# Topic Questions: 4.1 Integration of hyperbolic functions and expressions involving them. — WFM03 Integration > 27 WFM03 Integration topic questions (145 marks) on 4.1 Integration of hyperbolic functions and… — 15 papers, 2014–2026. Open the exact question in the… - Canonical HTML: https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/integration/4-1-integration-of-hyperbolic-functions-and-expressions-involving-them/ - Markdown mirror: https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/integration/4-1-integration-of-hyperbolic-functions-and-expressions-involving-them/index.md --- Edexcel IAL · Mathematics · WFM03 · Integration 27 WFM03 Integration topic questions are tagged to this syllabus point across 15 papers (2014–2026). Only the parts whose knowledge graph matches this syllabus statement are counted, and the table shows which parts of each question are involved. - 27 topic questions - 15 papers - 145 tagged marks - 23.5% of topic questions - 28.2% of topic marks - 2014–2026 - Syllabus 2014–current - [All WFM03 Integration topic questions](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/integration/) - [All paper codes](https://www.examsci.com/topics/) Core finding **This Integration syllabus point appears in 15 WFM03 papers across 2014–2026, contributing 27 topic questions and 145 marks.** The most recent appearance is WFM03/01 January 2026. That equals 23.5% of the 115 topic questions and 28.2% of the 515 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 | | --- | --- | --- | --- | --- | --- | --- | | [**WFM03/01** January 2026 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2026-january-wfm03-01/#q-5) | **Q5** Arc Length and Surface of Revolution - Edexcel IAL FP3 Jan 2026 Q5 | FRQ | 2 of 3 parts ((b), (c)) | 7 of 12 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=fef100ce-ae1f-4eda-8b03-fb1220056d55&question_id=c5e7b183-a13f-478a-a31c-517acad6adcb&source_detail=WFM03%2F01+January+2026) | | [**WFM03/02** January 2026 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2026-january-wfm03-02/#q-2) | **Q2** Integration of Algebraic and Quadratic Surd Fractions - Edexcel IAL FP3 Jan 2026 Q2 | FRQ | 1 of 2 parts ((b)) | 7 of 12 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=bd27cc0c-ad2c-4810-9040-17c7618428b2&question_id=8117f430-5547-47ed-984f-489c6eb9cc5d&source_detail=WFM03%2F02+January+2026) | | [**WFM03/02** January 2026 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2026-january-wfm03-02/#q-6) | **Q6** Arc Length and Surface Area of Revolution - Edexcel IAL FP3 Jan 2026 Q6 | FRQ | 1 of 3 parts ((c)) | 7 of 12 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=bd27cc0c-ad2c-4810-9040-17c7618428b2&question_id=2fd90a76-b478-4cc9-af4c-f7b02025b138&source_detail=WFM03%2F02+January+2026) | | [**WFM03/01** June 2025 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2025-june-wfm03-01/#q-7) | **Q7** Surface Area of Revolution - Edexcel IAL F3 2025 Q7 | FRQ | 1 of 2 parts ((b)) | 7 of 9 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=321dde8b-e2d5-4735-b634-f4645608cc26&question_id=31e9b211-2ee1-4b7a-9ad5-29f3dcc701eb&source_detail=WFM03%2F01+June+2025) | | [**WFM03/01** January 2025 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2025-january-wfm03-01/#q-3) | **Q3** Integration of Algebraic Surds and Fractions - Edexcel IAL FP3 Jan 2025 Q3 | FRQ | 1 of 2 parts ((ii)) | 6 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=13d75753-e4c1-45b2-95df-47669cf01e00&question_id=d31dd5b8-9e2e-49a9-be6f-a38fb9ee98f5&source_detail=WFM03%2F01+January+2025) | | [**WFM03/01** June 2024 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2024-june-wfm03-01/#q-7) | **Q7** Arc Length of Hyperbolic Curve - Edexcel IAL FP3 2024 Jun Q7 | FRQ | 1 of 2 parts ((b)) | 4 of 8 on the paper | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c1c493df-2716-407c-92e0-04993a02fdbe&question_id=d754e3a7-616c-443b-96ce-5aa8c2ba49ed&source_detail=WFM03%2F01+June+2024) | | [**WFM03/01** January 