# 9709/62 October/November 2016

> 9709/62 October/November 2016: 6 questions, 50 marks. Difficulty 0.39, deviation 0.15, algebraic 0.27, text density 0.41. CIE IAL Mathematics 9709 P6.

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CIE IAL · Mathematics · 2016 October/November

This Mathematics 9709 Paper 6 (Probability & Statistics 1) paper contains 6 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
- 6 questions
- 50 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=4b7421ee-4aba-455e-b6f6-f98dceb5b2c7)
- [All 9709 P6 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p6/)

Core finding

**9709/62 October/November 2016 is a past paper for CIE IAL Mathematics 9709 Paper 6 (Probability & Statistics 1), with 6 questions worth 50 marks.** Its mark-weighted Difficulty Measure is 0.39 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.15 and a mark split of 32.0% Easy, 58.0% Medium and 10.0% Hard. Algebraic complexity averages 0.27; text density and modelling average 0.41. All five measures use 14 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 14 parts carrying 50 part marks. Difficulty tags cover 14 parts, algebraic tags 14 and text-density tags 14. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.39 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.15 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 32.0 / 58.0 / 10.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.27 — 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** | 0.39 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.15 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 32.0% Easy / 58.0% Medium / 10.0% 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** | 0.41 | 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 | [3 Probability](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 5 | 0.45 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=4b7421ee-4aba-455e-b6f6-f98dceb5b2c7&question_id=38ac4c17-ff1c-477d-9f3c-be3ce15948df&source_detail=9709%2F62+October%2FNovember+2016) |
| **Q2** FRQ | [3 Probability](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 7 | 0.34 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=4b7421ee-4aba-455e-b6f6-f98dceb5b2c7&question_id=d3fb6ecc-fd17-4bd7-af1a-bc2fa24ef596&source_detail=9709%2F62+October%2FNovember+2016) |
| **Q3** FRQ | [4 Discrete random variables](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 8 | 0.36 Medium | 0.36 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=4b7421ee-4aba-455e-b6f6-f98dceb5b2c7&question_id=9f686c37-1c98-4e60-8b36-d41ed4ce480c&source_detail=9709%2F62+October%2FNovember+2016) |
| **Q4** FRQ | [5 The normal distribution](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 9 | 0.28 Easy | 0.28 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=4b7421ee-4aba-455e-b6f6-f98dceb5b2c7&question_id=1f45dd05-7fc7-4d6b-9c17-3c59ff79b6c6&source_detail=9709%2F62+October%2FNovember+2016) |
| **Q5** FRQ | [1 Representation of data](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 9 | 0.34 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=4b7421ee-4aba-455e-b6f6-f98dceb5b2c7&question_id=583a2494-47ba-42ce-b20d-96c8f5803c11&source_detail=9709%2F62+October%2FNovember+2016) |
| **Q6** FRQ | [2 Permutations and combinations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 12 | 0.55 Medium | 0.30 Low | 0.30 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=4b7421ee-4aba-455e-b6f6-f98dceb5b2c7&question_id=56ebc7a4-93cc-4f7c-b3ee-95e0fb7c085d&source_detail=9709%2F62+October%2FNovember+2016) |

## Topics in this paper

- [3 Probability](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/)
- [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/)

## Related papers

- [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
- [9709/63](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p6/2016-october-november-9709-63/) — October/November 2016 — 7 questions · 50 marks — Free
- [9709/61](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p6/2016-may-june-9709-61/) — May/June 2016 — 7 questions · 50 marks — Free
- [9709/62](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p6/2016-may-june-9709-62/) — May/June 2016 — 7 questions · 50 marks — Free
- [9709/63](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p6/2016-may-june-9709-63/) — May/June 2016 — 7 questions · 50 marks — Free
- [9709/62](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p6/2016-march-9709-62/) — March 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 0.39 from 14 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 0.15, 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 32.0% Easy, 58.0% 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-p6/2016-october-november-9709-62/