Skip to content
VirtusAcademy

Proportion in Context

FoundationHigherAQAEdexcelOCR

This free Foundation and Higher GCSE Maths worksheet on proportion in context helps you revise applying proportion in context. Questions build from straightforward to exam standard, with full worked answers in the mark scheme — ideal for revision or homework. Suitable for AQA, Edexcel and OCR. Find the value of one unit first, then scale up.

Free downloads

These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

Proportion in context means applying direct or inverse proportion to a real situation, and the first task is deciding which one applies.

Ask what happens when one quantity increases. If the other increases too, the proportion is direct. If it decreases, the proportion is inverse. Getting this wrong turns a straightforward question into a wrong answer.

Once identified, the method is the same as usual: find the constant, then use it. The unitary method — finding the value for one unit first — often gives the clearest working and earns method marks even if the final arithmetic slips.

Revision notes

Deciding which proportion applies

Increasing one quantity that increases the other means direct proportion; one that decreases the other means inverse.

More petrol means more distance, so that is direct. More taps filling a bath means less time, so that is inverse.

The unitary method

Find the value for one unit, then scale up.

If \(5\) books cost \(£40\), one costs \(£8\), so \(9\) cost \(£72\). Showing the one-unit step makes the method visible.

Checking the answer makes sense

In direct proportion, more input gives a larger answer. In inverse, more input gives a smaller one.

If you expected fewer hours and got more, the wrong type of proportion was used.

Key points

  • Decide whether the proportion is direct or inverse first.
  • Direct: both quantities increase together.
  • Inverse: one increases as the other decreases.
  • The unitary method finds the value for one unit.
  • Show the one-unit step for method marks.
  • Sense-check the direction of the answer.

Worked examples

Example 1

\(6\) pens cost \(£4.50\). Find the cost of \(10\) pens.

Working

\[4.50 \div 6 = £0.75\]find the cost of one pen
\[0.75 \times 10\]multiply by the number wanted
\[= £7.50\]state the answer

Example 2

\(3\) taps fill a tank in \(40\) minutes. How long would \(5\) taps take?

Working

\[3 \times 40 = 120 \text{ tap-minutes}\]this is inverse proportion, so find the constant product
\[120 \div 5\]divide by the new number of taps
\[= 24 \text{ minutes}\]more taps means less time

Example 3

\(4\) litres of paint cover \(30\text{m}^2\). How much covers \(45\text{m}^2\)?

Working

\[30 \div 4 = 7.5\text{m}^2 \text{ per litre}\]find the coverage of one litre
\[45 \div 7.5\]divide the area by the rate
\[= 6 \text{ litres}\]state the answer

Common mistakes

  • Using direct proportion for an inverse situation.

    More workers means less time, so multiplying gives an answer in the wrong direction.

  • Skipping the unitary step.

    Finding the value for one unit makes the method visible and earns marks.

  • Not checking the direction of the answer.

    If more taps gave more time, something has gone wrong.

  • Mixing units.

    Convert everything to the same unit before calculating.

Exam tips

  • Ask whether one quantity going up makes the other go up or down.
  • Use the unitary method to show clear working.
  • Sense-check the direction of your answer before writing it.
  • Include units in the final answer.

Key terms

Direct proportion
Both quantities increase together.
Inverse proportion
One increases as the other decreases.
Unitary method
Finding the value for one unit first.
Rate
The amount per single unit.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.