GCSE Maths Study Guide

GCSEs in England are set by exam boards and regulated by Ofqual, and the subject content for each GCSE is published by the Department for Education (DfE). This guide covers GCSE Mathematics from the two boards most students sit: AQA (specification 8300) and Pearson Edexcel (specification 1MA1).

The 9 to 1 scale

GCSEs in England are graded 9 to 1, with 9 the highest. A student who does not reach the standard for grade 1 is recorded as U (unclassified) and receives no certificate. The scale is not a straight swap for the old A* to G letters, but the DfE and Ofqual give three fixed comparison points:

• The bottom of grade 7 is aligned with the bottom of the old grade A.
• The bottom of grade 4 is aligned with the bottom of the old grade C.
• The bottom of grade 1 is aligned with the bottom of the old grade G.

Grade 9 is awarded to fewer students than the old A*. The DfE recognises grade 4 and above as a "standard pass" in all subjects, and tells employers, colleges and universities that the nearest equivalent to an old grade C is a grade 4.

Why grade 4 in maths matters

Maths and English are treated differently from other GCSEs. If you finish Year 11 without a grade 4 in maths, you will keep studying maths after 16. Under the DfE's 16 to 19 funding rules for the 2026 to 2027 academic year, students with a grade 3 must study towards the GCSE again, and students with grade 2 or below may study towards either the GCSE or Functional Skills level 2. If you need that grade 4 sooner, the November series is your first chance to resit after the summer.

What is the same on every board

AQA's specification says its subject content "matches that set out in the Department for Education's Mathematics GCSE subject content" and that this content "is common to all exam boards". The assessment objectives are set by Ofqual and are the same across boards, and the topic weightings are prescribed by Ofqual too. So the maths you need to learn is the same for AQA and Edexcel. What differs is the style of the questions, the paper codes and where to find past papers.

It is a linear qualification

GCSE Maths is linear: you sit all three papers at the end of the course, in the same series and at the same tier. There are no modules banked along the way. You can resit as many times as you like within the life of the specification.

Both boards use the same structure. Each paper can test content from any part of the specification, and each is worth one third of the GCSE.

Paper	Calculator	Time	Marks	AQA code	Edexcel code
Paper 1	Not allowed	1 hour 30 minutes	80	8300/1F or 8300/1H	1MA1/1F or 1MA1/1H
Paper 2	Allowed	1 hour 30 minutes	80	8300/2F or 8300/2H	1MA1/2F or 1MA1/2H
Paper 3	Allowed	1 hour 30 minutes	80	8300/3F or 8300/3H	1MA1/3F or 1MA1/3H

F means Foundation tier and H means Higher tier. Your grade comes from your total mark across all three papers; individual papers are not graded. Ofqual requires that between 33 and 50 per cent of the total marks are for questions done without a calculator; both boards meet this with one non-calculator paper out of three.

Summer 2027 dates

GCSE exams sit in common timetable slots agreed by all the exam boards through the Joint Council for Qualifications (JCQ). Both AQA's May/June 2027 GCSE timetable and Pearson's final Summer 2027 GCSE timetable put the maths papers on the same mornings:

Paper	Date	Session
Paper 1 (non-calculator)	Friday 14 May 2027	Morning
Paper 2 (calculator)	Thursday 27 May 2027	Morning
Paper 3 (calculator)	Monday 14 June 2027	Morning

On AQA's timetable the GCSE written exams run from 10 May to 18 June 2027. The boards have named Wednesday 23 June 2027 as the contingency day, so you must stay available until then in case an exam has to be moved. AQA sends GCSE results to students on Thursday 19 August 2027.

November 2026 resit dates

Paper	Date	Session
Paper 1 (non-calculator)	Wednesday 4 November 2026	Morning
Paper 2 (calculator)	Friday 6 November 2026	Morning
Paper 3 (calculator)	Monday 9 November 2026	Morning

These dates are the same on AQA's and Pearson's final November 2026 timetables. AQA releases November 2026 results to students on Wednesday 13 January 2027. You can only enter the November series if you were at least 16 on the previous 31 August (so for November 2026, 16 or over on 31 August 2026). This is an Ofqual rule for GCSE Mathematics, not just a board policy.

What to bring

AQA's specification expects you to have a pencil (for diagrams only), a ruler, a pair of compasses and a protractor for every paper. For Papers 2 and 3 you need a calculator with, as a minimum, the four operations and square, square root, reciprocal and power functions, brackets, a memory, and exponential, trigonometric and statistical functions. The calculator must be one permitted under the JCQ Instructions for conducting examinations.

Ofqual requires GCSE Mathematics to be tiered, using an "overlapping tiers model". Every paper is either Foundation or Higher, and you sit all three papers at the same tier. You cannot mix them.

