L3 Differentiation Past Papers
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AS91578Differentiation past exam papers
Every NZQA exam for AS91578 (Apply differentiation methods in solving problems) from 2013 to 2025, with its marking schedule, and from 2021 the examiners’ report, which says where students lost marks.
Papers by year
2020Archived copy
2019Archived copy
2018Archived copy
2017Archived copy
2016Archived copy
2015Archived copy
2014Archived copy
2013Archived copy
Marked student answers at each grade (NZQA exemplars), 2024: Achievement · Merit · Excellence.
What the examiners keep saying
Getting the derivative right is only half the job: many students then can’t solve the equation it gives. Practise solving these by hand, because unknown constants in the question stop the calculator doing it for you.
Reports: 2021–2025A dropped chain-rule factor, or missing that the product or quotient rule is needed, gives a wrong derivative, and a wrong derivative gets no credit for that part.
Reports: 2021–2025In optimisation, sort out which letters are variables and which are constants, and write the quantity in terms of one variable before you differentiate.
Reports: 2021–2025Tangent and normal questions catch students out every year, especially a tangent drawn from a point that isn’t on the curve. Only put a point’s x-value into the gradient function if the point is on the curve.
Reports: 2021–2025In “prove” or “show that” questions, finish the argument formally, for example by testing that a stationary point really is a maximum.
Reports: 2021–2025Use brackets when you write out the product, quotient and chain rules. Missing brackets keep turning good working into wrong answers.
Reports: 2021–2025If the question says you don’t need to simplify the derivative, don’t. Students who simplify anyway make slips and lose the grade.
Reports: 2023–2025
How to use these papers
- Start with the most recent papers. They are the closest to this year’s exam.
- Sit a whole paper without notes, then mark it with its schedule. The schedule shows what earns Achievement, Merit and Excellence in each part, not only the answer.
- After marking, read that year’s examiners’ report to see where other students lost marks.
- Check the 2026 assessment specification for what this year’s exam covers. An older paper can include something that has since changed.
About the older papers
NZQA takes papers off its website after five years. The older ones here are NZQA’s own files as saved by the Internet Archive, a non-profit library of the web, so they can be slow to open. We could only find the examiners’ reports from 2021 on. We couldn’t find a copy of the 2014 marking schedule.
Practise each topic in AS91578 with worked answers.
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