L2 Calculus Past Papers
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AS91262Calculus past exam papers
Every NZQA exam for AS91262 (Apply calculus methods in solving problems) from 2012 to 2025, with its marking schedule, and from 2020 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
2012Archived copy
What the examiners keep saying
Always write + c, then find its value from the information given and show how. Leaving it out was on the Not Achieved list in 2024 and 2025.
Reports: 2021, 2023, 2024 and 2025For Excellence, show whether a turning point is a maximum or a minimum (with the second derivative or the gradient either side), even when the question doesn’t ask, including in optimisation.
Reports: 2021, 2023, 2024 and 2025The algebra after the calculus is often what stops students: solving the cubic, quadratic, simultaneous or linear equation that comes out of it.
Reports: 2021, 2023, 2024 and 2025The derivative gives the gradient. Set it equal to the gradient you’re given; don’t substitute the gradient into f(x).
Reports: 2021, 2023, 2024 and 2025Finding the equation of a tangent is a Merit skill every year, so be fluent with the equation of a straight line.
Reports: 2021, 2023, 2024 and 2025Sketches need one smooth curve of the right shape, the correct x-intercepts and labelled axes.
Reports: 2021, 2023, 2024 and 2025Do kinematics questions with calculus. Physics formulas earn no credit.
Reports: 2021, 2023 and 2024
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 2020 on.
Practise each topic in AS91262 with worked answers.
Open the Calculus question bank →