Level 3 Differentiation Walkthrough

2024 NCEA Level 3 Differentiation Question 2(a)

2024 Paper

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Question

A function is defined parametrically by the pair of equations \[ x=3t^2+1 \quad \text{and} \quad y=\cos t. \]

Find an expression for \(\frac{dy}{dx}\).

First walkthrough idea

Hint to try first

Find \(\frac{dy}{dt}\) and \(\frac{dx}{dt}\) first.

Step 1

Differentiate \(x\) with respect to \(t\)

\(3t^2+1\) differentiates to \(6t\).

Show the first step’s working

\(3t^2+1\) differentiates to \(6t\).

Key result

\[ 6 t \]

Walkthrough overview

What this question practises

This 2024 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Parametric differentiation using \(\frac{dy/dt}{dx/dt}\).

This is Question 2(a) from the 2024 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.

Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91578.

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Learning summary

Review the method, not only the answer

This walkthrough helps you practise parametric differentiation using \(\frac{dy/dt}{dx/dt}\). 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 1(e) Question 2(b) →