MATHEMATICS-COMPULSO · HKDSE
MATHEMATICS-COMPULSO/11
(Conventional Questions)
Mathematics (Compulsory Part) · 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
150
210 min
Coordinate Geometry and Trigonometry
Cohort performance
Session statistics from official examination reports
Total marks
150
Duration
210 min
Session difficulty
3.8 / 5
Level 5**
~90% of max
Level 5*
~84% of max
Level 5
~76% of max
Key examiner messages
Top priorities from the principal examiner before you revise
The 2021 paper is rated as moderately difficult (4 stars). While Section A(1) and A(2) followed historical trends closely, Section B pushed the boundaries of algebraic complexity. In particular, the coordinate geometry of circles in Question 19 and the 3D folding problem in Quest
The 2021 paper is rated as moderately difficult (4 stars).
While Section A(1) and A(2) followed historical trends closely, Section B pushed the boundaries of algebraic complexity.
In particular, the coordinate geometry of circles in Question 19 and the 3D folding problem in Question 18 served as significant hurdles for high-achieving students.
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: 8100%Geometric Visualisation
Weight: 675%Interpretation Logical
Weight: 450%Proof & J
Weight: 225%Management
Weight: 113%
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 “Find” questions.
Give reasons and link mechanism to outcome; each point needs a because/so chain.
Match the expected response style for “Prove” questions.
Match the expected response style for “Simplify” questions.
Match the expected response style for “Factorize” questions.
Match the expected response style for “Make” 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: 1.4
Min per mark: 1.3
Syllabus traceability
Topics linked to questions and mark weighting in this session
Measures of dispersion
15 marks this session
More about Trigonometry
15 marks this session
Quadratic equations in one unknown
14 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
Measures of dispersion
Equations of circles
More about polynomials
More about Trigonometry
Plane geometry
Quadratic equations in one unknown
Mensuration (Area & Volume)
More about graphs of functions
Difficulty trend
How session difficulty has shifted across recent years
Paper comparison
Marks and duration breakdown across papers in this session
Paper 1 (Structured):
Paper 2 (MCQ):
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
Measures of dispersion
15 marks this session
Practise in RevuiMore about Trigonometry
15 marks this session
Practise in RevuiQuadratic equations in one unknown
14 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 paper is rated as moderately difficult (4 stars). While Section A(1) and A(2) followed historical trends closely, Section B pushed the boundaries of algebraic complexity. In particular, the coordinate geometry of circles in Question 19 and the 3D folding problem in Quest
- 2Message
The 2021 paper is rated as moderately difficult (4 stars).
- 3Message
While Section A(1) and A(2) followed historical trends closely, Section B pushed the boundaries of algebraic complexity.
- 4Message
In particular, the coordinate geometry of circles in Question 19 and the 3D folding problem in Question 18 served as significant hurdles for high-achieving students.
Teacher briefing pack
One-page session summary for tutors and classroom review
2021 2021
Mathematics (Compulsory Part)
The 2021 paper is rated as moderately difficult (4 stars). While Section A(1) and A(2) followed historical trends closely, Section B pushed the boundaries of algebraic complexity. In particular, the coordinate geometry of circles in Question 19 and the 3D folding problem in Quest
The 2021 paper is rated as moderately difficult (4 stars). While Section A(1) and A(2) followed historical trends closely, Section B pushed the boundaries of algebraic complexity. In particular, the coordinate geometry of circles in Question 19 and the 3D folding problem in Quest
The 2021 paper is rated as moderately difficult (4 stars).
While Section A(1) and A(2) followed historical trends closely, Section B pushed the boundaries of algebraic complexity.
- Total marks
- 150
- Duration
- 210 min
- Session difficulty
- 3.8 / 5
- Level 5**
- ~90% of max
- Level 5*
- ~84% of max
- Level 5
- ~76% of max
Session analysis
The 2021 paper is rated as moderately difficult (4 stars). While Section A(1) and A(2) followed historical trends closely, Section B pushed the boundaries of algebraic complexity. In particular, the coordinate geometry of circles in Question 19 and the 3D folding problem in Question 18 served as significant hurdles for high-achieving students.
Updated Jun 11, 2026
Paper breakdown
Paper 1 (Structured):
Paper 2 (MCQ):
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.
80% 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.
Paper 2 MCQ
45·45·30%
Paper 1 Section A
(1)
35·9·23%
Paper 1 Section A
(2)
35·5·23%
Paper 1 Section B
35·5·23%
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 A(1)
0.78 m/minPaper 1 Section A(2)
0.70 m/minPaper 1 Section B
0.60 m/minPaper 2 Section A
0.60 m/minTotal marks
115
Total time
170 min
Avg pace
0.68
Next-year prediction
Topics worth watching next year, with the reason shown directly below each bar.
3D Trigonometry & Bearings
90%90%
Loci & Circle Equations
85%85%
Linear Programming
80%80%
Difficulty Verdict
The 2021 paper is rated as moderately difficult (4 stars). While Section A(1) and A(2) followed historical trends closely, Section B pushed the boundaries of algebraic complexity. In particular, the coordinate geometry of circles in Question 19 and the 3D folding problem in Question 18 served as significant hurdles for high-achieving students.
Where the Marks Are
Standard questions in Section A, such as indices (Q1), change of subject (Q2), and factorization (Q3), provided quick, accessible marks. Candidates who mastered basic statistical measures (Q9 and Q11) and linear programming setup (Q16) secured a solid foundation of passing marks. The core of the differentiation, however, lies in the final sub-parts of Section B questions, which carried heavy weightings for precision and algebraic proofs.
Examiner notes & key calculations
- Premature Rounding: In sequence questions (Q17) involving logarithms, many candidates rounded off intermediate values too early, resulting in inaccurate final integer answers for k k k.
- Lack of Rigor in Geometric Proofs: In Q14(b), candidates often asserted similarity of 3D cones without verifying the ratio of corresponding linear dimensions, losing crucial method marks.
- Incomplete Conditions for Quadrilaterals: In Q19(c)(iii), to determine if STUV was a rectangle, many candidates only proved opposite sides were parallel or equal, completely forgetting to test the perpendicularity of adjacent sides.
Exam tips
Paper format
- Duration
- 2h 15min
- Total marks
- 105
Analysis is paraphrased for study purposes. Always verify against the official examiner report and mark scheme.