# WFM01/01 January 2020

> WFM01/01 January 2020: 9 questions, 75 marks. Difficulty 0.38, deviation 0.19, algebraic 0.40, text density 0.20. Edexcel IAL Mathematics FP1.

- Canonical HTML: https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/2020-january-wfm01-01/
- Markdown mirror: https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/2020-january-wfm01-01/index.md

---

Edexcel IAL · Mathematics · 2020 January

This Further Pure Mathematics 1 (WFM01) 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
- FP1
- 9 questions
- 75 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=0da4524e-0872-4b0a-a5bd-bdfdc7956755)
- [All FP1 papers](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/)

Core finding

**WFM01/01 January 2020 is a past paper for Edexcel IAL Further Pure Mathematics 1 (WFM01), with 9 questions worth 75 marks.** Its mark-weighted Difficulty Measure is 0.38 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.19 and a mark split of 42.7% Easy, 37.3% Medium and 20.0% Hard. Algebraic complexity averages 0.40; text density and modelling average 0.20. All five measures use 25 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 25 parts carrying 75 part marks. Difficulty tags cover 25 parts, algebraic tags 25 and text-density tags 25. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.38 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.19 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 42.7 / 37.3 / 20.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.40 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.20 — 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** | 0.19 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 42.7% Easy / 37.3% Medium / 20.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.40 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.20 | 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. Matrix algebra integration](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/matrix-algebra-integration/) | 6 | 0.20 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0da4524e-0872-4b0a-a5bd-bdfdc7956755&question_id=6285ff0c-564f-440f-a52b-40f09ce81bdd&source_detail=WFM01%2F01+January+2020) |
| **Q2** FRQ | [1. Complex numbers](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/complex-numbers/) | 6 | 0.37 Medium | 0.37 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0da4524e-0872-4b0a-a5bd-bdfdc7956755&question_id=70daf310-7706-40cb-a084-b2783dc7fd8a&source_detail=WFM01%2F01+January+2020) |
| **Q3** FRQ | [7. Series](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/series/) | 6 | 0.37 Medium | 0.37 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0da4524e-0872-4b0a-a5bd-bdfdc7956755&question_id=ab925093-9170-4e63-9995-7b278420a41b&source_detail=WFM01%2F01+January+2020) |
| **Q4** FRQ | [1. Complex numbers](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/complex-numbers/) | 7 | 0.24 Easy | 0.24 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0da4524e-0872-4b0a-a5bd-bdfdc7956755&question_id=3f41d76e-ff5a-4736-bc0e-ee56a0c1aa15&source_detail=WFM01%2F01+January+2020) |
| **Q5** FRQ | [3. Numerical solution of equations](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/numerical-solution-of-equations/) | 8 | 0.33 Medium | 0.33 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0da4524e-0872-4b0a-a5bd-bdfdc7956755&question_id=1ef8dd37-770a-453b-b377-683f1a69528a&source_detail=WFM01%2F01+January+2020) |
| **Q6** FRQ | [6. Transformations using matrices](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/transformations-using-matrices/) | 7 | 0.27 Easy | 0.20 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0da4524e-0872-4b0a-a5bd-bdfdc7956755&question_id=a23c8e92-27cb-4a4d-aed8-cf7ad22c157b&source_detail=WFM01%2F01+January+2020) |
| **Q7** FRQ | [2. Roots of quadratic equations](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/roots-of-quadratic-equations/) | 9 | 0.26 Easy | 0.26 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0da4524e-0872-4b0a-a5bd-bdfdc7956755&question_id=50a22498-84b6-43c0-b71c-5df7c79e5658&source_detail=WFM01%2F01+January+2020) |
| **Q8** FRQ | [4. Coordinate systems](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/coordinate-systems/) | 14 | 0.51 Medium | 0.51 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0da4524e-0872-4b0a-a5bd-bdfdc7956755&question_id=eb7f1b8b-848c-45a0-90eb-16b9ac7b761e&source_detail=WFM01%2F01+January+2020) |
| **Q9** FRQ | [8. Proof](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/proof/) | 12 | 0.75 Hard | 0.75 High | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0da4524e-0872-4b0a-a5bd-bdfdc7956755&question_id=00766bd5-005c-4306-b4dc-d6b2f9410d34&source_detail=WFM01%2F01+January+2020) |

## Topics in this paper

- [5. Matrix algebra integration](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/matrix-algebra-integration/)
- [1. Complex numbers](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/complex-numbers/)
- [7. Series](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/series/)
- [3. Numerical solution of equations](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/numerical-solution-of-equations/)
- [6. Transformations using matrices](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/transformations-using-matrices/)
- [2. Roots of quadratic equations](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/roots-of-quadratic-equations/)
- [4. Coordinate systems](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/coordinate-systems/)
- [8. Proof](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/proof/)

## Related papers

- [WFM01/01](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/2020-october-wfm01-01/) — October 2020 — 8 questions · 75 marks — Free
- [WFM01/01](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/2021-october-wfm01-01/) — October 2021 — 9 questions · 75 marks — Pro
- [WFM01/01](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/2021-june-wfm01-01/) — June 2021 — 8 questions · 75 marks — Pro
- [WFM01/01](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/2021-january-wfm01-01/) — January 2021 — 9 questions · 75 marks — Pro
- [WFM01/01](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/2019-june-wfm01-01/) — June 2019 — 9 questions · 75 marks — Free
- [WFM01/01](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/2019-january-wfm01-01/) — January 2019 — 9 questions · 75 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 0.38 from 25 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 0.19, 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 42.7% Easy, 37.3% Medium and 20.0% 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/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/2020-january-wfm01-01/