2024 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2024-january-wfm03-01/#q-5) | **Q5** Hyperbolic Identities and Reduction Formulae - Edexcel IAL FP3 Jan 2024 Q5 | FRQ | 2 of 3 parts ((b), (c)) | 8 of 11 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=1c4a0d21-4fcc-4068-b44d-9bcbaf24a9d2&question_id=2ebff379-25d4-46a2-845f-4b8f7aefe103&source_detail=WFM03%2F01+January+2024) | | [**WFM03/01** January 2024 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2024-january-wfm03-01/#q-8) | **Q8** Arc Length and Perimeter - Edexcel IAL FP3 Jan 2024 Q8 | FRQ | 1 of 2 parts ((b)) | 6 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=1c4a0d21-4fcc-4068-b44d-9bcbaf24a9d2&question_id=f801d0af-29cc-4e18-8e5a-a75b7a670336&source_detail=WFM03%2F01+January+2024) | | [**WFM03/01** June 2023 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2023-june-wfm03-01/#q-7) | **Q7** Reduction Formulae - Edexcel IAL FP3 June 2023 Q7 | FRQ | 2 parts ((a), (b)) | 9 | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2b8d47a2-0e9d-4609-a7aa-de9aa33edc00&question_id=ec26281f-1157-44e4-abf2-a9e03f3430b5&source_detail=WFM03%2F01+June+2023) | | [**WFM03/01** October 2021 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2021-october-wfm03-01/#q-1) | **Q1** Arc Length of Hyperbolic Curve - Edexcel IAL FP3 Oct 2021 Q1 | FRQ | 1 part | 6 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=08ba1e8a-94f0-4941-ac15-58f37b5f8a42&question_id=964e3b66-475e-4a8d-88e4-20d8a30ebf52&source_detail=WFM03%2F01+October+2021) | | [**WFM03/01** January 2021 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2021-january-wfm03-01/#q-4) | **Q4** Hyperbolic Integration Substitution - Edexcel IAL FP3 Jan 2021 Q4 | FRQ | 1 part | 6 | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=48e18848-8f77-40ca-a915-de8a4a8e6a18&question_id=a61b2289-b54f-4991-b51b-0b5aaf6e47f9&source_detail=WFM03%2F01+January+2021) | | [**WFM03/01** October 2020 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2020-october-wfm03-01/#q-7) | **Q7** Arc Length and Surface Area of Revolution - Edexcel IAL FP3 June 2020 Q7 | FRQ | 1 of 3 parts ((c)) | 7 of 12 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=89d9551c-7c22-401e-9033-f397b71ae7c0&question_id=a995a440-ab33-427a-83cc-bb8911028e51&source_detail=WFM03%2F01+October+2020) | | [**WFM03/01** June 2019 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2019-june-wfm03-01/#q-4) | **Q4** Arc Length and Hyperbolic Functions - Edexcel IAL Further Pure Mathematics F3 Jun 2019 Q4 | FRQ | 1 of 3 parts ((a)) | 5 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=665de0c4-932f-42c9-81d7-12776dbdd310&question_id=abdd1bd4-639d-4701-b437-3743271efbf8&source_detail=WFM03%2F01+June+2019) | | [**WFM03/01** June 2019 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2019-june-wfm03-01/#q-7) | **Q7** Reduction Formulae - Edexcel IAL Further Pure Mathematics F3 Jun 2019 Q7 | FRQ | 1 of 2 parts ((a)) | 6 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=665de0c4-932f-42c9-81d7-12776dbdd310&question_id=81909394-9443-4461-8348-a3a19bd76611&source_detail=WFM03%2F01+June+2019) | | [**WFM03/01** June 2018 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2018-june-wfm03-01/#q-6) | **Q6** Arc Length and Surface of Revolution - Edexcel IAL FP3 2018 Jun Q6 | FRQ | 1 of 2 parts ((b)) | 5 of 7 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=e3312792-17ad-40b1-b446-97027e94cb20&question_id=7857e75c-0f50-43ef-991f-299464982f1d&source_detail=WFM03%2F01+June+2018) | | [**WFM03/01** June 2016 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2016-june-wfm03-01/#q-3) | **Q3** Integration by Completing Square and Substitution - Edexcel June 2016 F3 Q3 | FRQ | 1 of 2 parts ((b)) | 7 of 12 