# 9709/33 May/June 2012

> 9709/33 May/June 2012: 10 questions, 75 marks. Difficulty 0.40, deviation 0.14, algebraic 0.51, text density 0.25. CIE IAL Mathematics 9709 P3.

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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=de827fc6-44ab-4de8-9ad4-66ec852f59b5)
- [All 9709 P3 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/)

Core finding

**9709/33 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 0.40 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.14 and a mark split of 26.7% Easy, 65.3% Medium and 8.0% Hard. Algebraic complexity averages 0.51; 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**: 0.40 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.14 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 26.7 / 65.3 / 8.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.51 — 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** | 0.40 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.14 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 26.7% Easy / 65.3% Medium / 8.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.51 | 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 | [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=de827fc6-44ab-4de8-9ad4-66ec852f59b5&question_id=f5ebb4c4-234d-4fb5-befd-09e62ef3e1f5&source_detail=9709%2F33+May%2FJune+2012) |
| **Q2** 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=de827fc6-44ab-4de8-9ad4-66ec852f59b5&question_id=29f6c0ea-4e9f-4c25-8308-36b7bd27f655&source_detail=9709%2F33+May%2FJune+2012) |
| **Q3** FRQ | [3 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/) | 5 | 0.45 Medium | 0.75 High | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=de827fc6-44ab-4de8-9ad4-66ec852f59b5&question_id=6b8435e4-9105-4598-a41b-9fdc3e520297&source_detail=9709%2F33+May%2FJune+2012) |
| **Q4** FRQ | [4 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differentiation/) | 6 | 0.20 Easy | 0.37 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=de827fc6-44ab-4de8-9ad4-66ec852f59b5&question_id=2235264c-10f2-42df-9b5a-7f6ccca23a43&source_detail=9709%2F33+May%2FJune+2012) |
| **Q5** FRQ | [8 Differential equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differential-equations/) | 8 | 0.45 Medium | 0.39 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=de827fc6-44ab-4de8-9ad4-66ec852f59b5&question_id=ea021653-8b69-4faa-988d-953e5a333907&source_detail=9709%2F33+May%2FJune+2012) |
| **Q6** FRQ | [3 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/) | 8 | 0.33 Medium | 0.48 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=de827fc6-44ab-4de8-9ad4-66ec852f59b5&question_id=ff582db0-0b5e-4beb-bdae-bfc9b425215e&source_detail=9709%2F33+May%2FJune+2012) |
| **Q7** FRQ | [5 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/) | 9 | 0.62 Hard | 0.57 Medium | 0.37 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=de827fc6-44ab-4de8-9ad4-66ec852f59b5&question_id=edd44b5c-d694-4adb-986b-baf3b37e25c7&source_detail=9709%2F33+May%2FJune+2012) |
| **Q8** 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=de827fc6-44ab-4de8-9ad4-66ec852f59b5&question_id=8f14c4ed-0313-49f6-89f3-b3ea433137a9&source_detail=9709%2F33+May%2FJune+2012) |
| **Q9** FRQ | [7 Vectors](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/) | 10 | 0.40 Medium | 0.40 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=de827fc6-44ab-4de8-9ad4-66ec852f59b5&question_id=87d7871b-f308-4045-abb8-bbb3a2d832ce&source_detail=9709%2F33+May%2FJune+2012) |
| **Q10** FRQ | [9 Complex numbers](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/) | 11 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=de827fc6-44ab-4de8-9ad4-66ec852f59b5&question_id=91abad35-e823-4413-95a6-78ecd51a8860&source_detail=9709%2F33+May%2FJune+2012) |

## Topics in this paper

- [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/)
- [3 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/)
- [4 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differentiation/)
- [8 Differential equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differential-equations/)
- [5 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/)
- [6 Numerical solution of equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/numerical-solution-of-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 0.40 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 0.14, 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 26.7% Easy, 65.3% 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-p3/2012-may-june-9709-33/