L2 Algebra Past Papers

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AS91261

Algebra past exam papers

Every NZQA exam for AS91261 (Apply algebraic methods in solving problems) from 2012 to 2025, with its marking schedule, and from 2020 the examiners’ report, which says where students lost marks.

NZQA keeps only the last five years (2025, 2024, 2023, 2022 and 2021) on its website. Older papers open as copies of NZQA’s own files kept by the Internet Archive, marked “Archived copy”.

Papers by year

What the examiners keep saying

From NZQA’s examiners’ reports on AS91261, 2021 to 2025, in our words. NZQA published no report for 2022. Each year’s full report is linked above.

• Logs and index laws come up every year. Changing a log into index form, using a common base or taking logs of both sides earns Achievement; Excellence answers showed how logs and indices connect.

  Reports: 2021, 2023, 2024 and 2025

• Working out the discriminant is Achievement. Using it to answer a question about the roots is where Merit and Excellence come from.

  Reports: 2021, 2023, 2024 and 2025

• Turning a worded situation into an equation is where Merit and Excellence are won, and it can draw on earlier maths such as area, volume or Pythagoras.

  Reports: 2021, 2023, 2024 and 2025

• Algebraic fractions come up at every grade: factorise first, then cancel, and expand carefully after cross-multiplying.

  Reports: 2021, 2023, 2024 and 2025

• Check that each solution makes sense in the context, and say which one works and why.

  Reports: 2021, 2023 and 2024

• Small slips cost grades: signs, substitution and brackets. In 2025 some students expanded (2y)³ as 2y³ instead of 8y³.

  Reports: 2023–2025

• Be able to work backwards from given roots to the factors, then form and expand the equation.

  Reports: 2024 and 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.

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