Differentiation Rules NCEA Practice Questions | Calc.nz

Skill overview

What these questions practise

Choose a question, attempt it independently, then compare the reasoning and restrictions in its walkthrough.

Relevant standards: NCEA Level 3 Differentiation — AS91578 · NCEA Level 2 Calculus — AS91262

This collection contains 26 matching walkthroughs across 8 examination years.

The grouping is based on the method recorded for each walkthrough. Use the linked NZQA standard and paper material for authoritative wording, diagrams, and assessment information.

Before you start

Common mistakes in these methods

Differentiate the whole expression, including any inner function, and check the variable and units of the derivative.

Related practice

Differentiation Rules questions from different years

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NCEA Level 3 · AS91578 2025 Differentiation 3 questions

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Question 1(b) — Related Rates Rewriting in power form and finding a rate of change. Question 2(a) — Logarithms Differentiating reciprocal and logarithmic terms. Question 2(e) — Radius of Curvature First and second derivatives in a radius of curvature problem.

NCEA Level 3 · AS91578 2024 Differentiation 2 questions

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Question 1(d) — Stationary Points and Optimisation Stationary points, the second derivative test, and classifying the point. Question 2(c) — Higher Derivatives First and second derivatives in a proof-style differential-equation question.

NCEA Level 3 · AS91578 2023 Differentiation 2 questions

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Question 2(d) — Logarithms Second derivatives and finding a logarithmic point of inflection. Question 3(d) — Stationary Points and Optimisation Stationary points and classifying them with the second derivative.

NCEA Level 3 · AS91578 2020 Differentiation 5 questions

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Question 1(b) — Tangents Trig derivatives and evaluating a tangent gradient. Question 2(b) — Exponential Differentiation Differentiating an exponential depreciation model. Question 2(e) — Parametric Differentiation Parametric first and second derivatives. Question 3(d) — Stationary Points and Optimisation Stationary points and second derivative classification. Question 3(e) — Differential Equations Proving a differential equation using first and second derivatives.

NCEA Level 3 · AS91578 2019 Differentiation 3 questions

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Question 1(b) — Logarithms Differentiating a logarithm and evaluating a rate at t = 4. Question 3(a) — Trigonometric Differentiation Differentiating a cosecant form. Question 3(d) — Differentiation and Motion Finding when acceleration is zero from a velocity model.

NCEA Level 3 · AS91578 2018 Differentiation 6 questions

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Question 1(a) — Chain Rule Negative powers with the power and chain rules. Question 1(b) — Higher Derivatives Second derivatives and proving an identity. Question 1(c) — Logarithms Logarithmic and trigonometric differentiation. Question 1(e) — Parametric Differentiation Parametric first and second derivatives. Question 2(a) — Radicals and Surds Differentiating a radical and a cosecant. Question 2(b) — Logarithms Finding velocity from a logarithmic distance function.

NCEA Level 3 · AS91578 2017 Differentiation 2 questions

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Question 3(b) — Power Rule Negative powers and evaluating a gradient at a point. Question 3(e) — Higher Derivatives Second derivatives and a differential-equation parameter.

NCEA Level 3 · AS91578 2016 Differentiation 1 question

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Question 1(a) — Power Rule Power rule differentiation with negative exponents.

NCEA Level 2 · AS91262 2025 Calculus 2 questions

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Question 1(a) — Power Rule Using the power rule term by term and evaluating the gradient at a point. Question 3(b) — Calculus Method Using the base–height relationship to find dA/dh, with area in cm² and height in cm.

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Page updated 24 September 2026.