Level 2 Calculus Walkthrough

2025 NCEA Level 2 Calculus Question 3(c)

2025 Paper — Maximise the volume of a lidless cuboid

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Walkthrough overview

What this question practises

This 2025 walkthrough is part of AS91262 — Apply calculus methods in solving problems.

Method: Using a surface-area constraint, writing volume in one variable, maximizing it, and proving the maximum.

This is Question 3(c) from the 2025 NCEA Level 2 Calculus paper for AS91262 — Apply calculus 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 AS91262.

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Learning summary

Review the method, not only the answer

This walkthrough helps you practise using a surface-area constraint, writing volume in one variable, maximizing it, and proving the maximum. Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Finding a stationary value is only part of an optimisation argument; justify that it is the required maximum and respect the domain.

Continue practising

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