# 9709/12 May/June 2011

> 9709/12 May/June 2011: 11 questions, 75 marks. Difficulty 0.42, deviation 0.16, algebraic 0.36, text density 0.27. CIE IAL Mathematics 9709 P1.

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CIE IAL · Mathematics · 2011 May/June

This Mathematics 9709 Paper 1 (Pure Mathematics 1) paper contains 11 questions worth 75 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 P1
- 11 questions
- 75 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=6183a128-bc5b-4c06-9484-0ce2bf8ceebc)
- [All 9709 P1 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/)

Core finding

**9709/12 May/June 2011 is a past paper for CIE IAL Mathematics 9709 Paper 1 (Pure Mathematics 1), with 11 questions worth 75 marks.** Its mark-weighted Difficulty Measure is 0.42 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.16 and a mark split of 22.7% Easy, 61.3% Medium and 16.0% Hard. Algebraic complexity averages 0.36; text density and modelling average 0.27. All five measures use 24 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 24 parts carrying 75 part marks. Difficulty tags cover 24 parts, algebraic tags 24 and text-density tags 24. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.42 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.16 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 22.7 / 61.3 / 16.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.36 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.27 — 0.20–0.75 · nearer Low

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** | 0.42 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.16 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 22.7% Easy / 61.3% Medium / 16.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.36 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.27 | 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 | [9 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/integration/) | 3 | 0.20 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6183a128-bc5b-4c06-9484-0ce2bf8ceebc&question_id=229b61aa-d749-4f8e-b369-280194878198&source_detail=9709%2F12+May%2FJune+2011) |
| **Q2** FRQ | [7 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/) | 5 | 0.30 Easy | 0.30 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6183a128-bc5b-4c06-9484-0ce2bf8ceebc&question_id=285c566f-c6fa-40a6-b349-4aead836a3ab&source_detail=9709%2F12+May%2FJune+2011) |
| **Q3** FRQ | [1 Quadratics](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/quadratics/) | 5 | 0.35 Medium | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6183a128-bc5b-4c06-9484-0ce2bf8ceebc&question_id=a4fe655b-a28d-421b-9cd7-38c9ce2c1a68&source_detail=9709%2F12+May%2FJune+2011) |
| **Q4** FRQ | [8 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/differentiation/) | 6 | 0.45 Medium | 0.37 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6183a128-bc5b-4c06-9484-0ce2bf8ceebc&question_id=75e860a9-1ffc-49b7-bef2-abc73475bedd&source_detail=9709%2F12+May%2FJune+2011) |
| **Q5** FRQ | [5 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/) | 6 | 0.45 Medium | 0.48 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6183a128-bc5b-4c06-9484-0ce2bf8ceebc&question_id=99dab179-58dd-4fa0-9a4b-993dc1aff023&source_detail=9709%2F12+May%2FJune+2011) |
| **Q6** FRQ | [2 Functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/) | 5 | 0.35 Medium | 0.35 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6183a128-bc5b-4c06-9484-0ce2bf8ceebc&question_id=b668a7d7-b0cb-4d49-9015-d27a3de2339c&source_detail=9709%2F12+May%2FJune+2011) |
| **Q7** FRQ | [3 Coordinate geometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/) | 7 | 0.38 Medium | 0.38 Medium | 0.38 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6183a128-bc5b-4c06-9484-0ce2bf8ceebc&question_id=27194c03-7aab-49d5-a653-daea74bc7ee5&source_detail=9709%2F12+May%2FJune+2011) |
| **Q8** FRQ | [6 Vectors](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/) | 8 | 0.39 Medium | 0.39 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6183a128-bc5b-4c06-9484-0ce2bf8ceebc&question_id=f73af264-07f4-4be5-8a40-b2e6d70be12e&source_detail=9709%2F12+May%2FJune+2011) |
| **Q9** FRQ | [2 Functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/) | 8 | 0.42 Medium | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6183a128-bc5b-4c06-9484-0ce2bf8ceebc&question_id=7d2f29ac-7f78-4488-981b-a6848ed839bc&source_detail=9709%2F12+May%2FJune+2011) |
| **Q10** FRQ | [4 Circular measure](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/circular-measure/) | 11 | 0.52 Medium | 0.40 Medium | 0.57 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6183a128-bc5b-4c06-9484-0ce2bf8ceebc&question_id=6eda2046-8f25-4af5-b38b-c162075f0a8f&source_detail=9709%2F12+May%2FJune+2011) |
| **Q11** FRQ | [8 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/differentiation/) | 11 | 0.58 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6183a128-bc5b-4c06-9484-0ce2bf8ceebc&question_id=18e8a7fa-e36c-479f-a23f-325286ca88bd&source_detail=9709%2F12+May%2FJune+2011) |

## Topics in this paper

- [9 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/integration/)
- [7 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/)
- [1 Quadratics](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/quadratics/)
- [8 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/differentiation/)
- [3 Coordinate geometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/)
- [5 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/)
- [2 Functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/)
- [6 Vectors](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/)
- [4 Circular measure](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/circular-measure/)

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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 0.42 from 24 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 0.16, 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 22.7% Easy, 61.3% Medium and 16.0% 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-p1/2011-may-june-9709-12/