9709 · Cambridge International AS Level
9709/21
Pure Mathematics 2 (9709/2)
Mathematics · June 2025 · Variant 1
Relative difficulty
Analysis source: Cambridge Assessment International Education
Analysis aligned to the official syllabus and assessment design.
3.5 / 5
125
185 min
Differentiation, Integration, and Parametric Functions
Cohort performance
Session statistics from official examination reports
Total marks
125
Duration
185 min
Session difficulty
3.5 / 5
Key examiner messages
Top priorities from the principal examiner before you revise
Key high-mark targets include Coordinate Geometry (specifically circle tangents in P11 Q8, worth 8 marks) and Parametric Differentiation (P21 Q6, worth 10 marks).
Candidates frequently lose marks on these high-tariff questions due to algebraic slips during simultaneous equations and failure to apply the chain rule correctly.
Another critical area is Composite Functions in Paper 11 Q10, where proving why a composite function cannot be formed requires rigorous comparisons of domains and ranges.
Question difficulty map
How candidates performed on each question in this series
No data available in official reports
Assessment objectives
Skill and AO weighting from official examiner commentary
Skill weighting
Shows the skill mix this paper tested most heavily.
Algebraic Manipulation
Weight: 9100%Calculus
Weight: 778%Fluency
Weight: 667%Coordinate Interpretation
Weight: 556%Trigonometric Graphical
Weight: 333%Sketching &
Weight: 111%
Method marks watchlist
Where working, steps, or method marks were commonly lost
No data available in official reports
Recurring mistakes across years
Themes examiners flag in multiple recent sessions for this subject
No data available in official reports
Question choice intelligence
Mean scores and popularity for optional questions (HKDSE electives)
No data available in official reports
Level exemplars
What candidate scripts at each grade level looked like
No data available in official reports
Grade & admission context
How marks relate to grade thresholds and entry standards
Report type
Cambridge Principal Examiner Report — component performance and international standards
Level A
Approx. 78% of maximum mark
Level B
Approx. 66% of maximum mark
Level C
Approx. 50% of maximum mark
Level D
Approx. 36% of maximum mark
Level E
Approx. 22% of maximum mark
Deep insights
What top candidates did
Techniques and approaches examiners rewarded in this series
No data available in official reports
Command word playbook
How to match each command word to the expected response style
Match the expected response style for “Find” questions.
Match the expected response style for “Solve” questions.
Match the expected response style for “Show” questions.
Match the expected response style for “Sketch” questions.
Match the expected response style for “State” questions.
Match the expected response style for “Prove” questions.
Give reasons and link mechanism to outcome; each point needs a because/so chain.
State features in sequence or list observable properties — do not explain causes unless asked.
Time traps
Sections where candidates spent disproportionate time relative to marks
No data available in official reports
Syllabus traceability
Topics linked to questions and mark weighting in this session
Differentiation (Pure Mathematics 2 (for Paper 2))
15 marks this session
Algebra (Pure Mathematics 2 (for Paper 2))
15 marks this session
Series (Pure Mathematics 1 (for Paper 1))
14 marks this session
MCQ trap analytics
Commonly chosen wrong options from examiner commentary
No data available in official reports
Topic heatmap across years
Mark concentration by topic and exam year for this subject
Mark intensity
Series (Pure Mathematics 1 (for Paper 1))
Integration (Pure Mathematics 2 (for Paper 2))
Differentiation (Pure Mathematics 1)
Differentiation (Pure Mathematics 1 (for Paper 1))
Differentiation (Pure Mathematics 2 (for Paper 2))
Algebra (Pure Mathematics 2 (for Paper 2))
Differentiation (Pure Mathematics 2)
Trigonometry (Pure Mathematics 1 (for Paper 1))
Difficulty trend
How session difficulty has shifted across recent years
Paper comparison
Marks and duration breakdown across papers in this session
Paper 11 Pure Mathematics 1:
Paper 21 Pure Mathematics 2:
Marks you can still earn
Where valid approaches outside the mark scheme may still gain credit
No data available in official reports
Practise what examiners flagged
Target weak topics from this report inside the Revui app
Differentiation (Pure Mathematics 2 (for Paper 2))
15 marks this session
Practise in RevuiAlgebra (Pure Mathematics 2 (for Paper 2))
15 marks this session
Practise in RevuiSeries (Pure Mathematics 1 (for Paper 1))
14 marks this session
Practise in RevuiSelf-diagnostic checklist
Key actions before you sit this paper — copy and tick off as you revise
- 1Message
Key high-mark targets include Coordinate Geometry (specifically circle tangents in P11 Q8, worth 8 marks) and Parametric Differentiation (P21 Q6, worth 10 marks).
