# 9709/13 May/June 2011

> 9709/13 May/June 2011: 10 questions, 75 marks. Difficulty 0.41, deviation 0.12, algebraic 0.35, text density 0.31. 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 10 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
- 10 questions
- 75 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=562e3cf1-49d8-4b8f-8e8f-1cabdc4bc125)
- [All 9709 P1 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/)

Core finding

**9709/13 May/June 2011 is a past paper for CIE IAL Mathematics 9709 Paper 1 (Pure Mathematics 1), with 10 questions worth 75 marks.** Its mark-weighted Difficulty Measure is 0.41 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.12 and a mark split of 20.0% Easy, 76.0% Medium and 4.0% Hard. Algebraic complexity averages 0.35; text density and modelling average 0.31. All five measures use 22 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 22 parts carrying 75 part marks. Difficulty tags cover 22 parts, algebraic tags 22 and text-density tags 22. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.41 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.12 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 20.0 / 76.0 / 4.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.35 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.31 — 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** | 0.41 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.12 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 20.0% Easy / 76.0% Medium / 4.0% 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** | 0.31 | 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 | [7 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/) | 5 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=562e3cf1-49d8-4b8f-8e8f-1cabdc4bc125&question_id=59102669-8d20-41c8-8d28-f98234a06f56&source_detail=9709%2F13+May%2FJune+2011) |
| **Q2** FRQ | [1 Quadratics](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/quadratics/) | 5 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=562e3cf1-49d8-4b8f-8e8f-1cabdc4bc125&question_id=25575663-b12a-4f21-a27b-36137c883345&source_detail=9709%2F13+May%2FJune+2011) |
| **Q3** FRQ | [3 Coordinate geometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/) | 5 | 0.45 Medium | 0.45 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=562e3cf1-49d8-4b8f-8e8f-1cabdc4bc125&question_id=a0afe37c-5667-4d32-bbaa-1f661a0729d0&source_detail=9709%2F13+May%2FJune+2011) |
| **Q4** FRQ | [8 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/differentiation/) | 7 | 0.20 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=562e3cf1-49d8-4b8f-8e8f-1cabdc4bc125&question_id=b4ba5d92-8a70-46f6-98ba-eb1f6bbc1d7f&source_detail=9709%2F13+May%2FJune+2011) |
| **Q5** FRQ | [6 Vectors](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/) | 7 | 0.45 Medium | 0.34 Medium | 0.31 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=562e3cf1-49d8-4b8f-8e8f-1cabdc4bc125&question_id=12174dff-bb8a-4090-b06e-3765a7d18314&source_detail=9709%2F13+May%2FJune+2011) |
| **Q6** FRQ | [7 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/) | 8 | 0.45 Medium | 0.45 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=562e3cf1-49d8-4b8f-8e8f-1cabdc4bc125&question_id=b890c0bd-3b6a-437c-af27-2bba4f552f42&source_detail=9709%2F13+May%2FJune+2011) |
| **Q7** FRQ | [4 Circular measure](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/circular-measure/) | 8 | 0.33 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=562e3cf1-49d8-4b8f-8e8f-1cabdc4bc125&question_id=f54aed5b-5d9b-4838-99dd-61602628b6a5&source_detail=9709%2F13+May%2FJune+2011) |
| **Q8** FRQ | [5 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/) | 7 | 0.58 Medium | 0.58 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=562e3cf1-49d8-4b8f-8e8f-1cabdc4bc125&question_id=a6d72193-9cdf-425a-90c3-ebb8dddf9e19&source_detail=9709%2F13+May%2FJune+2011) |
| **Q9** FRQ | [9 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/integration/) | 11 | 0.40 Medium | 0.29 Low | 0.34 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=562e3cf1-49d8-4b8f-8e8f-1cabdc4bc125&question_id=d4463ebf-9de1-4914-b01a-196bd81f19bc&source_detail=9709%2F13+May%2FJune+2011) |
| **Q10** FRQ | [2 Functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/) | 12 | 0.41 Medium | 0.28 Low | 0.26 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=562e3cf1-49d8-4b8f-8e8f-1cabdc4bc125&question_id=d9e2b14b-0ec9-4814-8fcb-e56c530ac862&source_detail=9709%2F13+May%2FJune+2011) |

## Topics in this paper

- [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/)
- [3 Coordinate geometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/)
- [8 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/differentiation/)
- [9 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/integration/)
- [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/)
- [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/)

## Related papers

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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 22 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 0.12, 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 20.0% Easy, 76.0% Medium and 4.0% 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-9709-13/