Series: past paper questions

Real questions on series

The newest 20 of 78 written questions. Open one to see it on the real paper.

1. 9709/12 · May/June 2026 · Q4a(i)[2]
   (a) (i) Find the first three terms, in ascending powers of $x$, in the expansion of ${\left(3-\frac{1}{2}x\right)}^4$.See it on the paper →
2. 9709/12 · May/June 2026 · Q4a(ii)[1]
   (ii) Find the first three terms, in ascending powers of $x$, in the expansion of $(2+ax{)}^3$. Give your answer in terms of the constant $a$.See it on the paper →
3. 9709/12 · May/June 2026 · Q4b[4]

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

   See it on the paper →
4. 9709/12 · May/June 2026 · Q7b(ii)[3]
   (b) The second, third and fourth terms of a geometric progression are $9$, $k+4$ and $k^2$ respectively, where $k$ is a negative constant. (ii) Find the sum to infinity of the progression.See it on the paper →
5. 9709/11 · October/November 2025 · Q2b[2]

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

   See it on the paper →
6. 9709/12 · October/November 2025 · Q8b(i)[5]

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

   See it on the paper →
7. 9709/13 · October/November 2025 · Q1a[3]

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

   See it on the paper →
8. 9709/13 · October/November 2025 · Q1b[2]

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

   See it on the paper →
9. 9709/31 · October/November 2025 · Q10a[6]

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

   See it on the paper →
10. 9709/31 · October/November 2025 · Q10b[5]

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

    See it on the paper →
11. 9709/11 · May/June 2025 · Q3a[5]

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

    See it on the paper →
12. 9709/11 · May/June 2025 · Q3b[2]

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

    See it on the paper →
13. 9709/12 · May/June 2025 · Q3[4]

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

    See it on the paper →
14. 9709/13 · May/June 2025 · Q2[4]

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

    See it on the paper →
15. 9709/13 · May/June 2025 · Q4a[3]

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

    See it on the paper →
16. 9709/13 · May/June 2025 · Q4b[3]

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

    See it on the paper →
17. 9709/13 · May/June 2025 · Q6[6]

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

    See it on the paper →
18. 9709/22 · May/June 2025 · Q4b[3]

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

    See it on the paper →
19. 9709/32 · May/June 2025 · Q2b[1]

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

    See it on the paper →
20. 9709/33 · May/June 2025 · Q7b[4]

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

    See it on the paper →

What examiners said

The correct use of the binomial expansion was seen in nearly all scripts for both of parts (i) and (ii). A few errors in dealing with powers and the negative term were noted and there were still candidates who produced every term of both expansions or forgot that ‘1’ is a term in x 0 .

— Examiner report, October/November 2023, 9709/13 Q4(a) (Cambridge)

The correct use of the binomial expansion was seen in nearly all scripts for both of parts (i) and (ii). A few errors in dealing with powers and the negative term were noted and there were still candidates who produced every term of both expansions or forgot that ‘1’ is a term in x 0 .

— Examiner report, October/November 2023, 9709/13 Q4(a) (Cambridge)

The correct formula for the sum to infinity was almost always used. The appropriate value of p was nearly always used correctly to find the first term of the series but less frequently to find the common ratio. Here some candidates chose to use their fractional value of p as r, rather than finding it from one of their expressions for r from part (a).

— Examiner report, October/November 2023, 9709/13 Q5(b) (Cambridge)