# Topic Questions: • use the expansion of $(1+x)^n$, where $n$ is a rational number and $|x|<1$ — 9709 P3 Algebra

> 32 9709 P3 Algebra topic questions (107 marks) on use the expansion of …, where … is a rational… — 22 papers, 2020–2026. Open the exact question in the…

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CIE IAL · Mathematics · 9709 P3 · Algebra

32 9709 P3 Algebra topic questions are tagged to this syllabus point across 22 papers (2020–2026). Only the parts whose knowledge graph matches this syllabus statement are counted, and the table shows which parts of each question are involved.

- 32 topic questions
- 22 papers
- 107 tagged marks
- 20.5% of topic questions
- 18.7% of topic marks
- 2020–2026
- Syllabus 2020–2027
- [All 9709 P3 Algebra topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/)
- [All paper codes](https://www.examsci.com/topics/)

Core finding

**This Algebra syllabus point appears in 22 9709 P3 papers across 2020–2026, contributing 32 topic questions and 107 marks.** The most recent appearance is 9709/33 May/June 2026. That equals 20.5% of the 156 topic questions and 18.7% of the 573 marks tagged to Algebra. Only parts tagged to this subtopic are counted, so a four-part question can contribute one item and one part's marks. The table lists every matching question, its tagged parts and marks, with a link back to the paper page. Sessions are newest first, so the statement can be traced back through the full paper history.

## Topic questions by session

Newest sessions first. Parts and marks count only the parts tagged to this subtopic; “x of y parts” shows how much of the question is tagged elsewhere. Select the paper cell to open the matching question on the paper page, or use **Go to Practice Hub** to answer that exact question in the Interactive Practice Hub.

