GCSE maths · strand
Ratio and Proportion
15 topics, each with printable practice questions and a full answer key. Every sheet is generated, so you can make a fresh one whenever you need it.
- Best Buy Questions
- Compound Interest and Depreciation
- Exchange Rates
- Flow Rates and Compound Units
- Percentages
- Ratio
- Repeated Percentage Change
- Reverse Percentages
- Simple Interest
- Writing and Simplifying Ratio
All strands by tier: Foundation tier · Higher tier
- A14
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plot and interpret graphs (including reciprocal graphs and exponential graphs) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration
- G14
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use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.)
- N2
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apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers – all both positive and negative; understand and use place value (e.g. when working with very large or very small numbers, and when calculating with decimals)
- N11
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identify and work with fractions in ratio problems
- N12
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interpret fractions and percentages as operators
- N13
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use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate
- R1
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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
Conversions and Units · Flow Rates and Compound Units · Speed and Density
- R3
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express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
- R4
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use ratio notation, including reduction to simplest form
Ratio · Writing a Ratio as a Fraction or Linear Function · Writing and Simplifying Ratio
- R5
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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)
Conversions and Units · Exchange Rates · Ratio · Writing a Ratio as a Fraction or Linear Function
- R6
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express a multiplicative relationship between two quantities as a ratio or a fraction
Writing a Ratio as a Fraction or Linear Function · Writing and Simplifying Ratio
- R7
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understand and use proportion as equality of ratios
- R8
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relate ratios to fractions and to linear functions
- R9
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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
Compound Interest and Depreciation · Percentages · Repeated Percentage Change · Reverse Percentages · Simple Interest
- R10
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solve problems involving direct and inverse proportion, including graphical and algebraic representations
Conversions and Units · Direct and Inverse Proportion · Exchange Rates · Proportion
- R11
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use compound units such as speed, rates of pay, unit pricing, density and pressure
Best Buy Questions · Flow Rates and Compound Units · Proportion · Speed and Density
- R12
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compare lengths, areas and volumes using ratio notation; make links to similarity (including trigonometric ratios) and scale factors
- R13
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understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y; construct and interpret equations that describe direct and inverse proportion
- R14
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interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion
- R16
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set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes
Compound Interest and Depreciation · Repeated Percentage Change
Statements from the Department for Education's GCSE mathematics subject content. Contains public sector information licensed under the Open Government Licence v3.0.