# 9709/13 May/June 2019

> 9709/13 May/June 2019: 10 questions, 75 marks. Difficulty 0.45, deviation 0.16, algebraic 0.45, text density 0.29. CIE IAL Mathematics 9709 P1.

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CIE IAL · Mathematics · 2019 May/June

This Mathematics 9709 Paper 1 (Pure Mathematics 1) 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 P1
- 10 questions
- 75 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=1e85967c-5fb9-4d24-a8c6-a88e9d5b4927)
- [All 9709 P1 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/)

Core finding

**9709/13 May/June 2019 is a past paper for CIE IAL Mathematics 9709 Paper 1 (Pure Mathematics 1), with 10 questions worth 75 marks.** Its mark-weighted Difficulty Measure is 0.45 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.16 and a mark split of 18.7% Easy, 58.7% Medium and 22.6% Hard. Algebraic complexity averages 0.45; text density and modelling average 0.29. All five measures use 27 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 27 parts carrying 75 part marks. Difficulty tags cover 27 parts, algebraic tags 27 and text-density tags 27. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.45 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.16 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 18.7 / 58.7 / 22.6 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.45 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.29 — 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** | 0.45 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.16 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 18.7% Easy / 58.7% Medium / 22.6% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.45 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.29 | 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 Quadratics](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/quadratics/) | 5 | 0.35 Medium | 0.35 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=1e85967c-5fb9-4d24-a8c6-a88e9d5b4927&question_id=25bde077-937b-4167-beee-e53ce79ea089&source_detail=9709%2F13+May%2FJune+2019) |
| **Q2** FRQ | [7 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/) | 5 | 0.30 Easy | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=1e85967c-5fb9-4d24-a8c6-a88e9d5b4927&question_id=9ab31e01-d583-49ae-81af-7519242c0eaf&source_detail=9709%2F13+May%2FJune+2019) |
| **Q3** FRQ | [4 Circular measure](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/circular-measure/) | 6 | 0.45 Medium | 0.33 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=1e85967c-5fb9-4d24-a8c6-a88e9d5b4927&question_id=6b4d82ab-3eac-4d27-bbaa-a08f451aacfe&source_detail=9709%2F13+May%2FJune+2019) |
| **Q4** FRQ | [2 Functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/) | 5 | 0.40 Medium | 0.40 Medium | 0.30 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=1e85967c-5fb9-4d24-a8c6-a88e9d5b4927&question_id=0ad76407-f71c-43c2-b338-1e4135eb43e3&source_detail=9709%2F13+May%2FJune+2019) |
| **Q5** FRQ | [7 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/) | 7 | 0.55 Medium | 0.41 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=1e85967c-5fb9-4d24-a8c6-a88e9d5b4927&question_id=40b507ff-e571-44a0-9e3f-ba4f9f563fe9&source_detail=9709%2F13+May%2FJune+2019) |
| **Q6** FRQ | [6 Vectors](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/) | 7 | 0.34 Medium | 0.34 Medium | 0.31 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=1e85967c-5fb9-4d24-a8c6-a88e9d5b4927&question_id=fa6a291a-fdaf-45e8-b0f0-033f50c23360&source_detail=9709%2F13+May%2FJune+2019) |
| **Q7** FRQ | [3 Coordinate geometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/) | 9 | 0.39 Medium | 0.39 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=1e85967c-5fb9-4d24-a8c6-a88e9d5b4927&question_id=651dff27-60f6-48c7-b89c-daf9851c0ccc&source_detail=9709%2F13+May%2FJune+2019) |
| **Q8** FRQ | [8 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/differentiation/) | 8 | 0.75 Hard | 0.75 High | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=1e85967c-5fb9-4d24-a8c6-a88e9d5b4927&question_id=60353926-fcd9-4253-aeb2-2daaa2b56d0c&source_detail=9709%2F13+May%2FJune+2019) |
| **Q9** FRQ | [2 Functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/) | 10 | 0.40 Medium | 0.33 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=1e85967c-5fb9-4d24-a8c6-a88e9d5b4927&question_id=060beb3c-7541-414f-b664-7be2f1db05e4&source_detail=9709%2F13+May%2FJune+2019) |
| **Q10** FRQ | [8 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/differentiation/) | 13 | 0.54 Medium | 0.57 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=1e85967c-5fb9-4d24-a8c6-a88e9d5b4927&question_id=b4c873b3-3d35-4e2b-bf6a-2ffd5cf897f1&source_detail=9709%2F13+May%2FJune+2019) |

## Topics in this paper

- [1 Quadratics](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/quadratics/)
- [7 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/)
- [4 Circular measure](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/circular-measure/)
- [5 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/)
- [2 Functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/functions/)
- [6 Vectors](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/)
- [3 Coordinate geometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/)
- [8 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/differentiation/)
- [9 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/integration/)

## 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 0.45 from 27 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 0.16, 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 18.7% Easy, 58.7% Medium and 22.7% 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-p1/2019-may-june-9709-13/