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.
Topic position
Section 3 of 10
Practice
9 questions
Recall
10 flashcards
Drawing a Tangent to Estimate Gradient
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.