GCSE Maths: Number
Number is the warm-up that runs through every other topic. Get it secure and you free up marking-scheme bandwidth for the harder questions on algebra and geometry.
Fractions, decimals and percentages must be interchangeable. You should be able to add/subtract/multiply/divide fractions, convert between recurring decimals and fractions (higher tier), and calculate percentage change, reverse percentage and repeated percentage change (compound interest, depreciation).
Indices — laws of indices, negative indices, fractional indices — are heavily tested. Memorise xᵃ × xᵇ = xᵃ⁺ᵇ, xᵃ / xᵇ = xᵃ⁻ᵇ, (xᵃ)ᵇ = xᵃᵇ, x⁰ = 1, x⁻¹ = 1/x, x^(1/n) = ⁿ√x.
Standard form is a guaranteed mark. Practise converting in both directions and performing arithmetic on numbers in standard form (without calculator for non-calc papers).
Surds (higher tier) — simplifying, rationalising the denominator, multiplying — appear on most higher papers. Three rules cover most questions: √a × √b = √(ab), √a / √b = √(a/b), and rationalising by multiplying by the conjugate.
HCF/LCM by prime factorisation, estimation, and upper/lower bounds (with the rule 'lower of two upper bounds for division') round out the topic. Upper and lower bounds are a common trap — always identify whether you need the larger or smaller bound at each step.
What you'll learn
- The full Number sub-topic map and how it sits within GCSE Maths
- What examiners reward in Number questions, command word by command word
- The most common Number mistakes — and how to avoid them in your answers
- How to revise Number with notes, flashcards, exam-style questions and the AI Study Coach
- How OES generates Maths resources without using official copyrighted past papers
Who this is for
- Students revising Number as part of GCSE Maths
- Anyone retaking GCSE Maths who needs a focused review of Number
- Parents and tutors supporting Maths students on Number
Learning objectives
By the end of this topic you should be able to:
- Convert between fractions, decimals and percentages including recurring decimals
- Apply the laws of indices including fractional and negative indices
- Convert numbers between standard form and ordinary form, and calculate with them
- Simplify and manipulate surds including rationalising the denominator
- Calculate the HCF and LCM by prime factorisation
- Calculate upper and lower bounds and apply them to compound problems
Common mistakes
- Adding fractions without a common denominator
- Treating x⁻¹ as −x instead of 1/x
- Errors with standard form arithmetic (subtracting powers when multiplying)
- Forgetting to rationalise the denominator
- Using the wrong bound for division (the lower bound divides by the upper bound for the minimum)
Revision tips
- Spend 10 minutes a day on fraction arithmetic until it is automatic
- Make a one-page index laws cheat sheet and re-derive each law from scratch
- Drill standard form non-calculator questions weekly
- Practise three surd questions per session for two weeks before the exam
- Memorise the upper/lower bound rule for each operation (+, −, ×, ÷)
How OES helps
AI Revision Notes
Concise, spec-aligned notes for every Maths topic, written to match what examiners reward.
Smart Flashcards
Adaptive Maths flashcards that prioritise the cards you keep forgetting using spaced repetition.
Exam-Style Papers
AI-generated Maths practice papers in the style of real exams — not official copyrighted past papers — with mark-scheme aware feedback.
Personal AI Study Coach
A 24/7 coach that plans every Maths session, explains anything you ask and adapts to your weakest topics.
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Frequently asked questions
Is Number on every GCSE Maths specification?
Yes. Number is a core part of the GCSE Maths specification across AQA, Edexcel and OCR. Some boards weight sub-topics slightly differently, but the content on this page maps to all three.
How long should I spend revising Number?
Most students need 4–6 focused sessions to feel confident on Number: one for the notes, one or two for flashcards, and two for exam-style questions. The AI Study Coach can build a schedule for you that fits the time you have left before the exam.
Does OES use official Maths past papers for Number questions?
No. OES does not redistribute official copyrighted past papers. We generate fresh exam-style questions in the style of real AQA, Edexcel and OCR papers, marked against the published mark scheme conventions.
What are the most common mistakes on Number questions?
Adding fractions without a common denominator Treating x⁻¹ as −x instead of 1/x The full list — and how to avoid each — is in the "Common mistakes" section above.
Is this topic harder for higher-tier or foundation students?
Most of Number is on both tiers. Higher-tier papers add a few stretch sub-topics and more demanding command words ("evaluate", "explain in detail"). The OES content is tier-aware — questions can be generated at foundation, higher or mixed difficulty.
How do I know if I've actually understood Number, not just memorised it?
The fastest test is to attempt a fresh exam-style question and self-mark it against the mark scheme. If you can hit every mark point in your own words, you understand it. If you keep dropping the same marks, the AI Study Coach can target those gaps directly.
Where should I go next after Number?
Related topics like algebra, ratio, statistics build directly on Number, so they are a strong next step. You can also drill Maths exam-style papers to combine Number with everything else you have revised.
Ready to start?
Jump straight into the OES tools built for this topic.
Revise Number with the AI Study Coach