeaways
- Free 11 plus maths practice is easy to find, but worked methods are rare: this guide shows where to look and how to mark at home.
- Percentage questions reward a fixed two-step habit: divide by 100 to find 1%, then multiply by the percentage needed.
- GL, CEM and independent school papers differ in structure and timing, so practise the format your target school actually uses.
- Mark with the method, not just the answer, and keep an error log by topic to spot repeated mistakes.
- A workable baseline is 40-60 questions a week in Year 4, rising to 60-100 across mixed-topic timed sets in Year 5.
This guide explains what 11 plus maths covers, where to find free questions and answers, and how to solve and mark percentage questions step by step, with worked examples and the most common mistake at each step, so you can review at home without a tutor.
What topics appear most often in 11 plus maths papers?
Most 11+ maths papers draw from the Key Stage 2 curriculum, taken slightly beyond age expectations. GL Assessment sets 11+ tests for many grammar schools, and maths is a common subject alongside English and reasoning, though which subjects are tested varies by school. The same topic clusters recur whether your child sits GL, CEM-style or independent school papers.
Core number topics: fractions, decimals and percentages
Fractions of quantities, converting between decimals and percentages, and percentage increase questions appear in nearly every paper. This is why the percentages section below gets its own walkthrough.
Word problems, ratio and multi-step reasoning
Expect two- and three-step problems: sharing money in a ratio, then finding a fraction of one share. Reading the question matters as much as the arithmetic.
Shape, area and problem-solving questions
Perimeter, area of compound shapes, angle facts and volume of cuboids are the usual suspects.
Exact weighting varies by school and provider, so check your target school's published guidance.
Where can you find free 11 plus maths questions with answers?
Free sample papers from publishers and schools
Publishers often release free sample 11+ maths papers, and many grammar schools and consortia release past papers or familiarisation materials directly. These are the closest match to the real exam, because they come from the same question styles your child will face. The catch is volume: a sample paper or two runs out quickly, and answers are often a bare number with no method shown.
Free question banks and forums
Online parent forums share papers, answers and marking advice, and some platforms offer free taster content to let you try before paying. Forum quality varies, so check answers yourself before marking your child's work against them.
What free sources lack: worked methods
Much of the free material does not explain how to reach the answer, or which step children usually get wrong. That matters most in topics like percentages, where a right answer reached by a wrong method hides a gap. Sagito gives an explanation with each answer, and its 2,000 free questions need no account.
How do you solve 11 plus percentage questions step by step?
Finding a percentage of an amount
Teach the two-step method: find 1% by dividing by 100, then multiply by the percentage you need. For 15% of £240: 240 ÷ 100 = 2.40, then 2.40 × 15 = £36. The common error is dividing by 10 instead of 100, which gives £360, or multiplying by the percentage before dividing.
Percentage increase and decrease
For an increase, find the percentage and add it on. A £60 jumper rising by 20%: 60 ÷ 100 = 0.60, 0.60 × 20 = 12, so the new price is £72. For a decrease, subtract instead. The most common error is dividing the change by the wrong amount. A rise from £50 to £60 is 10 ÷ 50 = 20%, because you divide by the starting price. Reversed, a fall from £60 to £50 is 10 ÷ 60 = 16.7%, not 20%. Children who divide by the new price instead of the starting price get both wrong.
Percentage problems written as word problems
Word problems hide the operation. "A coat costs £80 after a 25% discount. What was the original price?" means £80 is 75% of the original, so divide by 75 and multiply by 100: £106.67. The common error is taking 25% off £80 again, which assumes the discount applied to the sale price.
Percentage questions appear in most 11 plus maths papers, and CEM-style tests tend to favour multi-step word problems over plain calculation. Practise the divide-by-100 habit until it is automatic.
How do GL, CEM and independent school maths questions differ?
GL format: standard and multiple choice
GL papers follow predictable topic splits: number, fractions, percentages, measurement, and problem-solving, usually as one-question-one-answer items. Practice should mirror that structure, so your child gets used to answering cleanly on a separate sheet or grid at a steady pace.
CEM format: mixed topics and timing pressure
CEM-style papers shuffle topics question by question, so a fractions question can sit next to a shape question with no section headings. They are also deliberately tight on time, which punishes children who linger. Practise short, mixed-topic drills against a timer rather than long topic blocks.
Independent school papers: longer multi-step questions
Independent school papers ask fewer questions with more steps each, often requiring written working to earn method marks. Train your child to show every step and label answers clearly. Most schools publish past papers on their own websites, so build practice around the actual target school's format.
What are the most common mistakes in 11 plus maths answers?
