# 9709/23 May/June 2016

> 9709/23 May/June 2016: 7 questions, 50 marks. Difficulty 0.40, deviation 0.14, algebraic 0.38, text density 0.31. CIE IAL Mathematics 9709 P2.

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CIE IAL · Mathematics · 2016 May/June

This Mathematics 9709 Paper 2 (Pure Mathematics 2) paper contains 7 questions worth 50 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 P2
- 7 questions
- 50 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=8ae56d4c-81b8-451f-b42d-af39221feda8)
- [All 9709 P2 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/)

Core finding

**9709/23 May/June 2016 is a past paper for CIE IAL Mathematics 9709 Paper 2 (Pure Mathematics 2), with 7 questions worth 50 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 26.0% Easy, 66.0% Medium and 8.0% Hard. Algebraic complexity averages 0.38; text density and modelling average 0.31. All five measures use 17 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 17 parts carrying 50 part marks. Difficulty tags cover 17 parts, algebraic tags 17 and text-density tags 17. 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**: 26.0 / 66.0 / 8.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.38 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.31 — 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** | 26.0% Easy / 66.0% Medium / 8.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.38 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.31 | 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-p2/logarithmic-and-exponential-functions/) | 3 | 0.20 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=8ae56d4c-81b8-451f-b42d-af39221feda8&question_id=1069c81e-d574-46fb-ab4d-b1d159925b8a&source_detail=9709%2F23+May%2FJune+2016) |
| **Q2** FRQ | [1 Algebra](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/algebra/) | 5 | 0.30 Easy | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=8ae56d4c-81b8-451f-b42d-af39221feda8&question_id=419b7260-f804-4f1f-bd0c-048e259f5a33&source_detail=9709%2F23+May%2FJune+2016) |
| **Q3** FRQ | [1 Algebra](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/algebra/) | 5 | 0.30 Easy | 0.30 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=8ae56d4c-81b8-451f-b42d-af39221feda8&question_id=00119a9b-685d-46aa-95e0-700cebc5e7ae&source_detail=9709%2F23+May%2FJune+2016) |
| **Q4** FRQ | [3 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/trigonometry/) | 8 | 0.39 Medium | 0.39 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=8ae56d4c-81b8-451f-b42d-af39221feda8&question_id=2baa116a-40d2-4df3-9936-c4c6739a59bb&source_detail=9709%2F23+May%2FJune+2016) |
| **Q5** FRQ | [2 Logarithmic and exponential functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/logarithmic-and-exponential-functions/) | 9 | 0.39 Medium | 0.39 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=8ae56d4c-81b8-451f-b42d-af39221feda8&question_id=c79917f2-73dc-4033-a548-ceec4c38c2d2&source_detail=9709%2F23+May%2FJune+2016) |
| **Q6** FRQ | [5 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/integration/) | 10 | 0.45 Medium | 0.38 Medium | 0.28 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=8ae56d4c-81b8-451f-b42d-af39221feda8&question_id=0c551e14-69ed-4420-bbcb-f4899dc4ac2d&source_detail=9709%2F23+May%2FJune+2016) |
| **Q7** FRQ | [3 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/trigonometry/) | 10 | 0.55 Medium | 0.40 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=8ae56d4c-81b8-451f-b42d-af39221feda8&question_id=914fec4e-eaf6-49d7-835c-ca2f72e20907&source_detail=9709%2F23+May%2FJune+2016) |

## Topics in this paper

- [2 Logarithmic and exponential functions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/logarithmic-and-exponential-functions/)
- [1 Algebra](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/algebra/)
- [3 Trigonometry](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/trigonometry/)
- [4 Differentiation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/differentiation/)
- [6 Numerical solution of equations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/numerical-solution-of-equations/)
- [5 Integration](https://www.examsci.com/topics/cie-ial/mathematics/9709-p2/integration/)

## Related papers

- [9709/21](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2016-october-november-9709-21/) — October/November 2016 — 7 questions · 50 marks — Free
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- [9709/21](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2016-may-june-9709-21/) — May/June 2016 — 7 questions · 50 marks — Free
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- [9709/22](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p2/2016-march-9709-22/) — March 2016 — 8 questions · 50 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 0.40 from 17 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 26.0% Easy, 66.0% 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-p2/2016-may-june-9709-23/