NCEA maths skill practice
Differential Equations NCEA practice questions
Practise solving separable differential equations and verifying proposed relationships with first or second derivatives.
Skill overview
What these questions practise
The matched Integration methods explicitly name separation or a differential equation, while matched Differentiation methods verify or prove a differential-equation relationship.
Relevant standards: NCEA Level 3 Differentiation — AS91578 · NCEA Level 3 Integration — AS91579
This collection contains 23 matching walkthroughs across 9 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
- Separate the variables consistently before integrating, without dropping factors that belong with either differential.
- Retain the integration constant and apply the supplied condition, then check the resulting branch and domain in context.
- For verification, calculate the required derivatives and substitute them into both sides of the stated differential equation.
Related practice
Differential Equations 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
2024 Differentiation
NCEA Level 3 · AS91578
2023 Differentiation
NCEA Level 3 · AS91578
2020 Differentiation
NCEA Level 3 · AS91578
2017 Differentiation
NCEA Level 3 · AS91579
2025 Integration
NCEA Level 3 · AS91579
2024 Integration
NCEA Level 3 · AS91579
2023 Integration
NCEA Level 3 · AS91579
2022 Integration
NCEA Level 3 · AS91579
2021 Integration
NCEA Level 3 · AS91579
2020 Integration
NCEA Level 3 · AS91579
2019 Integration
NCEA Level 3 · AS91579
2018 Integration
NCEA Level 3 · AS91579
2017 Integration
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