GCSE maths · Checklist · AQA, Edexcel, OCR

GCSE maths topic checklist:
every topic, both tiers

The full list of GCSE maths topics for students sitting the exams in summer 2027 or the November 2026 resit series, grouped into the six content areas and marked where a topic is Higher tier only. It works for AQA, Pearson Edexcel and OCR alike.

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The short answer

What is a GCSE maths topic checklist for?

A GCSE maths topic checklist turns "revise maths" into a list of named topics, sorted by how secure each one is. Your child goes through every line below and rates it red (can't start it), amber (can do it with notes or a worked example) or green (can answer an unseen exam question on it, without help). The reds and ambers become the revision list.

Topics marked (Higher) are only examined on the Higher tier. Everything unmarked appears on both tiers, so every student needs it. A Foundation student can simply skip the Higher lines.

The same list works for every board. The Department for Education publishes one set of GCSE mathematics subject content that AQA (8300), Pearson Edexcel (1MA1) and OCR (J560) must all follow; Higher-only content is the part printed in bold there.

The checklist

Every GCSE maths topic, area by area

Six content areas, as the subject content sets them out. Rate each line red, amber or green. The weightings quoted are Pearson Edexcel's published ranges for 1MA1; the other boards publish theirs differently.

1. Number

Worth roughly a quarter of the marks on Foundation papers and much less on Higher, where it mostly appears inside other questions.

  • Place value; ordering integers, decimals and negative numbers
  • The four operations with integers, decimals and negatives, by written methods without a calculator
  • Order of operations, including powers and brackets
  • Factors, multiples and primes; writing a number as a product of prime factors
  • Highest common factor and lowest common multiple, including with Venn diagrams
  • Squares, cubes, square roots and cube roots
  • Laws of indices with whole-number powers, including zero and negative powers
  • Fractional indices, such as 272/3 and 16−1/2 (Higher)
  • Standard form: converting, and calculating with and without a calculator
  • Fractions: equivalence, simplifying, all four operations, mixed numbers
  • Moving between fractions, decimals and percentages; terminating decimals
  • Converting recurring decimals to fractions by the algebraic method (Higher)
  • Simplifying surds, such as √48 = 4√3, and exact calculation with them (Higher)
  • Rationalising a denominator, such as 6/√3 or 1/(2 + √3) (Higher)
  • Rounding to decimal places and significant figures; estimating answers
  • Error intervals written as inequalities, such as 6.5 ≤ x < 7.5
  • Upper and lower bounds in calculations, such as the greatest possible speed (Higher)
  • Listing outcomes systematically
  • The product rule for counting, such as how many four-digit codes exist (Higher)
  • Calculator skills: fractions, powers, roots, standard form and the memory

2. Algebra

The largest area on Higher papers, at around 27–33% of the marks, and home to most of the Higher-only content.

  • Algebraic notation; simplifying and collecting like terms
  • Substituting values into expressions and formulae
  • Expanding a single bracket and factorising into one
  • Expanding double brackets, such as (x + 3)(x − 5)
  • Expanding the product of three binomials (Higher)
  • Factorising x² + bx + c, including the difference of two squares
  • Factorising ax² + bx + c where a is not 1 (Higher)
  • Solving linear equations, including unknowns on both sides and brackets
  • Changing the subject of a formula
  • Changing the subject when it appears twice or needs factorising (Higher)
  • Solving quadratics by factorising
  • Solving quadratics with the quadratic formula (Higher)
  • Completing the square, and using it to find a turning point (Higher)
  • Linear simultaneous equations, by elimination and by substitution
  • Simultaneous equations where one is quadratic, including a circle (Higher)
  • Linear inequalities, solved and shown on a number line
  • Quadratic inequalities, such as x² − x − 12 < 0 (Higher)
  • Inequalities as regions on a graph; set notation (Higher)
  • Identities (≡) and "show that" questions
  • Algebraic proof, such as the sum of three consecutive integers being a multiple of 3 (Higher)
  • Algebraic fractions: simplifying, adding, multiplying, and equations containing them (Higher)
  • Function machines and simple functions
  • Composite functions fg(x) and inverse functions f−1(x) (Higher)
  • Term-to-term and position-to-term rules; the nth term of a linear sequence
  • Triangular, square, cube, Fibonacci-type and simple geometric sequences
  • The nth term of a quadratic sequence (Higher)
  • Straight-line graphs: y = mx + c, gradient, intercept, the equation through two points
  • Parallel lines; perpendicular gradients that multiply to −1 (Higher)
  • Quadratic graphs: plotting, and reading roots, intercepts and turning points
  • Recognising and sketching cubic and reciprocal graphs
  • Exponential graphs and the graphs of sin x, cos x and tan x (Higher)
  • The equation of a circle centred at the origin, and of a tangent to it (Higher)
  • Graph transformations: f(x) + a, f(x + a), −f(x), f(−x) (Higher)
  • Iteration to find approximate solutions (Higher)
  • Real-life graphs: distance–time, conversion graphs, what the gradient means
  • Gradients of curves using tangents, and the area under a graph (Higher)