	Foundation	Higher
Grades available	1 to 5, or U	4 to 9, or U (a grade 3 is allowed if you are a small number of marks below the 4/3 boundary)
How the marks are targeted on each paper	50% at grade 1 to the lower part of grade 3; 50% at the upper part of grade 3 to grade 5	50% at grades 4 to 6; 50% at grades 7 to 9
Content	Foundation content only	All content, including the higher-only topics

The overlap at grades 4 and 5

Ofqual says grades 4 and 5 are the only grades designed to be reachable from either tier, and boards must make sure a 4 or a 5 means the same standard whichever tier it came from. A Higher candidate who just misses grade 4 may get a grade 3, but Ofqual is clear that grade 3 is not actively targeted on Higher papers. Below that, a Higher candidate is unclassified.

How to think about your tier

• Aiming for 6 or above? You must sit Higher. Foundation cannot give more than a 5.
• Aiming for a secure 4 or 5? Both tiers can give it. On Foundation, half of every paper is aimed at grades 3 to 5. On Higher, half of every paper is aimed at grades 7 to 9, so a student working at grade 4 will find much of each Higher paper out of reach.
• Working around grade 3 to 4? Higher offers only a narrow safety net below grade 4. If you fall further than a few marks short you get U, while the same performance on Foundation could still earn a grade.

Your school makes the entry, usually based on mock results. If you are unsure, ask your teacher which tier your mock marks point to, and why.

The content is split into six areas, and AQA's references show which is which: N for Number, A for Algebra, R for Ratio, proportion and rates of change, G for Geometry and measures, P for Probability and S for Statistics. Any topic can appear on any of the three papers, and questions often combine areas.

The weightings below apply to your tier as a whole, not to each paper. Pearson publishes them as ranges and AQA as approximate single figures; they describe the same Ofqual rule.

Content area	Foundation (Pearson)	Foundation (AQA, approx.)	Higher (Pearson)	Higher (AQA, approx.)
Number	22 to 28%	25%	12 to 18%	15%
Algebra	17 to 23%	20%	27 to 33%	30%
Ratio, proportion and rates of change	22 to 28%	25%	17 to 23%	20%
Geometry and measures	12 to 18%	15%	17 to 23%	20%
Probability and statistics (combined)	12 to 18%	15%	12 to 18%	15%

What the weightings tell you

• Foundation is about half Number and Ratio. Fractions, decimals, percentages, ratio, proportion and money problems are where most Foundation marks are.
• Higher moves the weight to Algebra, which is the biggest single area at about 30%. Geometry and Ratio follow at about 20% each.
• Probability and statistics together are about 15% on both tiers.

The three assessment objectives

Assessment objective	Foundation	Higher
AO1: Use and apply standard techniques	50%	40%
AO2: Reason, interpret and communicate mathematically	25%	30%
AO3: Solve problems within mathematics and in other contexts	25%	30%

On Higher, 60% of the marks are for reasoning and problem solving rather than routine methods. Learning methods alone is not enough for a top grade: you need practice at multi-step questions where you have to decide which method to use.

Higher-only topics

Comparing the Foundation and Higher content lists in Pearson's specification, these statements appear only on Higher:

• Sketching translations and reflections of a given function
• Gradients of graphs and areas under graphs, including distance-time and velocity-time graphs (no calculus)
• The equation of a circle centred at the origin and the tangent to a circle at a given point
• Approximate solutions to equations by iteration
• Combinations of rotations, reflections and translations
• Circle theorems, including proving them
• The sine rule, the cosine rule and area of a triangle = ½ab sin C
• Conditional probability from two-way tables, tree diagrams and Venn diagrams
• Instantaneous and average rates of change from gradients of tangents and chords
• Histograms (including unequal class widths) and cumulative frequency graphs

Many shared topics also go further on Higher. Foundation solves quadratics by factorising; Higher adds completing the square and the quadratic formula. Foundation works with roots and integer indices; Higher adds fractional indices, surds and rationalising denominators. Higher adds inverse and composite functions, quadratic inequalities, linear and quadratic simultaneous equations, and vector proofs.

What Ofqual decided

In November 2024 Ofqual confirmed that students sitting GCSE Mathematics in 2025, 2026 and 2027 do not have to memorise the formulae, and that exam boards must give students a formulae sheet. For GCSE Mathematics this also covers the November 2025, 2026 and 2027 exams. Boards must publish the sheets in advance so students can get used to them, and must provide clean copies with the exam papers. In May 2026 Ofqual decided that the sheets will continue for exams from 2028 onwards, for the lifetime of the current qualifications, including resits.

Ofqual says the sheets set out the formulae students must memorise in a normal year, as in the DfE subject content and on the sheets used in 2022, 2023 and 2024, and that they should stay consistent between years and between specifications.

