Ratio, proportion and rates of change

    AQA
    GCSE

    This domain focuses on multiplicative reasoning and the comparison of quantities, serving as a fundamental bridge between numerical calculation and algebraic thinking. It encompasses the study of relationships between variables, including direct and inverse proportion, and the quantification of change through compound measures and gradients. Mastery of this topic requires fluency in converting between representations (fractions, decimals, percentages) and applying proportional logic to model real-world contexts such as finance, kinematics, and geometry.

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    Objectives
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    Exam Tips
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    Pitfalls
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    Key Terms
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    Mark Points

    Learning Objectives

    What you need to know and understand

    • Change freely between related standard units and compound units in numerical and algebraic contexts
    • Use scale factors, scale diagrams and maps
    • Express one quantity as a fraction of another
    • Use ratio notation, including reduction to simplest form and dividing a quantity into parts
    • Understand and use proportion as equality of ratios; relate ratios to fractions and linear functions
    • Solve problems involving percentage change, including simple interest
    • Solve problems involving direct and inverse proportion
    • Construct and interpret equations that describe direct and inverse proportion
    • Set up, solve and interpret growth and decay problems, including compound interest

    Key Terminology

    Essential terms to know

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