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Improving the Accuracy of Tangent Estimates (Higher)

Part of Gradients of Curves · GCSE GCSE Mathematics revision

This deep dive covers Improving the Accuracy of Tangent Estimates (Higher) 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 6 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 6 of 10

Practice

9 questions

Recall

10 flashcards

Improving the Accuracy of Tangent Estimates (Higher)

The accuracy of a gradient estimate from a tangent depends on how carefully the tangent is drawn. To improve accuracy:

Choose two points on the tangent that are as far apart as possible — this reduces the relative effect of any small drawing error
Make sure the line truly touches the curve at one point and does not cross it
Use a ruler and read coordinates precisely from the axis scales
Where a gradient is asked as a rate of change (e.g. speed from a distance-time graph), state the units clearly

Different tangent drawings at the same point by different students should give very similar gradient values if drawn carefully — typical GCSE mark schemes accept answers within a range of ±1 of the expected gradient.

Practice Questions for Gradients of Curves

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

Quick Recall Flashcards

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.

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.

Improving the Accuracy of Tangent Estimates (Higher)

Improving the Accuracy of Tangent Estimates (Higher)

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Practice Questions for Gradients of Curves

Quick Recall Flashcards

9 questions on Gradients of Curves — practise free