# WFM01/01 January 2016

> WFM01/01 January 2016: 9 questions, 75 marks. Difficulty 0.41, deviation 0.13, algebraic 0.40, text density 0.22. Edexcel IAL Mathematics FP1.

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Edexcel IAL · Mathematics · 2016 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
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Core finding

**WFM01/01 January 2016 is a past paper for Edexcel IAL Further Pure Mathematics 1 (WFM01), with 9 questions worth 75 marks.** Its mark-weighted Difficulty Measure is 0.41 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.13 and a mark split of 22.6% Easy, 70.7% Medium and 6.7% Hard. Algebraic complexity averages 0.40; text density and modelling average 0.22. All five measures use 22 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 22 parts carrying 75 part marks. Difficulty tags cover 22 parts, algebraic tags 22 and text-density tags 22. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.41 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.13 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 22.6 / 70.7 / 6.7 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.40 — 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** | 0.41 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.13 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 22.6% Easy / 70.7% Medium / 6.7% 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** | 0.22 | 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 | [1. Complex numbers](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/complex-numbers/) | 9 | 0.31 Easy | 0.31 Low | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=298d6be7-3aa2-42a1-82f9-da5f87143957&question_id=24579d5a-78bb-45a6-9182-30143a4d41a4&source_detail=WFM01%2F01+January+2016) |
| **Q2** FRQ | [3. Numerical solution of equations](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/numerical-solution-of-equations/) | 7 | 0.38 Medium | 0.38 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=298d6be7-3aa2-42a1-82f9-da5f87143957&question_id=ddaa6902-b23a-41c4-ac80-502456ba5f21&source_detail=WFM01%2F01+January+2016) |
| **Q3** FRQ | [2. Roots of quadratic equations](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/roots-of-quadratic-equations/) | 11 | 0.36 Medium | 0.36 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=298d6be7-3aa2-42a1-82f9-da5f87143957&question_id=81b2e320-c9a2-4eee-979e-88d9d4b19796&source_detail=WFM01%2F01+January+2016) |
| **Q4** FRQ | [6. Transformations using matrices](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/transformations-using-matrices/) | 8 | 0.42 Medium | 0.33 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=298d6be7-3aa2-42a1-82f9-da5f87143957&question_id=1118a9b0-05ba-4e4f-9716-ee33caea8a4c&source_detail=WFM01%2F01+January+2016) |
| **Q5** FRQ | [7. Series](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/series/) | 8 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=298d6be7-3aa2-42a1-82f9-da5f87143957&question_id=12f80abd-4756-4341-99ef-eef06c8e0d78&source_detail=WFM01%2F01+January+2016) |
| **Q6** FRQ | [4. Coordinate systems](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/coordinate-systems/) | 9 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=298d6be7-3aa2-42a1-82f9-da5f87143957&question_id=1f57829b-efd3-49a6-a88b-4d2e9db00384&source_detail=WFM01%2F01+January+2016) |
| **Q7** FRQ | [1. Complex numbers](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/complex-numbers/) | 9 | 0.39 Medium | 0.39 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=298d6be7-3aa2-42a1-82f9-da5f87143957&question_id=e2c693e2-55ae-4c75-bc85-502b2b409a70&source_detail=WFM01%2F01+January+2016) |
| **Q8** FRQ | [4. Coordinate systems](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/coordinate-systems/) | 8 | 0.49 Medium | 0.54 Medium | 0.36 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=298d6be7-3aa2-42a1-82f9-da5f87143957&question_id=d72cbab5-2fd7-4d14-bb4b-2c2498b355d3&source_detail=WFM01%2F01+January+2016) |
| **Q9** FRQ | [8. Proof](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/proof/) | 6 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=298d6be7-3aa2-42a1-82f9-da5f87143957&question_id=b5f38885-2c8d-44d7-8b31-6ec9d61514c1&source_detail=WFM01%2F01+January+2016) |

## Topics in this paper

- [1. Complex numbers](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/complex-numbers/)
- [3. Numerical solution of equations](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/numerical-solution-of-equations/)
- [2. Roots of quadratic equations](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/roots-of-quadratic-equations/)
- [6. Transformations using matrices](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/transformations-using-matrices/)
- [5. Matrix algebra integration](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/matrix-algebra-integration/)
- [7. Series](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/series/)
- [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-wfm01/2016-june-wfm01-01/) — June 2016 — 10 questions · 75 marks — Free
- [WFM01/01](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/2017-june-wfm01-01/) — June 2017 — 10 questions · 75 marks — Free
- [WFM01/01](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/2017-january-wfm01-01/) — January 2017 — 9 questions · 75 marks — Free
- [WFM01/01](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/2015-june-wfm01-01/) — June 2015 — 9 questions · 75 marks — Free
- [WFM01/01](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/2015-january-wfm01-01/) — January 2015 — 8 questions · 75 marks — Free
- [WFM01/01](https://www.examsci.com/past-papers/edexcel-ial/mathematics/further-pure-mathematics-1-wfm01/2018-june-wfm01-01/) — June 2018 — 10 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 0.41 from 22 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 0.13, 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 22.7% Easy, 70.7% Medium and 6.7% 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-1-wfm01/2016-january-wfm01-01/