# 9709/61 October/November 2015

> 9709/61 October/November 2015: 7 questions, 50 marks. Difficulty 0.38, deviation 0.16, algebraic 0.23, text density 0.41. CIE IAL Mathematics 9709 P6.

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CIE IAL · Mathematics · 2015 October/November

This Mathematics 9709 Paper 6 (Probability & Statistics 1) paper contains 7 questions worth 50 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 P6
- 7 questions
- 50 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=0a7733b0-4f00-4a49-b07a-592c743d9c39)
- [All 9709 P6 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p6/)

Core finding

**9709/61 October/November 2015 is a past paper for CIE IAL Mathematics 9709 Paper 6 (Probability & Statistics 1), with 7 questions worth 50 marks.** Its mark-weighted Difficulty Measure is 0.38 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.16 and a mark split of 36.0% Easy, 54.0% Medium and 10.0% Hard. Algebraic complexity averages 0.23; text density and modelling average 0.41. All five measures use 15 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 15 parts carrying 50 part marks. Difficulty tags cover 15 parts, algebraic tags 15 and text-density tags 15. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.38 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.16 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 36.0 / 54.0 / 10.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.23 — 0.20–0.75 · nearer Low
- **Text Density and Modelling Measure**: 0.41 — 0.20–0.75 · nearer Medium

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** | 0.38 | 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** | 36.0% Easy / 54.0% Medium / 10.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.23 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.41 | 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 | [4 Discrete random variables](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 4 | 0.45 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0a7733b0-4f00-4a49-b07a-592c743d9c39&question_id=2fddb4d1-7cdd-4752-b4db-b13c9e781742&source_detail=9709%2F61+October%2FNovember+2015) |
| **Q2** FRQ | [5 The normal distribution](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 4 | 0.45 Medium | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0a7733b0-4f00-4a49-b07a-592c743d9c39&question_id=aa687269-e445-403e-8fd0-24d571d944d5&source_detail=9709%2F61+October%2FNovember+2015) |
| **Q3** FRQ | [1 Representation of data](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 6 | 0.20 Easy | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0a7733b0-4f00-4a49-b07a-592c743d9c39&question_id=7099d10f-43cf-4088-a032-200e689a9278&source_detail=9709%2F61+October%2FNovember+2015) |
| **Q4** FRQ | [1 Representation of data](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 7 | 0.20 Easy | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0a7733b0-4f00-4a49-b07a-592c743d9c39&question_id=a1cb8ebb-03eb-42d6-b53b-2cdef58d3134&source_detail=9709%2F61+October%2FNovember+2015) |
| **Q5** FRQ | [2 Permutations and combinations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 9 | 0.45 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0a7733b0-4f00-4a49-b07a-592c743d9c39&question_id=337e8632-b592-4b95-9588-efafe02bd1b9&source_detail=9709%2F61+October%2FNovember+2015) |
| **Q6** FRQ | [3 Probability](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 9 | 0.31 Easy | 0.20 Low | 0.39 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0a7733b0-4f00-4a49-b07a-592c743d9c39&question_id=334c662b-41bf-45f2-86f8-16df562c23b2&source_detail=9709%2F61+October%2FNovember+2015) |
| **Q7** FRQ | [3 Probability](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 11 | 0.56 Medium | 0.31 Low | 0.38 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0a7733b0-4f00-4a49-b07a-592c743d9c39&question_id=81fcae11-54f7-47c1-889a-6fcd1684a4ec&source_detail=9709%2F61+October%2FNovember+2015) |

## Topics in this paper

- [4 Discrete random variables](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/)
- [5 The normal distribution](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/)
- [1 Representation of data](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/)
- [2 Permutations and combinations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/)
- [3 Probability](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/)

## Related papers

- [9709/62](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p6/2015-october-november-9709-62/) — October/November 2015 — 7 questions · 50 marks — Free
- [9709/63](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p6/2015-october-november-9709-63/) — October/November 2015 — 7 questions · 50 marks — Free
- [9709/61](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p6/2015-may-june-9709-61/) — May/June 2015 — 7 questions · 50 marks — Free
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- [9709/63](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p6/2015-may-june-9709-63/) — May/June 2015 — 7 questions · 50 marks — Free
- [9709/61](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p6/2016-october-november-9709-61/) — October/November 2016 — 7 questions · 50 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 0.38 from 15 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 36.0% Easy, 54.0% Medium and 10.0% 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-p6/2015-october-november-9709-61/