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9231 · Cambridge International A Level

9231/31

Structured Questions

Mathematics - Further · June 2025 · Variant 1

Relative difficulty

Demanding · 4.0/5

Analysis source: Cambridge Assessment International Education

Analysis aligned to the official syllabus and assessment design.

Relative difficulty

4.0 / 5

Total marks

250

Duration

420 min

Most tested topic

Differential equations

Cohort performance

Session statistics from official examination reports

Total marks

250

Duration

420 min

Session difficulty

4.0 / 5

Key examiner messages

Top priorities from the principal examiner before you revise

1

Rigorous and well-structured examination series testing deep algebraic manipulation, exact calculus methods, applied multi-stage mechanics, and detailed non-parametric statistical tests.

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

Algebraic Manipulation9
Calculus and7
Geometric Reasoning6
Statistical Inference4
Mathematical2
Proof1

Skill weighting

Shows the skill mix this paper tested most heavily.

Algebraic ManipulationAlgebraicManipulationCalculus andCalculus andGeometric ReasoningGeometricReasoningStatistical InferenceStatisticalInferenceMathematicalMathematicalProofProof
SkillWeightShare
  • Algebraic Manipulation

    Weight: 9100%
  • Calculus and

    Weight: 778%
  • Geometric Reasoning

    Weight: 667%
  • Statistical Inference

    Weight: 444%
  • Mathematical

    Weight: 222%
  • Proof

    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. 84% of maximum mark

Level A

Approx. 70% of maximum mark

Level B

Approx. 56% of maximum mark

Level C

Approx. 47% of maximum mark

Level D

Approx. 38% of maximum mark

Level E

Approx. 28% 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

FindFrequency: 17

Match the expected response style for “Find” questions.

thatFrequency: 12

Match the expected response style for “that” questions.

SketchFrequency: 4

Match the expected response style for “Sketch” questions.

DeduceFrequency: 3

Match the expected response style for “Deduce” questions.

ProveFrequency: 2

Match the expected response style for “Prove” questions.

VerifyFrequency: 2

Match the expected response style for “Verify” questions.

StateFrequency: 1

Match the expected response style for “State” questions.

CommentFrequency: 1

Match the expected response style for “Comment” questions.

Time traps

Sections where candidates spent disproportionate time relative to marks

Paper 31 (Further M90m / 50 marks

Min per mark: 1.8

Paper 41 (Further P90m / 50 marks

Min per mark: 1.8

Syllabus traceability

Topics linked to questions and mark weighting in this session

Differential equations

20 marks this session

Integration (Further Pure Mathematics 2)

16 marks this session

Vectors

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

LowHigh
Topic
2023
2024
2025
Σ

Integration (Further Pure Mathematics 2)

15
21
16
52

Differential equations (Further Pure Mathematics 2)

18
20
38

Differential equations

20
20

Vectors

16
16

Matrices (Further Pure Mathematics 2)

16
16

Circular motion (Further Mechanics)

16
16

Rational functions and graphs (Further Pure Mathematics 1)

15
15

Paper comparison

Marks and duration breakdown across papers in this session

Paper 11 Further Pure Mathematics 1:

75 marks120 min

Paper 21 Further Pure Mathematics 2:

75 marks120 min

Paper 31 Further Mechanics:

50 marks90 min

Paper 41 Further Probability & Statistics:

50 marks90 min

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

Self-diagnostic checklist

Key actions before you sit this paper — copy and tick off as you revise

  • 1Message

    Rigorous and well-structured examination series testing deep algebraic manipulation, exact calculus methods, applied multi-stage mechanics, and detailed non-parametric statistical tests.

Teacher briefing pack

One-page session summary for tutors and classroom review

June 2025 2025

Mathematics - Further

Rigorous and well-structured examination series testing deep algebraic manipulation, exact calculus methods, applied multi-stage mechanics, and detailed non-parametric statistical tests.

  • Rigorous and well-structured examination series testing deep algebraic manipulation, exact calculus methods, applied multi-stage mechanics, and detailed non-parametric statistical tests.

Total marks
250
Duration
420 min
Session difficulty
4.0 / 5

Session analysis

Rigorous and well-structured examination series testing deep algebraic manipulation, exact calculus methods, applied multi-stage mechanics, and detailed non-parametric statistical tests.

Updated Jun 12, 2026

Paper breakdown

Paper 11 Further Pure Mathematics 1:

75 marks120 min

Paper 21 Further Pure Mathematics 2:

75 marks120 min

Paper 31 Further Mechanics:

50 marks90 min

Paper 41 Further Probability & Statistics:

50 marks90 min

Top chapters

Differential equations20 marks
Integration (Further Pure Mathematics 2)16 marks
Vectors16 marks

Exam structure insights

Marks by chapter

See where the marks were concentrated so revision time goes to the highest-value topics.

Summation of series8 marks
Roots of polynomial equations7 marks
Proof by induction7 marks
Matrices (FPM1)9 marks
Polar coordinates13 marks
Vectors16 marks
Rational functions and graphs15 marks
Complex numbers11 marks

Mark accessibility

Estimate which marks were basic, mid-level, or high-difficulty.

80% within easy or medium reach

75
125
50
Easy: 75 marksMedium: 125 marksHard: 50 marks

Command word frequency

Spot common command words so answers match the expected response style.

Find17 times
that12 times
Sketch4 times
Deduce3 times
Prove2 times
Verify2 times
State1 times
Comment1 times

Question type mix

Compare the mark share of each paper section and question type.

250Marks
  • Long Structured

    120·10·48%

  • Medium Structured

    97·12·39%

  • Short Answer

    33·6·13%

Study ROI

Bigger bubbles recur more often; higher bubbles carry more marks, helping you rank revision priorities.

DifficultyRecurrence %Differential equat…VectorsRational functions…Circular motionContinuous random …

Difficulty trend

Compare difficulty across recent years.

4.520133.820143.82015420164.220173.820183.820194.220203.820214.220224.120234.5202442025

Time vs marks

Compare marks with suggested time allocation to plan exam pacing.

MarksMinutesMarks / min

Paper 31 (Further M

0.56 m/min
50
90

Paper 41 (Further P

0.56 m/min
50
90

Total marks

100

Total time

180 min

Avg pace

0.56

Next-year prediction

Topics worth watching next year, with the reason shown directly below each bar.

Matrices (Paper 1)

95%

95%

Proof by induction

90%

90%

Non-parametric tests

85%

85%

Analysis is paraphrased for study purposes. Always verify against the official examiner report and mark scheme.

9231/31 — Cambridge International A Level Mathematics - Further (June 2025) | Revui