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

Open a question for hints and a progressive worked solution, or use the standard and paper links to return to its assessment context.

NCEA Level 2 · AS91262

2025 Calculus

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

NCEA Level 3 · AS91579

2025 Integration

Question 1(b) · Integrating a derivative and using an Integrating a derivative and using an initial condition. Question 2(b) · Integrating a rate function and fitting Integrating a rate function and fitting the constant. Question 2(d) · Velocity and displacement from 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

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

NCEA Level 3 · AS91579

2023 Integration

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

NCEA Level 3 · AS91579

2022 Integration

Question 2(a) · Integrating an exponential term and a Integrating an exponential term and a square-root term.

NCEA Level 3 · AS91579

2021 Integration

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

NCEA Level 3 · AS91579

2020 Integration

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

NCEA Level 3 · AS91579

2019 Integration

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

NCEA Level 3 · AS91579

2018 Integration

Question 1(a) · Negative powers and the integration Negative powers and the integration constant. Question 2(d) · Velocity and distance from acceleration Building velocity and distance from acceleration.

NCEA Level 3 · AS91579

2017 Integration

Question 1(c) · Velocity and displacement from 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 19 July 2026.