# 9709/31 October/November 2020

> 9709/31 October/November 2020: 11 questions, 75 marks. Difficulty 0.43, deviation 0.14, algebraic 0.47, text density 0.29. CIE IAL Mathematics 9709 P3.

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CIE IAL · Mathematics · 2020 October/November

This Mathematics 9709 Paper 3 (Pure Mathematics 3) paper contains 11 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 P3
- 11 questions
- 75 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=6d3dbf03-a763-4245-9cd4-e9bb82088912)
- [All 9709 P3 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/)

Core finding

**9709/31 October/November 2020 is a past paper for CIE IAL Mathematics 9709 Paper 3 (Pure Mathematics 3), with 11 questions worth 75 marks.** Its mark-weighted Difficulty Measure is 0.43 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.14 and a mark split of 17.3% Easy, 68.0% Medium and 14.7% Hard. Algebraic complexity averages 0.47; text density and modelling average 0.29. All five measures use 17 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 17 parts carrying 75 part marks. Difficulty tags cover 17 parts, algebraic tags 17 and text-density tags 17. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.43 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.14 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 17.3 / 68.0 / 14.7 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.47 — 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** | 0.43 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.14 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 17.3% Easy / 68.0% Medium / 14.7% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.47 | 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 | [3.1 Algebra](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/) | 4 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6d3dbf03-a763-4245-9cd4-e9bb82088912&question_id=f84eb731-ba15-429d-ad77-30662e5e3790&source_detail=9709%2F31+October%2FNovember+2020) |
| **Q2** FRQ | [3.9 Complex numbers](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/) | 4 | 0.20 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6d3dbf03-a763-4245-9cd4-e9bb82088912&question_id=9b6dcac3-3be1-42d5-bdff-171ef8d0d17d&source_detail=9709%2F31+October%2FNovember+2020) |
| **Q3** FRQ | [3.4 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differentiation/) | 5 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6d3dbf03-a763-4245-9cd4-e9bb82088912&question_id=d89b346d-55ba-4898-bc8e-4517bdad22f2&source_detail=9709%2F31+October%2FNovember+2020) |
| **Q4** FRQ | [3.2 Logarithmic and exponential functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/logarithmic-and-exponential-functions/) | 6 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6d3dbf03-a763-4245-9cd4-e9bb82088912&question_id=ba53fabb-d395-4410-bad3-67ff1b253e09&source_detail=9709%2F31+October%2FNovember+2020) |
| **Q5** FRQ | [3.6 Numerical solution of equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/numerical-solution-of-equations/) | 5 | 0.30 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6d3dbf03-a763-4245-9cd4-e9bb82088912&question_id=08537ede-a29e-4b84-8739-a31228faded4&source_detail=9709%2F31+October%2FNovember+2020) |
| **Q6** FRQ | [3.3 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/) | 7 | 0.34 Medium | 0.34 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6d3dbf03-a763-4245-9cd4-e9bb82088912&question_id=89694fa2-0c2f-4283-9b45-2d58adda25cb&source_detail=9709%2F31+October%2FNovember+2020) |
| **Q7** FRQ | [3.9 Complex numbers](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/) | 7 | 0.34 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6d3dbf03-a763-4245-9cd4-e9bb82088912&question_id=68eed276-c90f-4dfa-ad29-776a5dbfe20b&source_detail=9709%2F31+October%2FNovember+2020) |
| **Q8** FRQ | [3.8 Differential equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differential-equations/) | 6 | 0.45 Medium | 0.45 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6d3dbf03-a763-4245-9cd4-e9bb82088912&question_id=4fe63ff8-80c3-42f1-ba7c-6ae67bf96e47&source_detail=9709%2F31+October%2FNovember+2020) |
| **Q9** FRQ | [3.1 Algebra](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/) | 10 | 0.45 Medium | 0.75 High | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6d3dbf03-a763-4245-9cd4-e9bb82088912&question_id=ecb748ef-0c90-49cd-8a6a-9588df01c0e0&source_detail=9709%2F31+October%2FNovember+2020) |
| **Q10** FRQ | [3.4 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differentiation/) | 10 | 0.57 Medium | 0.45 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6d3dbf03-a763-4245-9cd4-e9bb82088912&question_id=807dfb00-35d1-4fe9-8266-066044ae2bb9&source_detail=9709%2F31+October%2FNovember+2020) |
| **Q11** FRQ | [3.7 Vectors](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/) | 11 | 0.58 Medium | 0.61 High | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6d3dbf03-a763-4245-9cd4-e9bb82088912&question_id=6981fda4-c850-4a06-b8ec-fc6be77cba56&source_detail=9709%2F31+October%2FNovember+2020) |

## Topics in this paper

- [3.1 Algebra](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/)
- [3.9 Complex numbers](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/)
- [3.4 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differentiation/)
- [3.3 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/)
- [3.2 Logarithmic and exponential functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/logarithmic-and-exponential-functions/)
- [3.6 Numerical solution of equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/numerical-solution-of-equations/)
- [3.8 Differential equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differential-equations/)
- [3.5 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/)
- [3.7 Vectors](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/)

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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 0.43 from 17 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 0.14, 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 17.3% Easy, 68.0% Medium and 14.7% 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-p3/2020-october-november-9709-31/