# Topic Questions: • understand the definition and properties of $\mathrm{e}^x$ and $\ln x$, including their relationship as inverse functions and their graphs — 9709 P2 Logarithmic and exponential functions

> 32 9709 P2 Logarithmic and exponential functions topic questions (123 marks) on understand the definition and properties of … and… — 24 papers, 2020–2026.…

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CIE IAL · Mathematics · 9709 P2 · Logarithmic and exponential functions

32 9709 P2 Logarithmic and exponential functions topic questions are tagged to this syllabus point across 24 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
- 24 papers
- 123 tagged marks
- 25.6% of topic questions
- 28.4% of topic marks
- 2020–2026
- Syllabus 2020–2027
- [All 9709 P2 Logarithmic and exponential functions topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/logarithmic-and-exponential-functions/)
- [All paper codes](https://www.examsci.com/topics/)

Core finding

**This Logarithmic and exponential functions syllabus point appears in 24 9709 P2 papers across 2020–2026, contributing 32 topic questions and 123 marks.** The most recent appearance is 9709/21 May/June 2026. That equals 25.6% of the 125 topic questions and 28.4% of the 433 marks tagged to Logarithmic and exponential functions. 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 |
| --- | --- | --- | --- | --- | --- | --- |
| [**9709/21** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2026-may-june-9709-21/#q-6) | **Q6** Parametric Differentiation of Exponential Function - CIE A Level Maths 2026 Jun Paper 21 Q6 | FRQ | 2 of 3 parts ((b), (c)) | 6 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=be6f9351-4b56-44f4-a190-4c173afbab5c&question_id=4127a8c0-b08d-43ab-95e6-e4e94f7ea439&source_detail=9709%2F21+May%2FJune+2026) |
| [**9709/23** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2026-may-june-9709-23/#q-5) | **Q5** Solving Modulus and Logarithmic Inequalities - CIE Pure Mathematics 2026 Jun Paper 23 Q5 | FRQ | 1 of 2 parts ((b)) | 3 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=71967dfb-f245-4aa9-8687-a354bca203f4&question_id=a1e120b9-0017-4eff-9551-e18ff3c6d557&source_detail=9709%2F23+May%2FJune+2026) |
| [**9709/25** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2026-may-june-9709-25/#q-5) | **Q5** Modulus Inequality and Logarithmic Application - CIE 9709 Pure Mathematics 2026 Jun Paper 25 Q5 | FRQ | 1 of 2 parts ((b)) | 3 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=676df908-86e2-4c2a-80d5-ab947b294392&question_id=6026a92f-0ff9-4d0b-b27a-a352fab08bec&source_detail=9709%2F25+May%2FJune+2026) |
| [**9709/22** March 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2026-march-9709-22/#q-3) | **Q3** Linear Form Transformation of Exponential Model - CIE 9709 P22 2026 Q3 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b409e69d-9e6f-4ba0-8cd6-579cf789e935&question_id=b05e0702-eda5-43ce-b77d-a1bcb2e1dc3e&source_detail=9709%2F22+March+2026) |
| [**9709/22** March 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2026-march-9709-22/#q-7) | **Q7** Exponential Definite Integral and Iterative Method - CIE 9709 P22 2026 Q7 | FRQ | 1 of 3 parts ((a)) | 5 of 10 on the paper | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b409e69d-9e6f-4ba0-8cd6-579cf789e935&question_id=c7ca0b6d-6244-4aa6-abc3-01609a683ca7&source_detail=9709%2F22+March+2026) |
| [**9709/22** March 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2026-march-9709-22/#q-8) | **Q8** Tangent Line to Logarithmic Curve - CIE 9709 P22 2026 Q8 | FRQ | 1 part | 8 | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b409e69d-9e6f-4ba0-8cd6-579cf789e935&question_id=d16753c8-b3ae-4846-a1cb-5652475a6f27&source_detail=9709%2F22+March+2026) |
