MATHEMATICS-II-B-C · Common Test for University Admissions (大学入学共通テスト)
MATHEMATICS-II-B-C/11
Mathematics II, Mathematics B and Mathematics C
Mathematics II, B & C · 2022 · Variant 1
Relative difficulty
Analysis source: National Center for University Entrance Examinations (DNC)
Analysis aligned to the official syllabus and assessment design.
5.0 / 5
100
70 min
Calculus applications, sequences and vectors dominate preparation value, especially when questions ask you to connect a graph, formula and parameter condition.
Cohort performance
Session statistics from official examination reports
Total marks
100
Duration
70 min
Session difficulty
5.0 / 5
Calculator policy
Scientific calculators permitted only where specified in the DNC implementation guidelines; programming functions and CAS are prohibited. En
Key examiner messages
Top priorities from the principal examiner before you revise
数学II・数学B・数学C covers advanced algebra and functions, exponential/logarithmic and trigonometric functions, differentiation and integration, sequences, statistics, vectors and complex-plane/plane-curve ideas from the selected curriculum. R7 Common Test mathematics emphasizes sele…
The R7 Mathematics II/B/C paper is 70 minutes for 100 marks, so long chained questions require early recognition of the mathematical structure.
For calculus, the most common calculation chain is derivative -> critical point -> monotonicity -> max/min or graph shape -> area/integral.
When integrating between curves, solve intersections exactly first; wrong limits are more damaging than a minor arithmetic slip.
The DNC Problem Evaluation Committee publishes per-subject reports after each January session, rating alignment with the Course of Study (学習指導要領), item difficulty balance, and whether items discriminate without exceeding syllabus scope.
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
Cognitive skills emphasised in official test design.
Function and calculus reasoning
Weight: 38100%Algebraic calculation
Weight: 2463%Representation switching
Weight: 2258%Modeling and interpretation
Weight: 1642%
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
Calculus: Solving f′(x)=0 and assuming every solution is a maximum or minimum. — Check sign changes, second derivative or endpoints withi…
Integration: Integrating lower minus upper or using wrong intersection limits. — Sketch the region and write area = integral of top - bot…
Sequences: Confusing nth term with partial sum. — Label a_n and S_n separately and use a_n = S_n - S_{n-1} when needed.
Vectors: Treating position vectors and direction vectors as interchangeable. — Mark points as position vectors from origin and sides as d…
Logarithms: Accepting roots that make log arguments non-positive. — Write domain restrictions on the first line and test final roots.
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
Official body
National Center for University Entrance Examinations (DNC)
Grading system
DNC raw score 0–100 per mathematics paper; deviation values used for university admission
Scale band
0–100 raw
Scale band
Deviation 50 = mean
Scale band
University cut-off
Deep insights
What top candidates did
Techniques and approaches examiners rewarded in this series
Choose the representation
Before calculating, decide whether the problem is easier as an equation, graph, table, vector diagram or sequence recurrence. R7-style items often reward switching representation.
Run the calculus template
For max/min: define function, identify domain, differentiate, solve f′(x)=0, check endpoints and interpret. For area: sketch curves, find intersections, integrate upper minus lower.
Classify sequences early
Check for arithmetic, geometric, recurrence, partial sums or difference patterns. Write the first three terms if the type is not obvious.
Use vectors structurally
Draw origin, basis vectors, position vectors and parameters. For collinearity, set one vector as a scalar multiple of another; for perpendicularity, use dot product zero.
Keep logarithm/exponential domains visible
Write positivity restrictions before transforming equations. Many distractors include algebraic roots outside the domain.
Protect arithmetic accuracy
Because questions are chained, one derivative or sign error can corrupt several boxes. Check each derived expression against the graph or a simple value.