- 2Message
Candidates frequently lose marks on these high-tariff questions due to algebraic slips during simultaneous equations and failure to apply the chain rule correctly.
- 3Message
Another critical area is Composite Functions in Paper 11 Q10, where proving why a composite function cannot be formed requires rigorous comparisons of domains and ranges.
Teacher briefing pack
One-page session summary for tutors and classroom review
June 2025 2025
Mathematics
Key high-mark targets include Coordinate Geometry (specifically circle tangents in P11 Q8, worth 8 marks) and Parametric Differentiation (P21 Q6, worth 10 marks). Candidates frequently lose marks on these high-tariff questions due to algebraic slips during simultaneous equations
Key high-mark targets include Coordinate Geometry (specifically circle tangents in P11 Q8, worth 8 marks) and Parametric Differentiation (P21 Q6, worth 10 marks).
Candidates frequently lose marks on these high-tariff questions due to algebraic slips during simultaneous equations and failure to apply the chain rule correctly.
Another critical area is Composite Functions in Paper 11 Q10, where proving why a composite function cannot be formed requires rigorous comparisons of domains and ranges.
- Total marks
- 125
- Duration
- 185 min
- Session difficulty
- 3.5 / 5
Session analysis
Key high-mark targets include Coordinate Geometry (specifically circle tangents in P11 Q8, worth 8 marks) and Parametric Differentiation (P21 Q6, worth 10 marks). Candidates frequently lose marks on these high-tariff questions due to algebraic slips during simultaneous equations and failure to apply the chain rule correctly. Another critical area is Composite Functions in Paper 11 Q10, where proving why a composite function cannot be formed requires rigorous comparisons of domains and ranges.
Updated Jun 12, 2026
Paper breakdown
Paper 11 Pure Mathematics 1:
Paper 21 Pure Mathematics 2:
Top chapters
Exam structure insights
Marks by chapter
See where the marks were concentrated so revision time goes to the highest-value topics.
Mark accessibility
Estimate which marks were basic, mid-level, or high-difficulty.
80% within easy or medium reach
Command word frequency
Spot common command words so answers match the expected response style.
Question type mix
Compare the mark share of each paper section and question type.
Coordinate Geometry & Trigonometric Functions
39·5·31%
Functions, Series & Sequences
37·5·30%
Calculus and Curve Integration
31·4·25%
Algebraic Proofs and Identities
18·3·14%
Study ROI
Bigger bubbles recur more often; higher bubbles carry more marks, helping you rank revision priorities.
Next-year prediction
Topics worth watching next year, with the reason shown directly below each bar.
Integration by Trapezium Rule (Pure 2)
85%85%
Trigonometric Proofs and Identities (Pure 1)
80%80%
Examiner notes & key calculations
- Exact vs. Rounded Values: In P21 Q4(a), the question explicitly asks for the exact coordinate. Rounding to decimal forms such as x=1.386 x = 1.386 x=1.386 instead of leaving it as ln(4) \ln(4) ln(4) results in an immediate loss of accuracy marks.
- Calculator Settings: Numerical iteration in P21 Q3(c) must be conducted strictly in radian mode. Running the process in degrees yields nonsense values.
- Incomplete Quadratics: When solving quadratic inequalities or finding discriminant ranges (as in P11 Q6b), failing to correctly formulate the three-term quadratic in terms of the variable coefficient k k k prevents access to method marks.
Exam tips
Paper format
- Duration
- 1h 15min
- Total marks
- 50
Analysis is paraphrased for study purposes. Always verify against the official examiner report and mark scheme.