The Complete GCSE & IGCSE Maths Topic List (Foundation and Higher)
If you're trying to get a clear picture of everything that's on GCSE or IGCSE Maths — whether that's to plan your revision, understand the difference between Foundation and Higher, or compare GCSE to IGCSE — this is the page for you.
Below is every topic covered across both qualifications, organised by subject area and tier. All of these are available to practise in the students section.
Foundation vs Higher: What's the Difference?
GCSE Maths is split into two tiers, and it matters which one you're sitting.
Foundation covers grades 1–5. It includes all the core topics, from basic number work through to quadratics, trigonometry, and statistics. Higher covers grades 3–9 and includes everything on Foundation plus additional content that only appears at the top grades — things like circle theorems, vectors, proof, and quadratic inequalities.
If you're not sure which tier you're sitting, ask your teacher. Most schools enter students for a mixture, so it's really worth knowing before you start revising.
In the app, you can set your tier in your account settings and the content will be filtered accordingly — so you'll only see topics relevant to your exam.
GCSE vs IGCSE: What's the Difference?
GCSE (General Certificate of Secondary Education) is the standard qualification in England and Wales, examined by boards including Edexcel, AQA, and OCR.
IGCSE (International General Certificate of Secondary Education) is common in independent and international schools worldwide.
Around 90% of the content overlaps, but there are some differences:
| Topic | GCSE | IGCSE |
|---|---|---|
| Iteration | ✓ | — |
| Trapezium rule | ✓ | — |
| Arithmetic sequences | — | ✓ |
| Intersecting chords | — | ✓ |
| Differentiation | — | ✓ |
You can switch between GCSE and IGCSE mode in your settings, so you'll only ever practise topics relevant to your exam.
Full GCSE & IGCSE Maths Topic List
Topics are listed roughly in order of difficulty, from grade 1 upwards. Foundation students cover everything up to grade 5; Higher students cover everything.
Number
Foundation and Higher
- Converting between numbers and words
- Times tables
- Addition and subtraction
- Ordering numbers
- Negative numbers
- Squares, square roots, cubes, and cube roots
- Multiples of pi
- Simplifying fractions
- Equivalent fractions
- Adding and subtracting fractions
- Multiplying fractions
- Dividing fractions
- Fractions, decimals, and percentages
- Basic percentages
- Percentage change (increase and decrease)
- Compound growth and decay
- Reverse percentages
- Prime factor decomposition
- Highest Common Factor (HCF)
- Lowest Common Multiple (LCM)
- Basic indices (powers)
- Indices (laws of indices)
- Standard form
- Rounding (decimal places and significant figures)
- Estimation
- Error intervals
- Converting standard units
Higher only
- Fractional and negative indices
- Surds (simplifying, expanding, rationalising)
- Bounds (upper and lower bounds)
- Recurring decimals (converting to fractions)
Algebra
Foundation and Higher
- Simplifying expressions
- Substitution
- Expanding single brackets
- Factorising (single bracket)
- Expanding quadratics (double brackets)
- Factorising quadratics
- Solving linear equations
- Simultaneous equations (linear)
- Linear inequalities
- Finding the nth term (linear sequences)
- Quadratic sequences
- Equation of a straight line (y = mx + c)
- Gradients and intercepts
- Parallel and perpendicular lines
- Solving quadratics (factorising, formula, completing the square)
- Changing the subject of a formula
- Function notation
- Composite functions
- Inverse functions
- Common graphs (quadratic, cubic, reciprocal)
- Solving quadratics graphically
- Transformations of graphs
- Speed–time graphs
- Direct and inverse proportion
Higher only
- Fractional and negative indices (algebraic)
- Algebraic fractions
- Manipulating algebraic fractions
- Expanding triple brackets
- Factorising harder quadratics (non-monic)
- Difference of two squares
- Completing the square
- Quadratic inequalities
- Equation of a circle
- Iteration (finding approximate solutions)
- Gradients as rates of change
- Trapezium rule (estimating areas under curves)
Ratio, Proportion and Rates of Change
Foundation and Higher
- Ratios (simplifying, dividing in a ratio)
- Proportion (direct and inverse)
- Speed, distance, and time
- Compound units (density, pressure)
- Percentage and ratio problems
- Ratios and similar shapes (scale factors)
Geometry and Measures
Foundation and Higher
- Coordinates
- Angle facts (angles on a line, in a triangle, in parallel lines)
- Polygons (interior and exterior angles)
- Circumference of a circle
- Area of a circle
- Arcs and sectors
- Area of a triangle
- Areas and volumes of 2D and 3D shapes
- Pythagoras' theorem
- Trigonometry (SOH CAH TOA)
- Exact trigonometric values (30°, 45°, 60°)
- Translations
- Reflections
- Rotations
- Bearings
Higher only
- Area of a triangle using ½ab sin C
- The sine rule
- The cosine rule
- Circle theorems
- Vectors
- Equation of a circle (x² + y² = r²)
Probability
Foundation and Higher
- Theoretical probability
- Experimental probability
- The probability sum (P(A) + P(not A) = 1)
- Probability trees
- Product rule for counting
- Set notation and Venn diagrams
Statistics
Foundation and Higher
- Mean, median, mode, and range
- Interquartile range
- Cumulative frequency diagrams
- Box plots
- Scatter graphs and correlation
- Populations and samples
What Grade Are These Topics?
Here's a rough guide to how topics map to grade levels in the student section:
| Grade | Topics included |
|---|---|
| Grade 1 | Basic number, coordinates, times tables |
| Grade 2 | Fractions, basic algebra, ordering numbers |
| Grade 3 | Factorising, Pythagoras, fractions, rounding |
| Grade 4 | Quadratics, simultaneous equations, trigonometry basics, probability |
| Grade 5 | Higher-level functions, surds intro, proportion, speed–time graphs |
| Grade 6 | Sine/cosine rules, circle theorems intro, algebraic fractions |
| Grade 7+ | Vectors, iteration, quadratic inequalities, circle equations |
One thing worth knowing about grades 8 and 9: the questions at that level aren't just harder versions of the same topics — they tend to combine three or more topics in a single question. If any individual area has a gap in it, those multi-topic questions are where it tends to show up. Getting to a grade 8 or 9 is less about learning new content and more about making sure every topic you've covered is properly consolidated.
Practise Every Topic
The student section covers all of the topics listed above for both GCSE and IGCSE. Set your tier and curriculum in your account settings, and you'll only see questions relevant to your exam. Questions are graded by difficulty, so you can start where you are and build up — whether you're targeting a grade 4 pass or pushing for a 9.