Level 3 Differentiation Walkthrough

2020 NCEA Level 3 Differentiation Question 2(e)

2020 Paper

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Question

Scanned exam prompt asking for exact coordinates on a parametrically defined curve using first and second derivatives.

First walkthrough idea

Focus to try first

Parametric first and second derivatives.

Step 1

Use parametric differentiation

Find \(\frac{dy}{dx}\) using parametric differentiation.

Show the first step’s working
\[ \frac{dx}{dt}=\frac{1}{t} \] \[ \frac{dy}{dt}=18t^2 \] \[ \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{18t^2}{1/t} = 18t^3 \]

Walkthrough overview

What this question practises

This 2020 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Parametric first and second derivatives.

This is Question 2(e) from the 2020 NCEA Level 3 Differentiation paper for AS91578 — Apply differentiation methods in solving problems. Use the guided hints to practise the method before revealing the full working.

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Learning summary

Review the method, not only the answer

This walkthrough helps you practise parametric first and second derivatives. Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Check each step against the original condition, preserve signs and restrictions, and confirm that the final result answers the question asked.

Continue practising

← Question 2(d) Question 3(a) →