CIE IAL · Mathematics · 2025 May/June
9709/33 May/June 2025
This Mathematics 9709 Paper 3 (Pure Mathematics 3) paper contains 11 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 the mark scheme require Pro access.
Core finding
9709/33 May/June 2025 is a past paper for CIE IAL Mathematics 9709 Paper 3 (Pure Mathematics 3), with 11 questions worth 75 marks. Its mark-weighted Difficulty Measure is 0.44 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.15 and a mark split of 16.0% Easy, 65.3% Medium and 18.7% Hard. Algebraic complexity averages 0.49; text density and modelling average 0.24. All five measures use 23 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 23 parts carrying 75 part marks. Difficulty tags cover 23 parts, algebraic tags 23 and text-density tags 23. 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 | 0.15 | √(Σwi(di − μ)2 / Σwi) |
| Difficulty Ratio | 16.0% Easy / 65.3% Medium / 18.7% Hard | marks in band / all tagged marks |
| Algebraic Complexity Measure | 0.49 | Σ(ci × marksi) / Σmarksi, with c = 0.20 / 0.45 / 0.75 |
| Text Density and Modelling Measure | 0.24 | 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 |
3.1 Algebra | 4 | 0.39Medium | 0.39Medium | 0.20Low | Go to Practice Hub |
| Q2 FRQ |
3.2 Logarithmic and exponential functions | 4 | 0.45Medium | 0.45Medium | 0.20Low | Go to Practice Hub |
| Q3 FRQ |
3.3 Trigonometry | 4 | 0.45Medium | 0.45Medium | 0.20Low | Go to Practice Hub |
| Q4 FRQ |
3.9 Complex numbers | 6 | 0.45Medium | 0.33Medium | 0.20Low | Go to Practice Hub |
| Q5 FRQ |
3.4 Differentiation | 6 | 0.45Medium | 0.45Medium | 0.20Low | Go to Practice Hub |
| Q6 FRQ |
3.9 Complex numbers | 6 | 0.75Hard | 0.75High | 0.20Low | Go to Practice Hub |
| Q7 FRQ |
3.1 Algebra | 8 | 0.33Medium | 0.57Medium | 0.20Low | Go to Practice Hub |
| Q8 FRQ |
3.3 Trigonometry | 8 | 0.45Medium | 0.60Medium | 0.20Low | Go to Practice Hub |
| Q9 FRQ |
3.7 Vectors | 8 | 0.39Medium | 0.33Medium | 0.45Medium | Go to Practice Hub |
| Q10 FRQ |
3.5 Integration | 10 | 0.66Hard | 0.69High | 0.20Low | Go to Practice Hub |
| Q11 FRQ |
3.4 Differentiation | 11 | 0.34Medium | 0.34Medium | 0.29Low | Go to Practice Hub |
Full questions and mark scheme
This paper is from 2025. Question text, options and the mark scheme are available with Pro access. The metadata above is public so you can still plan revision by topic and difficulty.
Open this paperPaper 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 23 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 16.0% Easy, 65.3% Medium and 18.7% 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.