Antidifferentiation NCEA Practice Questions | Calc.nz

Skill overview

What these questions practise

The matched methods explicitly name antidifferentiation, antiderivatives, or integration of a derivative, gradient, rate, velocity, or acceleration. They include both Level 2 Calculus and Level 3 Integration questions.

Relevant standards: NCEA Level 2 Calculus — AS91262 · NCEA Level 3 Integration — AS91579

This collection contains 25 matching walkthroughs across 9 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

Include the constant of integration, then use the supplied point or initial condition to determine it.
Track which quantity is being recovered from the rate and keep the initial value and units attached to that quantity.
For a power antiderivative, increase the exponent and divide by the new exponent before applying any condition.

Related practice

Antidifferentiation questions from different years

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NCEA Level 2 · AS91262 2025 Calculus 1 question

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Question 2(b) — Antidifferentiation Antidifferentiating and using a point on the graph to find the constant.

NCEA Level 3 · AS91579 2025 Integration 4 questions

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Question 1(b) — Integration with Conditions Integrating a derivative and using an initial condition. Question 2(b) — Integration with Conditions Integrating a rate function and fitting the constant. Question 2(d) — Integration and Kinematics Building velocity and displacement from acceleration with initial conditions. Question 3(b) — Logarithms Logarithmic antiderivatives with a linear inside.

NCEA Level 3 · AS91579 2024 Integration 2 questions

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Question 1(c) — Integration and Kinematics Integrating velocity and using a position condition. Question 3(a) — Exponential Integration Integrating exponential terms with different inside coefficients.

NCEA Level 3 · AS91579 2023 Integration 3 questions

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Question 1(a) — Algebraic Integration Splitting an integral into three familiar antiderivatives. Question 1(b) — Integration and Kinematics Integrating velocity to get position, then using the starting distance. Question 3(d) — Integration and Kinematics Integrating acceleration to velocity with an initial condition.

NCEA Level 3 · AS91579 2022 Integration 1 question

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Question 2(a) — Radical Integration Integrating an exponential term and a square-root term.

NCEA Level 3 · AS91579 2021 Integration 3 questions

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Question 1(a) — Algebraic Integration Integrating a linear term and a reciprocal term. Question 1(b)(i) — Integration with Conditions Integrating a gradient function and fitting the constant. Question 1(c) — Integration and Kinematics Integrating acceleration twice with initial conditions.

NCEA Level 3 · AS91579 2020 Integration 5 questions

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Question 1(a) — Logarithms Power, constant, and logarithmic antiderivatives. Question 1(b) — Integration and Kinematics Integrating velocity and using the initial displacement. Question 2(a) — Power Rule Integration Integrating a reciprocal-square term. Question 3(b) — Integration with Conditions Integrating a gradient and using an initial condition. Question 3(c) — Integration and Kinematics Integrating acceleration to find velocity.

NCEA Level 3 · AS91579 2019 Integration 2 questions

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Question 1(a) — Radicals and Surds Rewriting a radical denominator and integrating a power. Question 3(d) — Integration with Conditions Integrating a derivative and using an initial condition.

NCEA Level 3 · AS91579 2018 Integration 2 questions

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Question 1(a) — Algebraic Integration Negative powers and the integration constant. Question 2(d) — Integration and Kinematics Building velocity and distance from acceleration.

NCEA Level 3 · AS91579 2017 Integration 2 questions

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Question 1(c) — Integration and Kinematics Building velocity and displacement from acceleration. Question 3(a) — Polynomial and Exponential Integration Integrating polynomial and exponential terms.

Keep practising

Integration techniques Differential equations

Page updated 9 August 2026.