Know what to revise. Then practise answering questions.
Use this topic map to plan your GCSE Maths revision from the foundations through to Higher-tier challenge. Each short question gives you an immediate check and a worked method.
The list is organised by the grade at which a topic commonly becomes important. Foundation students can focus on Grades 1-5; Higher students can use the full map. Exact topic ordering varies by exam board and tier, so use this as a revision guide alongside the relevant specification.
Grades 8-9
28 revision topics
Quadratic simultaneous equations
Transforming graphs y=f(x)
Proof
Completing the square
The nth term of a quadratic sequence
Quadratic inequalities
Velocity-time graphs
Proof of circle theorems
Perpendicular lines and the equation of a tangent
Vectors proof questions
Probability equation questions
Surds
Bounds
Direct and inverse proportion
Quadratic formula
Factorising harder quadratics
Algebraic fractions
Rearranging harder formulae
Trigonometric and exponential graphs
Inverse and composite functions
Iteration
Finding the area of any triangle
The sine rule
The cosine rule
Congruent triangles
3D Pythagoras and trigonometry
Histograms
Conditional probability
Grade 7
13 revision topics
Recurring decimals to fractions
Fractional and negative indices
The product rule for counting
Repeated percentage change
Expanding triple brackets
Parallel and perpendicular lines
Inequalities on graphs
Similar shapes (area and volume)
Enlarging with negative scale factors
Circle theorems
Cumulative frequency
Box plots
Capture-recapture
Grade 6
23 revision topics
Writing a ratio as a fraction or linear function
Direct and inverse proportion
Reverse percentages
Standard form
Speed and density
Changing the subject of a formula
Expanding and factorising quadratics
Solving quadratics
Drawing quadratic graphs
Drawing other graphs: cubic and reciprocal
Simultaneous equations
Solving simultaneous equations graphically
Midpoint of a line segment
Gradient of a line
Equation of a line
Spheres and cones
Sector areas and arc lengths
Similar shapes (lengths)
SOHCAHTOA (trigonometry)
Exact trigonometric values
Vectors
Probability trees
Venn diagrams
Grade 5
20 revision topics
Compound interest and depreciation
Indices
Prime factors, HCF and LCM
Real-life and distance-time graphs
Inequalities
Forming and solving equations
Sequences (nth term)
Expanding and factorising
Pythagoras
Angles in parallel lines
Angles in polygons
Surface area
Volume of a prism
Cylinders
Loci and construction
Bearings
Plans and elevations
Averages from frequency tables
Probability
Scatter graphs
Grade 4
20 revision topics
Error intervals
Fractions
Estimating
Writing and simplifying ratio
Ratio
Proportion
Percentages
Percentage change
Exchange rates
Conversions and units
Scale drawings
Best buy questions
Substitution
Solving equations
Drawing graphs
Area and circumference of circles
Transformations
Area of compound shapes
Frequency trees
Two-way tables
Grade 3
5 revision topics
Rotations
Reflections
Enlargements
Translations
Mixed transformations
Grade 2
17 revision topics
Calculation problems
Using a calculator
Systematic listing
Fractions of an amount
Fractions, decimals and percentages
Simplifying algebra
Writing an expression
Function machines
Solving one-step equations
Angles
Area and perimeter
Probability
Frequency polygons
Averages
Bar charts
Stem and leaf
Pie charts
Grade 1
12 revision topics
Addition and subtraction
Multiplication and division
Time
Writing, simplifying and ordering fractions
Place value
Rounding
Negative numbers
Powers and roots
BIDMAS
Factors and multiples
Coordinates
Pictograms
Practise
Answer a question, then check your method.
Have a go without looking at the method first. These are quick confidence-builders; a tutor can help turn any difficult topic into a step-by-step plan.
Percentage change
Question 1
Increase £80 by 15%.
Show method
15% of 80 is 12. Add 12 to 80: £92.
Solving equations
Question 2
Solve 4x + 7 = 31.
Show method
Subtract 7 to get 4x = 24, then divide by 4: x = 6.
Fractions of an amount
Question 3
Find 3/5 of 45.
Show method
One fifth of 45 is 9. Three fifths is 3 × 9 = 27.
Pythagoras
Question 4
A right-angled triangle has shorter sides 6 cm and 8 cm. Find the hypotenuse.
Show method
6² + 8² = 36 + 64 = 100. √100 = 10 cm.
Ratio
Question 5
Share £42 in the ratio 2:5. What is the smaller share?
Show method
There are 7 parts. £42 ÷ 7 = £6 per part; 2 parts = £12.
Standard form
Question 6
Write 0.00056 in standard form.
Show method
Move the decimal four places right to make 5.6, so use 10⁻⁴.
Probability
Question 7
A fair six-sided die is rolled. What is the probability of rolling an even number?
Show method
There are three even results (2, 4, 6) from six possible results: 3/6 = 1/2.
Area of a circle
Question 8
Find the area of a circle with radius 3 cm. Give your answer in terms of π.
Show method
Area = πr² = π × 3² = 9π cm².
About this resource
Practice connected to structured GCSE Maths support.
This free resource is published by National Rising Scholars to help students identify topics and check short methods. It is educational guidance rather than an official exam-board specification.
Bring a school question, a mock-paper result or a topic that feels stuck. We will identify the missing step and practise it until the method makes sense.
