# 9709/11 October/November 2020

> 9709/11 October/November 2020: 12 questions, 75 marks. Difficulty 0.40, deviation 0.16, algebraic 0.36, text density 0.29. CIE IAL Mathematics 9709 P1.

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CIE IAL · Mathematics · 2020 October/November

This Mathematics 9709 Paper 1 (Pure Mathematics 1) paper contains 12 questions worth 75 marks. The profile below reports five mark-weighted difficulty and complexity measures, and every question row repeats them. Full question text and mark scheme open in the Interactive Practice Hub.

- CIE IAL
- 9709 P1
- 12 questions
- 75 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=2e5391be-26d5-4420-ba3f-8d90950de6a0)
- [All 9709 P1 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/)

Core finding

**9709/11 October/November 2020 is a past paper for CIE IAL Mathematics 9709 Paper 1 (Pure Mathematics 1), with 12 questions worth 75 marks.** Its mark-weighted Difficulty Measure is 0.40 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.16 and a mark split of 29.3% Easy, 57.4% Medium and 13.3% Hard. Algebraic complexity averages 0.36; text density and modelling average 0.29. All five measures use 23 part-level tags, not candidate results. Every question row below repeats them and opens the Interactive Practice Hub for that question.

## Difficulty & complexity profile

All five measures are mark-weighted and calculated from 23 parts carrying 75 part marks. Difficulty tags cover 23 parts, algebraic tags 23 and text-density tags 23. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.40 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.16 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 29.3 / 57.4 / 13.3 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.36 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.29 — 0.20–0.75 · nearer Low

Scale: Easy 0.20 · Medium 0.45 · Hard 0.75, and Low 0.20 · Medium 0.45 · High 0.75 for the two complexity measures. [How each band is defined and how the values are calculated →](https://www.examsci.com/guides/difficulty-and-complexity-measures/)

### Definitions and calculation

| Measure | Paper value | Formula |
| --- | --- | --- |
| **Difficulty Measure** | 0.40 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.16 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 29.3% Easy / 57.4% Medium / 13.3% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.36 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.29 | Σ(t_i × marks_i) / Σmarks_i, with t = 0.20 / 0.45 / 0.75 |

w_i equals the part marks, except for a Hard part worth 4 or more marks, where w_i = marks^0.75 to offset the accessible starter steps inside long structured questions.

## Question list

Each measure is recalculated from the parts of that question and uses the same weights as the paper profile.

