Category Archives: Ch 7: Differential calculus

Methods: Unit 2 Topic 3

Aim: Explore the gradient of a chord or secant and generalise. Visually see the gradient of the tangent as the limiting value as the two points get closer together.
Apps: InteractiveDiffCalc, Main
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Solution
InteractiveDiffCalc is an application that was added in version 3 of the Classpad operating system. The strength in the InteractiveDiffcalc app is being able to follow the first principles approach visually. By dynamically moving the points closer together students can see the secant getting closer to the tangent.
It also supports the development of the idea of the gradient function and taking time to understand the plotting of the gradient at specific points is a neat way of encouraging students to develop this concept.

I would use this to introduce differential calculus at Year 11 or as a refresher in Year 12.

Newton Raphson

Aim: Investigate the Newton-Raphson method for approximating roots
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Solution

Activity 28: Average speed

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Activity 29: Speed at an instant

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Activity 30: Gradient of a tangent

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Activity 32: Differentiate

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Activity 33: Tangents

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Activity 34: Modelling motion

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