# 9709/51 October/November 2020

> 9709/51 October/November 2020: 7 questions, 50 marks. Difficulty 0.35, deviation 0.12, algebraic 0.27, text density 0.33. CIE IAL Mathematics 9709 P5.

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CIE IAL · Mathematics · 2020 October/November

This Mathematics 9709 Paper 5 (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 P5
- 7 questions
- 50 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=2d049f0a-8457-4297-a56c-b821534b4a02)
- [All 9709 P5 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/)

Core finding

**9709/51 October/November 2020 is a past paper for CIE IAL Mathematics 9709 Paper 5 (Probability & Statistics 1), with 7 questions worth 50 marks.** Its mark-weighted Difficulty Measure is 0.35 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 0.33. All five measures use 18 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 18 parts carrying 50 part marks. Difficulty tags cover 18 parts, algebraic tags 18 and text-density tags 18. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.35 — 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**: 0.33 — 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** | 0.35 | 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** | 0.33 | 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 | [5.3 Probability](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/probability/) | 4 | 0.20 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2d049f0a-8457-4297-a56c-b821534b4a02&question_id=5aa7b19a-47ba-466c-bc44-fa66315ba670&source_detail=9709%2F51+October%2FNovember+2020) |
| **Q2** FRQ | [5.3 Probability](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/probability/) | 5 | 0.35 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2d049f0a-8457-4297-a56c-b821534b4a02&question_id=a329a97b-f9e9-4d5d-9bbd-4a11984ce468&source_detail=9709%2F51+October%2FNovember+2020) |
| **Q3** FRQ | [5.4 Discrete random variables](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/discrete-random-variables/) | 5 | 0.35 Medium | 0.35 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2d049f0a-8457-4297-a56c-b821534b4a02&question_id=be168ec2-eac3-4a98-a34c-05a936742fbe&source_detail=9709%2F51+October%2FNovember+2020) |
| **Q4** FRQ | [5.4 Discrete random variables](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/discrete-random-variables/) | 6 | 0.37 Medium | 0.37 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2d049f0a-8457-4297-a56c-b821534b4a02&question_id=4960fd77-c55c-4d0a-84d8-7a4d21baf63d&source_detail=9709%2F51+October%2FNovember+2020) |
| **Q5** FRQ | [5.5 The normal distribution](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/the-normal-distribution/) | 9 | 0.37 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2d049f0a-8457-4297-a56c-b821534b4a02&question_id=a93d62bc-3761-435e-95e1-3aef4600c9a0&source_detail=9709%2F51+October%2FNovember+2020) |
| **Q6** FRQ | [5.1 Representation of data](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/representation-of-data/) | 10 | 0.35 Medium | 0.35 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2d049f0a-8457-4297-a56c-b821534b4a02&question_id=65d0bcfb-d6b9-4238-a337-48888ef0ab34&source_detail=9709%2F51+October%2FNovember+2020) |
| **Q7** FRQ | [5.2 Permutations and combinations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/permutations-and-combinations/) | 11 | 0.36 Medium | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2d049f0a-8457-4297-a56c-b821534b4a02&question_id=68efb32c-fbe1-4e53-922d-76c7adb30036&source_detail=9709%2F51+October%2FNovember+2020) |

## Topics in this paper

- [5.3 Probability](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/probability/)
- [5.4 Discrete random variables](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/discrete-random-variables/)
- [5.5 The normal distribution](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/the-normal-distribution/)
- [5.1 Representation of data](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/representation-of-data/)
- [5.2 Permutations and combinations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/permutations-and-combinations/)

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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 0.35 from 18 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-p5/2020-october-november-9709-51/