2025 NCEA Level 2 Calculus

2025 Calculus AS91262 worked answers

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

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Paper overview

Work through the 2025 questions one step at a time

This page contains 12 independent worked question walkthroughs for NCEA Level 2 Calculus (AS91262). 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 Calculus questions

Choose a question part to open its guided worked solution.

Question 1

Question 1 walkthroughs

Question 1(a) worked solution Using the power rule term by term and evaluating the gradient at a point. Question 1(b) worked solution Finding the point of tangency, the gradient, and the tangent equation. Question 1(c) worked solution Finding critical points, identifying the minimum, and solving for the constant. Question 1(d) worked solution Writing displacement equations, solving when they are equal, and answering in context.

Question 2

Question 2 walkthroughs

Question 2(a) worked solution Sketching the derivative from stationary points, signs, and changes in concavity. Question 2(b) worked solution Antidifferentiating and using a point on the graph to find the constant. Question 2(c) worked solution Differentiating, evaluating a rate, and using derivatives to justify the minimum turning point. Question 2(d) worked solution Using a stationary point and an x-intercept to find constants, then classifying the other stationary point.

Question 3

Question 3 walkthroughs

Question 3(a) worked solution Differentiating, solving for the given gradient, and finding the coordinate on the curve. Question 3(b) worked solution Forming an area expression, finding the height from the given area, and evaluating the rate of change. Question 3(c) worked solution Using a surface-area constraint, writing volume in one variable, maximizing it, and proving the maximum. Question 3(d) worked solution Differentiating, factorising, classifying critical points, and finding where the function is decreasing.

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Stationary points and optimisation Antidifferentiation

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