# 9709/72 March 2016

> 9709/72 March 2016: 7 questions, 50 marks. Difficulty 0.40, deviation 0.10, algebraic 0.27, text density 0.38. CIE IAL Mathematics 9709 P7.

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CIE IAL · Mathematics · 2016 March

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=d9760089-e998-4165-a32f-5a10afc1452c)
- [All 9709 P7 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p7/)

Core finding

**9709/72 March 2016 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 0.40 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.10 and a mark split of 20.0% Easy, 80.0% Medium and 0.0% Hard. Algebraic complexity averages 0.27; text density and modelling average 0.38. 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**: 0.40 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.10 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 20.0 / 80.0 / 0.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.27 — 0.20–0.75 · nearer Low
- **Text Density and Modelling Measure**: 0.38 — 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** | 0.40 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.10 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 20.0% Easy / 80.0% 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** | 0.38 | 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 | 2 Linear combinations of random variables | 5 | 0.45 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d9760089-e998-4165-a32f-5a10afc1452c&question_id=156a1bd5-b10f-4019-a876-253951f5f650&source_detail=9709%2F72+March+2016) |
| **Q2** FRQ | 5 Hypothesis tests | 5 | 0.45 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d9760089-e998-4165-a32f-5a10afc1452c&question_id=71ae0742-36a1-4ec2-82b0-121f93e1dd8e&source_detail=9709%2F72+March+2016) |
| **Q3** FRQ | 5 Hypothesis tests | 5 | 0.40 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d9760089-e998-4165-a32f-5a10afc1452c&question_id=788efa54-09cc-4742-9212-44eb8f95682f&source_detail=9709%2F72+March+2016) |
| **Q4** FRQ | 2 Linear combinations of random variables | 5 | 0.45 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d9760089-e998-4165-a32f-5a10afc1452c&question_id=4f659dac-7f41-4980-ac6f-6c9444358465&source_detail=9709%2F72+March+2016) |
| **Q5** FRQ | 4 Sampling and estimation | 8 | 0.39 Medium | 0.39 Medium | 0.42 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d9760089-e998-4165-a32f-5a10afc1452c&question_id=d2a96ed7-e242-41cc-b4f9-63e1f043f3e3&source_detail=9709%2F72+March+2016) |
| **Q6** FRQ | 1 The Poisson distribution | 11 | 0.36 Medium | 0.20 Low | 0.43 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d9760089-e998-4165-a32f-5a10afc1452c&question_id=444ee29e-b5b6-4d24-b20a-b3de0b3b34f0&source_detail=9709%2F72+March+2016) |
| **Q7** FRQ | 3 Continuous random variables | 11 | 0.38 Medium | 0.38 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d9760089-e998-4165-a32f-5a10afc1452c&question_id=0752a22b-c45b-44db-9ee1-4d311d54f83f&source_detail=9709%2F72+March+2016) |

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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 0.40 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 0.10, 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 20.0% Easy, 80.0% 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-p7/2016-march-9709-72/