Gradient = rate of change
On a distance–time graph the gradient is the speed; on a speed–time graph the gradient is the acceleration. A flat (horizontal) line means "stationary" (distance–time) or "constant speed" (speed–time).
Area under a speed–time graph = distance
Split the area into rectangles and triangles. A rectangle is speed × time; a triangle is base height.
speed = distance ÷ time
Rearrange as needed: , . Keep units consistent.
Drawn from real examiner reports.
Counting squares instead of the scale
A point was read as because it was "1 square along, 4 squares up" — but each square was not one unit, so the true values differed. Always use the axis scale.
Seen on June 2024 Paper 2H (Q25).
Treating times like 9 h 36 min as 9.36
h min is h (since ), not . Convert minutes to a fraction of an hour first.
Seen on June 2024 Paper 2H (Q3).
Wrong speed–distance–time arrangement
Writing instead of , or dividing the wrong way round.
Seen on June 2024 Paper 2H (Q3); the summary highlights manipulating the speed–distance–time formula.
Using speed × time for a triangle
On a speed–time graph the accelerating part is a triangle: distance base height. Using speed × time (the rectangle rule) for it doubles that distance.
Confusing gradient with area
On a speed–time graph the gradient is the acceleration and the area is the distance. Reading the area when acceleration is wanted (or the reverse) is a frequent mix-up.
Describe each segment by its gradient
Going up = speeding up / moving away; flat = constant; coming down to 0 on a speed–time graph = decelerating to rest. Read the gradient of each straight section in turn.
Convert time to hours before dividing
Turn minutes into a decimal of an hour first: min h, so h min h. Then apply speed distance time.
Split the area into simple shapes
For distance from a speed–time graph, break the region into rectangles (speed × time) and triangles ( base height), work out each, then add them together.
What does the gradient of a distance–time graph represent?
A train travels km in hour minutes at a steady speed. Find its average speed in km/h.