MATHEMATICS-M2-ALGEBRA-AND-CALCULUS · HKDSE
MATHEMATICS-M2-ALGEBRA-AND-CALCULUS/11
Paper 1
Mathematics M2 Algebra and Calculus · 2021 2021 · Variant 1
Relative difficulty
Analysis source: Hong Kong Examinations and Assessment Authority (HKEAA)
Analysis aligned to the official syllabus and assessment design.
3.8 / 5
100
150 min
Applications of differentiation
Cohort performance
Session statistics from official examination reports
Total marks
100
Duration
150 min
Session difficulty
3.8 / 5
Level 5**
~90% of max
Level 5*
~76% of max
Level 5
~65% of max
Key examiner messages
Top priorities from the principal examiner before you revise
The 2021 HKDSE Mathematics Module 2 (Algebra and Calculus) paper sits at a solid 4 out of 5 stars in difficulty. While Section A presented familiar, structured tasks, Section B demanded exceptional algebraic stamina and deep conceptual agility, particularly in the integration of
While Section A presented familiar, structured tasks, Section B demanded exceptional algebraic stamina and deep conceptual agility, particularly in the integration of trigonometric substitutions and related rates.
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: 10100%Geometric Visualisation
Weight: 880%Logical
Weight: 660%Deduction & Logical
Weight: 550%Calculus Application
Weight: 440%Matrix
Weight: 220%Operations
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
Reporting source
HKEAA Subject Examination Report — comments on candidates’ performance with marking schemes
Level 5**
Outstanding — competitive JUPAS programmes (medicine, law, top faculties)
Level 5*
Excellent — strong JUPAS profile for selective programmes
Level 5
Good — meets most university entrance requirements
Level 4
Satisfactory — foundation programmes or less selective routes
Level 3
Pass threshold for many sub-degree and vocational pathways
Admission context
Levels feed JUPAS and non-JUPAS university applications; 5** and 5* are most selective
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 “Prove” questions.
Match the expected response style for “Find” questions.
Weigh arguments for and against with evidence; end with a supported judgement.
Match the expected response style for “Solve” questions.
Support your choice with specific evidence from data or the scenario given.
Time traps
Sections where candidates spent disproportionate time relative to marks
Min per mark: 1.4
Syllabus traceability
Topics linked to questions and mark weighting in this session
Applications of differentiation
20 marks this session
Definite integration
19 marks this session
Applications of vectors
13 marks this session
Matrices
12 marks this session
Systems of linear equations
8 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
Definite integration
Applications of vectors
Applications of differentiation
Matrices
Systems of linear equations
Difficulty trend
How session difficulty has shifted across recent years
Paper comparison
Marks and duration breakdown across papers in this session
Module 2 (Algebra and Calculus):
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
Applications of differentiation
20 marks this session
Practise in RevuiDefinite integration
19 marks this session
Practise in RevuiApplications of vectors
13 marks this session
Practise in RevuiMatrices
12 marks this session
Practise in RevuiSystems of linear equations
8 marks this session
Practise in RevuiSelf-diagnostic checklist
Key actions before you sit this paper — copy and tick off as you revise
- 1Message
The 2021 HKDSE Mathematics Module 2 (Algebra and Calculus) paper sits at a solid 4 out of 5 stars in difficulty. While Section A presented familiar, structured tasks, Section B demanded exceptional algebraic stamina and deep conceptual agility, particularly in the integration of
- 2Message
While Section A presented familiar, structured tasks, Section B demanded exceptional algebraic stamina and deep conceptual agility, particularly in the integration of trigonometric substitutions and related rates.
Teacher briefing pack
One-page session summary for tutors and classroom review
2021 2021 2021
Mathematics M2 Algebra and Calculus
The 2021 HKDSE Mathematics Module 2 (Algebra and Calculus) paper sits at a solid 4 out of 5 stars in difficulty. While Section A presented familiar, structured tasks, Section B demanded exceptional algebraic stamina and deep conceptual agility, particularly in the integration of
The 2021 HKDSE Mathematics Module 2 (Algebra and Calculus) paper sits at a solid 4 out of 5 stars in difficulty. While Section A presented familiar, structured tasks, Section B demanded exceptional algebraic stamina and deep conceptual agility, particularly in the integration of
While Section A presented familiar, structured tasks, Section B demanded exceptional algebraic stamina and deep conceptual agility, particularly in the integration of trigonometric substitutions and related rates.
- Total marks
- 100
- Duration
- 150 min
- Session difficulty
- 3.8 / 5
- Level 5**
- ~90% of max
- Level 5*
- ~76% of max
- Level 5
- ~65% of max
Session analysis
The 2021 HKDSE Mathematics Module 2 (Algebra and Calculus) paper sits at a solid 4 out of 5 stars in difficulty. While Section A presented familiar, structured tasks, Section B demanded exceptional algebraic stamina and deep conceptual agility, particularly in the integration of trigonometric substitutions and related rates.
Updated Jun 11, 2026
Paper breakdown
Module 2 (Algebra and Calculus):
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.
75% 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.
Section A
(Short Questions)
50·8·50%
Section B
(Structured Questions)
50·4·50%
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.
Section A
0.71 m/minTotal marks
50
Total time
70 min
Avg pace
0.71
Next-year prediction
Topics worth watching next year, with the reason shown directly below each bar.
Scalar product and vector product
95%95%
Determinants
90%90%
Limits
85%85%
2021 M2 Difficulty Verdict
The 2021 HKDSE Mathematics Module 2 (Algebra and Calculus) paper sits at a solid 4 out of 5 stars in difficulty. While Section A presented familiar, structured tasks, Section B demanded exceptional algebraic stamina and deep conceptual agility, particularly in the integration of trigonometric substitutions and related rates.
Analysis is paraphrased for study purposes. Always verify against the official examiner report and mark scheme.