GCSE Maths topics: the full list

By The STEM-Tutor team · Updated October 2026

GCSE Maths content is set nationally and grouped into six areas. Here is what each covers, with the main Higher-only topics marked.

1. Number

• Place value, ordering and rounding
• Fractions, decimals and percentages
• Factors, multiples, primes, HCF and LCM
• Powers, roots and standard form
• Surds and bounds (Higher)

2. Algebra

• Expanding brackets, factorising and simplifying
• Solving linear equations and inequalities
• Straight-line graphs and sequences
• Quadratics: factorising and solving
• Simultaneous equations
• Quadratic formula, completing the square, functions and algebraic proof (Higher)

3. Ratio, proportion and rates of change

• Ratio, proportion and scale
• Percentage change, compound interest and growth
• Speed, density and pressure
• Direct and inverse proportion

4. Geometry and measures

• Angles, polygons and parallel lines
• Area, perimeter, volume and surface area
• Pythagoras' theorem and trigonometry (SOHCAHTOA)
• Transformations and constructions
• Sine rule, cosine rule, circle theorems and vectors (Higher)

5. Probability

• Probability scales and outcomes
• Tree diagrams and Venn diagrams
• Conditional probability (Higher)

6. Statistics

• Averages and range
• Charts and graphs, including scatter graphs
• Cumulative frequency, box plots and histograms (Higher)

Foundation or Higher?

Foundation papers cover grades 1 to 5, and Higher papers cover grades 4 to 9. Higher includes everything in Foundation plus the topics marked above. Your teacher will advise which tier suits you. Check your board's specification for the exact content and paper structure.

How to use this list

1. Tick each topic you can answer exam questions on without help.
2. Revise the unticked ones first. See our GCSE Maths revision plan.

A quick example from each area

Number: fractions

Work out 2⅓ × 1½.

• Convert to improper fractions: 7/3 × 3/2 = 21/6.
• = 3½.

Algebra: solving equations

Solve 5x − 7 = 2x + 8.

• 3x = 15, so x = 5.

Algebra: quadratics

Solve x² + 5x + 6 = 0.

• (x + 2)(x + 3) = 0, so x = −2 or x = −3.

Ratio: sharing

Share £60 in the ratio 2 : 3.

• 5 parts, so one part is £12. The shares are £24 and £36.

Ratio: percentage change

A £250 phone is reduced by 15%. Find the new price.

• 250 × 0.85 = £212.50.

Geometry: area of a circle

Find the area of a circle of radius 7 cm, to 1 decimal place.

• A = πr² = π × 49 ≈ 153.9 cm².

Probability: two events

A fair coin is flipped and a fair dice is rolled. Find P(heads and a 6).

• Independent events: ½ × ⅙ = 1/12.

Statistics: the mean

Find the mean of 4, 7, 9, 10, 15.

• Total 45, divided by 5 = 9.

Which topics carry the most marks?

The weightings are set nationally. On the Higher tier, algebra carries the largest share, about 30%, followed by number, ratio and geometry, with probability and statistics together making up the rest. On Foundation, number carries the largest share. This matters for revision: strong algebra helps in almost every question on Higher, and strong number skills do the same on Foundation. If you are short of time, focus there first.

Topics that often catch students out

• Reverse percentages: if a price after a 20% rise is £60, divide by 1.2, do not take 20% off.
• Bounds: 7 cm to the nearest cm lies between 6.5 cm and 7.5 cm.
• Standard form: 3.2 × 10⁴ is 32,000; the first number must be between 1 and 10.
• Circle theorems: name the theorem you use for each angle.
• Histograms: frequency density is frequency divided by class width.

Practice questions

Try each one before opening the answer.

Frequently asked questions

Is the content the same for every exam board?

Yes. AQA, Edexcel and OCR follow the same national subject content. The papers look different, so practise with your own board's past papers.

How many papers are there?

Three papers of equal weight: one non-calculator and two calculator papers, for each tier.

Key takeaways

• GCSE Maths has six content areas.
• Algebra is the biggest share on Higher; number on Foundation.
• Every board covers the same content.
• There are three papers: one non-calculator, two calculator.
• Use the topic list to check off what you have mastered.

Where to go next

Dive deeper into individual topics.

• Trigonometry
• Surds
• Vectors
• Circle theorems

The six areas in more detail

Number covers place value, fractions, decimals, percentages, powers, roots, standard form, factors, multiples, primes and, on Higher, surds and bounds. It underpins everything else, so fluent number skills save time on every paper.

Algebra covers expressions, equations, inequalities, sequences, graphs and functions. On Higher it extends to quadratic equations, simultaneous equations with a quadratic, algebraic fractions, iteration and functions. It is the largest area on the Higher tier.

Ratio, proportion and rates of change covers ratio, direct and inverse proportion, percentages in context, compound interest, speed, density and pressure. Many real-life problems sit here.

Geometry and measures covers angles, shapes, area and volume, transformations, constructions, Pythagoras, trigonometry, circle theorems and vectors. Diagrams help a lot in this area.

Probability covers simple probability, tree diagrams, Venn diagrams and, on Higher, conditional probability.

Statistics covers averages, charts, scatter graphs, and on Higher, cumulative frequency, box plots and histograms.

Planning your revision around the list

Print or copy the topic list and give each topic a colour: green for confident, amber for unsure and red for weak. Start revision with the red topics that carry the most marks, then work through the amber ones. Revisit green topics every few weeks so they stay secure. Update the colours as you go; seeing red turn to green is motivating and shows you exactly where your time is best spent.

Geometry: Pythagoras

A right-angled triangle has shorter sides 6 cm and 8 cm. Find the hypotenuse.

• h² = 36 + 64 = 100, so h = 10 cm.

Algebra: inequalities

Solve 3x + 4 < 19.

• 3x < 15, so x < 5.

Formulae you need to learn

GCSE Maths gives very few formulae in the exam. You need to know Pythagoras' theorem, the trigonometric ratios, the areas of common shapes, the circumference and area of a circle, the volume of prisms, the quadratic formula and, on Higher, the sine and cosine rules. A few formulae, such as the volume of a sphere or cone, are given in the question when needed. For GCSE exams in 2025 to 2027, a formulae sheet is provided with the papers, so check the sheet for your exam year, but learn the common formulae anyway so you can use them quickly.

Learning these early, and using them often in practice, means you will not waste time trying to remember them in the exam.

Finally, remember that the topics connect. A single exam question can use ratio, algebra and geometry together, so practise mixed questions once each topic feels secure.