3. Ratio, proportion and rates of change

The context-heavy area: recipes, best buys, exchange rates, speed. Edexcel gives it roughly 22–28% of Foundation marks and 17–23% of Higher.

  • Simplifying ratios; ratios as fractions; the form 1 : n
  • Sharing in a ratio, including when the difference or one share is given
  • Combining two ratios into a three-part ratio
  • Percentages of amounts; percentage increase and decrease; one quantity as a percentage of another
  • Reverse percentages, finding the original amount
  • Simple and compound interest, depreciation, repeated percentage change
  • Growth and decay with a multiplier, such as 5000 × 0.92n
  • Best buys and unit pricing
  • Direct and inverse proportion in problems and graphs; recognising y = kx and y = k/x
  • Proportion equations such as y ∝ x² or y ∝ 1/√x, finding k (Higher)
  • Compound measures: speed, density, pressure, with unit conversions
  • Converting units, including area and volume units such as cm³ to litres
  • Scale drawings and map scales
  • Similar shapes: length scale factors
  • Similar shapes: area and volume scale factors, k² and k³ (Higher)
  • The gradient of a curve at a point as a rate of change (Higher)

4. Geometry and measures

Big on both tiers. Foundation leans on angles, area and perimeter; Higher adds circle theorems, vector proof and trigonometry without a right angle.

  • Angles on a line, at a point, vertically opposite, in triangles and quadrilaterals
  • Angles in parallel lines — alternate, corresponding, co-interior — with reasons
  • Interior and exterior angles of polygons
  • Properties and symmetry of triangles and quadrilaterals
  • Perimeter and area of rectangles, triangles, parallelograms, trapezia and compound shapes
  • Circumference and area of a circle; arc length and sector area
  • Volume and surface area of cuboids, prisms and cylinders
  • Volume and surface area of spheres, cones and pyramids
  • Composite solids, including a frustum
  • Plans and elevations; faces, edges and vertices
  • Ruler-and-compass constructions: perpendicular bisector, angle bisector, perpendicular from a point
  • Loci: regions a set distance from a point or a line
  • Bearings
  • Reflection, rotation, translation by a column vector, and enlargement with positive or fractional scale factors
  • Enlargement with a negative scale factor; combined transformations; invariant points (Higher)
  • Congruent triangles: SSS, SAS, ASA, RHS
  • Congruence proofs (Higher)
  • Pythagoras' theorem in two dimensions
  • Right-angled trigonometry: finding sides and angles
  • Exact values of sin, cos and tan for 0°, 30°, 45°, 60° and 90° (tan up to 60°)
  • Pythagoras and trigonometry in three dimensions, such as the angle between a line and a plane (Higher)
  • The sine rule, the cosine rule and area = ½ab sin C (Higher)
  • Circle vocabulary: radius, chord, tangent, arc, sector, segment
  • Circle theorems, applied with reasons and proved (Higher)
  • Vectors: adding, subtracting, multiplying by a scalar, on diagrams
  • Vector proofs that points are collinear or lines parallel (Higher)

5. Probability

A smaller area where marks go on thin working. Tree diagrams and Venn diagrams turn up in almost every series.

