# 9709/52 May/June 2025

> 9709/52 May/June 2025: 7 questions, 50 marks. Difficulty 0.45, deviation 0.14, algebraic 0.33, text density 0.44. CIE IAL Mathematics 9709 P5.

- Canonical HTML: https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/2025-may-june-9709-52/
- Markdown mirror: https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/2025-may-june-9709-52/index.md

---

CIE IAL · Mathematics · 2025 May/June

This Mathematics 9709 Paper 5 (Probability & Statistics 1) 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 the mark scheme require Pro access.

- CIE IAL
- 9709 P5
- 7 questions
- 50 marks
- Pro paper
- [Open in Interactive Practice Hub](https://www.examsci.com/practice?set_id=d18a80f7-973f-40bf-87e2-4cd045ae79fc)
- [All 9709 P5 papers](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/)

Core finding

**9709/52 May/June 2025 is a past paper for CIE IAL Mathematics 9709 Paper 5 (Probability & Statistics 1), with 7 questions worth 50 marks.** Its mark-weighted Difficulty Measure is 0.45 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.14 and a mark split of 16.0% Easy, 72.0% Medium and 12.0% Hard. Algebraic complexity averages 0.33; text density and modelling average 0.44. All five measures use 16 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 16 parts carrying 50 part marks. Difficulty tags cover 16 parts, algebraic tags 16 and text-density tags 16. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.45 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.14 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 16.0 / 72.0 / 12.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.33 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.44 — 0.20–0.75 · nearer Medium

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** | 0.14 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 16.0% Easy / 72.0% Medium / 12.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.33 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.44 | 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 | [5.4 Discrete random variables](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/discrete-random-variables/) | 3 | 0.45 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d18a80f7-973f-40bf-87e2-4cd045ae79fc&question_id=44edea1f-49eb-4c24-964b-c8c8451ff8f4&source_detail=9709%2F52+May%2FJune+2025) |
| **Q2** FRQ | [5.5 The normal distribution](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/the-normal-distribution/) | 5 | 0.45 Medium | 0.45 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d18a80f7-973f-40bf-87e2-4cd045ae79fc&question_id=82b05da0-2848-42c7-b064-5379bbbcc3fa&source_detail=9709%2F52+May%2FJune+2025) |
| **Q3** FRQ | [5.3 Probability](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/probability/) | 5 | 0.35 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d18a80f7-973f-40bf-87e2-4cd045ae79fc&question_id=d658e35a-5927-45f0-8796-3c2c1be7fc27&source_detail=9709%2F52+May%2FJune+2025) |
| **Q4** FRQ | [5.3 Probability](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/probability/) | 6 | 0.37 Medium | 0.20 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d18a80f7-973f-40bf-87e2-4cd045ae79fc&question_id=2be4c3b5-e2d8-415c-8e9c-03f6109b0f11&source_detail=9709%2F52+May%2FJune+2025) |
| **Q5** FRQ | [5.1 Representation of data](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/representation-of-data/) | 10 | 0.35 Medium | 0.35 Medium | 0.40 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d18a80f7-973f-40bf-87e2-4cd045ae79fc&question_id=3067ae5c-f7df-4923-aa68-586fde24c272&source_detail=9709%2F52+May%2FJune+2025) |
| **Q6** FRQ | [5.2 Permutations and combinations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/permutations-and-combinations/) | 9 | 0.65 Hard | 0.45 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d18a80f7-973f-40bf-87e2-4cd045ae79fc&question_id=80d66b20-dca9-4ec9-b7a5-3379b7c2d043&source_detail=9709%2F52+May%2FJune+2025) |
| **Q7** FRQ | [5.5 The normal distribution](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/the-normal-distribution/) | 12 | 0.45 Medium | 0.30 Low | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d18a80f7-973f-40bf-87e2-4cd045ae79fc&question_id=5c3195c0-ec44-4056-b531-c50426921c71&source_detail=9709%2F52+May%2FJune+2025) |

## Full questions and mark scheme

This paper is from 2025. Question text, options and the mark scheme are available with Pro access. The metadata above is public so you can still plan revision by topic and difficulty.

[Open this paper](https://www.examsci.com/practice?set_id=d18a80f7-973f-40bf-87e2-4cd045ae79fc)

## Topics in this paper

- [5.4 Discrete random variables](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/discrete-random-variables/)
- [5.3 Probability](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/probability/)
- [5.5 The normal distribution](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/the-normal-distribution/)
- [5.2 Permutations and combinations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/permutations-and-combinations/)
- [5.1 Representation of data](https://www.examsci.com/topics/cie-ial/mathematics/9709-p5/representation-of-data/)

## Related papers

- [9709/51](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/2025-october-november-9709-51/) — October/November 2025 — 7 questions · 50 marks — Pro
- [9709/52](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/2025-october-november-9709-52/) — October/November 2025 — 7 questions · 50 marks — Pro
- [9709/53](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/2025-october-november-9709-53/) — October/November 2025 — 7 questions · 50 marks — Pro
- [9709/55](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/2025-october-november-9709-55/) — October/November 2025 — 6 questions · 50 marks — Pro
- [9709/51](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/2025-may-june-9709-51/) — May/June 2025 — 6 questions · 50 marks — Pro
- [9709/53](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/2025-may-june-9709-53/) — May/June 2025 — 7 questions · 50 marks — Pro

## 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 16 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 16.0% Easy, 72.0% Medium and 12.0% 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.

---

Full page with native tables, bar charts and Practice Hub links: https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p5/2025-may-june-9709-52/