# WMA13/01 January 2020

> WMA13/01 January 2020: 9 questions, 75 marks. Difficulty 0.45, deviation 0.20, algebraic 0.44, text density 0.22. Edexcel IAL Mathematics P3.

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Edexcel IAL · Mathematics · 2020 January

This Pure Mathematics 3 (WMA13) paper contains 9 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.

- Edexcel IAL
- P3
- 9 questions
- 75 marks
- Free paper
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Core finding

**WMA13/01 January 2020 is a past paper for Edexcel IAL Pure Mathematics 3 (WMA13), with 9 questions worth 75 marks.** Its mark-weighted Difficulty Measure is 0.45 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.20 and a mark split of 28.0% Easy, 40.0% Medium and 32.0% Hard. Algebraic complexity averages 0.44; text density and modelling average 0.22. 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**: 0.45 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.20 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 28.0 / 40.0 / 32.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.44 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.22 — 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** | 0.20 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 28.0% Easy / 40.0% Medium / 32.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.44 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.22 | 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 | [3. Exponential and logarithms](https://www.examsci.com/topics/edexcel-ial/mathematics/pure-mathematics-3-wma13/exponential-and-logarithms/) | 6 | 0.41 Medium | 0.37 Medium | 0.45 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=44a376ad-3a1b-44b2-906c-e3e264e10e0d&question_id=34df4af1-c5a7-4f20-9557-bd04210eca51&source_detail=WMA13%2F01+January+2020) |
| **Q2** FRQ | [1. Algebra and functions](https://www.examsci.com/topics/edexcel-ial/mathematics/pure-mathematics-3-wma13/algebra-and-functions/) | 8 | 0.39 Medium | 0.39 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=44a376ad-3a1b-44b2-906c-e3e264e10e0d&question_id=72583dcf-c1fc-495a-88ad-731f6f122827&source_detail=WMA13%2F01+January+2020) |
| **Q3** FRQ | [3. Exponential and logarithms](https://www.examsci.com/topics/edexcel-ial/mathematics/pure-mathematics-3-wma13/exponential-and-logarithms/) | 5 | 0.35 Medium | 0.35 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=44a376ad-3a1b-44b2-906c-e3e264e10e0d&question_id=2d73f9d8-8b9a-454d-9fc1-ede9a1748946&source_detail=WMA13%2F01+January+2020) |
| **Q4** FRQ | [4. Differentiation](https://www.examsci.com/topics/edexcel-ial/mathematics/pure-mathematics-3-wma13/differentiation/) | 11 | 0.56 Medium | 0.59 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=44a376ad-3a1b-44b2-906c-e3e264e10e0d&question_id=062dfa2a-f52a-4024-8964-42cd9631488f&source_detail=WMA13%2F01+January+2020) |
| **Q5** FRQ | [2. Trigonometry](https://www.examsci.com/topics/edexcel-ial/mathematics/pure-mathematics-3-wma13/trigonometry/) | 8 | 0.57 Medium | 0.60 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=44a376ad-3a1b-44b2-906c-e3e264e10e0d&question_id=a077e517-a53e-4b26-beb9-36794024ef8b&source_detail=WMA13%2F01+January+2020) |
| **Q6** FRQ | [1. Algebra and functions](https://www.examsci.com/topics/edexcel-ial/mathematics/pure-mathematics-3-wma13/algebra-and-functions/) | 9 | 0.49 Medium | 0.39 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=44a376ad-3a1b-44b2-906c-e3e264e10e0d&question_id=c1162b18-53d1-4ce5-adc0-bcb1e337c032&source_detail=WMA13%2F01+January+2020) |
| **Q7** FRQ | [6. Numerical methods](https://www.examsci.com/topics/edexcel-ial/mathematics/pure-mathematics-3-wma13/numerical-methods/) | 11 | 0.44 Medium | 0.34 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=44a376ad-3a1b-44b2-906c-e3e264e10e0d&question_id=77c2ceb9-4025-4cac-b41f-3a1a1b0afc22&source_detail=WMA13%2F01+January+2020) |
| **Q8** FRQ | [5. Integration](https://www.examsci.com/topics/edexcel-ial/mathematics/pure-mathematics-3-wma13/integration/) | 10 | 0.47 Medium | 0.53 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=44a376ad-3a1b-44b2-906c-e3e264e10e0d&question_id=c2035ca3-7feb-4bb0-a49c-b183a9b86cdb&source_detail=WMA13%2F01+January+2020) |
| **Q9** FRQ | [2. Trigonometry](https://www.examsci.com/topics/edexcel-ial/mathematics/pure-mathematics-3-wma13/trigonometry/) | 7 | 0.27 Easy | 0.27 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=44a376ad-3a1b-44b2-906c-e3e264e10e0d&question_id=9a235af8-b134-4603-a7bf-a59a5bb3df36&source_detail=WMA13%2F01+January+2020) |

## Topics in this paper

- [3. Exponential and logarithms](https://www.examsci.com/topics/edexcel-ial/mathematics/pure-mathematics-3-wma13/exponential-and-logarithms/)
- [4. Differentiation](https://www.examsci.com/topics/edexcel-ial/mathematics/pure-mathematics-3-wma13/differentiation/)
- [1. Algebra and functions](https://www.examsci.com/topics/edexcel-ial/mathematics/pure-mathematics-3-wma13/algebra-and-functions/)
- [2. Trigonometry](https://www.examsci.com/topics/edexcel-ial/mathematics/pure-mathematics-3-wma13/trigonometry/)
- [6. Numerical methods](https://www.examsci.com/topics/edexcel-ial/mathematics/pure-mathematics-3-wma13/numerical-methods/)
- [5. Integration](https://www.examsci.com/topics/edexcel-ial/mathematics/pure-mathematics-3-wma13/integration/)

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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 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 0.20, 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 28.0% Easy, 40.0% Medium and 32.0% 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/edexcel-ial/mathematics/pure-mathematics-3-wma13/2020-january-wma13-01/