# 9709/42 October/November 2016

> 9709/42 October/November 2016: 7 questions, 50 marks. Difficulty 0.39, deviation 0.23, algebraic 0.38, text density 0.52. CIE IAL Mathematics 9709 P4.

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CIE IAL · Mathematics · 2016 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=c6646917-526e-446b-b2d2-a91ccb57ac37)
- [All 9709 P4 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/)

Core finding

**9709/42 October/November 2016 is a past paper for CIE IAL Mathematics 9709 Paper 4 (Mechanics), with 7 questions worth 50 marks.** Its mark-weighted Difficulty Measure is 0.39 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.23 and a mark split of 46.0% Easy, 20.0% Medium and 34.0% Hard. Algebraic complexity averages 0.38; text density and modelling average 0.52. All five measures use 15 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 15 parts carrying 50 part marks. Difficulty tags cover 15 parts, algebraic tags 15 and text-density tags 15. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.39 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.23 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 46.0 / 20.0 / 34.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.38 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.52 — 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** | 0.39 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.23 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 46.0% Easy / 20.0% Medium / 34.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.38 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.52 | 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 | [3 Newton’s laws of motion](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/newton-s-laws-of-motion/) | 6 | 0.20 Easy | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c6646917-526e-446b-b2d2-a91ccb57ac37&question_id=fcd2029c-6ae9-42be-9ccb-2738d41f25be&source_detail=9709%2F42+October%2FNovember+2016) |
| **Q2** 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 | 0.20 Easy | 0.37 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c6646917-526e-446b-b2d2-a91ccb57ac37&question_id=950c6fc9-f147-4547-be8e-11170fbce1a4&source_detail=9709%2F42+October%2FNovember+2016) |
| **Q3** FRQ | [1 Forces and equilibrium](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/forces-and-equilibrium/) | 6 | 0.37 Medium | 0.37 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c6646917-526e-446b-b2d2-a91ccb57ac37&question_id=075a7571-a7dd-49d2-9e18-c431fe1babcd&source_detail=9709%2F42+October%2FNovember+2016) |
| **Q4** FRQ | [4 Energy, work and power](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/energy-work-and-power/) | 6 | 0.33 Medium | 0.33 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c6646917-526e-446b-b2d2-a91ccb57ac37&question_id=8532e75a-c070-4b7c-a25c-2d71e8f977e7&source_detail=9709%2F42+October%2FNovember+2016) |
| **Q5** FRQ | [1 Forces and equilibrium](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/forces-and-equilibrium/) | 6 | 0.75 Hard | 0.75 High | 0.75 High | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c6646917-526e-446b-b2d2-a91ccb57ac37&question_id=dff0a31e-ae87-45cd-a264-d688dc1cb7da&source_detail=9709%2F42+October%2FNovember+2016) |
| **Q6** FRQ | [4 Energy, work and power](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/energy-work-and-power/) | 8 | 0.49 Medium | 0.36 Medium | 0.64 High | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c6646917-526e-446b-b2d2-a91ccb57ac37&question_id=516563ea-ca19-41cc-b918-61091c69c5a8&source_detail=9709%2F42+October%2FNovember+2016) |
| **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/) | 12 | 0.49 Medium | 0.33 Medium | 0.60 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c6646917-526e-446b-b2d2-a91ccb57ac37&question_id=187c4df6-cbae-4694-a43c-a4d0ab466731&source_detail=9709%2F42+October%2FNovember+2016) |

## Topics in this paper

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

## Related papers

- [9709/41](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/2016-october-november-9709-41/) — October/November 2016 — 7 questions · 50 marks — Free
- [9709/43](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/2016-october-november-9709-43/) — October/November 2016 — 7 questions · 50 marks — Free
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- [9709/42](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/2016-may-june-9709-42/) — May/June 2016 — 7 questions · 50 marks — Free
- [9709/43](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/2016-may-june-9709-43/) — May/June 2016 — 7 questions · 50 marks — Free
- [9709/42](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/2016-march-9709-42/) — March 2016 — 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 0.39 from 15 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 0.23, 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 46.0% Easy, 20.0% Medium and 34.0% 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-p4/2016-october-november-9709-42/