# 9709 P3 Integration Topic Questions

> CIE IAL 9709 P3: every Integration topic question from 49 papers (2020–2026), grouped by syllabus point. 114 questions, 651 marks, with direct links into…

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CIE IAL · Mathematics · 9709 P3 · A Level

Every 9709 P3 Integration topic question from the 2020–2027 syllabus, drawn from 49 papers (2020–2026) and grouped by syllabus point. Each row opens a page listing the exact question numbers, marks and a direct link into the paper. These are questions by topic, not full papers, so you can revise one topic at a time.

- 9709 P3
- 6 subtopics
- 114 topic questions
- 49 papers
- 651 tagged marks
- [Back to Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/)
- [All paper codes](https://www.examsci.com/topics/)

Core finding

**recognise when an integrand can usefully be regarded as a product… is the most frequently assessed subtopic in Integration, with 36 topic questions and 209 marks across 35 papers.** extend the idea of ‘reverse differentiation’ to include the… follows with 35 topic questions and 197 marks. The topic contains 6 subtopics, 114 topic questions and 651 marks in total. Rows count only the parts tagged to that subtopic, keep the same colour in both charts and repeat paper count, tagged marks and year range in the native table.

## Topic question count and mark distribution

Subtopics are on the vertical axis and sorted from highest to lowest. Only the parts whose knowledge graph matches a subtopic are counted for it, and percentages are each row's share of the tagged total in that chart. A part tagged to several subtopics is counted in each bar, so the bars are not a partition of the topic total.

### Questions by subtopic

question items

- [• 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/) (35 papers) — 36 · 24.7%
- [• 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/) (29 papers) — 35 · 24.0%
- [• 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/) (21 papers) — 24 · 16.4%
- [• 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/) (20 papers) — 23 · 15.8%
- [• 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/) (15 papers) — 16 · 11.0%
- [• recognise an integrand of the form $\frac{k\mathrm{f}'(x)}{\mathrm{f}(x)}$, and integrate such functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/recognise-an-integrand-of-the-form-frac-k-mathrm-f-x-mathrm-f-x-and-integrate-such/) (12 papers) — 12 · 8.2%

### Marks by subtopic

marks

- [• 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/) (35 papers) — 209 · 25.0%
- [• 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/) (29 papers) — 197 · 23.6%
- [• 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/) (21 papers) — 138 · 16.5%
- [• 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/) (20 papers) — 128 · 15.3%
- [• 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/) (15 papers) — 87 · 10.4%
- [• recognise an integrand of the form $\frac{k\mathrm{f}'(x)}{\mathrm{f}(x)}$, and integrate such functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/recognise-an-integrand-of-the-form-frac-k-mathrm-f-x-mathrm-f-x-and-integrate-such/) (12 papers) — 76 · 9.1%

## Subtopic comparison matrix

Curriculum order is by syllabus number, then alphabetically. Every row links to the matching past-paper question list.

| Subtopic | Topic questions | Papers | Marks | Years | |
| --- | --- | --- | --- | --- | --- |
| **[• 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 | 29 | 197 | 2020–2026 | [Open topic questions](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/) |
| **[• 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 | 21 | 138 | 2020–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/integrate-rational-functions-by-means-of-decomposition-into-partial-fractions/) |
| **[• recognise an integrand of the form $\frac{k\mathrm{f}'(x)}{\mathrm{f}(x)}$, and integrate such functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/recognise-an-integrand-of-the-form-frac-k-mathrm-f-x-mathrm-f-x-and-integrate-such/)** | 12 | 12 | 76 | 2020–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/recognise-an-integrand-of-the-form-frac-k-mathrm-f-x-mathrm-f-x-and-integrate-such/) |
| **[• 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 | 35 | 209 | 2020–2026 | [Open topic questions](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/) |
| **[• 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 | 15 | 87 | 2021–2026 | [Open topic questions](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/) |
| **[• 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 | 20 | 128 | 2021–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/use-trigonometrical-relationships-in-carrying-out-integration/) |

## Browse every topic question

- [• 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 an integrand of the form $\frac{k\mathrm{f}'(x)}{\mathrm{f}(x)}$, and integrate such functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/recognise-an-integrand-of-the-form-frac-k-mathrm-f-x-mathrm-f-x-and-integrate-such/) — 12 question items · 12 papers — 76 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

## Other topics in 9709 P3

- [Algebra 156 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/)
- [Complex numbers 152 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/)
- [Differential equations 75 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differential-equations/)
- [Differentiation 134 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differentiation/)
- [Logarithmic and exponential functions 68 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/logarithmic-and-exponential-functions/)
- [Numerical solution of equations 131 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/numerical-solution-of-equations/)
- [Trigonometry 138 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/)
- [Vectors 133 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/)

## Topic question rules and edge cases

**How many subtopics does Integration contain?**

This page lists 6 subtopics tagged to the current syllabus. They are ordered by syllabus number, then alphabetically, and each row opens a page of matching past-paper questions.

**How are the subtopic question and mark totals calculated?**

A multiple-choice question contributes one item and its marks to every subtopic it is tagged with. A structured question contributes one item per tagged part, and that part’s marks; untagged parts of the same question are not counted here. A part tagged to several subtopics therefore appears under each of them.

**Why do some subtopics have no numbered prefix?**

Practical-skills statements and some syllabus bullets are unnumbered. Numbered statements come first; unnumbered statements and ties are sorted alphabetically.

**Is the LaTeX rendered without JavaScript?**

Yes. Subtopics that contain formulas are converted to static KaTeX HTML during the build, and the KaTeX stylesheet is served from the same site.

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