9231 · Cambridge International AS Level
9231/11
Further Pure Mathematics 1
Mathematics - Further · June 2024 · Variant 1
Relative difficulty
Analysis source: Cambridge Assessment International Education
4.2 / 5
150
240 min
Differential Equations
Cohort performance
Session statistics from official examination reports
Total marks
150
Duration
240 min
Session difficulty
4.2 / 5
Key examiner messages
Top priorities from the principal examiner before you revise
A substantial portion of the marks in Paper 1 was concentrated in Rational Functions and Graphs (15 marks) and Polar Coordinates (15 marks).
In Paper 2, the heaviest weightings lay in Differential Equations (24 marks) and Integration (19 marks).
In Paper 1, Q7 (Polar Coordinates) demanded integration by parts under substitution, which became a prime area for drop-off.
In Paper 2, Q6 and Q7 (Differential Equations) offered 10 marks each for finding particular solutions.
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%Fluency
Weight: 990%Logical
Weight: 880%Proof
Weight: 770%Graphical
Weight: 660%Analysis
Weight: 550%Calculus & Differentiation
Weight: 440%Integration Spatial Visualization
Weight: 330%
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. 79% of maximum mark
Level B
Approx. 60% of maximum mark
Level C
Approx. 52% of maximum mark
Level D
Approx. 43% 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 “that” questions.
Match the expected response style for “Find” 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.
Time traps
Sections where candidates spent disproportionate time relative to marks
Min per mark: 1.7
Min per mark: 1.7
Min per mark: 1.6
Min per mark: 1.6
Min per mark: 1.6
Min per mark: 1.6
Syllabus traceability
Topics linked to questions and mark weighting in this session
Differential equations (Further Pure Mathematics 2)
24 marks this session
Integration (Further Pure Mathematics 2)
19 marks this session
Matrices (Further Pure Mathematics 2)
16 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
Difficulty trend
How session difficulty has shifted across recent years
Paper comparison
Marks and duration breakdown across papers in this session
Paper 1 Further Pure Mathematics 11:
Paper 2 Further Pure Mathematics 21:
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 (Further Pure Mathematics 2)
24 marks this session
Practise in RevuiIntegration (Further Pure Mathematics 2)
19 marks this session
Practise in RevuiMatrices (Further Pure Mathematics 2)
16 marks this session
Practise in RevuiSelf-diagnostic checklist
Key actions before you sit this paper — copy and tick off as you revise
- 1Message
A substantial portion of the marks in Paper 1 was concentrated in Rational Functions and Graphs (15 marks) and Polar Coordinates (15 marks).
- 2Message
In Paper 2, the heaviest weightings lay in Differential Equations (24 marks) and Integration (19 marks).
- 3Message
In Paper 1, Q7 (Polar Coordinates) demanded integration by parts under substitution, which became a prime area for drop-off.
- 4Message
In Paper 2, Q6 and Q7 (Differential Equations) offered 10 marks each for finding particular solutions.
Teacher briefing pack
One-page session summary for tutors and classroom review
June 2024 2024
Mathematics - Further
A substantial portion of the marks in Paper 1 was concentrated in Rational Functions and Graphs (15 marks) and Polar Coordinates (15 marks). In Paper 2, the heaviest weightings lay in Differential Equations (24 marks) and Integration (19 marks). In Paper 1, Q7 (Polar Coordinates)
A substantial portion of the marks in Paper 1 was concentrated in Rational Functions and Graphs (15 marks) and Polar Coordinates (15 marks).
In Paper 2, the heaviest weightings lay in Differential Equations (24 marks) and Integration (19 marks).
In Paper 1, Q7 (Polar Coordinates) demanded integration by parts under substitution, which became a prime area for drop-off.
- Total marks
- 150
- Duration
- 240 min
- Session difficulty
- 4.2 / 5
Session analysis
A substantial portion of the marks in Paper 1 was concentrated in Rational Functions and Graphs (15 marks) and Polar Coordinates (15 marks). In Paper 2, the heaviest weightings lay in Differential Equations (24 marks) and Integration (19 marks). In Paper 1, Q7 (Polar Coordinates) demanded integration by parts under substitution, which became a prime area for drop-off. In Paper 2, Q6 and Q7 (Differential Equations) offered 10 marks each for finding particular solutions. Candidates who solidifed their algorithmic techniques for finding integrating factors and auxiliary roots secured high-yielding marks here.
Updated Jun 12, 2026
Paper breakdown
Paper 1 Further Pure Mathematics 11:
Paper 2 Further Pure Mathematics 21:
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.
70% 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.
Structured Calculations
108·18·72%
Show that / Prove
(Structured)
31·7·21%
Sketching
11·3·7%
Study ROI
Bigger bubbles recur more often; higher bubbles carry more marks, helping you rank revision priorities.
Time vs marks
Compare marks with suggested time allocation to plan exam pacing.
Paper 1 (Q1-Q3) Pol…
0.63 m/minPaper 1 (Q4-Q5) Mat…
0.60 m/minPaper 1 (Q6-Q7) Rat…
0.64 m/minPaper 2 (Q1-Q3) Com…
0.63 m/minPaper 2 (Q4-Q5) Int…
0.60 m/minPaper 2 (Q6-Q7) 1st…
0.64 m/minTotal marks
130
Total time
210 min
Avg pace
0.62
Next-year prediction
Topics worth watching next year, with the reason shown directly below each bar.
Vectors (Skew Lines and Intersections)
90%90%
Complex Numbers (De Moivre's Theorem Application)
85%85%
Examiner notes & key calculations
- Neglecting the Pre-requisite step in Integrating Factors: In Paper 2 Q7(b), many candidates failed to divide the equation xdydx−y=x2sinh−1x x \frac{dy}{dx} - y = x^2 \sinh^{-1}x xdxdy−y=x2sinh−1x by x x x before finding the integrating factor, leading to completely incorrect integrals.
- Method of Differences Misalignment: In Paper 1 Q3(b), the fractional term (14)r+1 \left(\frac{1}{4}\right)^{r+1} (41)r+1 caused severe confusion. Many students failed to factor out constant terms correctly, resulting in telescoping series terms that did not cancel correctly.
- Modulus Graph Cusps: In Paper 1 Q6(d), candidates frequently sketched the modulus function y=∣x2+ax+1x+2∣ y = \left|\frac{x^2+ax+1}{x+2}\right| y=∣∣∣∣x+2x2+ax+1∣∣∣∣ with smooth turning points at the x-intercepts instead of sharp cusps, losing key sketching marks.
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.