# 9709/21 October/November 2015

> 9709/21 October/November 2015: 7 questions, 50 marks. Difficulty 0.42, deviation 0.13, algebraic 0.43, text density 0.25. CIE IAL Mathematics 9709 P2.

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CIE IAL · Mathematics · 2015 October/November

This Mathematics 9709 Paper 2 (Pure Mathematics 2) 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 P2
- 7 questions
- 50 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=35410b08-3d3a-4302-a237-69424e1052b5)
- [All 9709 P2 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/)

Core finding

**9709/21 October/November 2015 is a past paper for CIE IAL Mathematics 9709 Paper 2 (Pure Mathematics 2), with 7 questions worth 50 marks.** Its mark-weighted Difficulty Measure is 0.42 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.13 and a mark split of 18.0% Easy, 76.0% Medium and 6.0% Hard. Algebraic complexity averages 0.43; text density and modelling average 0.25. 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**: 0.42 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.13 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 18.0 / 76.0 / 6.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.43 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.25 — 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** | 0.13 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 18.0% Easy / 76.0% Medium / 6.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.43 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.25 | 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 Logarithmic and exponential functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/logarithmic-and-exponential-functions/) | 4 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=35410b08-3d3a-4302-a237-69424e1052b5&question_id=892f0a2c-fdd5-4774-8817-fd4aefbd9b69&source_detail=9709%2F21+October%2FNovember+2015) |
| **Q2** FRQ | [4 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/differentiation/) | 5 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=35410b08-3d3a-4302-a237-69424e1052b5&question_id=2f922b59-7334-4505-a5ac-f427fe38eed9&source_detail=9709%2F21+October%2FNovember+2015) |
| **Q3** FRQ | [3 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/trigonometry/) | 7 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=35410b08-3d3a-4302-a237-69424e1052b5&question_id=9d5b9422-b2d4-4109-bad7-e18b657f2f12&source_detail=9709%2F21+October%2FNovember+2015) |
| **Q4** FRQ | [6 Numerical solution of equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/numerical-solution-of-equations/) | 7 | 0.27 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=35410b08-3d3a-4302-a237-69424e1052b5&question_id=c81c987f-8452-499d-91d3-602ea6a4ca0f&source_detail=9709%2F21+October%2FNovember+2015) |
| **Q5** FRQ | [5 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/integration/) | 7 | 0.31 Easy | 0.31 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=35410b08-3d3a-4302-a237-69424e1052b5&question_id=68175a57-f9dc-45ee-ba1b-abef304b73b8&source_detail=9709%2F21+October%2FNovember+2015) |
| **Q6** FRQ | [1 Algebra](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/algebra/) | 9 | 0.55 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=35410b08-3d3a-4302-a237-69424e1052b5&question_id=90b557cd-06a5-47ee-9cf8-6734151f9db0&source_detail=9709%2F21+October%2FNovember+2015) |
| **Q7** FRQ | [4 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/differentiation/) | 11 | 0.45 Medium | 0.59 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=35410b08-3d3a-4302-a237-69424e1052b5&question_id=62fc5291-eb52-4143-b5e9-7d5dff7a611a&source_detail=9709%2F21+October%2FNovember+2015) |

## Topics in this paper

- [2 Logarithmic and exponential functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/logarithmic-and-exponential-functions/)
- [4 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/differentiation/)
- [3 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/trigonometry/)
- [6 Numerical solution of equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/numerical-solution-of-equations/)
- [5 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/integration/)
- [1 Algebra](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/algebra/)

## 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 0.42 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 0.13, 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 18.0% Easy, 76.0% Medium and 6.0% 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-p2/2015-october-november-9709-21/