| [**9709/22** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-october-november-9709-22/#q-1) | **Q1** Logarithmic Equation with Exact Solution - CIE Pure Mathematics 2025 Paper 22 Q1 | FRQ | 1 part | 4 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=94e39d6f-4578-4f72-b7e3-69893082ab12&question_id=0ba3c07d-ea40-4ddf-bea7-1318ea0ef32a&source_detail=9709%2F22+October%2FNovember+2025) |
| [**9709/22** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-october-november-9709-22/#q-6) | **Q6** Definite Integral and Numerical Solution of Exponential Equation - CIE Pure Mathematics 2025 Paper 22 Q6 | FRQ | 1 of 3 parts ((a)) | 4 of 9 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=94e39d6f-4578-4f72-b7e3-69893082ab12&question_id=8e3fce9f-77c2-490b-833b-935865a8af66&source_detail=9709%2F22+October%2FNovember+2025) |
| [**9709/23** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-october-november-9709-23/#q-8) | **Q8** Stationary Point of Exponential Product Function - CIE P2 2025 Q8 | FRQ | 1 part | 6 | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2675658d-907a-4273-bfc6-3e2a56654ef3&question_id=1bc9e997-53be-4e84-bb11-bb337fe189ab&source_detail=9709%2F23+October%2FNovember+2025) |
| [**9709/25** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-october-november-9709-25/#q-5) | **Q5** Shaded Region Bounded by Exponential Curve and Line - CIE 9709 Pure Mathematics 2025 Nov Paper 25 Q5 | FRQ | 1 of 2 parts ((a)) | 2 of 7 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d8e07605-f00e-45fb-a2b1-de7bd8ea23b9&question_id=852127c9-eb0c-4747-b287-cd00a38caafa&source_detail=9709%2F25+October%2FNovember+2025) |
| [**9709/21** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-may-june-9709-21/#q-3) | **Q3** Intersection of Exponential and Secant Curves - CIE A-Level Maths 2025 Jun Paper 21 Q3 | FRQ | 1 of 3 parts ((a)) | 2 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=7cc2750a-19aa-484e-8c4b-2aed1e280b7f&question_id=9b9d58e1-2c69-4783-bf4a-975f91e2abc9&source_detail=9709%2F21+May%2FJune+2025) |
| [**9709/23** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-may-june-9709-23/#q-6) | **Q6** Implicit Differentiation and Tangent to Logarithmic Curve - CIE Pure Mathematics 2025 Jun Paper 23 Q6 | FRQ | 1 of 2 parts ((a)) | 3 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=af305940-211b-4b41-80d5-3d9e354abe46&question_id=ec3eaf62-487d-429f-91e3-7689792d2eca&source_detail=9709%2F23+May%2FJune+2025) |
| [**9709/25** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-may-june-9709-25/#q-6) | **Q6** Implicit Curve Analysis and Tangent Equation - CIE Pure Maths 2025 Jun P25 Q6 | FRQ | 1 of 2 parts ((a)) | 3 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=466aeb86-ac3e-43be-be29-b0ae625577fb&question_id=ed2a506a-83cb-45c4-872e-814536cc9b86&source_detail=9709%2F25+May%2FJune+2025) |
| [**9709/22** March 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-march-9709-22/#q-3) | **Q3** Intersection and Area of Exponential Curves - CIE A-Level Maths 2025 Mar Paper 22 Q3 | FRQ | 1 of 2 parts ((a)) | 2 of 5 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b6a2a173-49dc-4e3a-bd53-8608ce39b5e0&question_id=bcbe3d0a-aa02-4b4b-a8ee-7c84fae19452&source_detail=9709%2F22+March+2025) |
| [**9709/22** March 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-march-9709-22/#q-5) | **Q5** Iterative Method and Sign Change - CIE A-Level Maths 2025 Mar Paper 22 Q5 | FRQ | 1 of 4 parts ((a)) | 2 of 8 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b6a2a173-49dc-4e3a-bd53-8608ce39b5e0&question_id=ac8caba8-bf54-4395-bf88-ee5a5ad66605&source_detail=9709%2F22+March+2025) |
