NCEA Level 3 Integration — AS91579

Standard overview

Skills covered in AS91579

Use a range of integration methods to find functions, areas, volumes, and solutions to contextual or differential-equation problems.

• Recognise and apply substitution, reverse-chain-rule, trigonometric, and other integration methods.
• Use definite integrals for signed area, total area, and volume.
• Apply initial conditions and interpret an integrated model in context.

Official title: AS91579 — Apply integration methods in solving problems. View the official NZQA standard and assessment resources for AS91579.

More ways to practise

Browse related questions by method

Skill pages collect questions using the same method from different examination years.

Available examination years

Choose a Integration paper

Each year page links to every walkthrough currently available on Calc.nz.

Reasoning progression

Achieved, Merit, and Excellence thinking

The grade depends on the complete evidence in a response, not merely the apparent difficulty of a question part. Across these walkthroughs, the progression can be understood as:

• Achieved: Select an appropriate method, carry it out correctly, and communicate a valid solution to the problem.
• Merit: Connect methods and conditions, with the relational thinking needed to justify important steps and conclusions.
• Excellence: Develop, generalise, or prove a result using extended abstract thinking and a coherent chain of reasoning.

Always use the assessment schedule for the specific examination when checking grade evidence.

Exam preparation

Common mistakes to watch for

• Forgetting the constant of integration or failing to use an initial condition.
• Using bounds without checking sign, intersections, or whether total area is required.
• Choosing an integration method without first simplifying or matching the integrand's structure.