9231 · Cambridge International AS Level
9231/11
Further Pure Mathematics 1
Mathematics - Further · June 2025 · Variant 1
Relative difficulty
Analysis source: Cambridge Assessment International Education
Analysis aligned to the official syllabus and assessment design.
3.8 / 5
150
240 min
Differential equations
Cohort performance
Session statistics from official examination reports
Total marks
150
Duration
240 min
Session difficulty
3.8 / 5
Key examiner messages
Top priorities from the principal examiner before you revise
A comprehensive analysis of Cambridge International AS & A Level Further Mathematics (9231) Paper 1 (Further Pure Mathematics 1) and Paper 2 (Further Pure Mathematics 2) for May/June 2025.
The papers assess summation of series, roots of polynomials, proof by induction, transformations, polar coordinates, 3D vectors, rational graphs, complex roots, integration reduction formulas, differential equations, and matrices.
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
Weight: 10100%Rigorous Proof & Reasoning
Weight: 990%Calculus & Differentiation
Weight: 880%Integration
Weight: 770%Geometric & Graphical Reasoning
Weight: 660%Spatial Logical
Weight: 550%Proof & I
Weight: 330%Matrix Transformation
Weight: 220%Vector A
Weight: 110%
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. 76% of maximum mark
Level B
Approx. 60% of maximum mark
Level C
Approx. 51% of maximum mark
Level D
Approx. 42% of maximum mark
Level E
Approx. 34% 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 “Show” questions.
Match the expected response style for “Sketch” questions.
Match the expected response style for “Prove” questions.
Match the expected response style for “Deduce” questions.
Match the expected response style for “Verify” questions.
Match the expected response style for “State” questions.
Time traps
Sections where candidates spent disproportionate time relative to marks
Min per mark: 0
Syllabus traceability
Topics linked to questions and mark weighting in this session
Differential equations
20 marks this session
Integration
16 marks this session
Vectors
16 marks this session
Rational functions and graphs
15 marks this session
Hyperbolic functions
15 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
Differential equations (Further Pure Mathematics 2)
Integration (Further Pure Mathematics 2)
Matrices (Further Pure Mathematics 2)
Differential equations
Integration
Vectors
Rational functions and graphs
Hyperbolic functions
Paper comparison
Marks and duration breakdown across papers in this session
Paper 1 Further Pure Mathematics 1:
Paper 2 Further 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
Differential equations
20 marks this session
Practise in RevuiIntegration
16 marks this session
Practise in RevuiVectors
16 marks this session
Practise in RevuiRational functions and graphs
15 marks this session
Practise in RevuiHyperbolic functions
15 marks this session
Practise in RevuiSelf-diagnostic checklist
Key actions before you sit this paper — copy and tick off as you revise
- 1Message
A comprehensive analysis of Cambridge International AS & A Level Further Mathematics (9231) Paper 1 (Further Pure Mathematics 1) and Paper 2 (Further Pure Mathematics 2) for May/June 2025.
- 2Message
The papers assess summation of series, roots of polynomials, proof by induction, transformations, polar coordinates, 3D vectors, rational graphs, complex roots, integration reduction formulas, differential equations, and matrices.
Teacher briefing pack
One-page session summary for tutors and classroom review
June 2025 2025
Mathematics - Further
A comprehensive analysis of Cambridge International AS & A Level Further Mathematics (9231) Paper 1 (Further Pure Mathematics 1) and Paper 2 (Further Pure Mathematics 2) for May/June 2025. The papers assess summation of series, roots of polynomials, proof by induction, transforma
A comprehensive analysis of Cambridge International AS & A Level Further Mathematics (9231) Paper 1 (Further Pure Mathematics 1) and Paper 2 (Further Pure Mathematics 2) for May/June 2025.
The papers assess summation of series, roots of polynomials, proof by induction, transformations, polar coordinates, 3D vectors, rational graphs, complex roots, integration reduction formulas, differential equations, and matrices.
- Total marks
- 150
- Duration
- 240 min
- Session difficulty
- 3.8 / 5
Session analysis
A comprehensive analysis of Cambridge International AS & A Level Further Mathematics (9231) Paper 1 (Further Pure Mathematics 1) and Paper 2 (Further Pure Mathematics 2) for May/June 2025. The papers assess summation of series, roots of polynomials, proof by induction, transformations, polar coordinates, 3D vectors, rational graphs, complex roots, integration reduction formulas, differential equations, and matrices.
Updated Jun 12, 2026
Paper breakdown
Paper 1 Further Pure Mathematics 1:
Paper 2 Further 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.
77% 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.
Short Answer
(1-4 marks)
57·21·38%
Medium Answer
(5-7 marks)
53·9·35%
Long Answer
(8-10 marks)
40·4·27%
Study ROI
Bigger bubbles recur more often; higher bubbles carry more marks, helping you rank revision priorities.
Difficulty trend
Compare difficulty across recent years.
Time vs marks
Compare marks with suggested time allocation to plan exam pacing.
Paper 1 Further Pur…
37.55 m/minTotal marks
751
Total time
20 min
Avg pace
37.55
Cumulative marks ladder
The line is your running mark total question by question; dashed lines are the estimated grade cut-offs. See which question the line crosses your target grade at, so you know how far you must answer cleanly and which questions decide a band.
Next-year prediction
Topics worth watching next year, with the reason shown directly below each bar.
Skew Lines & Intersecting Lines
85%85%
Cayley-Hamilton Matrix Inverse
75%75%
Sum of Series by Method of Differences (alternate forms)
70%70%
Exam tips
Paper format
- Duration
- 2h
- Total marks
- 75
- Weighting
- 50%
- Question types
- Structured Questions
Analysis is paraphrased for study purposes. Always verify against the official examiner report and mark scheme.