# 9709/12 May/June 2018

> 9709/12 May/June 2018: 11 questions, 75 marks. Difficulty 0.38, deviation 0.17, algebraic 0.32, text density 0.27. CIE IAL Mathematics 9709 P1.

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CIE IAL · Mathematics · 2018 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=ac9f16c6-3c1c-4e89-9da9-ec7a3f18060a)
- [All 9709 P1 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/)

Core finding

**9709/12 May/June 2018 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 0.38 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.17 and a mark split of 38.7% Easy, 45.3% Medium and 16.0% Hard. Algebraic complexity averages 0.32; text density and modelling average 0.27. All five measures use 24 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 24 parts carrying 75 part marks. Difficulty tags cover 24 parts, algebraic tags 24 and text-density tags 24. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.38 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.17 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 38.7 / 45.3 / 16.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.32 — 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** | 0.38 | 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** | 38.7% Easy / 45.3% Medium / 16.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.32 | 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 | [7 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/) | 5 | 0.20 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ac9f16c6-3c1c-4e89-9da9-ec7a3f18060a&question_id=d7c2a7fa-dfb7-421a-8e36-c5704d5f86e8&source_detail=9709%2F12+May%2FJune+2018) |
| **Q2** FRQ | [1 Quadratics](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/quadratics/) | 5 | 0.20 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ac9f16c6-3c1c-4e89-9da9-ec7a3f18060a&question_id=d31a8de7-d925-4f03-af6a-0bce16436301&source_detail=9709%2F12+May%2FJune+2018) |
| **Q3** FRQ | [7 Series](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/series/) | 5 | 0.20 Easy | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ac9f16c6-3c1c-4e89-9da9-ec7a3f18060a&question_id=2637c535-ea96-4c5a-9810-4b1d4590fe54&source_detail=9709%2F12+May%2FJune+2018) |
| **Q4** FRQ | [5 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/) | 6 | 0.33 Medium | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ac9f16c6-3c1c-4e89-9da9-ec7a3f18060a&question_id=cf1da97f-4153-4c9c-9cfe-847985dadac2&source_detail=9709%2F12+May%2FJune+2018) |
| **Q5** FRQ | [6 Vectors](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/) | 6 | 0.37 Medium | 0.37 Medium | 0.28 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ac9f16c6-3c1c-4e89-9da9-ec7a3f18060a&question_id=8adfd439-c041-421c-b602-6bf0247d7c94&source_detail=9709%2F12+May%2FJune+2018) |
| **Q6** FRQ | [4 Circular measure](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/circular-measure/) | 6 | 0.45 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ac9f16c6-3c1c-4e89-9da9-ec7a3f18060a&question_id=8a6eaf7c-4c15-4e46-b397-7af57f9e95ac&source_detail=9709%2F12+May%2FJune+2018) |
| **Q7** FRQ | [1 Quadratics](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/quadratics/) | 7 | 0.31 Easy | 0.31 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ac9f16c6-3c1c-4e89-9da9-ec7a3f18060a&question_id=f7e4167c-515f-42de-8c83-9ff1c367888c&source_detail=9709%2F12+May%2FJune+2018) |
| **Q8** FRQ | [3 Coordinate geometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/) | 7 | 0.45 Medium | 0.45 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ac9f16c6-3c1c-4e89-9da9-ec7a3f18060a&question_id=83522f9c-1308-47d4-8c32-42e8d06d7d45&source_detail=9709%2F12+May%2FJune+2018) |
| **Q9** FRQ | [9 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/integration/) | 8 | 0.39 Medium | 0.33 Medium | 0.26 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ac9f16c6-3c1c-4e89-9da9-ec7a3f18060a&question_id=68900145-ecb8-413a-b3c9-ff9f03ef992e&source_detail=9709%2F12+May%2FJune+2018) |
| **Q10** FRQ | [5 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/) | 8 | 0.36 Medium | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ac9f16c6-3c1c-4e89-9da9-ec7a3f18060a&question_id=c596ff26-1417-475b-8280-1b741a359261&source_detail=9709%2F12+May%2FJune+2018) |
| **Q11** FRQ | [3 Coordinate geometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/) | 12 | 0.75 Hard | 0.60 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ac9f16c6-3c1c-4e89-9da9-ec7a3f18060a&question_id=f607f248-2470-48e6-9139-7430eb2459e3&source_detail=9709%2F12+May%2FJune+2018) |

## Topics in this paper

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

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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 0.38 from 24 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 38.7% Easy, 45.3% Medium and 16.0% 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-p1/2018-may-june-9709-12/