Ratio, proportion and rates of change – GCSE AQA Higher Maths revision notes

What this topic covers

Ratio, proportion and rates of change has 5 subtopics:

• Units, Scale and Similarity
• Ratio and Proportion Fundamentals
• Percentages and Financial Maths
• Direct and Inverse Proportion
• Rates of Change and Growth

Ratio, proportion and rates of change lessons by subtopic

23 lessons, grouped by subtopic.

Units, Scale and Similarity

• Converting Between Standard and Compound Units: Learn to change freely between related standard units (time, length, area, volume, mass) and compound units (speed, rates of pay, prices) in numerical contexts. Practice converting between different units and working with rates and compound measurements.
• Scale Factors, Scale Diagrams and Maps: Learn to work with scale factors in various contexts, interpret and create scale diagrams, and use map scales to calculate real distances and measurements.
• Working with Compound Units: Learn to calculate and use compound units including speed, rates of pay, and unit pricing in real-world problems
• Comparing and Scaling in 2D and 3D: Learn to compare lengths, areas and volumes using ratio notation and understand how scale factors affect different dimensions

Ratio and Proportion Fundamentals

• Expressing One Quantity as a Fraction of Another: Learn how to express one quantity as a fraction of another, including cases where the fraction is less than 1 or greater than 1. Practice with real-world examples and different types of quantities.
• Simplifying and Interpreting Ratios: Simplify ratios, scale them correctly, and interpret each part of a ratio as a share of the whole or a multiplicative comparison.
• Dividing Quantities Using Ratios: Learn how to divide a given quantity into two parts using part:part and part:whole ratios, and express divisions as ratios.
• Ratio in Real-World Contexts: Apply ratio skills to solve real-world problems involving conversion, comparison, scaling, mixing, and concentrations.
• Expressing Multiplicative Relationships as Ratios and Fractions: Learn to identify and express multiplicative relationships between two quantities using both ratio and fraction notation. Practice converting between different representations and understanding when to use each form.
• Understanding Proportion as Equality of Ratios: Learn what proportion means and how it relates to equal ratios. Explore how to identify when two ratios are in proportion and solve problems involving proportional relationships.
• Connecting Ratios, Fractions and Linear Functions: Explore the relationships between ratios, fractions and linear functions. Learn how to convert between these representations and understand their mathematical connections through practical examples and graphical interpretations.

Percentages and Financial Maths

• Percentage Basics and Percentage of Amounts: Interpret percentages, find percentages of amounts, and compare percentage values accurately in straightforward contexts.
• Comparing and Working with Percentages: Compare quantities using percentages and work confidently with percentages greater than 100%.
• Percentage Change and Financial Applications: Solve problems involving percentage increase and decrease, find original values, and apply percentage concepts to simple interest and financial mathematics.

Direct and Inverse Proportion

• Modelling Direct and Inverse Proportion: Recognise direct and inverse proportion relationships, write proportion statements, and model them in numerical and contextual problems.
• Working with Proportion Equations: Develop skills in interpreting and working with equations that describe direct and inverse proportion relationships, including higher-level applications.
• Solving Direct and Inverse Proportion Problems: Solve direct and inverse proportion problems algebraically and graphically, and explain how the relationship changes with scale.

Rates of Change and Growth

• Direct and Inverse Proportion Graphs: Recognise and interpret graphs that show direct and inverse proportion relationships, understanding their characteristic shapes and real-world applications.
• Gradient as a Rate of Change: Interpret gradient as a rate of change, calculate gradients from graphs and coordinates, and explain what they mean in context.
• Average and Instantaneous Rates of Change: Calculate average and instantaneous rates of change from chords and tangents, and interpret them in numerical, graphical, and contextual problems.
• Chords, Tangents and Rates of Change: Use chords and tangents on curves to distinguish between average and instantaneous rates of change and avoid common exam errors.
• Growth and Decay with Multipliers: Model exponential growth and decay using percentage multipliers and compound change in financial and scientific contexts.
• Compound Growth, Decay and Iteration: Solve harder repeated percentage-change problems and use iterative methods to model long-term growth and decay behaviour.

Revise Right Mocks '26

AQA GCSE Maths mock draft, 26–31 Oct. Draft coverage: Maths Paper 1 (Higher tier). Reviewed for an original-practice sitting; check student availability before registering. Marking and results will follow later, after separate approval. Eligible new accounts receive a five-day Pro trial when signup email verification completes. Previous trials keep their original expiry. After expiry, new papers need Pro unless you have an explicitly confirmed free sitting offer for this event. That offer adds no Pro time or AI learning. Saved attempts and released results remain readable. No card or automatic charge.

More in this course

Go back to the full GCSE AQA Higher Maths topic list, or practise this topic with past-paper questions.