Arithmetic slips under time pressure
Most lost marks are not hard maths. A child multiplies 7 × 8 as 54, or adds 45 + 38 as 73, and the whole question falls apart. Timed papers push children to rush the basics. Writing each calculation on its own line makes a slip easier to find, because it shows up at the exact line where it happened.
Misreading multi-step word problems
A question might ask for the change from £20 after two purchases and a discount. Children answer after step one. Ask your child to say what the question actually wants before they start, so you can check whether they solved the right problem.
Leaving answers in the wrong format
£1.50 written as 1.5, a fraction where a decimal was asked, or 0.375 where the paper wants a percentage. Check the format the question asks for before marking.
How should you mark and review practice answers at home?
Marking is where the practice actually pays off, but only if you go beyond a tick or cross.
Mark with the method, not just the answer
A correct answer reached by a wrong route will fail on a harder question. Ask your child to talk through their method on the two or three they got wrong, then compare it against the worked method on the answer. Note the exact step where the route diverged. That step is the teaching point, and it usually takes two minutes to fix.
Keep an error log by topic
Keep a simple notebook page per topic: percentages, fractions, ratio, word problems. Each time a question goes wrong, write one line: the topic, the question type, and the mistake in your child's words. After a fortnight, patterns appear. Most children make the same three or four errors repeatedly, and the log tells you which ones.
When to re-test a topic
Re-test a topic three to four days after reviewing it, using fresh questions, not the originals. If your child clears eight out of ten, move on. If not, review again and re-test after another week.
How many questions should a child practise per week before the exam?
A workable baseline is 3–4 short sessions a week of 15–20 minutes, roughly 40–60 questions, in Year 4, rising to 60–100 questions across 4–5 sessions in Year 5. Short, frequent practice beats one long weekend session because it keeps methods fresh without exhausting a 9 or 10 year old.
Year 4 vs Year 5 volumes
In Year 4, aim for two or three sessions covering one topic each, such as fractions or percentages, with answers marked the same day. In Year 5, add a weekly mixed set that mirrors exam conditions.
Scaling up in the final months
About three months out, move to one full timed paper a week plus topic top-ups on weak areas, and ease off in the final week. If practice is causing arguments, cut volume rather than consistency.
Where does Sagito fit alongside paid 11+ platforms?
What Sagito does well: no account, no ads
Sagito has 5,000 questions across maths, English, verbal reasoning and non-verbal reasoning, and 2,000 of them are free with no daily cap. Each answer comes with an explanation. There is no account to create and no ads, so your child can start practising straight away, and purchases sit behind a parent PIN. The collectible adventure on top is there to get practice opened daily, not to replace it.
Where Sagito falls short: no full mock papers
Sagito has short timed challenges (15, 30 or 45 minutes) but not full mock papers laid out like a real GL or CEM exam. If you want full mock papers under exam conditions, use past papers from your target school or a dedicated mock service. Sagito suits daily topic practice alongside those: the free 2,000 questions cost nothing, and Plus (£3.99 a month) unlocks all 5,000.
FAQ
Are 11 plus maths questions the same as SATs questions?
Both draw on the Key Stage 2 curriculum, but 11+ questions tend to push slightly beyond age expectations and lean harder on multi-step word problems. SATs papers follow a predictable format each May, while 11+ papers vary by provider, with GL, CEM and independent school styles each structuring and timing questions differently.
What is a good score in 11 plus maths?
There is no fixed pass mark. Grammar schools set their own qualifying scores, and raw marks are age-standardised, so what counts as good depends on the school, the cohort and the year. As a rough practice benchmark, a child consistently clearing eight out of ten questions on a topic has usually mastered it and can move on.
Can my child practise 11 plus maths without an account or app subscription?
Yes. Sagito needs no account and carries no ads, and 2,000 of its 5,000 questions are free with no daily cap, so practice can start immediately. Publishers also release free sample papers without sign-up, though their explanations are limited. Paying only becomes necessary if you want the full question bank or full timed mock papers.
When should Year 4 start 11 plus maths practice?
Year 4 is a sensible starting point, kept light: two or three short sessions a week of 15 to 20 minutes, roughly 40 to 60 questions, each covering a single topic and marked the same day. Serious volume can wait until Year 5, when mixed-topic sets and timed practice become useful.
Do grammar schools publish past 11+ maths papers?
Many do. Individual grammar schools and consortia often release past papers or familiarisation materials on their own websites, and these are the closest match to the real exam. Coverage is uneven, though, and published answers usually give a bare number with no worked method, so you may need to supply the explanation yourself.