# 9709/52 October/November 2011

> 9709/52 October/November 2011: 6 questions, 50 marks. Difficulty 0.46, deviation 0.15, algebraic 0.41, text density 0.54. CIE IAL Mathematics 9709 P5.

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CIE IAL · Mathematics · 2011 October/November

This Mathematics 9709 Paper 5 (Mechanics 2) paper contains 6 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
- 6 questions
- 50 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=87777a38-1f2e-4c73-a1f9-e7fb7d564fa9)
- [All 9709 P5 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/)

Core finding

**9709/52 October/November 2011 is a past paper for CIE IAL Mathematics 9709 Paper 5 (Mechanics 2), with 6 questions worth 50 marks.** Its mark-weighted Difficulty Measure is 0.46 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.15 and a mark split of 12.0% Easy, 66.0% Medium and 22.0% Hard. Algebraic complexity averages 0.41; text density and modelling average 0.54. All five measures use 14 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 14 parts carrying 50 part marks. Difficulty tags cover 14 parts, algebraic tags 14 and text-density tags 14. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.46 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.15 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 12.0 / 66.0 / 22.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.41 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.54 — 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** | 0.15 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 12.0% Easy / 66.0% Medium / 22.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.41 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.54 | 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 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=87777a38-1f2e-4c73-a1f9-e7fb7d564fa9&question_id=d50e6a21-f9d2-459f-aeb9-aca542878f35&source_detail=9709%2F52+October%2FNovember+2011) |
| **Q2** FRQ | [1 Motion of a projectile](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/) | 7 | 0.45 Medium | 0.34 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=87777a38-1f2e-4c73-a1f9-e7fb7d564fa9&question_id=26e9f860-c1fe-4a81-8671-15317bc2e11f&source_detail=9709%2F52+October%2FNovember+2011) |
| **Q3** FRQ | [4 Hooke’s law](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/) | 8 | 0.39 Medium | 0.39 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=87777a38-1f2e-4c73-a1f9-e7fb7d564fa9&question_id=820958db-4514-4d98-bffb-e95890ffee0f&source_detail=9709%2F52+October%2FNovember+2011) |
| **Q4** FRQ | [2 Equilibrium of a rigid body](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/) | 9 | 0.52 Medium | 0.51 Medium | 0.75 High | [Go to Practice Hub](https://www.examsci.com/practice?set_id=87777a38-1f2e-4c73-a1f9-e7fb7d564fa9&question_id=16e0fa7e-1578-466e-a55b-be3ff1b6a9c8&source_detail=9709%2F52+October%2FNovember+2011) |
| **Q5** FRQ | [5 Linear motion under a variable force](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/) | 10 | 0.45 Medium | 0.45 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=87777a38-1f2e-4c73-a1f9-e7fb7d564fa9&question_id=db5ad87d-e739-4214-a679-1244129e75fb&source_detail=9709%2F52+October%2FNovember+2011) |
| **Q6** FRQ | [3 Uniform motion in a circle](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/) | 11 | 0.58 Medium | 0.45 Medium | 0.61 High | [Go to Practice Hub](https://www.examsci.com/practice?set_id=87777a38-1f2e-4c73-a1f9-e7fb7d564fa9&question_id=e31e1a49-48bf-443b-ba2e-133f2f910ec7&source_detail=9709%2F52+October%2FNovember+2011) |

## Topics in this paper

- [2 Equilibrium of a rigid body](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/)
- [1 Motion of a projectile](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-p5/2011-october-november-9709-51/) — October/November 2011 — 6 questions · 50 marks — Free
- [9709/53](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/2011-october-november-9709-53/) — October/November 2011 — 7 questions · 50 marks — Free
- [9709/51](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/2011-may-june-9709-51/) — May/June 2011 — 7 questions · 50 marks — Free
- [9709/52](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/2011-may-june-9709-52/) — May/June 2011 — 6 questions · 50 marks — Free
- [9709/53](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/2011-may-june-9709-53/) — May/June 2011 — 7 questions · 50 marks — Free
- [9709/51](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/2012-october-november-9709-51/) — October/November 2012 — 7 questions · 50 marks — Free

## 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 14 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 0.15, 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 12.0% Easy, 66.0% Medium and 22.0% 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-p5/2011-october-november-9709-52/