# 9709/12 May/June 2020

> 9709/12 May/June 2020: 11 questions, 75 marks. Difficulty 0.34, deviation 0.12, algebraic 0.29, text density 0.27. CIE IAL Mathematics 9709 P1.

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CIE IAL · Mathematics · 2020 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=9275aff7-1c76-429c-8092-211f890344a0)
- [All 9709 P1 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/)

Core finding

**9709/12 May/June 2020 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 0.34 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.12 and a mark split of 45.3% Easy, 54.7% Medium and 0.0% Hard. Algebraic complexity averages 0.29; text density and modelling average 0.27. All five measures use 26 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 26 parts carrying 75 part marks. Difficulty tags cover 26 parts, algebraic tags 26 and text-density tags 26. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.34 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.12 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 45.3 / 54.7 / 0.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.29 — 0.20–0.75 · nearer Low
- **Text Density and Modelling Measure**: 0.27 — 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** | 0.34 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.12 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 45.3% Easy / 54.7% Medium / 0.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.29 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.27 | 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 | [1.6 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/) | 5 | 0.35 Medium | 0.35 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9275aff7-1c76-429c-8092-211f890344a0&question_id=2b048936-fd1e-4df9-b5f3-fa89fb18c583&source_detail=9709%2F12+May%2FJune+2020) |
| **Q2** FRQ | [1.5 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/) | 5 | 0.20 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9275aff7-1c76-429c-8092-211f890344a0&question_id=3699e3b3-c6a5-4803-98ab-e59baacb9c24&source_detail=9709%2F12+May%2FJune+2020) |
| **Q3** FRQ | [1.7 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/differentiation/) | 5 | 0.35 Medium | 0.35 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9275aff7-1c76-429c-8092-211f890344a0&question_id=e85a745b-8e11-4143-989f-bb2233f0d47c&source_detail=9709%2F12+May%2FJune+2020) |
| **Q4** FRQ | [1.6 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/) | 5 | 0.45 Medium | 0.45 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9275aff7-1c76-429c-8092-211f890344a0&question_id=82b6cd2e-f7b5-4120-8682-12797436c465&source_detail=9709%2F12+May%2FJune+2020) |
| **Q5** FRQ | [1.2 Functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/) | 6 | 0.20 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9275aff7-1c76-429c-8092-211f890344a0&question_id=3e1cd516-ae35-4bdc-9db0-93d1945ee475&source_detail=9709%2F12+May%2FJune+2020) |
| **Q6** FRQ | [1.1 Quadratics](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/quadratics/) | 6 | 0.33 Medium | 0.33 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9275aff7-1c76-429c-8092-211f890344a0&question_id=373f3f40-abf9-4d82-bcef-834156b53fa4&source_detail=9709%2F12+May%2FJune+2020) |
| **Q7** FRQ | [1.4 Circular measure](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/circular-measure/) | 7 | 0.38 Medium | 0.27 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9275aff7-1c76-429c-8092-211f890344a0&question_id=917422ed-6f51-4b9b-afb1-33a115e323b0&source_detail=9709%2F12+May%2FJune+2020) |
| **Q8** FRQ | [1.8 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/integration/) | 8 | 0.45 Medium | 0.36 Medium | 0.36 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9275aff7-1c76-429c-8092-211f890344a0&question_id=8ccfa7dd-b4d2-4233-b400-00a19aa3335d&source_detail=9709%2F12+May%2FJune+2020) |
| **Q9** FRQ | [1.2 Functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/) | 8 | 0.29 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9275aff7-1c76-429c-8092-211f890344a0&question_id=0b903255-bb30-4b4a-b850-236da6faccbc&source_detail=9709%2F12+May%2FJune+2020) |
| **Q10** FRQ | [1.7 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/differentiation/) | 9 | 0.28 Easy | 0.28 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9275aff7-1c76-429c-8092-211f890344a0&question_id=a5536c7c-daaf-462d-a4b8-e4d71c49331e&source_detail=9709%2F12+May%2FJune+2020) |
| **Q11** FRQ | [1.3 Coordinate geometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/) | 11 | 0.38 Medium | 0.27 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9275aff7-1c76-429c-8092-211f890344a0&question_id=d67b9909-4099-4f5a-91dc-6fc2eb94276b&source_detail=9709%2F12+May%2FJune+2020) |

## Topics in this paper

- [1.6 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/)
- [1.5 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/)
- [1.7 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/differentiation/)
- [1.2 Functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/)
- [1.1 Quadratics](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/quadratics/)
- [1.4 Circular measure](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/circular-measure/)
- [1.8 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/integration/)
- [1.3 Coordinate geometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/)

## 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 0.34 from 26 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 0.12, 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 45.3% Easy, 54.7% Medium and 0.0% 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-p1/2020-may-june-9709-12/