Ratio, proportion and rates of change

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What this unit covers

• Ratio, proportion and rates of change: [Higher only] Use compound units such as density and pressure.
• Ratio, proportion and rates of change: [Foundation and Higher] Use compound units such as speed, rates of pay and unit pricing.
• Ratio, proportion and rates of change: [Foundation and Higher] Use scale factors, scale diagrams and maps, including geometrical problems.
• Ratio, proportion and rates of change: [Foundation and Higher] Express one quantity as a fraction of another, including fractions less than 1 and greater than 1.
• Ratio, proportion and rates of change: [Foundation and Higher] Use ratio notation, including reducing ratios to simplest form.
• Ratio, proportion and rates of change: [Foundation and Higher] Apply ratio to contexts involving conversion, comparison, scaling, mixing, concentration and value for money.
• Ratio, proportion and rates of change: [Foundation and Higher] Divide a quantity into two parts in a part:part or part:whole ratio and express such divisions as ratios.
• Ratio, proportion and rates of change: [Foundation and Higher] Express a multiplicative relationship between two quantities as a ratio or a fraction.
• Ratio, proportion and rates of change: [Foundation and Higher] Understand and use proportion as equality of ratios.
• Ratio, proportion and rates of change: [Foundation and Higher] Relate ratios to fractions and to linear functions.
• Ratio, proportion and rates of change: [Foundation and Higher] Interpret percentages and percentage changes as fractions, decimals and multiplicative changes.
• Ratio, proportion and rates of change: [Foundation and Higher] Define percentage as parts per hundred and express one quantity as a percentage of another.
• Ratio, proportion and rates of change: [Foundation and Higher] Solve problems involving direct and inverse proportion, including graphical and algebraic representations.
• Ratio, proportion and rates of change: [Foundation and Higher] Compare lengths, areas and volumes using ratio notation and scale factors.
• Ratio, proportion and rates of change: [Higher only] Link length, area and volume ratios to similarity and trigonometric ratios.
• Ratio, proportion and rates of change: [Higher only] Construct equations that describe direct and inverse proportion.
• Ratio, proportion and rates of change: [Foundation and Higher] Interpret equations that describe direct and inverse proportion.
• Ratio, proportion and rates of change: [Foundation and Higher] Interpret the gradient of a straight-line graph as a rate of change.
• Ratio, proportion and rates of change: [Foundation and Higher] Recognise and interpret graphs that illustrate direct and inverse proportion.
• Ratio, proportion and rates of change: [Higher only] Apply average and instantaneous rate of change using gradients of chords and tangents.
• Ratio, proportion and rates of change: [Higher only] Interpret the gradient at a point on a curve as the instantaneous rate of change.
• Ratio, proportion and rates of change: [Higher only] Set up, solve and interpret growth and decay problems, including compound interest.
• Ratio, proportion and rates of change: [Higher only] Work with general iterative processes.
• Ratio, proportion and rates of change: [Foundation and Higher] Change freely between related standard units and compound units in numerical contexts.
• Ratio, proportion and rates of change: [Higher only] Change between compound units such as density and pressure in numerical and algebraic contexts.