Command word playbook
How to match each command word to the expected response style
No data available in official reports
Time traps
Sections where candidates spent disproportionate time relative to marks
No data available in official reports
Syllabus traceability
Topics linked to questions and mark weighting in this session
Mathematics II functions, equations and calculus
Official topic weighting
Sequences and mathematical induction-style reasoning
Official topic weighting
Statistics and probability distributions
Official topic weighting
Vectors, complex plane and geometric representation
Official topic weighting
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
Mathematics II functions, equations and calculus
Vectors, complex plane and geometric representation
Sequences and mathematical induction-style reasoning
Statistics and probability distributions
Difficulty trend
How session difficulty has shifted across recent years
Paper comparison
Marks and duration breakdown across papers in this session
Mathematics II, Mathematics B and Mathematics C: Functions, calculus, sequences, statistics, vectors and complex-plane/geometric tasks
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
Mathematics II functions, equations and calculus
Official topic weighting
Practise in RevuiSequences and mathematical induction-style reasoning
Official topic weighting
Practise in RevuiStatistics and probability distributions
Official topic weighting
Practise in RevuiVectors, complex plane and geometric representation
Official topic weighting
Practise in RevuiSelf-diagnostic checklist
Key actions before you sit this paper — copy and tick off as you revise
- 1Message
数学II・数学B・数学C covers advanced algebra and functions, exponential/logarithmic and trigonometric functions, differentiation and integration, sequences, statistics, vectors and complex-plane/plane-curve ideas from the selected curriculum. R7 Common Test mathematics emphasizes sele…
- 2Message
The R7 Mathematics II/B/C paper is 70 minutes for 100 marks, so long chained questions require early recognition of the mathematical structure.
- 3Message
For calculus, the most common calculation chain is derivative -> critical point -> monotonicity -> max/min or graph shape -> area/integral.
- 4Message
When integrating between curves, solve intersections exactly first; wrong limits are more damaging than a minor arithmetic slip.
- 5Message
The DNC Problem Evaluation Committee publishes per-subject reports after each January session, rating alignment with the Course of Study (学習指導要領), item difficulty balance, and whether items discriminate without exceeding syllabus scope.
- 6Pitfall
Calculus: Solving f′(x)=0 and assuming every solution is a maximum or minimum. — Check sign changes, second derivative or endpoints withi…
- 7Pitfall
Integration: Integrating lower minus upper or using wrong intersection limits. — Sketch the region and write area = integral of top - bot…
- 8Pitfall
Sequences: Confusing nth term with partial sum. — Label a_n and S_n separately and use a_n = S_n - S_{n-1} when needed.
- 9Pitfall
Vectors: Treating position vectors and direction vectors as interchangeable. — Mark points as position vectors from origin and sides as d…
- 10Pitfall
Logarithms: Accepting roots that make log arguments non-positive. — Write domain restrictions on the first line and test final roots.
- 11Strength
Choose the representation: Before calculating, decide whether the problem is easier as an equation, graph, table, vector diagra
- 12Strength
Run the calculus template: For max/min: define function, identify domain, differentiate, solve f′(x)=0, check endpoints and int
- 13Strength
Classify sequences early: Check for arithmetic, geometric, recurrence, partial sums or difference patterns. Write the first th
Teacher briefing pack
One-page session summary for tutors and classroom review
2022 2022
Mathematics II, B & C
数学II・数学B・数学C covers advanced algebra and functions, exponential/logarithmic and trigonometric functions, differentiation and integration, sequences, statistics, vectors and complex-plane/plane-curve ideas from the selected curriculum. R7 Common Test mathematics emphasizes selecti
数学II・数学B・数学C covers advanced algebra and functions, exponential/logarithmic and trigonometric functions, differentiation and integration, sequences, statistics, vectors and complex-plane/plane-curve ideas from the selected curriculum. R7 Common Test mathematics emphasizes sele…
The R7 Mathematics II/B/C paper is 70 minutes for 100 marks, so long chained questions require early recognition of the mathematical structure.
For calculus, the most common calculation chain is derivative -> critical point -> monotonicity -> max/min or graph shape -> area/integral.
Calculus: Solving f′(x)=0 and assuming every solution is a maximum or minimum. — Check sign changes, second derivative or endpoints withi…
Integration: Integrating lower minus upper or using wrong intersection limits. — Sketch the region and write area = integral of top - bot…
- Total marks
- 100
- Duration
- 70 min
- Session difficulty
- 5.0 / 5
- Calculator policy
- Scientific calculators permitted only where specified in the DNC implementation guidelines; programming functions and CAS are prohibited. En
Session analysis
数学II・数学B・数学C covers advanced algebra and functions, exponential/logarithmic and trigonometric functions, differentiation and integration, sequences, statistics, vectors and complex-plane/plane-curve ideas from the selected curriculum. R7 Common Test mathematics emphasizes selecting methods, connecting representations and interpreting multi-step results. National Center for University Entrance Examinations (DNC) emphasises calculus applications, sequences and vectors dominate preparation value, especially when questions ask you to connect a graph, formula and parameter condition.. Priority revision: Mathematics II functions, equations and calculus, Sequences and mathematical induction-style reasoning, Statistics and probability distributions, Vectors, complex plane and geometric representation. Before calculating, decide whether the problem is easier as an equation, graph, table, vector diagram or sequence recurrence. R7-style items often reward switching representation.
