Improving the estimate of the gradient of a curve
I can improve the estimate of the gradient by considering the gradient of the tangent at a fixed point.
Improving the estimate of the gradient of a curve
I can improve the estimate of the gradient by considering the gradient of the tangent at a fixed point.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- Since the gradient is improved by moving the points closer together, you could consider a point.
- By drawing the tangent to the graph at a given point, you can estimate the gradient at that point.
- The gradient at that point is estimated by calculating the gradient of the tangent.
Keywords
Tangent - A tangent to a curve at a given point is a line that intersects the curve at that point. Both the tangent and the curve have the same gradient at the given point.
Common misconception
Pupils may think a tangent to a curve at a given point cannot intersect the curve at another point.
Define the tangent at a point as the line which has the same gradient as the curve at that point. If the graph is cubic then it is possible for the tangent at a point to intersect the graph again. There are examples in the lesson that show this.
To help you plan your year 11 maths lesson on: Improving the estimate of the gradient of a curve, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Improving the estimate of the gradient of a curve, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
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The assessment exit quiz will test your pupils' understanding of the key learning points.
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Explore more key stage 4 maths lessons from the Real-life graphs unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Starter quiz
6 Questions
$$x=-2 \ \text{to} \ x=-1$$ -
$$4$$
$$x=-1 \ \text{to} \ x=1$$ -
$$1$$
$$x=0 \ \text{to} \ x=2$$ -
$$5\over2$$
$$x=2 \ \text{to} \ x=3$$ -
$$10$$
$$x=-1 \ \text{to} \ x=2$$ -
$$2$$
Exit quiz
6 Questions
