IGCSE Graph Skills
Graph questions award marks for the axes, the scale, the plotting and the line separately. Losing the scale mark costs nothing else, but choosing a scale that wastes half the grid costs a mark on almost every paper.
The same graph skills are marked in Biology, Chemistry, Physics and Mathematics, using the same criteria. This sheet sets out what each mark is awarded for and the errors that most often lose them.
Drawing the graph
| Element | What earns the mark | Common error |
|---|---|---|
| Axes | Independent variable on the horizontal, dependent on the vertical | Plotting them the wrong way round |
| Labels | Quantity and unit on both axes | Giving the quantity without its unit |
| Scale | Plotted points fill at least half the grid in both directions | Squeezing the data into one corner |
| Scale intervals | Sensible steps such as 1, 2, 5 or 10 per square | Using awkward steps such as 3 or 7 per square |
| Plotting | Small neat crosses or dots, accurate to half a small square | Large blobs that hide the true position |
| Line | One smooth curve or one straight ruled line of best fit | Joining the points dot to dot |
Reading the graph
| Task | Method | Note |
|---|---|---|
| Gradient of a straight line | Change in y divided by change in x, using two widely separated points on the line | Take the points from the drawn line, never from plotted crosses |
| Intercept | Read where the line crosses the vertical axis | Only valid if the horizontal axis starts at zero |
| Interpolation | Reading a value inside the range of the data | Reliable, because it is supported by the measurements |
| Extrapolation | Extending the line beyond the data | Unreliable, since there is no evidence the trend continues |
| Area under a line | Split into triangles and rectangles and add | On a speed-time graph the area gives distance |
| Gradient of a curve | Draw a tangent at the point, then find its gradient | State that a tangent was drawn |
Describing what a graph shows
| Shape | What to say | What not to say |
|---|---|---|
| Straight line through the origin | Directly proportional | Just says it goes up |
| Straight line not through the origin | Linear relationship with a constant added | Directly proportional |
| Rising then levelling off | Increasing until a limiting factor takes effect | Stops because it has finished |
| Steeper section | A faster rate of change over that interval | It is bigger there |
| Curve through the origin, getting steeper | Rate of change increasing with the variable | Exponential, unless you can justify it |
How to use this sheet
- Choose the scale before plotting anything. Check the largest value fits and that the points will fill at least half the grid.
- Avoid scale steps of 3 or 7 per square. They make every reading a calculation and invite errors.
- Take gradient readings from the line you drew, using points far apart, and show the triangle on the graph.
- Say directly proportional only when the line is straight and passes through the origin.
- Label anomalies rather than hiding them, and draw the line of best fit ignoring them.
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Frequently asked questions
How do I choose a scale for a graph?
Find the largest value on each axis and select a scale so the plotted points fill at least half the grid in both directions. Use steps of 1, 2, 5 or 10 per square, since awkward steps such as 3 or 7 make every point a calculation and cause plotting errors.
Should I join the points or draw a line of best fit?
Draw a single line or smooth curve of best fit, with roughly as many points above it as below. Joining the points dot to dot suggests the data has no underlying trend and loses the line mark in every subject.
How do I calculate a gradient correctly?
Choose two points on the drawn line, as far apart as the grid allows, and divide the change in the vertical quantity by the change in the horizontal one. Read from the line rather than from plotted crosses, and show the triangle on the graph as evidence.
When can I say two quantities are directly proportional?
Only when the graph is a straight line that passes through the origin. A straight line that crosses the vertical axis elsewhere shows a linear relationship, but doubling one quantity does not double the other, so it is not proportionality.
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Other reference sheets
Written to the published Cambridge IGCSE syllabuses. Always check the formula list and data sheet issued with your own paper, since the material provided differs between subjects and syllabus versions. Last reviewed 2026-08-12.