# 9709/41 October/November 2020

> 9709/41 October/November 2020: 7 questions, 50 marks. Difficulty 0.49, deviation 0.17, algebraic 0.40, text density 0.58. CIE IAL Mathematics 9709 P4.

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CIE IAL · Mathematics · 2020 October/November

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=6dc2ecb2-30ba-49da-82b7-aae79b7b8115)
- [All 9709 P4 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/)

Core finding

**9709/41 October/November 2020 is a past paper for CIE IAL Mathematics 9709 Paper 4 (Mechanics), with 7 questions worth 50 marks.** Its mark-weighted Difficulty Measure is 0.49 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.17 and a mark split of 14.0% Easy, 54.0% Medium and 32.0% Hard. Algebraic complexity averages 0.40; text density and modelling average 0.58. All five measures use 12 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 12 parts carrying 50 part marks. Difficulty tags cover 12 parts, algebraic tags 12 and text-density tags 12. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.49 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.17 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 14.0 / 54.0 / 32.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.40 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.58 — 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** | 0.17 | √(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** | 0.40 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.58 | 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 | [4.3 Momentum](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/momentum/) | 5 | 0.20 Easy | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6dc2ecb2-30ba-49da-82b7-aae79b7b8115&question_id=994049f4-fb05-49c3-a4d7-fc4c6b303a46&source_detail=9709%2F41+October%2FNovember+2020) |
| **Q2** FRQ | [4.5 Energy, work and power](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/energy-work-and-power/) | 5 | 0.35 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6dc2ecb2-30ba-49da-82b7-aae79b7b8115&question_id=0f92b5e8-27af-4d69-9ca6-aa8b839ea5a8&source_detail=9709%2F41+October%2FNovember+2020) |
| **Q3** FRQ | [4.1 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=6dc2ecb2-30ba-49da-82b7-aae79b7b8115&question_id=956faf1c-d116-42d5-a98f-4b2a222c5270&source_detail=9709%2F41+October%2FNovember+2020) |
| **Q4** FRQ | [4.2 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=6dc2ecb2-30ba-49da-82b7-aae79b7b8115&question_id=d558b54d-d62e-4cc5-97c8-b6fa11719d11&source_detail=9709%2F41+October%2FNovember+2020) |
| **Q5** FRQ | [4.4 Newton’s laws of motion](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/newton-s-laws-of-motion/) | 7 | 0.58 Medium | 0.45 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6dc2ecb2-30ba-49da-82b7-aae79b7b8115&question_id=21b3dab0-82da-4244-a98b-bb61860fb8ff&source_detail=9709%2F41+October%2FNovember+2020) |
| **Q6** FRQ | [4.5 Energy, work and power](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/energy-work-and-power/) | 9 | 0.59 Medium | 0.45 Medium | 0.75 High | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6dc2ecb2-30ba-49da-82b7-aae79b7b8115&question_id=e66d15a9-e6bd-4063-8091-711a3599de15&source_detail=9709%2F41+October%2FNovember+2020) |
| **Q7** FRQ | [4.1 Forces and equilibrium](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/forces-and-equilibrium/) | 12 | 0.61 Hard | 0.45 Medium | 0.75 High | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6dc2ecb2-30ba-49da-82b7-aae79b7b8115&question_id=75510894-3c0d-4ace-8370-540e82a8366e&source_detail=9709%2F41+October%2FNovember+2020) |

## Topics in this paper

- [4.3 Momentum](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/momentum/)
- [4.5 Energy, work and power](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/energy-work-and-power/)
- [4.4 Newton’s laws of motion](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/newton-s-laws-of-motion/)
- [4.1 Forces and equilibrium](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/forces-and-equilibrium/)
- [4.2 Kinematics of motion in a straight line](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/kinematics-of-motion-in-a-straight-line/)

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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 12 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 0.17, 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-p4/2020-october-november-9709-41/