# WFM03/01 June 2016

> WFM03/01 June 2016: 8 questions, 75 marks. Difficulty 0.49, deviation 0.12, algebraic 0.51, text density 0.23. Edexcel IAL Mathematics FP3.

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Edexcel IAL · Mathematics · 2016 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=cc87ae7a-efe2-4b64-b941-a913fa71b1de)
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Core finding

**WFM03/01 June 2016 is a past paper for Edexcel IAL Further Pure Mathematics 3 (WFM03), with 8 questions worth 75 marks.** Its mark-weighted Difficulty Measure is 0.49 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.12 and a mark split of 2.7% Easy, 77.3% Medium and 20.0% Hard. Algebraic complexity averages 0.51; text density and modelling average 0.23. All five measures use 15 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 15 parts carrying 75 part marks. Difficulty tags cover 15 parts, algebraic tags 15 and text-density tags 15. Tags are internal metadata, not official exam-board ratings.

- **Difficulty Measure**: 0.49 — 0.20–0.75 · nearer Medium
- **Difficulty Deviation**: 0.12 — 0 = uniform; higher = more mixed
- **Difficulty Ratio**: 2.7 / 77.3 / 20.0 — % Easy / Medium / Hard
- **Algebraic Complexity Measure**: 0.51 — 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** | 0.49 | Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75 |
| **Difficulty Deviation** | 0.12 | √(Σw_i(d_i − μ)^2 / Σw_i) |
| **Difficulty Ratio** | 2.7% Easy / 77.3% Medium / 20.0% Hard | marks in band / all tagged marks |
| **Algebraic Complexity Measure** | 0.51 | 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/) | 6 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cc87ae7a-efe2-4b64-b941-a913fa71b1de&question_id=ef3e5e30-7827-4172-bad9-3724334444c3&source_detail=WFM03%2F01+June+2016) |
| **Q2** FRQ | [2. Further coordinate systems](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/further-coordinate-systems/) | 11 | 0.58 Medium | 0.45 Medium | 0.34 Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cc87ae7a-efe2-4b64-b941-a913fa71b1de&question_id=bf6fc947-5134-4959-b9e1-1ea11b7bd92c&source_detail=WFM03%2F01+June+2016) |
| **Q3** FRQ | [4. Integration](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/integration/) | 12 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cc87ae7a-efe2-4b64-b941-a913fa71b1de&question_id=e8c635af-87b4-45a1-80e9-c83a4ac828b6&source_detail=WFM03%2F01+June+2016) |
| **Q4** FRQ | [6. Further matrix algebra](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/further-matrix-algebra/) | 9 | 0.45 Medium | 0.62 High | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cc87ae7a-efe2-4b64-b941-a913fa71b1de&question_id=aef57a77-53fc-4394-8495-e8b8cc7fa501&source_detail=WFM03%2F01+June+2016) |
| **Q5** FRQ | [3. Differentiation](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/differentiation/) | 7 | 0.54 Medium | 0.59 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cc87ae7a-efe2-4b64-b941-a913fa71b1de&question_id=077587a9-e3a9-4259-a315-2a7ff9f31807&source_detail=WFM03%2F01+June+2016) |
| **Q6** FRQ | [5. Vectors](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/vectors/) | 9 | 0.56 Medium | 0.45 Medium | 0.31 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cc87ae7a-efe2-4b64-b941-a913fa71b1de&question_id=ea459d65-dc80-4e62-bf0c-d8496e432fd9&source_detail=WFM03%2F01+June+2016) |
| **Q7** FRQ | [4. Integration](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/integration/) | 11 | 0.45 Medium | 0.64 High | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cc87ae7a-efe2-4b64-b941-a913fa71b1de&question_id=87cd78ee-bffc-48f3-84ed-03012c609d56&source_detail=WFM03%2F01+June+2016) |
| **Q8** FRQ | [4. Integration](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/integration/) | 10 | 0.45 Medium | 0.45 Medium | 0.20 Low | [Go to Practice Hub](https://www.examsci.com/practice?set_id=cc87ae7a-efe2-4b64-b941-a913fa71b1de&question_id=c4a1fcb0-c2bd-45b1-86c3-82ed75c85034&source_detail=WFM03%2F01+June+2016) |

## Topics in this paper

- [1. Hyperbolic functions](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/hyperbolic-functions/)
- [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/)
- [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/)
- [5. Vectors](https://www.examsci.com/topics/edexcel-ial/mathematics/further-pure-mathematics-3-wfm03/vectors/)

## Related papers

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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 0.49 from 15 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 0.12, 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 2.7% Easy, 77.3% 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.

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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-wfm03/2016-june-wfm03-01/