To find the gradient of a curve at a specific point:
- Mark the point on the curve
- Place a ruler so it just TOUCHES the curve at that point — the line should not cut through the curve (this is the tangent)
- Extend the tangent line well across the graph in both directions
- Choose two clear points on the tangent line (ideally at grid intersections, far apart)
- Calculate the gradient: m = (y₂ − y₁) ÷ (x₂ − x₁)
- Include appropriate units from the axis labels
Key principle: use points FAR APART on the tangent — this reduces the error caused by inaccurate drawing. Points that are very close together magnify any slight drawing errors.
Example: The tangent at a point on a distance-time graph passes through (2, 10) and (6, 50).
Gradient = (50 − 10) ÷ (6 − 2) = 40 ÷ 4 = 10 m/s
Interpretation: the object is travelling at 10 m/s at that instant.
This deep dive covers Drawing a Tangent to Estimate Gradient within Gradients of Curves for GCSE Mathematics. Revise Gradients of Curves in Graphs for GCSE Mathematics with 9 exam-style questions and 10 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 3 of 10 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Gradients of Curves
How do you find the gradient of a curve at a specific point?
Explain why the gradient of a chord between two points on a curve is only an estimate of the gradient at a point, and how this estimate can be improved.