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Gradients of Curves

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 pick up marks when it appears in mixed-topic papers.

Study this topic

1

How Fast is Fast Right Now?

Introduction2

Gradients of Curves — Essential Concepts

Key Facts3

Drawing a Tangent to Estimate Gradient

Deep Dive4

Interpreting the Gradient in Context

Deep Dive5

Chord vs Tangent — Average vs Instantaneous Rate

Deep Dive6

Introduction to Differentiation (Higher)

Deep Dive7

Exam Tips for Gradients of Curves

Exam Tips8

Worked Examples

Notes9

Common Misconceptions

Misconceptions10

Topic Summary: Gradients of Curves

Summary

Sample 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.

Sample Questions

How do you find the gradient of a curve at a specific point?

  • A. Draw a chord joining two points on the curve and find its gradient
  • B. Draw a tangent to the curve at that point and find the gradient of the tangent
  • C. Find the average of the y-values on either side of the point
  • D. Divide the y-coordinate by the x-coordinate of the point
1 markfoundation

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.

2 markshigher

9

exam-style questions

10

revision flashcards

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