NCEA Level 2 Calculus — AS91262

Standard overview

Skills covered in AS91262

Build confidence with differentiation and anti-differentiation, then use those methods to solve gradient, rate, stationary-point, and optimisation problems.

• Differentiate and anti-differentiate polynomial and power functions.
• Use gradients, tangents, stationary points, and rates of change.
• Form and optimise a model, then interpret the result in context.

Official title: AS91262 — Apply calculus methods in solving problems. View the official NZQA standard and assessment resources for AS91262.

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 Calculus 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

• Substituting into the original function when the question asks for a gradient or rate.
• Finding a stationary point without justifying whether it is a maximum or minimum.
• Forgetting the constant of integration or information needed to determine it.