- Choose points far apart on the tangent for the gradient calculation — nearby points introduce larger percentage errors from drawing inaccuracy
- Label your tangent clearly and show the two points you used for the gradient calculation
- Always include units: gradient has units formed from the axis labels (m/s, °C/min, etc.)
- Zero gradient = turning point: state "the rate of change is zero" or "the maximum/minimum occurs here"
- Mark scheme tolerance: gradient estimates from tangents are usually accepted within a range — check the question; answers within ±1 of the expected value typically earn the mark
This exam tips covers Exam Tips for 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 7 of 10 in this topic. Treat this as a marking guide for what examiners are looking for, not just a fact list.
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.
Quick recall flashcards
What is a tangent to a curve?
A straight line that touches the curve at exactly one point and has the same gradient as the curve at that point.
It does NOT cross through the curve at that point — it only touches it.
The gradient of the tangent = the gradient of the curve at that point.
Used to estimate the rate of change at an instant.
Steps to estimate the gradient of a curve at a point
1. Mark the point on the curve
2. Place a ruler so it just TOUCHES the curve at that point (tangent)
3. Make the tangent line extend well across the graph
4. Choose two clear points on the tangent line
5. Calculate: gradient = (y2 - y1)/(x2 - x1)
Tip: use points far apart on the tangent for greater accuracy.