CIE IAL · Mathematics · 2015 May/June
9709/32 May/June 2015
This Mathematics 9709 Paper 3 (Pure Mathematics 3) paper contains 10 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.
Core finding
9709/32 May/June 2015 is a past paper for CIE IAL Mathematics 9709 Paper 3 (Pure Mathematics 3), with 10 questions worth 75 marks. Its mark-weighted Difficulty Measure is 0.44 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.19 and a mark split of 26.7% Easy, 45.3% Medium and 28.0% Hard. Algebraic complexity averages 0.48; text density and modelling average 0.26. 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.
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 →
Definitions and calculation
| Measure | Paper value | Formula |
|---|---|---|
| Difficulty Measure | 0.44 | Σ(di × wi) / Σwi, with d = 0.20 / 0.45 / 0.75 |
| Difficulty Deviation | 0.19 | √(Σwi(di − μ)2 / Σwi) |
| Difficulty Ratio | 26.7% Easy / 45.3% Medium / 28.0% Hard | marks in band / all tagged marks |
| Algebraic Complexity Measure | 0.48 | Σ(ci × marksi) / Σmarksi, with c = 0.20 / 0.45 / 0.75 |
| Text Density and Modelling Measure | 0.26 | Σ(ti × marksi) / Σmarksi, with t = 0.20 / 0.45 / 0.75 |
wi equals the part marks, except for a Hard part worth 4 or more marks, where wi = marks0.75 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 Integration | 3 | 0.20Easy | 0.20Low | 0.20Low | Go to Practice Hub |
| Q2 FRQ |
2 Logarithmic and exponential functions | 4 | 0.20Easy | 0.45Medium | 0.20Low | Go to Practice Hub |
| Q3 FRQ |
4 Differentiation | 6 | 0.45Medium | 0.45Medium | 0.20Low | Go to Practice Hub |
| Q4 FRQ |
3 Trigonometry | 6 | 0.20Easy | 0.20Low | 0.20Low | Go to Practice Hub |
| Q5 FRQ |
3 Trigonometry | 8 | 0.29Easy | 0.29Low | 0.45Medium | Go to Practice Hub |
| Q6 FRQ |
5 Integration | 8 | 0.45Medium | 0.45Medium | 0.20Low | Go to Practice Hub |
| Q7 FRQ |
9 Complex numbers | 9 | 0.56Medium | 0.45Medium | 0.20Low | Go to Practice Hub |
| Q8 FRQ |
1 Algebra | 10 | 0.57Medium | 0.75High | 0.20Low | Go to Practice Hub |
| Q9 FRQ |
8 Differential equations | 10 | 0.53Medium | 0.58Medium | 0.45Medium | Go to Practice Hub |
| Q10 FRQ |
7 Vectors | 11 | 0.58Medium | 0.61High | 0.20Low | Go to Practice Hub |
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 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 0.19, 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 26.7% Easy, 45.3% Medium and 28.0% 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.