# 9709/12 May/June 2015

> 9709/12 May/June 2015: 11 questions, 75 marks. Difficulty 0.41, deviation 0.13, algebraic 0.37, text density 0.30. CIE IAL Mathematics 9709 P1.

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CIE IAL · Mathematics · 2015 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=bc3fd100-bc03-4285-978c-b342e0bd902e)
- [All 9709 P1 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/)

Core finding

**9709/12 May/June 2015 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 0.41 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.13 and a mark split of 22.7% Easy, 69.3% Medium and 8.0% Hard. Algebraic complexity averages 0.37; text density and modelling average 0.30. All five measures use 25 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 25 parts carrying 75 part marks. Difficulty tags cover 25 parts, algebraic tags 25 and text-density tags 25. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.41 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.13 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 22.7 / 69.3 / 8.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.37 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.30 — 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** | 0.13 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 22.7% Easy / 69.3% Medium / 8.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.37 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.30 | 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=bc3fd100-bc03-4285-978c-b342e0bd902e&question_id=ab3086a6-8f28-4bc5-9553-938179f4a8b0&source_detail=9709%2F12+May%2FJune+2015) |
| **Q2** FRQ | [4 Circular measure](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/circular-measure/) | 4 | 0.45 Medium | 0.45 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=bc3fd100-bc03-4285-978c-b342e0bd902e&question_id=6fd389bb-6733-4493-a39c-44577f1f6e67&source_detail=9709%2F12+May%2FJune+2015) |
| **Q3** FRQ | [7 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/) | 5 | 0.30 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=bc3fd100-bc03-4285-978c-b342e0bd902e&question_id=dce4bd92-e995-4e14-bdb3-79166ad3e4fe&source_detail=9709%2F12+May%2FJune+2015) |
| **Q4** FRQ | [8 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/differentiation/) | 5 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=bc3fd100-bc03-4285-978c-b342e0bd902e&question_id=314f0702-401a-4eb5-af02-31d01e3f3c7e&source_detail=9709%2F12+May%2FJune+2015) |
| **Q5** FRQ | [5 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/) | 5 | 0.40 Medium | 0.40 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=bc3fd100-bc03-4285-978c-b342e0bd902e&question_id=30ba3672-cf70-4a84-ac01-36ecc5179a1a&source_detail=9709%2F12+May%2FJune+2015) |
| **Q6** FRQ | [5 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/) | 6 | 0.33 Medium | 0.33 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=bc3fd100-bc03-4285-978c-b342e0bd902e&question_id=7c0b2ea0-b79d-431d-9db0-ccb81e46973e&source_detail=9709%2F12+May%2FJune+2015) |
| **Q7** FRQ | [3 Coordinate geometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/) | 7 | 0.45 Medium | 0.31 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=bc3fd100-bc03-4285-978c-b342e0bd902e&question_id=52dd61ba-ca7a-4ad9-9059-e4513813b23e&source_detail=9709%2F12+May%2FJune+2015) |
| **Q8** FRQ | [7 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/) | 9 | 0.39 Medium | 0.39 Medium | 0.39 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=bc3fd100-bc03-4285-978c-b342e0bd902e&question_id=4af613df-c35a-49bb-ac85-7fe36439fb36&source_detail=9709%2F12+May%2FJune+2015) |
| **Q9** FRQ | [6 Vectors](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/) | 9 | 0.42 Medium | 0.42 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=bc3fd100-bc03-4285-978c-b342e0bd902e&question_id=a362cc39-8ee5-4eef-82cf-a4a0b7b091fe&source_detail=9709%2F12+May%2FJune+2015) |
| **Q10** FRQ | [9 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/integration/) | 10 | 0.60 Medium | 0.45 Medium | 0.35 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=bc3fd100-bc03-4285-978c-b342e0bd902e&question_id=7a024be2-29bd-4669-bfb0-08bda32f5e30&source_detail=9709%2F12+May%2FJune+2015) |
| **Q11** FRQ | [1 Quadratics](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/quadratics/) | 12 | 0.37 Medium | 0.33 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=bc3fd100-bc03-4285-978c-b342e0bd902e&question_id=3d9e90f2-f4bb-4498-bba4-d7e43cbcfd6e&source_detail=9709%2F12+May%2FJune+2015) |

## Topics in this paper

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

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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 25 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 0.13, 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, 69.3% Medium and 8.0% 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-p1/2015-may-june-9709-12/