**Ratio, proportion and rates of change**

What students need to learn:

**R1** change freely between related standard units (e.g. time, length, area, volume/capacity, mass) and compound units (e.g. speed, rates of pay,

prices, density, pressure) in numerical and algebraic contexts

**R2** use scale factors, scale diagrams and maps

**R3** express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1

**R4** use ratio notation, including reduction to simplest form

**R5** divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio; apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)

**R6** express a multiplicative relationship between two quantities as a ratio or a fraction

**R7** understand and use proportion as equality of ratios

**R8** relate ratios to fractions and to linear functions

**R9** define percentage as ‘number of parts per hundred’; interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively; express one quantity as a percentage of another; compare two quantities using percentages; work with percentages greater than 100%; solve problems involving percentage change, including percentage increase/decrease and original value problems, and simple interest including in financial mathematics

**R10** solve problems involving direct and inverse proportion, including graphical and algebraic representations

**R11** use compound units such as speed, rates of pay, unit pricing, density and pressure

**R12** compare lengths, areas and volumes using ratio notation; make links to similarity (including trigonometric ratios) and scale factors

**R13** understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y; interpret equations that describe direct and inverse

proportion

**R14** interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion

**R16** set up, solve and interpret the answers in growth and decay problems, including compound interest

To see the split between Higher and Foundation please see the full specification **Edexcel GCSE 2015 Specification**