NCEA Level 3 Differentiation — AS91578

Standard overview

Skills covered in AS91578

Develop fluent differentiation and use derivatives to reason about graphs, motion, related rates, optimisation, and mathematical models.

• Apply chain, product, quotient, logarithmic, trigonometric, and parametric differentiation.
• Use first and second derivatives to analyse stationary points and inflection points.
• Solve related-rate, tangent, optimisation, and proof-style problems.

Official title: AS91578 — Apply differentiation methods in solving problems. View the official NZQA standard and assessment resources for AS91578.

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 Differentiation 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

• Applying a differentiation rule but omitting an inner derivative or one product term.
• Solving a derivative condition without checking the domain or interpreting the result.
• Claiming a maximum, minimum, or inflection point without the required sign or derivative evidence.