# 9709/33 May/June 2017

> 9709/33 May/June 2017: 11 questions, 75 marks. Difficulty 0.36, deviation 0.17, algebraic 0.49, text density 0.25. CIE IAL Mathematics 9709 P3.

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CIE IAL · Mathematics · 2017 May/June

This Mathematics 9709 Paper 3 (Pure Mathematics 3) 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 P3
- 11 questions
- 75 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=d42d00cd-40d1-40a0-9edc-d293b8180f19)
- [All 9709 P3 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/)

Core finding

**9709/33 May/June 2017 is a past paper for CIE IAL Mathematics 9709 Paper 3 (Pure Mathematics 3), with 11 questions worth 75 marks.** Its mark-weighted Difficulty Measure is 0.36 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.17 and a mark split of 42.7% Easy, 45.3% Medium and 12.0% Hard. Algebraic complexity averages 0.49; text density and modelling average 0.25. All five measures use 20 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 20 parts carrying 75 part marks. Difficulty tags cover 20 parts, algebraic tags 20 and text-density tags 20. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.36 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.17 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 42.7 / 45.3 / 12.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.49 — 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** | 0.36 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.17 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 42.7% Easy / 45.3% Medium / 12.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.49 | 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 | [3 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/) | 3 | 0.20 Easy | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d42d00cd-40d1-40a0-9edc-d293b8180f19&question_id=99fa2886-d66f-466f-b8f0-4647c2d100fa&source_detail=9709%2F33+May%2FJune+2017) |
| **Q2** FRQ | [1 Algebra](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/) | 4 | 0.20 Easy | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d42d00cd-40d1-40a0-9edc-d293b8180f19&question_id=f0b37cd8-e780-482c-8814-e1d5cb2578a8&source_detail=9709%2F33+May%2FJune+2017) |
| **Q3** FRQ | [2 Logarithmic and exponential functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/logarithmic-and-exponential-functions/) | 4 | 0.20 Easy | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d42d00cd-40d1-40a0-9edc-d293b8180f19&question_id=d9c2c395-fc16-4eae-8273-7928e6ea7ff5&source_detail=9709%2F33+May%2FJune+2017) |
| **Q4** FRQ | [5 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/) | 4 | 0.20 Easy | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d42d00cd-40d1-40a0-9edc-d293b8180f19&question_id=630582bb-d54a-40b9-898f-988b0788dd5d&source_detail=9709%2F33+May%2FJune+2017) |
| **Q5** FRQ | [4 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differentiation/) | 6 | 0.37 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d42d00cd-40d1-40a0-9edc-d293b8180f19&question_id=2387416c-460f-4c19-873b-55069f8f7766&source_detail=9709%2F33+May%2FJune+2017) |
| **Q6** FRQ | [6 Numerical solution of equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/numerical-solution-of-equations/) | 7 | 0.20 Easy | 0.27 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d42d00cd-40d1-40a0-9edc-d293b8180f19&question_id=628b6512-3247-4a07-b41e-771f8b3f313d&source_detail=9709%2F33+May%2FJune+2017) |
| **Q7** FRQ | [4 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differentiation/) | 8 | 0.23 Easy | 0.20 Low | 0.23 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d42d00cd-40d1-40a0-9edc-d293b8180f19&question_id=e35a058c-750d-4a70-a454-609e716ec43f&source_detail=9709%2F33+May%2FJune+2017) |
| **Q8** FRQ | [8 Differential equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differential-equations/) | 9 | 0.42 Medium | 0.42 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d42d00cd-40d1-40a0-9edc-d293b8180f19&question_id=d740f919-9de8-4b91-be76-3c6bdaac3018&source_detail=9709%2F33+May%2FJune+2017) |
| **Q9** FRQ | [1 Algebra](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/) | 10 | 0.45 Medium | 0.75 High | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d42d00cd-40d1-40a0-9edc-d293b8180f19&question_id=b0476468-7852-4e72-be08-1beb4185361c&source_detail=9709%2F33+May%2FJune+2017) |
| **Q10** FRQ | [7 Vectors](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/) | 10 | 0.57 Medium | 0.60 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d42d00cd-40d1-40a0-9edc-d293b8180f19&question_id=94d6b178-e028-48ba-8460-61489f7e6aee&source_detail=9709%2F33+May%2FJune+2017) |
| **Q11** FRQ | [9 Complex numbers](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/) | 10 | 0.55 Medium | 0.63 High | 0.30 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d42d00cd-40d1-40a0-9edc-d293b8180f19&question_id=bd3af816-6654-40a4-981d-94e844caaf04&source_detail=9709%2F33+May%2FJune+2017) |

## Topics in this paper

- [3 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/)
- [1 Algebra](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/)
- [2 Logarithmic and exponential functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/logarithmic-and-exponential-functions/)
- [5 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/)
- [4 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differentiation/)
- [6 Numerical solution of equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/numerical-solution-of-equations/)
- [8 Differential equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differential-equations/)
- [7 Vectors](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/)
- [9 Complex numbers](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/)

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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 0.36 from 20 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 0.17, 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 42.7% Easy, 45.3% 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.

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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-p3/2017-may-june-9709-33/