This topic summary covers Topic Summary: Gradients of Curves 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 10 of 10 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 10 of 10
Practice
9 questions
Recall
10 flashcards
Topic Summary: Gradients of Curves
Key Methods
- Tangent method: draw tangent, calculate gradient = rise ÷ run
- Differentiation: dy/dx = naxⁿ⁻¹ (power rule)
- Chord: average rate of change between two points
- Gradient at turning point = 0
Interpretation by Graph Type
- Distance-time → speed (m/s)
- Speed-time → acceleration (m/s²)
- Positive gradient → increasing quantity
- Negative gradient → decreasing quantity
- Zero gradient → turning point
Key Vocabulary
- Tangent: line touching curve at one point with same gradient
- Chord: line joining two points on a curve
- Instantaneous rate: rate at a single moment (tangent)
- Average rate: rate over an interval (chord)
- dy/dx: gradient function (derivative)
Common Errors
- Confusing tangent (touches) with chord (joins two points)
- Using nearby points on the tangent (magnifies drawing errors)
- Omitting units from gradient answers
- Confusing estimate (tangent) with exact value (differentiation)