# Topic Questions: • recognise an integrand of the form $\frac{k\mathrm{f}'(x)}{\mathrm{f}(x)}$, and integrate such functions — 9709 P3 Integration

> 12 9709 P3 Integration topic questions (76 marks) on recognise an integrand of the form …, and… — 12 papers, 2020–2026. Open the exact question in the…

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CIE IAL · Mathematics · 9709 P3 · Integration

12 9709 P3 Integration topic questions are tagged to this syllabus point across 12 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.

- 12 topic questions
- 12 papers
- 76 tagged marks
- 10.5% of topic questions
- 11.7% of topic marks
- 2020–2026
- Syllabus 2020–2027
- [All 9709 P3 Integration topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/)
- [All paper codes](https://www.examsci.com/topics/)

Core finding

**This Integration syllabus point appears in 12 9709 P3 papers across 2020–2026, contributing 12 topic questions and 76 marks.** The most recent appearance is 9709/32 March 2026. That equals 10.5% of the 114 topic questions and 11.7% of the 651 marks tagged to Integration. 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 |
| --- | --- | --- | --- | --- | --- | --- |
| [**9709/32** March 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2026-march-9709-32/#q-9) | **Q9** Integration by Trigonometric Substitution - CIE P3 2026 Mar Q9 | FRQ | 1 of 2 parts ((b)) | 5 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0fd758f5-8815-4e29-a05d-65b87156efed&question_id=f5473e09-b2e5-4eaa-a4b9-bfdc4550619a&source_detail=9709%2F32+March+2026) |
| [**9709/32** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-may-june-9709-32/#q-8) | **Q8** Separable Differential Equation - CIE A-Level Pure Mathematics 2025 May/June Paper 32 Q8 | FRQ | 1 part | 7 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b93317c4-369e-4279-a9c6-be0a47e5beeb&question_id=614d796e-7ca4-4061-bd9a-766b43734968&source_detail=9709%2F32+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-11) | **Q11** Solving Differential Equation with Inverse Tan and Logarithm - CIE A Level Mathematics | FRQ | 1 part | 8 | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2cdcf4cc-bb80-426a-8133-c75f6e9636f0&question_id=7094785d-1d57-4826-a502-cb33167383a9&source_detail=9709%2F35+May%2FJune+2025) |
| [**9709/32** March 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-march-9709-32/#q-10) | **Q10** Partial Fractions and Exact Definite Integration - CIE A-Level Math 2025 Mar Paper 32 Q10 | FRQ | 1 of 2 parts ((b)) | 6 of 11 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ebe23b18-f2b2-4e16-8e60-c5ac5649cb15&question_id=37374358-efb5-4b70-9902-1cd7bccf0980&source_detail=9709%2F32+March+2025) |
| [**9709/32** May/June 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-may-june-9709-32/#q-10) | **Q10** Differential Equations and Trigonometric Integration - CIE A Level Mathematics 2024 Jun P32 Q10 | FRQ | 1 of 2 parts ((b)) | 8 of 10 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b47257e0-776e-40f2-b0b7-69834ea85d57&question_id=6616cd61-7b59-46b8-822c-4eba12671639&source_detail=9709%2F32+May%2FJune+2024) |
| [**9709/32** October/November 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2023-october-november-9709-32/#q-5) | **Q5** Integration of Rational Function - CIE 9709 2023 Nov Paper 32 Q5 | FRQ | 1 part | 6 | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=3fb73dde-04cc-4e60-91c5-1ddfee06f24d&question_id=d4259eec-05b3-427a-b126-9ac7591c55d3&source_detail=9709%2F32+October%2FNovember+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-8) | **Q8** Separable Differential Equation - CIE Pure Mathematics 3 2023 Jun Q8 | FRQ | 1 part | 8 | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=38715021-d2e9-4b06-9487-8984689a84e7&question_id=d7d53a58-207f-4a97-9332-72386b62806c&source_detail=9709%2F33+May%2FJune+2023) |
| [**9709/32** October/November 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-october-november-9709-32/#q-10) | **Q10** Partial Fractions Decomposition and Integration - CIE Pure Mathematics 2022 Nov Paper 32 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=ec345ecb-a979-44f7-9e14-294a778ff934&question_id=17ff30b3-1922-4081-b343-91eb83fdf2d9&source_detail=9709%2F32+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-4) | **Q4** Separable Differential Equation with Initial Condition - CIE Pure Mathematics 2022 Jun Paper 31 Q4 | FRQ | 1 part | 7 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=09685b56-86ca-46e2-9c33-353cef143122&question_id=bd4dcd81-6ffb-4107-acf1-207bb5a9c9f1&source_detail=9709%2F31+May%2FJune+2022) |
| [**9709/33** May/June 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2021-may-june-9709-33/#q-7) | **Q7** Differential Equation from Geometric Properties - CIE 9709 2021 Jun Paper 33 Q7 | FRQ | 1 of 3 parts ((b)) | 6 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=279950d4-e630-466e-8074-e1e13ad3f5e6&question_id=28d4cdf5-e368-4461-8355-24fd8496bbd4&source_detail=9709%2F33+May%2FJune+2021) |
| [**9709/32** March 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2021-march-9709-32/#q-4) | **Q4** Separable Differential Equation - CIE A-Level Mathematics 2021 March Paper 32 Q4 | FRQ | 1 of 2 parts ((a)) | 6 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ab7133da-61cb-4438-b5f6-ad6909bb250e&question_id=c7ef615f-c894-4667-9e15-2b63ec0a0598&source_detail=9709%2F32+March+2021) |
| [**9709/31** May/June 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2020-may-june-9709-31/#q-7) | **Q7** Differentiation and Integration of Trigonometric Quotient - CIE 2020 Jun Paper 31 Q7 | FRQ | 1 of 2 parts ((b)) | 4 of 8 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=30d827e6-7a05-4ddb-93bb-64f6a01bb238&question_id=2993f8dd-33fb-4aea-820d-c1b08e173de3&source_detail=9709%2F31+May%2FJune+2020) |

## Related topic questions in Integration

- [• extend the idea of ‘reverse differentiation’ to include the integration of $\mathrm{e}^{ax+b}$, $\frac{1}{ax+b}$, $\sin(ax+b)$, $\cos(ax+b)$, $\sec^2(ax+b)$ and $\frac{1}{x^2+a^2}$](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/extend-the-idea-of-reverse-differentiation-to-include-the-integration-of-mathrm-e-ax/) — 35 question items · 29 papers — 197 marks · 2020–2026
- [• integrate rational functions by means of decomposition into partial fractions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/integrate-rational-functions-by-means-of-decomposition-into-partial-fractions/) — 24 question items · 21 papers — 138 marks · 2020–2026
- [• recognise when an integrand can usefully be regarded as a product, and use integration by parts](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/recognise-when-an-integrand-can-usefully-be-regarded-as-a-product-and-use-integration/) — 36 question items · 35 papers — 209 marks · 2020–2026
- [• use a given substitution to simplify and evaluate either a definite or an indefinite integral](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/use-a-given-substitution-to-simplify-and-evaluate-either-a-definite-or-an-indefinite/) — 16 question items · 15 papers — 87 marks · 2021–2026
- [• use trigonometrical relationships in carrying out integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/use-trigonometrical-relationships-in-carrying-out-integration/) — 23 question items · 20 papers — 128 marks · 2021–2026

## Topic question rules and edge cases

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

12 question stems cover this subtopic across 12 papers, but only 12 tagged parts and 76 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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