Updated 2026-07-03
Paper breakdown
Mathematics II, Mathematics B and Mathematics C: Functions, calculus, sequences, statistics, vectors and complex-plane/geometric tasks
Top chapters
Exam structure insights
Marks by syllabus topic
Revision priority from official test-design weighting.
Mark accessibility
Estimated difficulty spread based on official design.
Calculus applications, sequences and vectors dominate preparation value, especia
Paper structure
Official paper breakdown for this subject.
Mathematics II, Mathematics
100·10·100%
Official syllabus scope
数学II・数学B・数学C covers advanced algebra and functions, exponential/logarithmic and trigonometric functions, differentiation and integration, sequences, statistics, vectors and complex-plane/plane-curve ideas from the selected curriculum. R7 Common Test mathematics emphasizes selecting methods, connecting representations and interpreting multi-step results.
Difficulty verdict
Rated 5/5 for January sessions. Calculus applications, sequences and vectors dominate preparation value, especially when questions ask you to connect a graph, formula and parameter condition.
What examiners measure
1. Analyze functions using algebraic, graphical and calculus-based methods. 2. Solve sequence, vector, statistics and complex-number problems from given conditions. 3. Model situations and choose appropriate formulas or representations. 4. Carry out multi-step calculations accurately under time pressure. 5. Interpret mathematical results and constraints in the context of the problem.
Where the marks are
Highest-weight syllabus areas: Mathematics II functions, equations and calculus; Sequences and mathematical induction-style reasoning; Statistics and probability distributions; Vectors, complex plane and geometric representation.
Examiner notes & key calculations
- The R7 Mathematics II/B/C paper is 70 minutes for 100 marks, so long chained questions require early recognition of the mathematical structure.
- For calculus, the most common calculation chain is derivative -> critical point -> monotonicity -> max/min or graph shape -> area/integral.
- When integrating between curves, solve intersections exactly first; wrong limits are more damaging than a minor arithmetic slip.
- For sequences, sum formulas are frequent: arithmetic S_n = n(a_1 + a_n)/2, geometric S_n = a(1 - r^n)/(1 - r) when r != 1.
- Vector geometry often reduces to dot product, scalar multiple or section formula; write these before substituting numbers.
- Statistics items can require interpreting normal distribution standardization z = (x - mean) / standard deviation, not only reading a table.
- Complex-plane problems are geometric: modulus means distance, argument means angle, and multiplication rotates/scales.
- Paper 1: Mathematics II, Mathematics B and Mathematics C · 100 marks · 70 min · Functions, calculus, sequences, statistics, vectors and complex-plane/geometric tasks.
Exam tips
Paper format
- Duration
- 70 min
- Total marks
- 100
- Weighting
- 100%
- Question types
- Functions, calculus, sequences, statistics, vectors and complex-plane/geometric tasks
- Before calculating, decide whether the problem is easier as an equation, graph, table, vector diagram or sequence recurrence. R7-style items often reward switching representation.
- For max/min: define function, identify domain, differentiate, solve f′(x)=0, check endpoints and interpret. For area: sketch curves, find intersections, integrate upper minus lower.
- Check for arithmetic, geometric, recurrence, partial sums or difference patterns. Write the first three terms if the type is not obvious.
Common mistakes
Calculus
Solving f′(x)=0 and assuming every solution is a maximum or minimum.
How to avoid: Check sign changes, second derivative or endpoints within the domain.
Integration
Integrating lower minus upper or using wrong intersection limits.
How to avoid: Sketch the region and write area = integral of top - bottom over the correct interval.
Sequences
Confusing nth term with partial sum.
How to avoid: Label a_n and S_n separately and use a_n = S_n - S_{n-1} when needed.
Analysis is paraphrased for study purposes. Always verify against the official examiner report and mark scheme.