| Question | Topic | Marks | Difficulty Measure | Algebraic Complexity Measure | Text Density and Modelling Measure | Practice |
| --- | --- | --- | --- | --- | --- | --- |
| **Q1** FRQ | [1.1 Quadratics](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/quadratics/) | 3 | 0.45 Medium | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2e5391be-26d5-4420-ba3f-8d90950de6a0&question_id=2d716784-a96d-4f6f-bac1-f235d834e216&source_detail=9709%2F11+October%2FNovember+2020) |
| **Q2** FRQ | [1.8 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/integration/) | 4 | 0.20 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2e5391be-26d5-4420-ba3f-8d90950de6a0&question_id=a660eb89-c27f-45bb-b12f-4a0acb7b5809&source_detail=9709%2F11+October%2FNovember+2020) |
| **Q3** FRQ | [1.7 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/differentiation/) | 3 | 0.45 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2e5391be-26d5-4420-ba3f-8d90950de6a0&question_id=34ffb071-3cda-43c8-a3f2-1dceddafe65f&source_detail=9709%2F11+October%2FNovember+2020) |
| **Q4** FRQ | [1.2 Functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/) | 3 | 0.45 Medium | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2e5391be-26d5-4420-ba3f-8d90950de6a0&question_id=3b0cea55-0983-4db1-be47-ae7e963b19aa&source_detail=9709%2F11+October%2FNovember+2020) |
| **Q5** FRQ | [1.6 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/) | 5 | 0.40 Medium | 0.40 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2e5391be-26d5-4420-ba3f-8d90950de6a0&question_id=ed472f16-1753-4365-84cf-4f51928a50cf&source_detail=9709%2F11+October%2FNovember+2020) |
| **Q6** FRQ | [1.7 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/differentiation/) | 5 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2e5391be-26d5-4420-ba3f-8d90950de6a0&question_id=8b08425a-1b88-4723-934d-742e4db05f22&source_detail=9709%2F11+October%2FNovember+2020) |
| **Q7** FRQ | [1.5 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/) | 6 | 0.33 Medium | 0.33 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2e5391be-26d5-4420-ba3f-8d90950de6a0&question_id=6ba32a6a-f27a-4279-b89e-e9cf1f9bc1ff&source_detail=9709%2F11+October%2FNovember+2020) |
| **Q8** FRQ | [1.6 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/) | 7 | 0.34 Medium | 0.34 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2e5391be-26d5-4420-ba3f-8d90950de6a0&question_id=eb999e72-5f5d-4036-9dae-2f7438a933fb&source_detail=9709%2F11+October%2FNovember+2020) |
| **Q9** FRQ | [1.3 Coordinate geometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/) | 8 | 0.29 Easy | 0.29 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2e5391be-26d5-4420-ba3f-8d90950de6a0&question_id=880854c2-32ca-4699-b68c-00302e27d811&source_detail=9709%2F11+October%2FNovember+2020) |
| **Q10** FRQ | [1.4 Circular measure](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/circular-measure/) | 10 | 0.46 Medium | 0.30 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2e5391be-26d5-4420-ba3f-8d90950de6a0&question_id=ad231359-24d9-482c-8750-31c89852ddfa&source_detail=9709%2F11+October%2FNovember+2020) |
| **Q11** FRQ | [1.2 Functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/) | 9 | 0.42 Medium | 0.42 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2e5391be-26d5-4420-ba3f-8d90950de6a0&question_id=afb27db9-54d9-474a-8bbc-fc67a42fa5ac&source_detail=9709%2F11+October%2FNovember+2020) |
| **Q12** FRQ | [1.1 Quadratics](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/quadratics/) | 12 | 0.52 Medium | 0.56 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2e5391be-26d5-4420-ba3f-8d90950de6a0&question_id=5d4607b5-8867-458c-aedd-f5eb25ff7329&source_detail=9709%2F11+October%2FNovember+2020) |

## Topics in this paper

- [1.1 Quadratics](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/quadratics/)
- [1.8 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/integration/)
- [1.7 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/differentiation/)
- [1.2 Functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/)
- [1.5 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/)
- [1.6 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/)
- [1.3 Coordinate geometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/)
- [1.4 Circular measure](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/circular-measure/)

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## Paper FAQ

**How are the difficulty and complexity measures calculated?**

Each part is weighted by its official marks. Difficulty uses Easy 0.20, Medium 0.45 and Hard 0.75; algebraic complexity and text density and modelling use Low 0.20, Medium 0.45 and High 0.75. A Hard part worth 4 or more marks is down-weighted to marks^0.75, so the accessible starter steps inside a long structured question do not inflate the difficulty result. This paper's Difficulty Measure is 0.40 from 23 parts.

**What does the Difficulty Deviation show?**

It is the mark-weighted standard deviation of the part difficulty values around the paper mean. A value of 0 would mean every tagged part has the same difficulty; this paper's deviation is 0.16, so its parts are more mixed than a single-level paper.

**Is the Difficulty Ratio based on question counts or marks?**

It is based on official marks, not question counts. This paper's shares are 29.3% Easy, 57.3% Medium and 13.3% Hard; the three shares sum to 100% before rounding.

**Are these official difficulty ratings?**

No. They are derived from the platform's part-level difficulty and static-question-profile tags. They are not exam-board grade boundaries and are not calculated from candidate outcomes. Use them to compare the demand profile of papers, not to predict a grade.

**Why does each question row show its own measures?**

Each row recalculates the same mark-weighted formula from that question's parts. A single-part MCQ therefore shows the tag value directly, while a multi-part structured question blends the tags of its parts using the same Hard-part decay as the paper profile.

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Full page with native tables, bar charts and Practice Hub links: https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2020-october-november-9709-11/