# 9709/63 May/June 2015

> 9709/63 May/June 2015: 7 questions, 50 marks. Difficulty 0.50, deviation 0.19, algebraic 0.29, text density 0.45. CIE IAL Mathematics 9709 P6.

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CIE IAL · Mathematics · 2015 May/June

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=cf47561d-edc4-44f6-bacf-d7791bcbb5ad)
- [All 9709 P6 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p6/)

Core finding

**9709/63 May/June 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 0.50 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.19 and a mark split of 14.0% Easy, 48.0% Medium and 38.0% Hard. Algebraic complexity averages 0.29; text density and modelling average 0.45. 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**: 0.50 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.19 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 14.0 / 48.0 / 38.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.29 — 0.20–0.75 · nearer Low
- **Text Density and Modelling Measure**: 0.45 — 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** | 0.50 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.19 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 14.0% Easy / 48.0% Medium / 38.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.29 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.45 | 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 | [5 The normal distribution](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 3 | 0.45 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cf47561d-edc4-44f6-bacf-d7791bcbb5ad&question_id=828d6c5a-7460-4fe0-9638-d8186844a078&source_detail=9709%2F63+May%2FJune+2015) |
| **Q2** FRQ | [3 Probability](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 5 | 0.30 Easy | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cf47561d-edc4-44f6-bacf-d7791bcbb5ad&question_id=5722628b-c7e5-4213-afde-ddce67015967&source_detail=9709%2F63+May%2FJune+2015) |
| **Q3** FRQ | [5 The normal distribution](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=cf47561d-edc4-44f6-bacf-d7791bcbb5ad&question_id=1962cbd0-de61-4773-95df-9be31342bc6a&source_detail=9709%2F63+May%2FJune+2015) |
| **Q4** FRQ | [3 Probability](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 6 | 0.41 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cf47561d-edc4-44f6-bacf-d7791bcbb5ad&question_id=de29fcc4-0d1d-4853-9de5-dab5a0282eaa&source_detail=9709%2F63+May%2FJune+2015) |
| **Q5** FRQ | [4 Discrete random variables](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 9 | 0.62 Hard | 0.45 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cf47561d-edc4-44f6-bacf-d7791bcbb5ad&question_id=19a028b5-caeb-467b-9b12-f3475de02e68&source_detail=9709%2F63+May%2FJune+2015) |
| **Q6** FRQ | [1 Representation of data](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 11 | 0.48 Medium | 0.31 Low | 0.43 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cf47561d-edc4-44f6-bacf-d7791bcbb5ad&question_id=504311a4-b6b6-4b06-a4bf-dd269883e5eb&source_detail=9709%2F63+May%2FJune+2015) |
| **Q7** FRQ | [2 Permutations and combinations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/) | 11 | 0.65 Hard | 0.31 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cf47561d-edc4-44f6-bacf-d7791bcbb5ad&question_id=76c17799-3fae-4f12-af72-3bd4b3ed3614&source_detail=9709%2F63+May%2FJune+2015) |

## Topics in this paper

- [5 The normal distribution](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/)
- [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/)
- [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/)

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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 0.50 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 0.19, 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 14.0% Easy, 48.0% Medium and 38.0% 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-may-june-9709-63/