# 9709/41 May/June 2014

> 9709/41 May/June 2014: 7 questions, 50 marks. Difficulty 0.41, deviation 0.09, algebraic 0.35, text density 0.56. CIE IAL Mathematics 9709 P4.

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CIE IAL · Mathematics · 2014 May/June

This Mathematics 9709 Paper 4 (Mechanics) 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 P4
- 7 questions
- 50 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=a917008a-68f9-4e95-b94e-acd0260d12f1)
- [All 9709 P4 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/)

Core finding

**9709/41 May/June 2014 is a past paper for CIE IAL Mathematics 9709 Paper 4 (Mechanics), with 7 questions worth 50 marks.** Its mark-weighted Difficulty Measure is 0.41 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.09 and a mark split of 16.0% Easy, 84.0% Medium and 0.0% Hard. Algebraic complexity averages 0.35; text density and modelling average 0.56. All five measures use 13 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 13 parts carrying 50 part marks. Difficulty tags cover 13 parts, algebraic tags 13 and text-density tags 13. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.41 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.09 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 16.0 / 84.0 / 0.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.35 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.56 — 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** | 0.41 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.09 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 16.0% Easy / 84.0% Medium / 0.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.35 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.56 | 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 | [4 Energy, work and power](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/energy-work-and-power/) | 3 | 0.20 Easy | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a917008a-68f9-4e95-b94e-acd0260d12f1&question_id=8a42ce3d-5364-40ae-a088-87d6b0415d81&source_detail=9709%2F41+May%2FJune+2014) |
| **Q2** FRQ | [1 Forces and equilibrium](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/forces-and-equilibrium/) | 4 | 0.33 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a917008a-68f9-4e95-b94e-acd0260d12f1&question_id=f002f019-089c-46aa-b172-5862067763b4&source_detail=9709%2F41+May%2FJune+2014) |
| **Q3** FRQ | [1 Forces and equilibrium](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/forces-and-equilibrium/) | 6 | 0.45 Medium | 0.45 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a917008a-68f9-4e95-b94e-acd0260d12f1&question_id=557b44e5-a39a-4a29-b110-14aaa248697f&source_detail=9709%2F41+May%2FJune+2014) |
| **Q4** FRQ | [2 Kinematics of motion in a straight line](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/kinematics-of-motion-in-a-straight-line/) | 6 | 0.45 Medium | 0.45 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a917008a-68f9-4e95-b94e-acd0260d12f1&question_id=9cc0532b-a794-4c04-8146-5da2dace9cf5&source_detail=9709%2F41+May%2FJune+2014) |
| **Q5** FRQ | [4 Energy, work and power](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/energy-work-and-power/) | 8 | 0.45 Medium | 0.45 Medium | 0.75 High | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a917008a-68f9-4e95-b94e-acd0260d12f1&question_id=4b36a908-3fc4-42dc-a9c8-634baec00788&source_detail=9709%2F41+May%2FJune+2014) |
| **Q6** FRQ | [3 Newton’s laws of motion](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/newton-s-laws-of-motion/) | 10 | 0.45 Medium | 0.20 Low | 0.75 High | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a917008a-68f9-4e95-b94e-acd0260d12f1&question_id=f04fed5d-7d84-4543-96f4-5cea5e92776b&source_detail=9709%2F41+May%2FJune+2014) |
| **Q7** FRQ | [2 Kinematics of motion in a straight line](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/kinematics-of-motion-in-a-straight-line/) | 13 | 0.39 Medium | 0.39 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a917008a-68f9-4e95-b94e-acd0260d12f1&question_id=3aad4f9a-bb13-4f6a-87ac-9181d1f73482&source_detail=9709%2F41+May%2FJune+2014) |

## Topics in this paper

- [4 Energy, work and power](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/energy-work-and-power/)
- [1 Forces and equilibrium](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/forces-and-equilibrium/)
- [2 Kinematics of motion in a straight line](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/kinematics-of-motion-in-a-straight-line/)
- [3 Newton’s laws of motion](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/newton-s-laws-of-motion/)

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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 0.41 from 13 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 0.09, 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 16.0% Easy, 84.0% 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-p4/2014-may-june-9709-41/