L3 Integration Past Papers
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AS91579Integration past exam papers
Every NZQA exam for AS91579 (Apply integration methods in solving problems) from 2013 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
Marked student answers at each grade (NZQA exemplars), 2024: Achievement · Merit · Excellence.
What the examiners keep saying
Always write + c, don’t assume it is zero, and keep it consistent when you rearrange. In 2025 many wrongly took c = 0 because s = 0 when t = 0.
Reports: 2021–2025If a factor goes missing in the integration, that part gets no credit, even when the final answer comes out right.
Reports: 2021–2025Not every fraction integrates to a log. Some need long division or a substitution first.
Reports: 2021–2025Use a trig identity before integrating something like sin²(2x). Writing (1/3)sin³(2x) was a common wrong answer in 2022.
Reports: 2021–2025For differential equations, separate the variables, integrate both sides properly and use the given values to find the constant. Forming the equation yourself from a context is Excellence work.
Reports: 2021–2025Try every part rather than jumping to the Excellence ones. Students who attempted everything picked up credit on the harder parts.
Reports: 2021–2025Show the integration by hand: an answer straight from the graphics calculator is unlikely to get more than Achievement.
Reports: 2022–2025
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 2020 on.
Practise each topic in AS91579 with worked answers.
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