MATHEMATICS-I · Common Test for University Admissions (大学入学共通テスト)
MATHEMATICS-I/11
Mathematics I
Mathematics I · 2020 · Variant 1
Relative difficulty
Analysis source: National Center for University Entrance Examinations (DNC)
Analysis aligned to the official syllabus and assessment design.
3.0 / 5
100
70 min
Quadratic functions and their graph behavior, including vertex form, intersections, discriminants and domain-restricted maximum/minimum problems.
Cohort performance
Session statistics from official examination reports
Total marks
100
Duration
70 min
Session difficulty
3.0 / 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I covers numbers and expressions, quadratic functions, figures and measurement, and data analysis. R7 Common Test questions require students to understand mathematical concepts, use them in context, and explain relationships among formulas, graphs, diagrams and data.
Mathematics I is 70 minutes for 100 points; a target pace is about 1.4 points per minute, with routine algebra completed quickly.
The official style favors context-rich tasks, so translate words into variables before applying formulas.
For a quadratic f(x) = ax² + bx + c, the axis is x = -b/(2a), vertex value is f(-b/(2a)), and D = b² - 4ac gives intersection count.
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.
Algebraic and calculation
Weight: 30100%Function and Graphical reasoning
Weight: 30100%Geometry and measurement
Weight: 2273%Data interpretation
Weight: 1860%
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
Quadratics: Using discriminant conclusions without considering tangency or domain restrictions. — After calculating D, check whether inte…
Inequalities: Forgetting to reverse the inequality sign when multiplying or dividing by a negative. — Mark negative operations with an ar…
Trigonometry: Using the wrong side for sine, cosine or tangent. — Label sides relative to the given angle, not relative to the drawing or…
Data: Assuming a stronger correlation because the slope is steep. — Correlation depends on tightness around a line, not just slope.
Rounding: Rounding intermediate values and missing an exact answer. — Keep radicals and fractions exact until the last step.
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
Secure algebra speed
Factorization, expansion, completing the square and inequality manipulation should be automatic. Slow algebra drains time from interpretation items.
Use a quadratic checklist
For every quadratic, write: vertex, axis, intercepts, discriminant and domain. Most questions use one of these five facts.
Sketch before solving
A rough graph prevents sign and range errors. Mark the axis of symmetry and whether the parabola opens upward or downward.
Treat trigonometry as geometry
Draw the triangle, label opposite/adjacent/hypotenuse and check whether the angle is in degrees. Apply sine/cosine rules only after the figure is clear.
Read statistical displays exactly
For histograms, box plots and scatter plots, distinguish median, mean, quartiles, outliers, correlation and regression trend.
Check answer-box constraints
If the answer format expects integer boxes or fractional parts, use exact values and avoid decimal rounding until the final decision.
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
Numbers, expressions and equations
Official topic weighting
Quadratic functions
Official topic weighting
Figures, measurement and trigonometric ratios
Official topic weighting
Data analysis
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
Quadratic functions
Numbers, expressions and equations
Figures, measurement and trigonometric ratios
Data analysis
Difficulty trend
How session difficulty has shifted across recent years
Paper comparison
Marks and duration breakdown across papers in this session
Mathematics I: Algebra, quadratic functions, measurement, trigonometry and data analysis
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
Numbers, expressions and equations
Official topic weighting
Practise in RevuiQuadratic functions
Official topic weighting
Practise in RevuiFigures, measurement and trigonometric ratios
Official topic weighting
Practise in RevuiData analysis
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I covers numbers and expressions, quadratic functions, figures and measurement, and data analysis. R7 Common Test questions require students to understand mathematical concepts, use them in context, and explain relationships among formulas, graphs, diagrams and data.
- 2Message
Mathematics I is 70 minutes for 100 points; a target pace is about 1.4 points per minute, with routine algebra completed quickly.
- 3Message
The official style favors context-rich tasks, so translate words into variables before applying formulas.
- 4Message
For a quadratic f(x) = ax² + bx + c, the axis is x = -b/(2a), vertex value is f(-b/(2a)), and D = b² - 4ac gives intersection count.
- 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
Quadratics: Using discriminant conclusions without considering tangency or domain restrictions. — After calculating D, check whether inte…
- 7Pitfall
Inequalities: Forgetting to reverse the inequality sign when multiplying or dividing by a negative. — Mark negative operations with an ar…
- 8Pitfall
Trigonometry: Using the wrong side for sine, cosine or tangent. — Label sides relative to the given angle, not relative to the drawing or…
- 9Pitfall
Data: Assuming a stronger correlation because the slope is steep. — Correlation depends on tightness around a line, not just slope.
- 10Pitfall
Rounding: Rounding intermediate values and missing an exact answer. — Keep radicals and fractions exact until the last step.
