Topic 2 of 8
Graphs and calculations
Turn numbers into a trend, gradient or justified result.
O-Level 5086 / 5088 (2026) / SEC G3 K326 / K328 (2027)
Turn measurements into a graph or calculation
Keep the meaning of each axis, ratio and unit visible.
Put the independent variable on the horizontal axis and the measured or derived dependent variable on the vertical axis. Label each axis with a quantity and unit, use a clear uniform scale, and plot the actual points. A best-fit line or smooth curve represents a trend; do not force it through every point or through the origin without a reason.
| Time / s | Gas volume / cm3 |
|---|---|
| 0 | 0 |
| 20 | 24 |
| 40 | 39 |
| 60 | 45 |
| 80 | 48 |
An interval rate is a gradient between two points
Between 20 and 40 seconds, gas volume increases from 24 to 39 cubic centimetres. The horizontal change is 20 seconds and the vertical change is 15 cubic centimetres. The curve becomes less steep later.
Worked example
Calculate and interpret a gradient
Find the average gas-production rate between 20 and 40 s.
- Change in gas volume = 39 - 24 = 15 cm3.
- Time interval = 40 - 20 = 20 s. Average rate = 15 / 20 = 0.75 cm3 s-1.
- This is an interval average. A rate at one instant is the gradient of a tangent to the curve at that instant, where required.
0.75 cm3 s-1. The graph later becomes flatter, so the gas-production rate decreases.
Interpolation estimates a value within the measured range. Extrapolation extends a trend outside it and needs an extra assumption that the relationship continues. If a graph is linear, choose two well-separated points on the best-fit line for a gradient, not two close points chosen because they happen to be measurements.
Keep guard digits during working. Round the final answer to a precision justified by the inputs and any question instruction. A unit conversion changes the numerical value, not the physical quantity: 25.0 cm3 = 0.0250 dm3. Check dimensions before inserting numbers into a formula.