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Conversion Graphs

FoundationHigherAQAEdexcelOCR

This free Foundation and Higher GCSE Maths worksheet on conversion graphs helps you revise reading and using conversion graphs. 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. Read across then down from the axis to convert between quantities.

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

A conversion graph is a straight line used to change between two units or currencies. Because the relationship is proportional, the graph is a straight line through the origin.

Reading it works both ways. To convert from one unit to the other, go up from the horizontal axis to the line, then across to the vertical axis. To convert back, reverse the process.

The gradient is the conversion rate. If the graph converts pounds to euros and passes through \((10, 12)\), the gradient is \(1.2\), meaning one pound buys \(1.2\) euros — the same figure as the exchange rate itself.

Revision notes

Reading in both directions

Draw a line from your known value to the graph, then turn ninety degrees to read the other axis.

Leave those construction lines visible, because method marks are awarded for showing where you read from.

The gradient as the rate

Pick a clear point on the line and divide the vertical value by the horizontal one.

If the line passes through \((20, 32)\) on a miles-to-kilometres graph, the rate is \(32 \div 20 = 1.6\) kilometres per mile.

Extending beyond the graph

For values outside the drawn range, use the rate rather than the graph.

If \(1\) mile is \(1.6\) km, then \(50\) miles is \(80\) km, even if the graph only goes to \(30\). Scaling up a read value works too: double the reading for double the input.

Key points

  • A conversion graph is a straight line through the origin.
  • Read across and up, or up and across, to convert.
  • Show your construction lines.
  • The gradient is the conversion rate.
  • Use the rate for values beyond the graph.
  • Include units in every answer.

Worked examples

Example 1

A graph converts miles to kilometres and passes through \((10, 16)\). Find the rate.

Working

\[16 \div 10\]divide kilometres by miles
\[= 1.6 \text{ km per mile}\]state the rate with units

Example 2

Using that rate, convert \(35\) miles to kilometres.

Working

\[35 \times 1.6\]multiply the miles by the rate
\[= 56 \text{ km}\]state the answer with units

Example 3

Using the same graph, convert \(24\) km to miles.

Working

\[24 \div 1.6\]divide to convert back
\[= 15 \text{ miles}\]state the answer with units

Common mistakes

  • Reading from the wrong axis.

    Check which quantity is on which axis before starting.

  • Not showing construction lines.

    Marks are awarded for the lines drawn to and from the graph.

  • Multiplying when you should divide.

    Converting back requires dividing by the rate, not multiplying.

  • Omitting units.

    The answer describes a real quantity, so the unit is part of it.

Exam tips

  • Label which quantity is on each axis before reading.
  • Leave your construction lines on the diagram.
  • Work out the rate if you need values beyond the graph.
  • Sense-check whether the answer should be larger or smaller.

Key terms

Conversion graph
A straight-line graph for changing between units.
Rate
The amount of one quantity per unit of another.
Proportional
Increasing at a constant ratio, giving a line through the origin.
Construction lines
Lines drawn to show where a value was read.

Related topics

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