# WFM03/01 June 2018

> WFM03/01 June 2018: 8 questions, 75 marks. Difficulty 0.44, deviation 0.10, algebraic 0.52, text density 0.22. Edexcel IAL Mathematics FP3.

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Edexcel IAL · Mathematics · 2018 June

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=e3312792-17ad-40b1-b446-97027e94cb20)
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Core finding

**WFM03/01 June 2018 is a past paper for Edexcel IAL Further Pure Mathematics 3 (WFM03), with 8 questions worth 75 marks.** Its mark-weighted Difficulty Measure is 0.44 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.10 and a mark split of 9.3% Easy, 82.7% Medium and 8.0% Hard. Algebraic complexity averages 0.52; text density and modelling average 0.22. 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 75 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**: 0.44 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.10 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 9.3 / 82.7 / 8.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.52 — 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** | 0.44 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.10 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 9.3% Easy / 82.7% Medium / 8.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.52 | 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. Hyperbolic functions](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/hyperbolic-functions/) | 6 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=e3312792-17ad-40b1-b446-97027e94cb20&question_id=b3809ced-43cb-42ba-8160-d5f5e9337be1&source_detail=WFM03%2F01+June+2018) |
| **Q2** FRQ | [6. Further matrix algebra](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/further-matrix-algebra/) | 9 | 0.39 Medium | 0.39 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=e3312792-17ad-40b1-b446-97027e94cb20&question_id=0d0b08a6-185a-4433-856a-8d4119352086&source_detail=WFM03%2F01+June+2018) |
| **Q3** FRQ | [3. Differentiation](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/differentiation/) | 6 | 0.45 Medium | 0.75 High | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=e3312792-17ad-40b1-b446-97027e94cb20&question_id=a5c8791d-18ef-499a-9055-dce6374f7ec2&source_detail=WFM03%2F01+June+2018) |
| **Q4** FRQ | [2. Further coordinate systems](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/further-coordinate-systems/) | 12 | 0.39 Medium | 0.39 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=e3312792-17ad-40b1-b446-97027e94cb20&question_id=91d21a51-9371-4254-9638-482d87bacf01&source_detail=WFM03%2F01+June+2018) |
| **Q5** FRQ | [6. Further matrix algebra](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/further-matrix-algebra/) | 11 | 0.58 Medium | 0.75 High | 0.34 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=e3312792-17ad-40b1-b446-97027e94cb20&question_id=82db28ba-6e7e-43fb-a0e2-9bc4372b730c&source_detail=WFM03%2F01+June+2018) |
| **Q6** FRQ | [3. Differentiation](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/differentiation/) | 7 | 0.38 Medium | 0.38 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=e3312792-17ad-40b1-b446-97027e94cb20&question_id=7857e75c-0f50-43ef-991f-299464982f1d&source_detail=WFM03%2F01+June+2018) |
| **Q7** FRQ | [5. Vectors](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/vectors/) | 12 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=e3312792-17ad-40b1-b446-97027e94cb20&question_id=37e93bad-1368-4e5a-b483-38ca0aa33b9f&source_detail=WFM03%2F01+June+2018) |
| **Q8** FRQ | [4. Integration](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/integration/) | 12 | 0.45 Medium | 0.63 High | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=e3312792-17ad-40b1-b446-97027e94cb20&question_id=9f4718d2-cc44-4205-a58e-bc0d4f6ef405&source_detail=WFM03%2F01+June+2018) |

## Topics in this paper

- [1. Hyperbolic functions](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/hyperbolic-functions/)
- [6. Further matrix algebra](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/further-matrix-algebra/)
- [3. Differentiation](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/differentiation/)
- [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/)
- [4. Integration](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/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 0.44 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 0.10, 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 9.3% Easy, 82.7% Medium and 8.0% 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/further-pure-mathematics-3-wfm03/2018-june-wfm03-01/