Parametric Differentiation NCEA practice questions

Skill overview

What these questions practise

The matched methods explicitly use parametric gradients, tangent equations, gradient conditions, or parametric first and second derivatives.

Relevant standards: NCEA Level 3 Differentiation — AS91578

This collection contains 14 matching walkthroughs across 10 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

• Form the gradient as \(dy/dx=(dy/dt)/(dx/dt)\), keeping both derivatives at the same parameter value.
• For a parametric second derivative, differentiate \(dy/dx\) with respect to the parameter and divide by \(dx/dt\) again.
• After solving for the parameter, substitute it consistently into both coordinates before writing the tangent information.

Related practice

Parametric Differentiation 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.

Keep practising

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