A graph is a compact set of facts, and the marks go to readers who slow down. This checklist gives you a fixed order for reading any graph: labels, scale, then the gradient or area if the question needs them.
It is written for speed-time graphs first, but every step also works for distance-time, temperature, population and economics graphs.
The checklist
| Step | Ask yourself | Tick |
|---|---|---|
| 1 | What are the axis labels and units? Which is on the x-axis and which on the y-axis? | |
| 2 | What is the value of one small square on each axis? | |
| 3 | Where does the graph start? Is the origin zero, or does an axis start higher? | |
| 4 | What is the shape of each section: flat, straight up, straight down or curved? | |
| 5 | Does the question need a value, a gradient or an area? | |
| 6 | Did I write the unit with the answer? | |
| 7 | Is the answer sensible for the situation? |
Gradient = change in y ÷ change in x, using two points far apart on a straight section.
Area = use rectangles (base × height), triangles (½ × base × height) or trapeziums (½ × (a + b) × h).
Filled example: a speed-time graph
A cyclist’s journey has three sections.
| Section | Time interval | Speed |
|---|---|---|
| A | 0 s to 5 s | rises steadily from 0 to 10 m/s |
| B | 5 s to 9 s | constant 10 m/s |
| C | 9 s to 11 s | falls steadily from 10 to 0 m/s |
Axes: x is time in seconds, y is speed in m/s. The graph starts at the origin.
Section A, acceleration. Gradient = (10 − 0) ÷ (5 − 0) = 2 m/s².
Section A, distance. It is a triangle: ½ × 5 × 10 = 25 m.
Section B, distance. It is a rectangle: 4 × 10 = 40 m.
Section C, deceleration. Gradient = (0 − 10) ÷ (11 − 9) = −10 ÷ 2 = −5 m/s². The negative sign shows slowing down, so the deceleration is 5 m/s².
Section C, distance. Triangle: ½ × 2 × 10 = 10 m.
Total distance: 25 + 40 + 10 = 75 m.
Reasonableness: the highest speed is 10 m/s for a total time of 11 s, so the distance must be under 110 m. The value of 75 m fits.
Common misreadings
- Reading gradient as height. Steepness, not height, tells you acceleration.
- Using grid squares as whole units without checking the scale.
- Forgetting the time axis when taking a rectangle’s base.
- Calling deceleration negative distance. Distance stays positive here. Only the gradient is negative.
- Speed-only data cannot give direction. To describe displacement, you need information about direction.
Try the motion and energy graph explorer for original piecewise data: it calculates segment areas and slopes, and explains each step. Combine this with the formula and unit checklist, and find other templates on the resources page.
Reading a graph well is a skill that can be coached quickly when someone watches your method. That is one thing our teachers look at in online one-to-one tuition.