Gradient as rate of change
Edexcel 1MA1 examines this on both tiers, but the contextual interpretation work mostly sits on Paper 2H or 3H. The skill: read a gradient from a graph and translate it into a real-world rate.
Gradient = rate of change
The gradient of a graph tells you how the y-quantity changes per unit increase in the x-quantity.
- On a distance-time graph: gradient = speed.
- On a velocity-time graph: gradient = acceleration.
- On a "cost vs items" graph: gradient = price per item.
- On a "depth vs time" graph: gradient = rate of filling/draining.
Computing gradient from a graph
Pick two clear points on the line, (x₁, y₁) and (x₂, y₂):
m = (y₂ − y₁) / (x₂ − x₁) — and INCLUDE THE UNITS.
E.g. on a distance-time graph: m = (50 − 0) m / (10 − 0) s = 5 m/s.
Curves — average vs instantaneous
- Average rate of change between A and B: gradient of the chord AB.
- Instantaneous rate at a point: gradient of the tangent at that point.
For curves, draw the tangent carefully and pick two points on it (not on the curve!) to compute its gradient.
Direct proportion graphs
If y is directly proportional to x, the graph is a straight line through the origin. The gradient equals the constant of proportionality k in y = kx.
Common Edexcel mark-scheme phrasing
- M1 for picking valid coordinates on the line / tangent.
- M1 for computing rise / run.
- A1 for the gradient with correct units.
- B1 for an interpretation in context (e.g. "speed of 5 m/s").
⚠Common mistakes— Common errors
- Reading rise / run from squares without using the axis scales.
- Picking two points off the tangent line accidentally on the curve (gives wrong gradient).
- Stating gradient without units in a context question.
- Using a chord and calling it the instantaneous rate.
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