# 9709 P1 Functions Topic Questions

> CIE IAL 9709 P1: every Functions topic question from 49 papers (2020–2026), grouped by syllabus point. 218 questions, 562 marks, with direct links into the…

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CIE IAL · Mathematics · 9709 P1 · A Level

Every 9709 P1 Functions 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 P1
- 5 subtopics
- 218 topic questions
- 49 papers
- 562 tagged marks
- [Back to Functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/)
- [All paper codes](https://www.examsci.com/topics/)

Core finding

**understand and use the transformations of the graph of … given by …… is the most frequently assessed subtopic in Functions, with 73 topic questions and 200 marks across 42 papers.** identify the range of a given function in simple cases, and… follows with 66 topic questions and 159 marks. The topic contains 5 subtopics, 218 topic questions and 562 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

- [• understand and use the transformations of the graph of $y=\mathrm{f}(x)$ given by $y=\mathrm{f}(x)+a$, $y=\mathrm{f}(x+a)$, $y=a\mathrm{f}(x)$, $y=\mathrm{f}(ax)$ and simple combinations of these](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/understand-and-use-the-transformations-of-the-graph-of-y-mathrm-f-x-given-by-y-mathrm/) (42 papers) — 73 · 32.2%
- [• identify the range of a given function in simple cases, and find the composition of two given functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/identify-the-range-of-a-given-function-in-simple-cases-and-find-the-composition-of/) (39 papers) — 66 · 29.1%
- [• determine whether or not a given function is one-one, and find the inverse of a one-one function in simple cases](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/determine-whether-or-not-a-given-function-is-one-one-and-find-the-inverse-of-a-one/) (41 papers) — 51 · 22.5%
- [• understand the terms function, domain, range, one-one function, inverse function and composition of functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/understand-the-terms-function-domain-range-one-one-function-inverse-function-and/) (24 papers) — 30 · 13.2%
- [• illustrate in graphical terms the relation between a one-one function and its inverse](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/illustrate-in-graphical-terms-the-relation-between-a-one-one-function-and-its-inverse/) (7 papers) — 7 · 3.1%

### Marks by subtopic

marks

- [• understand and use the transformations of the graph of $y=\mathrm{f}(x)$ given by $y=\mathrm{f}(x)+a$, $y=\mathrm{f}(x+a)$, $y=a\mathrm{f}(x)$, $y=\mathrm{f}(ax)$ and simple combinations of these](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/understand-and-use-the-transformations-of-the-graph-of-y-mathrm-f-x-given-by-y-mathrm/) (42 papers) — 200 · 34.2%
- [• identify the range of a given function in simple cases, and find the composition of two given functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/identify-the-range-of-a-given-function-in-simple-cases-and-find-the-composition-of/) (39 papers) — 159 · 27.2%
- [• determine whether or not a given function is one-one, and find the inverse of a one-one function in simple cases](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/determine-whether-or-not-a-given-function-is-one-one-and-find-the-inverse-of-a-one/) (41 papers) — 149 · 25.5%
- [• understand the terms function, domain, range, one-one function, inverse function and composition of functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/understand-the-terms-function-domain-range-one-one-function-inverse-function-and/) (24 papers) — 62 · 10.6%
- [• illustrate in graphical terms the relation between a one-one function and its inverse](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/illustrate-in-graphical-terms-the-relation-between-a-one-one-function-and-its-inverse/) (7 papers) — 14 · 2.4%

## 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 | |
| --- | --- | --- | --- | --- | --- |
| **[• determine whether or not a given function is one-one, and find the inverse of a one-one function in simple cases](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/determine-whether-or-not-a-given-function-is-one-one-and-find-the-inverse-of-a-one/)** | 51 | 41 | 149 | 2020–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/determine-whether-or-not-a-given-function-is-one-one-and-find-the-inverse-of-a-one/) |
| **[• identify the range of a given function in simple cases, and find the composition of two given functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/identify-the-range-of-a-given-function-in-simple-cases-and-find-the-composition-of/)** | 66 | 39 | 159 | 2020–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/identify-the-range-of-a-given-function-in-simple-cases-and-find-the-composition-of/) |
| **[• illustrate in graphical terms the relation between a one-one function and its inverse](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/illustrate-in-graphical-terms-the-relation-between-a-one-one-function-and-its-inverse/)** | 7 | 7 | 14 | 2021–2025 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/illustrate-in-graphical-terms-the-relation-between-a-one-one-function-and-its-inverse/) |
| **[• understand and use the transformations of the graph of $y=\mathrm{f}(x)$ given by $y=\mathrm{f}(x)+a$, $y=\mathrm{f}(x+a)$, $y=a\mathrm{f}(x)$, $y=\mathrm{f}(ax)$ and simple combinations of these](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/understand-and-use-the-transformations-of-the-graph-of-y-mathrm-f-x-given-by-y-mathrm/)** | 73 | 42 | 200 | 2020–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/understand-and-use-the-transformations-of-the-graph-of-y-mathrm-f-x-given-by-y-mathrm/) |
| **[• understand the terms function, domain, range, one-one function, inverse function and composition of functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/understand-the-terms-function-domain-range-one-one-function-inverse-function-and/)** | 30 | 24 | 62 | 2020–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/understand-the-terms-function-domain-range-one-one-function-inverse-function-and/) |

## Browse every topic question

- [• determine whether or not a given function is one-one, and find the inverse of a one-one function in simple cases](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/determine-whether-or-not-a-given-function-is-one-one-and-find-the-inverse-of-a-one/) — 51 question items · 41 papers — 149 marks · 2020–2026
- [• identify the range of a given function in simple cases, and find the composition of two given functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/identify-the-range-of-a-given-function-in-simple-cases-and-find-the-composition-of/) — 66 question items · 39 papers — 159 marks · 2020–2026
- [• illustrate in graphical terms the relation between a one-one function and its inverse](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/illustrate-in-graphical-terms-the-relation-between-a-one-one-function-and-its-inverse/) — 7 question items · 7 papers — 14 marks · 2021–2025
- [• understand and use the transformations of the graph of $y=\mathrm{f}(x)$ given by $y=\mathrm{f}(x)+a$, $y=\mathrm{f}(x+a)$, $y=a\mathrm{f}(x)$, $y=\mathrm{f}(ax)$ and simple combinations of these](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/understand-and-use-the-transformations-of-the-graph-of-y-mathrm-f-x-given-by-y-mathrm/) — 73 question items · 42 papers — 200 marks · 2020–2026
- [• understand the terms function, domain, range, one-one function, inverse function and composition of functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/understand-the-terms-function-domain-range-one-one-function-inverse-function-and/) — 30 question items · 24 papers — 62 marks · 2020–2026

## Other topics in 9709 P1

- [Circular measure 102 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/circular-measure/)
- [Coordinate geometry 186 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/)
- [Differentiation 183 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/differentiation/)
- [Integration 100 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/integration/)
- [Quadratics 182 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/quadratics/)
- [Series 198 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/)
- [Trigonometry 154 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/)

## Topic question rules and edge cases

**How many subtopics does Functions contain?**

This page lists 5 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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