2021 NCEA Level 3 Differentiation

2021 Differentiation AS91578 worked answers

Guided, step-by-step worked solutions for Apply differentiation methods in solving problems.

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Paper overview

Work through the 2021 questions one step at a time

This page contains 15 independent worked question walkthroughs for NCEA Level 3 Differentiation (AS91578). Each walkthrough offers hints, reveals the full working in a logical sequence, and focuses on the method described below.

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Worked question index

2021 Differentiation questions

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Question 1

Question 1 walkthroughs

Question 1(a) worked solution Product rule with exponential and trigonometric chain rules. Question 1(b) worked solution Reading stationary points, concavity, and limits from a graph. Question 1(c) worked solution Product and chain rules for stationary points. Question 1(d) worked solution Parametric differentiation and evaluating a tangent gradient. Question 1(e) worked solution Cone and cylinder optimisation with a maximum-volume proof.

Question 2

Question 2 walkthroughs

Question 2(a) worked solution Chain rule differentiation of a composite polynomial. Question 2(b) worked solution Quotient rule and stationary points. Question 2(c) worked solution Product rule and finding the equation of a normal. Question 2(d) worked solution Related rates for the volume and radius of a sphere. Question 2(e) worked solution Tangent geometry on \(y=\sqrt{2x-4}\).

Question 3

Question 3 walkthroughs

Question 3(a) worked solution Quotient rule with \(\cot x\) and \(\csc^2 x\). Question 3(b) worked solution Stationary point on a radical function. Question 3(c) worked solution Using the derivative sign to find where a function is increasing. Question 3(d) worked solution Quotient rule with a parameter and a given tangent gradient. Question 3(e) worked solution Lamp and table optimisation using product and chain rules.

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Chain rule Product and quotient rules Related rates Stationary points and optimisation Parametric differentiation

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