GCSE AQA Mathematics: Complete Topic Guide & Revision Tips

1. Number

Covers basic arithmetic, properties of numbers, and calculations with decimals, fractions, and percentages.

• Understand place value and work confidently with large and small numbers.
• Perform calculations with integers, decimals, and fractions.
• Use factors, multiples, primes, squares, cubes, and roots.
• Apply the four operations (add, subtract, multiply, divide) to all number types.
• Work with powers, indices, and standard form.
• Calculate and interpret percentages, percentage change, and reverse percentages.
• Understand ratio and proportion in real-life contexts.
• Round numbers to a given degree of accuracy (decimal places, significant figures).
• Estimate answers and check calculations for reasonableness.
• Use surds and exact values where required.

2. Algebra

Focuses on expressions, equations, sequences, and graphs.

• Simplify and manipulate algebraic expressions, including expanding and factorising.
• Solve linear and quadratic equations and inequalities.
• Work with algebraic fractions and rearrange formulae.
• Generate and use sequences, including arithmetic and geometric progressions.
• Plot and interpret linear, quadratic, cubic, and reciprocal graphs.
• Understand and use function notation and composite functions.
• Solve simultaneous equations (algebraically and graphically).
• Recognise and use the equation of a straight line (y = mx + c).
• Apply algebra to real-life problems and modelling.
• Use inequalities on number lines and solve quadratic inequalities.

3. Ratio, Proportion and Rates of Change

Involves comparing quantities, scaling, and working with rates.

• Simplify ratios and divide quantities in a given ratio.
• Use direct and inverse proportion in calculations.
• Solve problems involving best buys and value for money.
• Work with compound measures (speed, density, pressure).
• Apply percentage increase/decrease and repeated percentage change.
• Use scale factors for enlargements and maps.
• Convert between currencies and units.
• Interpret and use gradient as a rate of change.
• Set up and solve problems involving proportionality.
• Apply ratio and proportion to real-life contexts (recipes, mixtures).

4. Geometry and Measures

Covers properties of shapes, transformations, and measurement.

• Classify and work with angles, triangles, quadrilaterals, and polygons.
• Calculate perimeters, areas, and volumes of 2D and 3D shapes.
• Use circle theorems, arc length, and sector area.
• Apply Pythagoras’ theorem and trigonometry in right-angled triangles.
• Work with vectors and vector notation.
• Understand and use congruence and similarity.
• Perform and describe transformations: translation, reflection, rotation, enlargement.
• Convert between metric units and use compound units.
• Calculate surface area and volume of prisms, cylinders, spheres, cones, and pyramids.
• Interpret and construct scale drawings and bearings.

5. Probability

Study the likelihood of events and how to calculate probabilities.

• Understand and use the probability scale from 0 to 1.
• Calculate probabilities of single and combined events.
• Use sample space diagrams, Venn diagrams, and tree diagrams.
• Apply the addition and multiplication rules of probability.
• Work with mutually exclusive and independent events.
• Calculate expected outcomes and relative frequency.
• Estimate probabilities from experimental data.
• Understand conditional probability and use two-way tables.
• Recognise and avoid common probability misconceptions.
• Apply probability to real-life situations and risk assessment.

6. Statistics

Focuses on data collection, representation, and interpretation.

• Collect, classify, and tabulate data effectively.
• Construct and interpret bar charts, pie charts, histograms, and frequency polygons.
• Calculate averages: mean, median, mode, and range.
• Work with grouped and ungrouped data.
• Draw and interpret cumulative frequency and box plots.
• Understand and use scatter graphs and correlation.
• Estimate the mean from grouped data.
• Identify outliers and interpret their effect on data.
• Compare data sets using averages and spread.
• Apply statistical techniques to real-world problems and surveys.

Further Support

For detailed notes, practice questions, and interactive resources on every GCSE AQA Mathematics topic, visit TRH Learning.