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12
42 ÷ 7 = 6; 2 × 6 = 12.
O Level · English Medium · Pearson Edexcel · Mathematics
Ratio, proportion and algebra
Use ratios, unit rates and algebra to express a relationship.
About this lesson and its coverage
Shared cross-level core and stretch unit. Start with the core questions, then use the stretch example for deeper work. The same unit is available in related class and board pathways; it is not a full grade-specific or examination-specification course. A teacher should select the appropriate depth and further topics.
Learn the idea
A ratio compares quantities in a stated order. A unit rate gives an amount per one unit. Direct proportion has the form y = kx and passes through the origin; inverse proportion has xy = k. Convert units before using either relationship.
Worked example
Red:blue counters = 2:3 and total counters = 25. Five ratio parts share 25, so each part is 5: red = 10 and blue = 15. If y = 4x, doubling x doubles y.
- Label the order and units.
- Find one part or the constant.
- Substitute and check the original relationship.
Stretch example
If y varies inversely as x and y = 6 when x = 4, then xy = 24 and y = 24/x. A power model y = kx² instead multiplies y by four when x doubles.
Your written practice
Show your working on paper. Check your answer, then choose Next.
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25
75 ÷ 3 = 25.
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28
4 × 7 = 28.
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5a
Combine like terms.
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At zero distance the fixed fee remains, so the relationship does not pass through the origin.
Link direct proportion to zero intercept.
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3
24 ÷ 8 = 3.
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Treat x² as a new horizontal variable u; then y = ku, a line through the origin.
Identify the transformed variable and constant gradient.
Progress and browser storage
Notebook challenge, sources and further study
Test a relationship
Construct a table for one direct and one inverse relationship using positive x.
Review with a guardian or teacher
- State the constant.
- Calculate at least four pairs.
- Check whether y/x or xy stays constant.
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