| [**9709/22** March 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2025-march-9709-22/#q-8) | **Q8** Implicit Differentiation and Stationary Points - CIE A-Level Maths 2025 Mar Paper 22 Q8 | FRQ | 1 of 2 parts ((b)) | 3 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b6a2a173-49dc-4e3a-bd53-8608ce39b5e0&question_id=55bc3342-0492-4684-87c8-2e095b69e23f&source_detail=9709%2F22+March+2025) |
| [**9709/21** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2024-october-november-9709-21/#q-5) | **Q5** Definite Integral and Iterative Method - A-Level Mathematics Q5 | FRQ | 1 of 2 parts ((a)) | 5 of 8 on the paper | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=34cf943f-dad2-4a92-a3d3-3dd9a2603fc1&question_id=edcad465-1f94-457e-8e1e-cbc3dc556265&source_detail=9709%2F21+October%2FNovember+2024) |
| [**9709/22** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2024-october-november-9709-22/#q-4) | **Q4** Exponential and Modulus Graphs - CIE Pure Maths 2024 Nov Paper 22 Q4 | FRQ | 1 of 3 parts ((a)) | 2 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0904e585-d89a-413e-b330-5ca7eecd992d&question_id=be2bba87-aab0-4db2-85b2-0ebc6dc60229&source_detail=9709%2F22+October%2FNovember+2024) |
| [**9709/23** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2024-october-november-9709-23/#q-5) | **Q5** Integration with Logarithmic Limits and Numerical Iteration - CIE Pure Mathematics Q5 | FRQ | 1 of 2 parts ((a)) | 5 of 8 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c75889a7-bc8c-400d-b75e-64d9bd9276ca&question_id=d17983c6-edc8-409a-97ca-f10cfb8c9596&source_detail=9709%2F23+October%2FNovember+2024) |
| [**9709/23** May/June 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2024-may-june-9709-23/#q-3) | **Q3** Exponential Curve Area and Gradient - CIE Pure Mathematics 2024 Jun Paper 23 Q3 | FRQ | 1 of 2 parts ((b)) | 5 of 8 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=68e9e6a6-c5e7-435e-ae19-09955e66fea6&question_id=ffe3fc42-b81a-4db9-99de-94c32c5c083b&source_detail=9709%2F23+May%2FJune+2024) |
| [**9709/23** October/November 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2023-october-november-9709-23/#q-7) | **Q7** | FRQ | 1 of 4 parts ((a)) | 4 of 11 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6960ef2a-4ff5-4f3d-9627-9be49c72cf4e&question_id=92ae430e-0b39-4b34-a760-0bf53362c684&source_detail=9709%2F23+October%2FNovember+2023) |
| [**9709/21** May/June 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2023-may-june-9709-21/#q-3) | **Q3** Definite Integral and Iteration - CIE A-Level Mathematics 2023 Jun Paper 21 Q3 | FRQ | 1 of 2 parts ((a)) | 4 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c04aa92d-8253-4bc2-ae3b-9903b11f4ea7&question_id=7e96bbc0-8584-4ef0-97c5-05ef1a2e28c6&source_detail=9709%2F21+May%2FJune+2023) |
| [**9709/22** March 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2023-march-9709-22/#q-6) | **Q6** Stationary Points on Exponential Curve - CIE Pure Maths 2 2023 Mar Paper 22 Q6 | FRQ | 1 of 2 parts ((b)) | 4 of 8 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b4382735-9fe1-4e8c-abd7-e655c2a7e551&question_id=1642c620-831f-4af3-af11-d81886445562&source_detail=9709%2F22+March+2023) |
| [**9709/21** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2022-may-june-9709-21/#q-5) | **Q5** Numerical Solution of Modulus Equation - CIE A Level Mathematics 2022 May Paper 21 Q5 | FRQ | 1 of 4 parts ((a)) | 3 of 9 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=12a191ee-c681-4394-a61e-8c35dee03851&question_id=d9b31bd8-c6c0-4b2c-bd27-b9b09c6c1b2f&source_detail=9709%2F21+May%2FJune+2022) |
| [**9709/21** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2022-may-june-9709-21/#q-6) | **Q6** Stationary Point Exponential Quotient - CIE A Level Mathematics 2022 May Paper 21 Q6 | FRQ | 1 of 2 parts ((b)) | 4 of 8 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=12a191ee-c681-4394-a61e-8c35dee03851&question_id=a9fa2600-f2f5-4eac-9c02-963d7c96809d&source_detail=9709%2F21+May%2FJune+2022) |
