NCEA maths skill practice
Parametric Differentiation NCEA practice questions
Practise finding gradients and tangent information when both coordinates are expressed using a parameter.
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
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14 matching questions shown.
NCEA Level 3 · AS91578 2025 Differentiation 3 questions
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NCEA Level 3 · AS91578 2024 Differentiation 1 question
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NCEA Level 3 · AS91578 2023 Differentiation 2 questions
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NCEA Level 3 · AS91578 2022 Differentiation 1 question
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NCEA Level 3 · AS91578 2021 Differentiation 1 question
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NCEA Level 3 · AS91578 2020 Differentiation 1 question
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NCEA Level 3 · AS91578 2019 Differentiation 1 question
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NCEA Level 3 · AS91578 2018 Differentiation 2 questions
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NCEA Level 3 · AS91578 2017 Differentiation 1 question
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NCEA Level 3 · AS91578 2016 Differentiation 1 question
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