# 9709/31 October/November 2010

> 9709/31 October/November 2010: 10 questions, 75 marks. Difficulty 0.40, deviation 0.13, algebraic 0.44, text density 0.30. CIE IAL Mathematics 9709 P3.

- Canonical HTML: https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2010-october-november-9709-31/
- Markdown mirror: https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2010-october-november-9709-31/index.md

---

CIE IAL · Mathematics · 2010 October/November

This Mathematics 9709 Paper 3 (Pure Mathematics 3) paper contains 10 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
- 10 questions
- 75 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=c3bdbf0d-308a-4293-8125-23f3e24c0bf7)
- [All 9709 P3 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/)

Core finding

**9709/31 October/November 2010 is a past paper for CIE IAL Mathematics 9709 Paper 3 (Pure Mathematics 3), with 10 questions worth 75 marks.** Its mark-weighted Difficulty Measure is 0.40 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.13 and a mark split of 24.0% Easy, 70.7% Medium and 5.3% Hard. Algebraic complexity averages 0.44; text density and modelling average 0.30. 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**: 0.13 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 24.0 / 70.7 / 5.3 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.44 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.30 — 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** | 0.13 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 24.0% Easy / 70.7% Medium / 5.3% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.44 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.30 | 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 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=c3bdbf0d-308a-4293-8125-23f3e24c0bf7&question_id=00322c2b-206c-4bbb-a599-3f9ae14f0a17&source_detail=9709%2F31+October%2FNovember+2010) |
| **Q2** FRQ | [2 Logarithmic and exponential functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/logarithmic-and-exponential-functions/) | 4 | 0.20 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c3bdbf0d-308a-4293-8125-23f3e24c0bf7&question_id=a8c463db-d575-4be0-8b64-c2156fc684ee&source_detail=9709%2F31+October%2FNovember+2010) |
| **Q3** FRQ | [3 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/) | 5 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c3bdbf0d-308a-4293-8125-23f3e24c0bf7&question_id=529f688d-953f-418d-984e-2ae6700f81c4&source_detail=9709%2F31+October%2FNovember+2010) |
| **Q4** FRQ | [6 Numerical solution of equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/numerical-solution-of-equations/) | 7 | 0.27 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c3bdbf0d-308a-4293-8125-23f3e24c0bf7&question_id=3ad470c8-02ba-4019-bdf2-fcaaf81253a4&source_detail=9709%2F31+October%2FNovember+2010) |
| **Q5** FRQ | [5 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/) | 7 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c3bdbf0d-308a-4293-8125-23f3e24c0bf7&question_id=3fdc1b44-dfad-46a3-99b4-9c1711db8960&source_detail=9709%2F31+October%2FNovember+2010) |
| **Q6** FRQ | [9 Complex numbers](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/) | 9 | 0.37 Medium | 0.37 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c3bdbf0d-308a-4293-8125-23f3e24c0bf7&question_id=f0e16e1e-bed5-4119-8c76-0dd07f007b8e&source_detail=9709%2F31+October%2FNovember+2010) |
| **Q7** FRQ | [7 Vectors](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/) | 9 | 0.53 Medium | 0.56 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c3bdbf0d-308a-4293-8125-23f3e24c0bf7&question_id=37f74b40-20a1-434a-ba64-2fcbbc5ec813&source_detail=9709%2F31+October%2FNovember+2010) |
| **Q8** FRQ | [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=c3bdbf0d-308a-4293-8125-23f3e24c0bf7&question_id=bd2bbcf5-625b-4e50-94f8-912a4639b56a&source_detail=9709%2F31+October%2FNovember+2010) |
| **Q9** FRQ | [4 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differentiation/) | 10 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c3bdbf0d-308a-4293-8125-23f3e24c0bf7&question_id=a039a715-c4b2-4761-81d8-d244e5162699&source_detail=9709%2F31+October%2FNovember+2010) |
| **Q10** FRQ | [8 Differential equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differential-equations/) | 10 | 0.33 Medium | 0.33 Medium | 0.75 High | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c3bdbf0d-308a-4293-8125-23f3e24c0bf7&question_id=e906022f-052e-4292-a326-5e8fb6b53618&source_detail=9709%2F31+October%2FNovember+2010) |

## Topics in this paper

- [1 Algebra](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/)
- [2 Logarithmic and exponential functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/logarithmic-and-exponential-functions/)
- [3 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/)
- [6 Numerical solution of equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/numerical-solution-of-equations/)
- [5 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/)
- [9 Complex numbers](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/)
- [7 Vectors](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/)
- [4 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differentiation/)
- [8 Differential equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differential-equations/)

## Related papers

- [9709/32](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2010-october-november-9709-32/) — October/November 2010 — 10 questions · 75 marks — Free
- [9709/33](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2010-october-november-9709-33/) — October/November 2010 — 10 questions · 75 marks — Free
- [9709/31](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2010-may-june-9709-31/) — May/June 2010 — 10 questions · 75 marks — Free
- [9709/32](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2010-may-june-9709-32/) — May/June 2010 — 10 questions · 75 marks — Free
- [9709/33](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2010-may-june-9709-33/) — May/June 2010 — 10 questions · 75 marks — Free
- [9709/31](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2011-october-november-9709-31/) — October/November 2011 — 10 questions · 75 marks — Free

## 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 0.13, 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 24.0% Easy, 70.7% Medium and 5.3% 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.

---

Full page with native tables, bar charts and Practice Hub links: https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2010-october-november-9709-31/