| [**9709/23** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2022-may-june-9709-23/#q-4) | **Q4** Trapezium Rule with Logarithms - CIE P2 2022 Jun Q4 | FRQ | 1 of 2 parts ((b)) | 2 of 6 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=11942891-33a9-4c3a-b252-567ad1ff81c6&question_id=e5c21905-2dc3-4b7a-8bf4-a695cc5b7a16&source_detail=9709%2F23+May%2FJune+2022) |
| [**9709/22** March 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2022-march-9709-22/#q-2) | **Q2** Tangent to Logarithmic Curve - CIE A-Level Mathematics Q2 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9f37a63e-4459-4d3f-ac95-87a61d538eab&question_id=4ed040d8-c988-4a48-be36-9c88c5426b10&source_detail=9709%2F22+March+2022) |
| [**9709/22** March 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2022-march-9709-22/#q-7) | **Q7** Implicit Differentiation and Numerical Iteration - CIE A-Level Mathematics Q7 | FRQ | 1 of 4 parts ((c)) | 4 of 12 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9f37a63e-4459-4d3f-ac95-87a61d538eab&question_id=c2bb06cc-71cf-4edf-9aa7-e9b837a4b6f1&source_detail=9709%2F22+March+2022) |
| [**9709/21** May/June 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2021-may-june-9709-21/#q-7) | **Q7** Polynomial Factorisation and Exponential Equation - CIE 9709 P21 2021 Jun Q7 | FRQ | 1 of 3 parts ((c)) | 4 of 9 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=494b1fa8-6a0d-40e7-b32e-99e138b84ea7&question_id=005628eb-62c0-4070-99d4-cf0f388d46e2&source_detail=9709%2F21+May%2FJune+2021) |
| [**9709/22** May/June 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2021-may-june-9709-22/#q-6) | **Q6** Logarithmic Curve Stationary Points and Gradients - CIE Math 2021 Jun Paper 22 Q6 | FRQ | 1 of 2 parts ((a)) | 6 of 8 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2646d336-680b-4771-b6c2-3441e98dce59&question_id=299418af-b48c-4ba2-a786-774539adf7ad&source_detail=9709%2F22+May%2FJune+2021) |
| [**9709/21** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2020-october-november-9709-21/#q-3) | **Q3** Area of Shaded Region under Exponential Curve - CIE Pure Mathematics 2020 Nov Paper 21 Q3 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=4898eed1-24a8-40de-bf43-8e9d5d44f2c0&question_id=6e00a8b8-ba7c-432c-b012-ded211cba0a7&source_detail=9709%2F21+October%2FNovember+2020) |

## Related topic questions in Logarithmic and exponential functions

- [• understand the relationship between logarithms and indices, and use the laws of logarithms (excluding change of base)](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/logarithmic-and-exponential-functions/understand-the-relationship-between-logarithms-and-indices-and-use-the-laws-of/) — 31 question items · 24 papers — 117 marks · 2020–2026
- [• use logarithms to solve equations and inequalities in which the unknown appears in indices](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/logarithmic-and-exponential-functions/use-logarithms-to-solve-equations-and-inequalities-in-which-the-unknown-appears-in/) — 35 question items · 30 papers — 99 marks · 2020–2026
- [• use logarithms to transform a given relationship to linear form, and hence determine unknown constants by considering the gradient and/or intercept](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/logarithmic-and-exponential-functions/use-logarithms-to-transform-a-given-relationship-to-linear-form-and-hence-determine/) — 15 question items · 12 papers — 56 marks · 2021–2026

## Topic question rules and edge cases

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

31 question stems cover this subtopic across 24 papers, but only 32 tagged parts and 123 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.

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