What is on AQA's 2027 sheets

AQA published its sheets for 2027 exams on 1 September 2026, with the same content as 2026. Each tier has its own sheet:

Formula	Foundation sheet	Higher sheet
Area of a trapezium; volume of a prism	Yes	Yes
Circumference and area of a circle	Yes	Yes
Pythagoras' theorem; sin, cos and tan in a right-angled triangle	Yes	Yes
Compound interest	Yes	Yes
P(A or B) = P(A) + P(B) minus P(A and B)	Yes	Yes
P(A and B) = P(A given B) P(B)	No	Yes
Quadratic formula	No	Yes
Sine rule, cosine rule, area = ½ab sin C	No	Yes

Formulae such as the curved surface area and volume of a cone and the surface area and volume of a sphere were never on the "must memorise" list: both specifications say they are given in the question when needed. AQA's specification also gives the constant acceleration (kinematics) formulae in the question.

What you still need to know

The sheet is not a list of everything. The specifications still expect you to know, for example:

• The area of a triangle (½ × base × height), parallelogram and rectangle, and the volume of a cuboid
• Arc length and sector area, worked out as a fraction of the full circle
• Exact values of sin and cos for 0°, 30°, 45°, 60° and 90°, and of tan for 0°, 30°, 45° and 60°
• Using y = mx + c for straight-line graphs
• Compound units such as speed, density and pressure

A formula on the sheet only helps if you can choose it, substitute into it and rearrange it. Those are the skills the marks are for.

Grade boundaries are set by the boards after the papers have been marked, and they move from year to year to reflect how hard each paper was. No one can tell you in advance the exact mark for a 4 or a 7. What you can use is how the marks are aimed and weighted, which is fixed by Ofqual's rules.

Target grade 4 (Foundation)

• Half of every Foundation paper is aimed at grades 1 to 3. Those marks should be secure first: arithmetic with fractions, decimals and negatives, percentages, simple ratio, reading charts and tables, basic angles and area.
• Number and ratio together are about half of Foundation. Percentage change, best-buy and proportion problems, ratio sharing and money contexts deserve more time than any other area.
• Half of Foundation marks are for AO1 standard techniques. Fluent, accurate methods pay off more on Foundation than on Higher.
• Practise Paper 1 skills without a calculator every week: written multiplication and division, fraction operations, and estimating.

Target grade 5

• On Foundation, grade 5 is the top grade, and it means scoring well on the second half of the paper, aimed at grades 3 to 5. Make sure the harder Foundation topics are covered: forming and solving equations from a context, linear simultaneous equations, Pythagoras and right-angled trigonometry, compound interest and growth and decay, tree diagrams, and transformations including enlargement.
• On Higher, half of each paper is aimed at grades 4 to 6. If you are on Higher, make sure every grade 4 to 6 topic is solid before you touch grade 8 and 9 material: expanding and factorising, solving linear and quadratic equations, straight-line graphs, similarity, volume and surface area, and probability.

Target grade 7 (Higher)

• Algebra is about 30% of Higher. Quadratics in every form (factorising, completing the square, the formula), simultaneous equations including one quadratic, algebraic fractions, and rearranging formulae.
• Work through the higher-only topics in Unit 4: circle theorems, the sine and cosine rules, histograms and cumulative frequency, conditional probability, surds and fractional indices.
• AO2 and AO3 together are 60% of Higher. Practise questions that ask you to "show that", explain, or solve an unfamiliar problem, and write each step down.

Target grade 9

• Half of every Higher paper is aimed at grades 7 to 9, and these questions usually come towards the end. Your time on them should go up as your grade 4 to 6 marks become reliable.
• Proof appears in several statements: algebraic arguments and proofs, proving circle theorems, and using vectors to construct geometric proofs. Practise writing complete, logical proofs.
• Expect function work (inverse and composite functions, transformations of graphs), iteration, the equation of a circle and its tangent, gradients and areas under curves, and quadratic inequalities.
• Accuracy matters at the top. A dropped negative sign or an early rounding can cost the final accuracy mark on a long question.

Where to find official papers

• AQA 8300: the assessment resources page for GCSE Mathematics 8300 lists past question papers, mark schemes, examiner reports and specimen papers.
• Pearson Edexcel 1MA1: Pearson's past papers search covers question papers and mark schemes; choose GCSE, then Mathematics (2015). The Sample Assessment Materials booklet has a full Foundation and Higher set (Papers 1 to 3) with mark schemes. Pearson keeps its most recent papers for teachers only for a period after each series, so ask your teacher for those.

A four-step method

1. Learn by topic using the content list in your specification.
2. Practise by topic with questions from several past papers.
3. Sit full papers under timed conditions, Paper 1 with no calculator, and your board's formulae sheet beside you.
4. Mark strictly with the official mark scheme, then read the examiner report for that series to see the common errors.