2025 NCEA Level 3 Differentiation

2025 Differentiation AS91578 worked answers

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

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Paper overview

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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

2025 Differentiation questions

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Question 1

Question 1 walkthroughs

Question 1(a) worked solution Chain rule differentiation of a composite polynomial. Question 1(b) worked solution Rewriting in power form and finding a rate of change. Question 1(c) worked solution Product rule and the gradient of a normal. Question 1(d) worked solution Finding a tangent and its x-intercept. Question 1(e) worked solution Parametric differentiation with stationary inflection points.

Question 2

Question 2 walkthroughs

Question 2(a) worked solution Differentiating reciprocal and logarithmic terms. Question 2(b) worked solution Product rule and deciding whether a model is increasing or decreasing. Question 2(c) worked solution Quotient rule and tangents with a given gradient. Question 2(d) worked solution Parametric gradients and tangent equations. Question 2(e) worked solution First and second derivatives in a radius of curvature problem.

Question 3

Question 3 walkthroughs

Question 3(a) worked solution Reading differentiability, stationary points, and a limit from a graph. Question 3(b) worked solution Stationary points on a logarithmic curve. Question 3(c) worked solution Related rates for the volume of a sphere. Question 3(d) worked solution Solving a parametric gradient condition. Question 3(e) worked solution Maximising the area of a rectangle inside a curve.

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

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