# 9709/72 May/June 2019

> 9709/72 May/June 2019: 7 questions, 50 marks. Difficulty 0.46, deviation 0.16, algebraic 0.40, text density 0.46. CIE IAL Mathematics 9709 P7.

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CIE IAL · Mathematics · 2019 May/June

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=8c388a9c-2478-476c-92da-20552bf45fd1)
- [All 9709 P7 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p7/)

Core finding

**9709/72 May/June 2019 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 0.46 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.16 and a mark split of 14.0% Easy, 62.0% Medium and 24.0% Hard. Algebraic complexity averages 0.40; text density and modelling average 0.46. All five measures use 19 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 19 parts carrying 50 part marks. Difficulty tags cover 19 parts, algebraic tags 19 and text-density tags 19. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.46 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.16 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 14.0 / 62.0 / 24.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.40 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.46 — 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** | 0.46 | 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** | 14.0% Easy / 62.0% Medium / 24.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.40 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.46 | 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 | 3 | 0.37 Medium | 0.37 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=8c388a9c-2478-476c-92da-20552bf45fd1&question_id=f291c006-3706-4b2b-a010-83c80e96cfab&source_detail=9709%2F72+May%2FJune+2019) |
| **Q2** FRQ | 4 Sampling and estimation | 4 | 0.39 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=8c388a9c-2478-476c-92da-20552bf45fd1&question_id=4e4e72e0-139d-4431-b7fd-a4207bed4825&source_detail=9709%2F72+May%2FJune+2019) |
| **Q3** FRQ | 4 Sampling and estimation | 8 | 0.45 Medium | 0.45 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=8c388a9c-2478-476c-92da-20552bf45fd1&question_id=45f76499-29a0-4a3b-be29-9da0c977b2b0&source_detail=9709%2F72+May%2FJune+2019) |
| **Q4** FRQ | 2 Linear combinations of random variables | 7 | 0.75 Hard | 0.45 Medium | 0.75 High | [Go to Practice Hub](https://www.examsci.com/practice?set_id=8c388a9c-2478-476c-92da-20552bf45fd1&question_id=9a288c3b-929b-4fc3-98d3-7a2dc60e9ebc&source_detail=9709%2F72+May%2FJune+2019) |
| **Q5** FRQ | 5 Hypothesis tests | 8 | 0.39 Medium | 0.39 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=8c388a9c-2478-476c-92da-20552bf45fd1&question_id=f4fc5a02-9a5c-4bae-b712-d0d40cf1db4c&source_detail=9709%2F72+May%2FJune+2019) |
| **Q6** FRQ | 3 Continuous random variables | 9 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=8c388a9c-2478-476c-92da-20552bf45fd1&question_id=a0e76e6e-28d5-45cd-b45e-abb7d7efc5d7&source_detail=9709%2F72+May%2FJune+2019) |
| **Q7** FRQ | 1 The Poisson distribution | 11 | 0.48 Medium | 0.38 Medium | 0.59 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=8c388a9c-2478-476c-92da-20552bf45fd1&question_id=ace985bc-49c6-4e52-902b-1c2b7cb5f3a8&source_detail=9709%2F72+May%2FJune+2019) |

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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 0.46 from 19 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 14.0% Easy, 62.0% Medium and 24.0% 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-p7/2019-may-june-9709-72/