Marks on graph questions go to students who read slowly and in order. This checklist gives you that order: 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 ride 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.
The motion and energy graph explorer works out segment areas and slopes and explains each step. Pair it with the formula and unit checklist. More templates are on the resources page.
Most graph errors happen in the first few seconds, when you pick a scale or a point. In online one-to-one tuition, a teacher watches those first steps live and corrects them straight away.