| Paper | Question | Type | Parts | Marks | Difficulty | Practice |
| --- | --- | --- | --- | --- | --- | --- |
| [**9709/33** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2026-may-june-9709-33/#q-9) | **Q9** Partial Fractions and Binomial Expansion - CIE Pure Mathematics 2026 Q9 | FRQ | 2 of 3 parts ((b), (c)) | 5 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=1cab28c8-892b-458b-b5a9-59aac0e92474&question_id=4ac9d7b9-505c-47f3-a62e-51ef5f39156f&source_detail=9709%2F33+May%2FJune+2026) |
| [**9709/32** March 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2026-march-9709-32/#q-4) | **Q4** Binomial Expansion Coefficients - CIE P3 2026 Mar Q4 | FRQ | 3 parts ((a), (b), (c)) | 6 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0fd758f5-8815-4e29-a05d-65b87156efed&question_id=f92c61c6-e1f5-4ecf-80a9-dd199598d415&source_detail=9709%2F32+March+2026) |
| [**9709/31** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-october-november-9709-31/#q-10) | **Q10** Partial Fractions and Binomial Expansion - CIE Pure Mathematics 2025 Nov Q10 | FRQ | 1 of 2 parts ((b)) | 5 of 11 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=7ffa0858-5cbd-490e-9150-de28164f7cda&question_id=f1272783-7f82-41ee-a390-2034a27ac7a5&source_detail=9709%2F31+October%2FNovember+2025) |
| [**9709/32** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-may-june-9709-32/#q-2) | **Q2** Binomial Expansion - CIE A-Level Pure Mathematics 2025 May/June Paper 32 Q2 | FRQ | 2 parts ((a), (b)) | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b93317c4-369e-4279-a9c6-be0a47e5beeb&question_id=7dc421ba-1431-4ab7-89ff-2776646a6d33&source_detail=9709%2F32+May%2FJune+2025) |
| [**9709/33** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-may-june-9709-33/#q-7) | **Q7** Partial Fractions and Binomial Series - CIE A-Level Math 2025 Jun Paper 33 Q7 | FRQ | 2 of 3 parts ((b), (c)) | 5 of 8 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b947d72f-ec97-4d00-ae14-757145ba0aa9&question_id=5fbf4296-0b39-4774-9dd5-f473e7659ac5&source_detail=9709%2F33+May%2FJune+2025) |
| [**9709/35** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-may-june-9709-35/#q-9) | **Q9** Partial Fraction Decomposition and Binomial Expansion - CIE A Level Mathematics | FRQ | 1 of 2 parts ((b)) | 4 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2cdcf4cc-bb80-426a-8133-c75f6e9636f0&question_id=a9825232-0078-4667-b7c8-3015af9d885d&source_detail=9709%2F35+May%2FJune+2025) |
| [**9709/31** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-october-november-9709-31/#q-7) | **Q7** Partial Fractions and Binomial Expansion - CIE A-Level Maths 2024 Nov Paper 31 Q7 | FRQ | 1 of 2 parts ((b)) | 4 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=70a34762-5adb-4bbc-a073-ccdcbf562e7c&question_id=1b938f1b-db7c-4cab-95f7-de424478af2a&source_detail=9709%2F31+October%2FNovember+2024) |
| [**9709/33** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-october-november-9709-33/#q-8) | **Q8** Partial Fractions and Binomial Expansion - CIE A-Level Pure Mathematics 2024 Nov Q8 | FRQ | 2 of 3 parts ((b), (c)) | 5 of 8 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=eea0ef07-a2e6-40ec-b1f1-0940ce02a199&question_id=c3714890-e8d3-45ee-9be6-f7a830b35d40&source_detail=9709%2F33+October%2FNovember+2024) |
| [**9709/31** May/June 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-may-june-9709-31/#q-1) | **Q1** Binomial Expansion - CIE A-Level Maths 2024 Jun Paper 31 Q1 | FRQ | 1 part | 4 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d001bb3e-de7a-4991-8014-a2761a618aba&question_id=5d38ec84-7925-4f47-bde7-c482f58ee5a9&source_detail=9709%2F31+May%2FJune+2024) |
| [**9709/32** March 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-march-9709-32/#q-2) | **Q2** Binomial Expansion Validity - CIE 9709 March 2024 Paper 32 Q2 | FRQ | 2 parts ((a), (b)) | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=e042eca9-7da3-4a8b-b612-449ce3e020fd&question_id=1892de5c-ab58-4d6e-9b6c-607b382a2af2&source_detail=9709%2F32+March+2024) |
| [**9709/33** October/November 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2023-october-november-9709-33/#q-9) | **Q9** Partial Fractions and Binomial Expansion - CIE A-Level Maths 2023 Q9 | FRQ | 2 of 3 parts ((b), (c)) | 6 of 11 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=719f9f72-ffe6-4873-b35f-05b84c1bcd86&question_id=cd7ac9b3-951f-452c-bc66-4f6ebc9937f9&source_detail=9709%2F33+October%2FNovember+2023) |
| [**9709/31** May/June 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2023-may-june-9709-31/#q-3) | **Q3** Binomial Expansion Coefficient - CIE Pure Mathematics 2023 Q3 | FRQ | 1 part | 4 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cfca2669-2cc1-43c6-a0cc-6132556376c3&question_id=0d3acc3b-4e6f-4fe1-8d14-d5049558c425&source_detail=9709%2F31+May%2FJune+2023) |
| [**9709/33** May/June 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2023-may-june-9709-33/#q-10) | **Q10** Partial Fractions and Binomial Expansion - CIE Pure Mathematics 3 2023 Jun Q10 | FRQ | 1 of 2 parts ((b)) | 5 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=38715021-d2e9-4b06-9487-8984689a84e7&question_id=c4db1f91-e6db-4e9d-a100-5f8a9ae21881&source_detail=9709%2F33+May%2FJune+2023) |
| [**9709/33** October/November 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-october-november-9709-33/#q-2) | **Q2** Binomial Expansion of Rational Square Root - CIE Pure Mathematics 3 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=955ef535-8636-46dc-9b2a-f083375bbec1&question_id=6f8397ab-9d96-4482-83f8-7d656d6fa4bd&source_detail=9709%2F33+October%2FNovember+2022) |
| [**9709/31** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-may-june-9709-31/#q-2) | **Q2** Binomial Expansion of Fractional Power - CIE Pure Mathematics 2022 Jun Paper 31 Q2 | FRQ | 2 parts ((a), (b)) | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=09685b56-86ca-46e2-9c33-353cef143122&question_id=4177a807-0033-4b76-b959-f9efb438a0b2&source_detail=9709%2F31+May%2FJune+2022) |
| [**9709/33** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-may-june-9709-33/#q-7) | **Q7** Partial Fractions and Binomial Expansion - CIE A Level Mathematics 2022 Jun Paper 33 Q7 | FRQ | 1 of 2 parts ((b)) | 5 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9659571c-b4b6-458e-b3ff-de05ece281b2&question_id=aefb9599-8517-443f-a2a6-7e429f5606ee&source_detail=9709%2F33+May%2FJune+2022) |
| [**9709/32** May/June 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2021-may-june-9709-32/#q-9) | **Q9** Partial Fractions and Binomial Expansion - CIE 9709 2021 Jun Paper 32 Q9 | FRQ | 1 of 2 parts ((b)) | 5 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=193dfa4e-69a9-4d3a-8797-abee668ebcf8&question_id=d6cdff7a-a4e5-435d-89d9-c0920a4e6f56&source_detail=9709%2F32+May%2FJune+2021) |
| [**9709/33** May/June 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2021-may-june-9709-33/#q-1) | **Q1** Binomial Expansion - CIE 9709 2021 Jun Paper 33 Q1 | FRQ | 1 part | 4 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=279950d4-e630-466e-8074-e1e13ad3f5e6&question_id=d262026e-5869-4a92-b7ba-2e26b72a4e77&source_detail=9709%2F33+May%2FJune+2021) |
| [**9709/31** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2020-october-november-9709-31/#q-9) | **Q9** Partial Fractions and Binomial Expansion - CIE 9709 W20 P31 Q9 | FRQ | 1 of 2 parts ((b)) | 5 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6d3dbf03-a763-4245-9cd4-e9bb82088912&question_id=ecb748ef-0c90-49cd-8a6a-9588df01c0e0&source_detail=9709%2F31+October%2FNovember+2020) |
| [**9709/33** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2020-october-november-9709-33/#q-9) | **Q9** Partial Fractions and Binomial Expansion - CIE Pure Mathematics 2020 Nov Paper 33 Q9 | FRQ | 1 of 2 parts ((b)) | 5 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=086627cb-e617-484f-abc7-431aab41e928&question_id=9377cc2a-6d6e-4d82-8041-77ab7759656b&source_detail=9709%2F33+October%2FNovember+2020) |
| [**9709/31** May/June 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2020-may-june-9709-31/#q-2) | **Q2** Binomial Expansion - CIE 2020 Jun Paper 31 Q2 | FRQ | 2 parts ((a), (b)) | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=30d827e6-7a05-4ddb-93bb-64f6a01bb238&question_id=c80cbcbd-7d14-4d6d-882f-099be53b1553&source_detail=9709%2F31+May%2FJune+2020) |
| [**9709/32** March 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2020-march-9709-32/#q-9) | **Q9** Partial Fractions and Binomial Expansion - CIE Pure Mathematics 3 March 2020 Q9 | FRQ | 1 of 2 parts ((b)) | 5 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=11f225a5-63c6-446a-9114-463175a53c07&question_id=e3a29dd0-c3d8-4b64-843d-fabaafabc4f2&source_detail=9709%2F32+March+2020) |

