# WFM03/01 October 2020

> WFM03/01 October 2020: 8 questions, 75 marks. Difficulty 0.46, deviation 0.15, algebraic 0.46, text density 0.23. Edexcel IAL Mathematics FP3.

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Edexcel IAL · Mathematics · 2020 October

This Further Pure Mathematics 3 (WFM03) paper contains 8 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
- FP3
- 8 questions
- 75 marks
- Free paper
- [Practise this paper](https://www.examsci.com/practice?set_id=89d9551c-7c22-401e-9033-f397b71ae7c0)
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Core finding

**WFM03/01 October 2020 is a past paper for Edexcel IAL Further Pure Mathematics 3 (WFM03), with 8 questions worth 75 marks.** Its mark-weighted Difficulty Measure is 0.46 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.15 and a mark split of 13.3% Easy, 65.3% Medium and 21.4% Hard. Algebraic complexity averages 0.46; text density and modelling average 0.23. All five measures use 19 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 19 parts carrying 75 part marks. Difficulty tags cover 19 parts, algebraic tags 19 and text-density tags 19. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.46 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.15 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 13.3 / 65.3 / 21.4 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.46 — 0.20–0.75 · nearer Medium
- **Text Density and Modelling Measure**: 0.23 — 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** | 0.46 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.15 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 13.3% Easy / 65.3% Medium / 21.4% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.46 | Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75 |
| **Text Density and Modelling Measure** | 0.23 | 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 | [1. Hyperbolic functions](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/hyperbolic-functions/) | 7 | 0.38 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=89d9551c-7c22-401e-9033-f397b71ae7c0&question_id=bdeaa7df-c9c3-4dc9-b00e-3233a75ca0f0&source_detail=WFM03%2F01+October+2020) |
| **Q2** FRQ | [4. Integration](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/integration/) | 8 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=89d9551c-7c22-401e-9033-f397b71ae7c0&question_id=3cc35ebf-5199-4c97-b179-972268f6d750&source_detail=WFM03%2F01+October+2020) |
| **Q3** FRQ | [6. Further matrix algebra](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/further-matrix-algebra/) | 9 | 0.37 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=89d9551c-7c22-401e-9033-f397b71ae7c0&question_id=6724d96e-b230-4c11-a4da-0555a0a5c5af&source_detail=WFM03%2F01+October+2020) |
| **Q4** FRQ | [4. Integration](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/integration/) | 9 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=89d9551c-7c22-401e-9033-f397b71ae7c0&question_id=afbe4d02-17fb-46e6-a8bb-7775acc875ed&source_detail=WFM03%2F01+October+2020) |
| **Q5** FRQ | [2. Further coordinate systems](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/further-coordinate-systems/) | 12 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=89d9551c-7c22-401e-9033-f397b71ae7c0&question_id=c675f5c0-3f34-4454-9bf6-25af18017d8b&source_detail=WFM03%2F01+October+2020) |
| **Q6** FRQ | [6. Further matrix algebra](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/further-matrix-algebra/) | 8 | 0.57 Medium | 0.45 Medium | 0.33 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=89d9551c-7c22-401e-9033-f397b71ae7c0&question_id=74158cff-939b-4a76-9693-068181bf9366&source_detail=WFM03%2F01+October+2020) |
| **Q7** FRQ | [1. Hyperbolic functions](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/hyperbolic-functions/) | 12 | 0.45 Medium | 0.52 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=89d9551c-7c22-401e-9033-f397b71ae7c0&question_id=a995a440-ab33-427a-83cc-bb8911028e51&source_detail=WFM03%2F01+October+2020) |
| **Q8** FRQ | [5. Vectors](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/vectors/) | 10 | 0.57 Medium | 0.45 Medium | 0.33 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=89d9551c-7c22-401e-9033-f397b71ae7c0&question_id=4051983b-9a0a-4b73-ba3d-455c093fffcf&source_detail=WFM03%2F01+October+2020) |

## Topics in this paper

- [1. Hyperbolic functions](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/hyperbolic-functions/)
- [4. Integration](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/integration/)
- [6. Further matrix algebra](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/further-matrix-algebra/)
- [2. Further coordinate systems](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/further-coordinate-systems/)
- [5. Vectors](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/vectors/)
- [3. Differentiation](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/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 0.46 from 19 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 0.15, 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 13.3% Easy, 65.3% Medium and 21.3% 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/further-pure-mathematics-3-wfm03/2020-october-wfm03-01/