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cc87ae7a-efe2-4b64-b941-a913fa71b1de&question_id=e8c635af-87b4-45a1-80e9-c83a4ac828b6&source_detail=WFM03%2F01+June+2016) | | [**WFM03/01** June 2016 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2016-june-wfm03-01/#q-5) | **Q5** Derivative and Integration of Inverse Hyperbolic Function - Edexcel June 2016 F3 Q5 | FRQ | 1 of 2 parts ((b)) | 5 of 7 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cc87ae7a-efe2-4b64-b941-a913fa71b1de&question_id=077587a9-e3a9-4259-a315-2a7ff9f31807&source_detail=WFM03%2F01+June+2016) | | [**WFM03/01** June 2016 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2016-june-wfm03-01/#q-8) | **Q8** Reduction Formula for Hyperbolic Integral - Edexcel June 2016 F3 Q8 | FRQ | 2 parts ((a), (b)) | 10 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cc87ae7a-efe2-4b64-b941-a913fa71b1de&question_id=c4a1fcb0-c2bd-45b1-86c3-82ed75c85034&source_detail=WFM03%2F01+June+2016) | | [**WFM03/01** June 2015 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2015-june-wfm03-01/#q-4) | **Q4** Reduction Formula for Hyperbolic Integration - Edexcel IAL FP3 2015 Jun Q4 | FRQ | 2 parts ((a), (b)) | 10 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=25480c7d-dfbb-4d33-9daf-3c7de1e2f335&question_id=8755094a-4b69-40f2-9f02-cead91afe5a7&source_detail=WFM03%2F01+June+2015) | | [**WFM03/01** June 2015 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2015-june-wfm03-01/#q-8) | **Q8** Integration by Hyperbolic Substitution - Edexcel IAL FP3 2015 Jun Q8 | FRQ | 2 parts ((a), (b)) | 11 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=25480c7d-dfbb-4d33-9daf-3c7de1e2f335&question_id=717d5f69-b503-401b-aa45-99c1c032e364&source_detail=WFM03%2F01+June+2015) | | [**WFM03/01** June 2014 · Edexcel IAL](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/2014-june-wfm03-01/#q-7) | **Q7** Integration Applications - Edexcel F3 June 2014 Q7 | FRQ | 1 of 3 parts ((c)) | 6 of 13 on the paper | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=453279c4-d96a-4b7c-b2e4-15bb564db6bb&question_id=359ecaf8-a03b-4461-ac2e-751b574eb023&source_detail=WFM03%2F01+June+2014) | ## Related topic questions in Integration - [4.2 Integration of inverse trigonometric and hyperbolic functions.](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/integration/4-2-integration-of-inverse-trigonometric-and-hyperbolic-functions/) — 28 question items · 16 papers — 114 marks · 2014–2026 - [4.3 Integration using hyperbolic and trigonometric substitutions.](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/integration/4-3-integration-using-hyperbolic-and-trigonometric-substitutions/) — 16 question items · 13 papers — 85 marks · 2014–2026 - [4.4 Use of substitution for integrals involving quadratic surds.](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/integration/4-4-use-of-substitution-for-integrals-involving-quadratic-surds/) — 21 question items · 14 papers — 92 marks · 2015–2026 - [4.5 The derivation and use of simple reduction formulae.](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/integration/4-5-the-derivation-and-use-of-simple-reduction-formulae/) — 40 question items · 19 papers — 185 marks · 2014–2026 - [4.6 The calculation of arc length and the area of a surface of revolution.](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/integration/4-6-the-calculation-of-arc-length-and-the-area-of-a-surface-of-revolution/) — 38 question items · 20 papers — 176 marks · 2014–2026 ## Topic question rules and edge cases **How many topic questions cover this syllabus point?** 21 question stems cover this subtopic across 15 papers, but only 27 tagged parts and 145 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 2014–2026. 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. --- Full page with native tables, bar charts and Practice Hub links: https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/integration/4-1-integration-of-hyperbolic-functions-and-expressions-involving-them/