# 9709/72 October/November 2015

> 9709/72 October/November 2015: 7 questions, 50 marks. Difficulty 0.34, deviation 0.12, algebraic 0.27, text density 0.39. CIE IAL Mathematics 9709 P7.

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CIE IAL · Mathematics · 2015 October/November

This Mathematics 9709 Paper 7 (Probability & Statistics 2) 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 P7
- 7 questions
- 50 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=311bf99d-e5bc-4a38-bee4-12572f38d08d)
- [All 9709 P7 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p7/)

Core finding

**9709/72 October/November 2015 is a past paper for CIE IAL Mathematics 9709 Paper 7 (Probability & Statistics 2), with 7 questions worth 50 marks.** Its mark-weighted Difficulty Measure is 0.34 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.12 and a mark split of 42.0% Easy, 58.0% Medium and 0.0% Hard. Algebraic complexity averages 0.27; text density and modelling average 0.39. All five measures use 16 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 16 parts carrying 50 part marks. Difficulty tags cover 16 parts, algebraic tags 16 and text-density tags 16. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.34 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.12 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 42.0 / 58.0 / 0.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.27 — 0.20–0.75 · nearer Low
- **Text Density and Modelling Measure**: 0.39 — 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** | 0.34 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.12 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 42.0% Easy / 58.0% Medium / 0.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.27 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.39 | 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 The Poisson distribution | 4 | 0.45 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=311bf99d-e5bc-4a38-bee4-12572f38d08d&question_id=cbc65052-0bc1-406d-9260-5938fe8cfcc4&source_detail=9709%2F72+October%2FNovember+2015) |
| **Q2** FRQ | 4 Sampling and estimation | 6 | 0.20 Easy | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=311bf99d-e5bc-4a38-bee4-12572f38d08d&question_id=33b71b71-e989-4e12-8b1e-f214d64b8ac8&source_detail=9709%2F72+October%2FNovember+2015) |
| **Q3** FRQ | 4 Sampling and estimation | 6 | 0.20 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=311bf99d-e5bc-4a38-bee4-12572f38d08d&question_id=bf66a316-bbe4-4cfa-96bb-9a883afe4f73&source_detail=9709%2F72+October%2FNovember+2015) |
| **Q4** FRQ | 3 Continuous random variables | 7 | 0.34 Medium | 0.34 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=311bf99d-e5bc-4a38-bee4-12572f38d08d&question_id=f3eb2b01-becd-425b-94c4-017362a05088&source_detail=9709%2F72+October%2FNovember+2015) |
| **Q5** FRQ | 1 The Poisson distribution | 7 | 0.45 Medium | 0.34 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=311bf99d-e5bc-4a38-bee4-12572f38d08d&question_id=4d510de4-cf8e-4de1-ae43-ccdc7d267567&source_detail=9709%2F72+October%2FNovember+2015) |
| **Q6** FRQ | 2 Linear combinations of random variables | 9 | 0.45 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=311bf99d-e5bc-4a38-bee4-12572f38d08d&question_id=305ef4e5-c47a-4033-bf9d-7214c91ccb67&source_detail=9709%2F72+October%2FNovember+2015) |
| **Q7** FRQ | 4 Sampling and estimation | 11 | 0.31 Easy | 0.31 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=311bf99d-e5bc-4a38-bee4-12572f38d08d&question_id=f323675f-8fde-4080-b7d4-13e09ce0d6a5&source_detail=9709%2F72+October%2FNovember+2015) |

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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 0.34 from 16 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 0.12, 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 42.0% Easy, 58.0% Medium and 0.0% 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-p7/2015-october-november-9709-72/