# 9709/42 May/June 2015

> 9709/42 May/June 2015: 7 questions, 50 marks. Difficulty 0.41, deviation 0.15, algebraic 0.33, text density 0.49. CIE IAL Mathematics 9709 P4.

- Canonical HTML: https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/2015-may-june-9709-42/
- Markdown mirror: https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/2015-may-june-9709-42/index.md

---

CIE IAL · Mathematics · 2015 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=73e787c0-492e-4785-8715-bfc523ff1955)
- [All 9709 P4 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/)

Core finding

**9709/42 May/June 2015 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 0.15 and a mark split of 26.0% Easy, 62.0% Medium and 12.0% Hard. Algebraic complexity averages 0.33; text density and modelling average 0.49. All five measures use 16 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 16 parts carrying 50 part marks. Difficulty tags cover 16 parts, algebraic tags 16 and text-density tags 16. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.41 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.15 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 26.0 / 62.0 / 12.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.33 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.49 — 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** | 0.15 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 26.0% Easy / 62.0% Medium / 12.0% 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** | 0.49 | 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 Kinematics of motion in a straight line](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/kinematics-of-motion-in-a-straight-line/) | 4 | 0.20 Easy | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=73e787c0-492e-4785-8715-bfc523ff1955&question_id=a829791c-05d0-415c-b69b-851cb260cfa8&source_detail=9709%2F42+May%2FJune+2015) |
| **Q2** FRQ | [4 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=73e787c0-492e-4785-8715-bfc523ff1955&question_id=92b4e89e-1bb9-46f4-a839-0f81171ee94a&source_detail=9709%2F42+May%2FJune+2015) |
| **Q3** FRQ | [4 Energy, work and power](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/energy-work-and-power/) | 5 | 0.30 Easy | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=73e787c0-492e-4785-8715-bfc523ff1955&question_id=851894fe-4b1e-49ae-a609-0ce0bcd167ee&source_detail=9709%2F42+May%2FJune+2015) |
| **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/) | 7 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=73e787c0-492e-4785-8715-bfc523ff1955&question_id=62920047-9c16-4dc1-81b3-c19b24321aa7&source_detail=9709%2F42+May%2FJune+2015) |
| **Q5** 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 | 0.37 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=73e787c0-492e-4785-8715-bfc523ff1955&question_id=da5576fb-6b19-4c58-b5a2-f6ce7f1eb2e2&source_detail=9709%2F42+May%2FJune+2015) |
| **Q6** 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/) | 11 | 0.52 Medium | 0.34 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=73e787c0-492e-4785-8715-bfc523ff1955&question_id=f2673014-b945-48cc-9ac3-5da81fab2118&source_detail=9709%2F42+May%2FJune+2015) |
| **Q7** FRQ | [1 Forces and equilibrium](https://www.examsci.com/topics/cie-ial/mathematics/9709-p4/forces-and-equilibrium/) | 12 | 0.45 Medium | 0.45 Medium | 0.75 High | [Go to Practice Hub](https://www.examsci.com/practice?set_id=73e787c0-492e-4785-8715-bfc523ff1955&question_id=6ee51772-b049-4a52-9865-e745b55d36cc&source_detail=9709%2F42+May%2FJune+2015) |

## Topics in this paper

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

## Related papers

- [9709/41](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/2015-october-november-9709-41/) — October/November 2015 — 7 questions · 50 marks — Free
- [9709/42](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/2015-october-november-9709-42/) — October/November 2015 — 7 questions · 50 marks — Free
- [9709/43](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/2015-october-november-9709-43/) — October/November 2015 — 7 questions · 50 marks — Free
- [9709/41](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/2015-may-june-9709-41/) — May/June 2015 — 7 questions · 50 marks — Free
- [9709/43](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/2015-may-june-9709-43/) — May/June 2015 — 7 questions · 50 marks — Free
- [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

## 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 16 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 26.0% Easy, 62.0% Medium and 12.0% 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.

---

Full page with native tables, bar charts and Practice Hub links: https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p4/2015-may-june-9709-42/