9231 · Cambridge International AS Level
9231/21
Further Pure Mathematics 2
Mathematics - Further · June 2023 · 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
Integration
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
The 2023 Further Mathematics series presents a balanced but rigorous test of algebraic stamina and conceptual mastery.
Rated at a 4-star difficulty, Paper 1 and Paper 2 demand not just rote learning of formulas, but deep structural understanding—especially in vectors, polar coordinate calculus, and parametric integration.
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: 7100%Stamina
Weight: 686%Logical
Weight: 571%Proof & R
Weight: 457%Geometric Sketching
Weight: 343%Integration Proficiency
Weight: 114%
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. 81% of maximum mark
Level B
Approx. 70% of maximum mark
Level C
Approx. 59% of maximum mark
Level D
Approx. 49% of maximum mark
Level E
Approx. 38% 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 “Obtain” questions.
Match the expected response style for “Verify” questions.
Match the expected response style for “Deduce” questions.
Time traps
Sections where candidates spent disproportionate time relative to marks
Min per mark: 1.6
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
Integration (Further Pure Mathematics 2)
23 marks this session
Differential equations (Further Pure Mathematics 2)
18 marks this session
Vectors (Further Pure Mathematics 1)
15 marks this session
Matrices (Further Pure Mathematics 2)
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
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
Integration (Further Pure Mathematics 2)
23 marks this session
Practise in RevuiDifferential equations (Further Pure Mathematics 2)
18 marks this session
Practise in RevuiVectors (Further Pure Mathematics 1)
15 marks this session
Practise in RevuiMatrices (Further Pure Mathematics 2)
15 marks this session
Practise in RevuiSelf-diagnostic checklist
Key actions before you sit this paper — copy and tick off as you revise
- 1Message
The 2023 Further Mathematics series presents a balanced but rigorous test of algebraic stamina and conceptual mastery.
- 2Message
Rated at a 4-star difficulty, Paper 1 and Paper 2 demand not just rote learning of formulas, but deep structural understanding—especially in vectors, polar coordinate calculus, and parametric integration.
Teacher briefing pack
One-page session summary for tutors and classroom review
June 2023 2023
Mathematics - Further
The 2023 Further Mathematics series presents a balanced but rigorous test of algebraic stamina and conceptual mastery. Rated at a 4-star difficulty, Paper 1 and Paper 2 demand not just rote learning of formulas, but deep structural understanding—especially in vectors, polar coord
The 2023 Further Mathematics series presents a balanced but rigorous test of algebraic stamina and conceptual mastery.
Rated at a 4-star difficulty, Paper 1 and Paper 2 demand not just rote learning of formulas, but deep structural understanding—especially in vectors, polar coordinate calculus, and parametric integration.
- Total marks
- 150
- Duration
- 240 min
- Session difficulty
- 3.8 / 5
Session analysis
The 2023 Further Mathematics series presents a balanced but rigorous test of algebraic stamina and conceptual mastery. Rated at a 4-star difficulty, Paper 1 and Paper 2 demand not just rote learning of formulas, but deep structural understanding—especially in vectors, polar coordinate calculus, and parametric integration.
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.
73% 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.
Calculation / Solve
89·23·59%
Proof / Show that
53·13·35%
Sketching / Graphing
8·3·5%
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 Section 1 (…
0.63 m/minPaper 1 Section 2 (…
0.62 m/minPaper 1 Section 3 (…
0.63 m/minPaper 2 Section 1 (…
0.63 m/minPaper 2 Section 2 (…
0.62 m/minTotal marks
128
Total time
205 min
Avg pace
0.62
Next-year prediction
Topics worth watching next year, with the reason shown directly below each bar.
Continuous random variables
85%85%
Probability generating functions
80%80%
Linear motion under a variable force
75%75%
Difficulty Verdict
The 2023 Further Mathematics series presents a balanced but rigorous test of algebraic stamina and conceptual mastery. Rated at a 4-star difficulty, Paper 1 and Paper 2 demand not just rote learning of formulas, but deep structural understanding—especially in vectors, polar coordinate calculus, and parametric integration.
Examiner notes & key calculations
- Vector Line Equations: A surprisingly common oversight was omitting the prefix r=\mathbf{r} =r= when writing the vector equation of a line. This leads to an automatic loss of the final accuracy mark.
- Polar Areas: Candidates routinely forget the crucial 12\frac{1}{2}21 factor in the polar area integral A=12∫r2dθA = \frac{1}{2} \int r^2 d\thetaA=21∫r2dθ.
- Parametric Second Derivatives: When differentiating parametrically, many fail to divide the t-derivative of dydx\frac{dy}{dx}dxdy by dxdt\frac{dx}{dt}dtdx, leading to highly complex and incorrect expressions for d2ydx2\frac{d^2y}{dx^2}dx2d2y.
- Induction Hypotheses: Leaving the induction assumption vague or failing to link the base case directly to n=1n=1n=1 remains a frequent source of dropped 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.