  • The 0 to 1 scale; probabilities of all outcomes summing to 1
  • Listing outcomes; sample space diagrams
  • Relative frequency, expected outcomes, fairness and bias
  • Two-way tables and frequency trees
  • Venn diagrams and set notation: ∪, ∩, A′ and the universal set
  • Tree diagrams for independent events and for "without replacement"
  • Conditional probability from tables, trees and Venn diagrams (Higher)

6. Statistics

Calculation plus interpretation. A "compare the distributions" question wants two comparisons, one of an average and one of spread, each in context.

  • Types of data; populations and samples; sampling and bias
  • Bar charts, pictograms, pie charts, vertical line charts and time series
  • Mean, median, mode and range from lists and frequency tables
  • Estimated mean and modal class from grouped data
  • Scatter graphs: correlation, lines of best fit, interpolation against extrapolation
  • Comparing distributions using an average and a measure of spread
  • Cumulative frequency graphs, with the median and interquartile range (Higher)
  • Box plots, drawn and compared (Higher)
  • Histograms with unequal class widths, using frequency density (Higher)

Tiering follows the DfE's GCSE mathematics subject content, in which Higher-only content is shown in bold. Area weightings are the approximate ranges Pearson Edexcel publishes for 1MA1. Check your board's specification if a line matters to a decision.

Using it

How to use the checklist: rate, test, then fix the roots

The checklist decides what to revise first. It is not itself a test, and it only works if the ratings are honest.

Boards

The topics match across boards; the papers do not

The content is identical for AQA, Pearson Edexcel and OCR. What differs is how the three papers are built, which is why practising on your own board's papers matters.

AQA (8300)Pearson Edexcel (1MA1)OCR (J560)
Papers3, each 1 hour 30 minutes3, each 1 hour 30 minutes3, each 1 hour 30 minutes
Marks per paper8080100
Non-calculatorPaper 1Paper 1The middle paper: Paper 2 (Foundation) or Paper 5 (Higher)
Paper numbering1F–3F, 1H–3H1F–3F, 1H–3HFoundation 1–3, Higher 4–6

From each board's published specification. Every board supplies a formulae sheet in all three papers, and Ofqual has confirmed that continues for the life of the current specifications — see the GCSE maths formula sheet for what is and isn't on it. If you don't know the board, look at the front of a school mock paper.

With a teacher

A ClassArc teacher can turn the reds into a weekly plan

Lots of red and amber in Year 10 is normal, and it is fixable. In ClassArc's free first class, a GCSE teacher works with your child for 55 minutes, one-to-one, starting just above where the school has reached and going back until the ground holds — which is this checklist done live, with the method visible.

After that, the same teacher takes every class, checks the school's current unit beforehand, and sets homework on that day's topic. GCSE-year classes are from £14 each on the largest block.

“

A red on rearranging formulae is never only one red. It shows up in trigonometry, speed and simultaneous equations too.

Why the roots come first

Next

After the checklist: plan, reference, decide

GCSE maths revision guide

Turns a filled-in checklist into a twelve-week plan, week one being this page.

Build the plan

Foundation or Higher?

If the tier is still open, the evidence to look at and the questions to ask school.

Read the post

GCSE maths tutor

One-to-one classes on your child's board and tier, with the same teacher every week.

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All UK maths resources

Every guide and checklist from Year 1 to A-Level.

Browse them

Checklist questions

Does this GCSE maths checklist work for AQA, Edexcel and OCR?
Yes. All three boards teach the same Department for Education subject content, so the topics on the checklist are the same whichever board your child sits. The boards differ in paper layout, marks per paper and question style, not in what is examined.
Which topics can a Foundation student skip?
Every line marked (Higher). Those topics are only examined on the Higher tier. Everything unmarked can appear on Foundation papers and should be secure before exam season.
When should my child fill in the checklist?
Once near the start of Year 11 is a good default, then every four to six weeks after that. In Year 10 it is still useful, but expect more red simply because some topics haven't been taught yet.
My child rated almost everything green. Is that right?
Possibly, but test it. Choose three green topics and do one past-paper question on each without notes. If any go wrong, the ratings were optimistic and the whole list is worth a second pass.
Is there a printable version?
Not as a separate download at the moment. The page prints cleanly from the browser, and many families simply copy the lines their child rates red and amber into a notebook.
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