## Related topic questions in Algebra

- [• divide a polynomial, of degree not exceeding 4, by a linear or quadratic polynomial, and identify the quotient and remainder (which may be zero)](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/divide-a-polynomial-of-degree-not-exceeding-4-by-a-linear-or-quadratic-polynomial-and/) — 24 question items · 21 papers — 82 marks · 2020–2026
- [• recall an appropriate form for expressing rational functions in partial fractions, and carry out the decomposition, in cases where the denominator is no more complicated than – $(ax+b)(cx+d)(ex+f)$ – $(ax+b)(cx+d)^2$ – $(ax+b)(cx^2+d)$](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/recall-an-appropriate-form-for-expressing-rational-functions-in-partial-fractions-and/) — 36 question items · 34 papers — 178 marks · 2020–2026
[**• understand the meaning of $|x|$, sketch the graph of $y=|ax+b|$ and use relations such as $|a|=|b|\Leftrightarrow a^2=b^2$ and $|x-a|** 32 question items · 23 papers 88 marks · 2020–2026](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/understand-the-meaning-of-x-sketch-the-graph-of-y-ax-b-and-use-relations-such-as-a-b/)
[**• use the factor theorem and the remainder theorem** 22 question items · 15 papers 82 marks · 2021–2026](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/use-the-factor-theorem-and-the-remainder-theorem/)

## Topic question rules and edge cases

**How many topic questions cover this syllabus point?**

22 question stems cover this subtopic across 22 papers, but only 32 tagged parts and 107 marks belong to it. Other parts of the same questions are assessed under different statements and are excluded from this page.

**Which papers include this subtopic?**

The table lists every matching session from 2020–2026. Each row links to the question anchor on the paper page, where the full paper context and practice entry point are available.

**Why can one question appear under several subtopics?**

The parts of one question can assess different syllabus statements. Each part is counted under its own subtopics, so the same question stem can appear on several subtopic pages while each page lists only the parts and marks tagged to that statement.

**Can I practise these questions with AI marking?**

Yes. Open a paper from the table and use the Interactive Practice Hub entry point. The page itself is static HTML so search engines and retrieval agents can read the full question list without executing JavaScript.

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Full page with native tables, bar charts and Practice Hub links: https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/use-the-expansion-of-1-x-n-where-n-is-a-rational-number-and-x-1/