# 9709/52 March 2016

> 9709/52 March 2016: 7 questions, 50 marks. Difficulty 0.49, deviation 0.18, algebraic 0.33, text density 0.45. CIE IAL Mathematics 9709 P5.

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CIE IAL · Mathematics · 2016 March

This Mathematics 9709 Paper 5 (Mechanics 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 P5
- 7 questions
- 50 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=a53a2981-7dd2-4f2c-92cb-781406ce05f7)
- [All 9709 P5 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/)

Core finding

**9709/52 March 2016 is a past paper for CIE IAL Mathematics 9709 Paper 5 (Mechanics 2), with 7 questions worth 50 marks.** Its mark-weighted Difficulty Measure is 0.49 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.18 and a mark split of 14.0% Easy, 54.0% Medium and 32.0% Hard. Algebraic complexity averages 0.33; text density and modelling average 0.45. All five measures use 17 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 17 parts carrying 50 part marks. Difficulty tags cover 17 parts, algebraic tags 17 and text-density tags 17. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.49 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.18 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 14.0 / 54.0 / 32.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.33 — 0.20–0.75 · nearer Medium
- **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** | 0.49 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.18 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 14.0% Easy / 54.0% Medium / 32.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.33 | 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 | [1 Motion of a projectile](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/) | 5 | 0.45 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a53a2981-7dd2-4f2c-92cb-781406ce05f7&question_id=4d712e4f-62b4-489e-ae42-4c6e14468c33&source_detail=9709%2F52+March+2016) |
| **Q2** FRQ | [2 Equilibrium of a rigid body](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/) | 5 | 0.35 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a53a2981-7dd2-4f2c-92cb-781406ce05f7&question_id=fa7a7f61-67d2-476b-8f2b-e0a2b91a2d14&source_detail=9709%2F52+March+2016) |
| **Q3** FRQ | [1 Motion of a projectile](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/) | 5 | 0.45 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a53a2981-7dd2-4f2c-92cb-781406ce05f7&question_id=487af4e0-de3e-4943-8449-5a7925b7858f&source_detail=9709%2F52+March+2016) |
| **Q4** FRQ | [2 Equilibrium of a rigid body](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/) | 7 | 0.41 Medium | 0.34 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a53a2981-7dd2-4f2c-92cb-781406ce05f7&question_id=b9cc93b0-4f1a-476d-90da-b3f853765764&source_detail=9709%2F52+March+2016) |
| **Q5** FRQ | [4 Hooke’s law](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/) | 9 | 0.61 Hard | 0.39 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a53a2981-7dd2-4f2c-92cb-781406ce05f7&question_id=f5376069-d68c-41e6-85fb-22f77283a58d&source_detail=9709%2F52+March+2016) |
| **Q6** FRQ | [5 Linear motion under a variable force](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/) | 9 | 0.59 Medium | 0.39 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a53a2981-7dd2-4f2c-92cb-781406ce05f7&question_id=6f91875f-3b79-4690-9d68-e0056ba8328d&source_detail=9709%2F52+March+2016) |
| **Q7** FRQ | [2 Equilibrium of a rigid body](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/) | 10 | 0.49 Medium | 0.40 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a53a2981-7dd2-4f2c-92cb-781406ce05f7&question_id=b08911e3-60fe-4e5c-ab2d-d870c350c81c&source_detail=9709%2F52+March+2016) |

## Topics in this paper

- [1 Motion of a projectile](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/)
- [2 Equilibrium of a rigid body](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/)
- [4 Hooke’s law](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/)
- [5 Linear motion under a variable force](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/)
- [3 Uniform motion in a circle](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/)

## Related papers

- [9709/51](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/2016-october-november-9709-51/) — October/November 2016 — 7 questions · 50 marks — Free
- [9709/52](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/2016-october-november-9709-52/) — October/November 2016 — 7 questions · 50 marks — Free
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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 0.49 from 17 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 0.18, 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, 54.0% Medium and 32.0% 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-p5/2016-march-9709-52/