Algebra: past paper questions

Real questions on algebra

The newest 20 of 187 written questions. Open one to see it on the real paper.

1. 9709/12 · May/June 2026 · Q10b(i)[2]

   2-mark question — its maths and diagrams are best seen on the paper.

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2. 9709/12 · May/June 2026 · Q10b(ii)[4]
   A function f is defined by $$f(x)=p{x}^2-2x+p+4$$ for $x\in \mathbb{R}$, where $p$ is a constant. (ii) Given that $p=2$ and $g^{-1}$ does exist, find an expression for $g^{-1}(x)$.See it on the paper →
3. 9709/11 · October/November 2025 · Q9a[4]

   4-mark “Find” question — its maths and diagrams are best seen on the paper.

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4. 9709/11 · October/November 2025 · Q9b[4]

   4-mark question — its maths and diagrams are best seen on the paper.

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5. 9709/12 · October/November 2025 · Q4a[1]

   1-mark “Find” question — its maths and diagrams are best seen on the paper.

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6. 9709/13 · October/November 2025 · Q4a[2]

   2-mark question — its maths and diagrams are best seen on the paper.

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7. 9709/13 · October/November 2025 · Q4b[4]

   4-mark question — its maths and diagrams are best seen on the paper.

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8. 9709/21 · October/November 2025 · Q2[3]

   3-mark “Solve” question — its maths and diagrams are best seen on the paper.

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9. 9709/21 · October/November 2025 · Q3a[3]

   3-mark “Solve” question — its maths and diagrams are best seen on the paper.

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10. 9709/21 · October/November 2025 · Q7a[2]

    2-mark “Find” question — its maths and diagrams are best seen on the paper.

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11. 9709/21 · October/November 2025 · Q7b[4]

    4-mark “State” question — its maths and diagrams are best seen on the paper.

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12. 9709/21 · October/November 2025 · Q7c[2]

    2-mark “Show” question — its maths and diagrams are best seen on the paper.

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13. 9709/22 · October/November 2025 · Q3a[4]

    4-mark “Solve” question — its maths and diagrams are best seen on the paper.

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14. 9709/23 · October/November 2025 · Q3a[3]

    3-mark “Solve” question — its maths and diagrams are best seen on the paper.

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15. 9709/31 · October/November 2025 · Q6[5]

    5-mark “Solve” question — its maths and diagrams are best seen on the paper.

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16. 9709/32 · October/November 2025 · Q5b[5]

    5-mark “Find” question — its maths and diagrams are best seen on the paper.

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17. 9709/32 · October/November 2025 · Q9a[5]

    5-mark question — its maths and diagrams are best seen on the paper.

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18. 9709/51 · October/November 2025 · Q7a[1]

    1-mark question — its maths and diagrams are best seen on the paper.

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19. 9709/51 · October/November 2025 · Q7b[3]

    3-mark question — its maths and diagrams are best seen on the paper.

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20. 9709/51 · October/November 2025 · Q7c[3]

    3-mark question — its maths and diagrams are best seen on the paper.

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What examiners said

For most candidates, this question provided a straightforward introduction to the paper and a good source of marks. Some candidates, however, did not realise that an interval was required and omitted this part of the solution entirely.

— Examiner report, February/March 2025, 9709/12 Q1 (Cambridge)

The majority of candidates used correct expressions for the second term and sum to infinity of a geometric progression. Elimination of a to form a quadratic equation in r was the more straightforward approach. The question asked candidates to find a single common ratio and so they needed to reject r = 32 as it was invalid for a convergent progression. Unfortunately, a significant majority rejected...

— Examiner report, February/March 2025, 9709/12 Q8(a) (Cambridge)

Some candidates chose to subtract the sum of the first 9 terms from the sum to infinity, while others found a new first term (the 10th term of the original progression) and used that to find the new sum to infinity. Negative signs were often omitted. As the answer to this part was exact, this meant that candidates who gave the answer as a decimal and rounded it to three significant figures were un...

— Examiner report, February/March 2025, 9709/12 Q8(b) (Cambridge)