NCEA maths skill practice
Related Rates NCEA practice questions
Practise connecting changing geometric or physical quantities through a shared equation and rates measured with respect to time.
Skill overview
What these questions practise
The catalogue includes sphere, cone, angle, height, area, and motion contexts. Each matched method is explicitly identified as related rates, so the grouping does not infer the topic from a generic rate question.
Relevant standards: NCEA Level 3 Differentiation — AS91578
This collection contains 12 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
- Differentiate the relationship with respect to time before substituting values from the particular instant.
- Keep each geometric quantity distinct and attach the correct units to its rate of change.
- For an angular rate, differentiate the trigonometric relationship before evaluating the angle and other measurements.
Related practice
Related Rates 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.
NCEA Level 3 · AS91578
2025 Differentiation
NCEA Level 3 · AS91578
2024 Differentiation
NCEA Level 3 · AS91578
2023 Differentiation
NCEA Level 3 · AS91578
2022 Differentiation
NCEA Level 3 · AS91578
2021 Differentiation
NCEA Level 3 · AS91578
2020 Differentiation
NCEA Level 3 · AS91578
2019 Differentiation
NCEA Level 3 · AS91578
2018 Differentiation
NCEA Level 3 · AS91578
2017 Differentiation
NCEA Level 3 · AS91578
2016 Differentiation
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