# 9709/32 May/June 2012

> 9709/32 May/June 2012: 10 questions, 75 marks. Difficulty 0.51, deviation 0.18, algebraic 0.56, text density 0.26. CIE IAL Mathematics 9709 P3.

- Canonical HTML: https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2012-may-june-9709-32/
- Markdown mirror: https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2012-may-june-9709-32/index.md

---

CIE IAL · Mathematics · 2012 May/June

This Mathematics 9709 Paper 3 (Pure Mathematics 3) 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 P3
- 10 questions
- 75 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=31cfdfc4-6524-4424-978c-1c30d6a3915a)
- [All 9709 P3 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/)

Core finding

**9709/32 May/June 2012 is a past paper for CIE IAL Mathematics 9709 Paper 3 (Pure Mathematics 3), with 10 questions worth 75 marks.** Its mark-weighted Difficulty Measure is 0.51 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.18 and a mark split of 10.7% Easy, 48.0% Medium and 41.3% Hard. Algebraic complexity averages 0.56; text density and modelling average 0.26. All five measures use 18 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 18 parts carrying 75 part marks. Difficulty tags cover 18 parts, algebraic tags 18 and text-density tags 18. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.51 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.18 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 10.7 / 48.0 / 41.3 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.56 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.26 — 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** | 0.51 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.18 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 10.7% Easy / 48.0% Medium / 41.3% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.56 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.26 | 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-p3/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=31cfdfc4-6524-4424-978c-1c30d6a3915a&question_id=757f4856-a0c0-4ce4-a818-5789c020dadc&source_detail=9709%2F32+May%2FJune+2012) |
| **Q2** FRQ | [3 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/) | 5 | 0.30 Easy | 0.20 Low | 0.30 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=31cfdfc4-6524-4424-978c-1c30d6a3915a&question_id=30b6b55c-3922-40ad-98ee-ae48a1678427&source_detail=9709%2F32+May%2FJune+2012) |
| **Q3** FRQ | [1 Algebra](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/) | 5 | 0.45 Medium | 0.75 High | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=31cfdfc4-6524-4424-978c-1c30d6a3915a&question_id=a7d67121-0c93-4962-b05e-b3dfdb2bdbd9&source_detail=9709%2F32+May%2FJune+2012) |
| **Q4** FRQ | [3 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/) | 6 | 0.75 Hard | 0.75 High | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=31cfdfc4-6524-4424-978c-1c30d6a3915a&question_id=fc1135fd-3148-41e9-8898-a34cb2910975&source_detail=9709%2F32+May%2FJune+2012) |
| **Q5** FRQ | [8 Differential equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differential-equations/) | 6 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=31cfdfc4-6524-4424-978c-1c30d6a3915a&question_id=ee206a93-7deb-4865-bf07-b6ef6c1bdc24&source_detail=9709%2F32+May%2FJune+2012) |
| **Q6** FRQ | [4 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differentiation/) | 8 | 0.65 Hard | 0.68 High | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=31cfdfc4-6524-4424-978c-1c30d6a3915a&question_id=23b5a7ea-abfc-48db-9326-25238b98e98d&source_detail=9709%2F32+May%2FJune+2012) |
| **Q7** FRQ | [9 Complex numbers](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/) | 8 | 0.29 Easy | 0.29 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=31cfdfc4-6524-4424-978c-1c30d6a3915a&question_id=91505fa1-9c99-412b-ae66-d0e6bfad8185&source_detail=9709%2F32+May%2FJune+2012) |
| **Q8** FRQ | [5 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/) | 10 | 0.60 Medium | 0.63 High | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=31cfdfc4-6524-4424-978c-1c30d6a3915a&question_id=698c2879-fd05-4ca8-8d6c-bf767bf44337&source_detail=9709%2F32+May%2FJune+2012) |
| **Q9** FRQ | [4 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differentiation/) | 11 | 0.61 Hard | 0.64 High | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=31cfdfc4-6524-4424-978c-1c30d6a3915a&question_id=d9fb9254-d25a-4930-a068-67e5fd5e21ac&source_detail=9709%2F32+May%2FJune+2012) |
| **Q10** FRQ | [7 Vectors](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/) | 12 | 0.57 Medium | 0.60 Medium | 0.33 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=31cfdfc4-6524-4424-978c-1c30d6a3915a&question_id=635cf971-0f35-420e-b5ff-b682184dbcf4&source_detail=9709%2F32+May%2FJune+2012) |

## Topics in this paper

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

## Related papers

- [9709/31](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2012-october-november-9709-31/) — October/November 2012 — 10 questions · 75 marks — Free
- [9709/32](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2012-october-november-9709-32/) — October/November 2012 — 10 questions · 75 marks — Free
- [9709/33](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2012-october-november-9709-33/) — October/November 2012 — 10 questions · 75 marks — Free
- [9709/31](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2012-may-june-9709-31/) — May/June 2012 — 10 questions · 75 marks — Free
- [9709/33](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2012-may-june-9709-33/) — May/June 2012 — 10 questions · 75 marks — Free
- [9709/31](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2013-october-november-9709-31/) — October/November 2013 — 10 questions · 75 marks — Free

## 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 0.51 from 18 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 0.18, 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 10.7% Easy, 48.0% Medium and 41.3% 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.

---

Full page with native tables, bar charts and Practice Hub links: https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2012-may-june-9709-32/