- 11Strength
Secure algebra speed: Factorization, expansion, completing the square and inequality manipulation should be automatic. Slo
- 12Strength
Use a quadratic checklist: For every quadratic, write: vertex, axis, intercepts, discriminant and domain. Most questions use on
- 13Strength
Sketch before solving: A rough graph prevents sign and range errors. Mark the axis of symmetry and whether the parabola ope
Teacher briefing pack
One-page session summary for tutors and classroom review
2020 2020
Mathematics I
数学I covers numbers and expressions, quadratic functions, figures and measurement, and data analysis. R7 Common Test questions require students to understand mathematical concepts, use them in context, and explain relationships among formulas, graphs, diagrams and data. National C
数学I covers numbers and expressions, quadratic functions, figures and measurement, and data analysis. R7 Common Test questions require students to understand mathematical concepts, use them in context, and explain relationships among formulas, graphs, diagrams and data.
Mathematics I is 70 minutes for 100 points; a target pace is about 1.4 points per minute, with routine algebra completed quickly.
The official style favors context-rich tasks, so translate words into variables before applying formulas.
Quadratics: Using discriminant conclusions without considering tangency or domain restrictions. — After calculating D, check whether inte…
Inequalities: Forgetting to reverse the inequality sign when multiplying or dividing by a negative. — Mark negative operations with an ar…
- Total marks
- 100
- Duration
- 70 min
- Session difficulty
- 3.0 / 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I covers numbers and expressions, quadratic functions, figures and measurement, and data analysis. R7 Common Test questions require students to understand mathematical concepts, use them in context, and explain relationships among formulas, graphs, diagrams and data. National Center for University Entrance Examinations (DNC) emphasises quadratic functions and their graph behavior, including vertex form, intersections, discriminants and domain-restricted maximum/minimum problems.. Priority revision: Numbers, expressions and equations, Quadratic functions, Figures, measurement and trigonometric ratios, Data analysis. Factorization, expansion, completing the square and inequality manipulation should be automatic. Slow algebra drains time from interpretation items.
Updated 2026-07-03
Paper breakdown
Mathematics I: Algebra, quadratic functions, measurement, trigonometry and data analysis
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.
Quadratic functions and their graph behavior, including vertex form, intersectio
Paper structure
Official paper breakdown for this subject.
Mathematics I
100·10·100%
Official syllabus scope
数学I covers numbers and expressions, quadratic functions, figures and measurement, and data analysis. R7 Common Test questions require students to understand mathematical concepts, use them in context, and explain relationships among formulas, graphs, diagrams and data.
Difficulty verdict
Rated 3/5 for January sessions. Quadratic functions and their graph behavior, including vertex form, intersections, discriminants and domain-restricted maximum/minimum problems.
What examiners measure
1. Manipulate algebraic expressions and equations accurately. 2. Analyze quadratic functions, graphs, maximum/minimum and intersections. 3. Apply trigonometric ratios and geometric measurement in figures. 4. Interpret statistical data, graphs and summary measures. 5. Connect formulas, diagrams and real-world situations through mathematical reasoning.
Where the marks are
Highest-weight syllabus areas: Numbers, expressions and equations; Quadratic functions; Figures, measurement and trigonometric ratios; Data analysis.
Examiner notes & key calculations
- Mathematics I is 70 minutes for 100 points; a target pace is about 1.4 points per minute, with routine algebra completed quickly.
- The official style favors context-rich tasks, so translate words into variables before applying formulas.
- For a quadratic f(x) = ax² + bx + c, the axis is x = -b/(2a), vertex value is f(-b/(2a)), and D = b² - 4ac gives intersection count.
- Restricted-domain maximum/minimum requires comparing vertex and endpoints. Do not stop at the vertex formula.
- In data questions, mean changes with every value, median depends on order position, and standard deviation depends on spread.
- Geometry items may combine trigonometric ratios with area: triangle area = 1/2 ab sin C is often faster than height construction.
- When a problem includes a student dialogue, underline the mathematical claim being checked; some dialogue sentences are explanatory, not conditions.
- Paper 1: Mathematics I · 100 marks · 70 min · Algebra, quadratic functions, measurement, trigonometry and data analysis.
Exam tips
Paper format
- Duration
- 70 min
- Total marks
- 100
- Weighting
- 100%
- Question types
- Algebra, quadratic functions, measurement, trigonometry and data analysis
- Factorization, expansion, completing the square and inequality manipulation should be automatic. Slow algebra drains time from interpretation items.
- For every quadratic, write: vertex, axis, intercepts, discriminant and domain. Most questions use one of these five facts.
- A rough graph prevents sign and range errors. Mark the axis of symmetry and whether the parabola opens upward or downward.
Common mistakes
Quadratics
Using discriminant conclusions without considering tangency or domain restrictions.
How to avoid: After calculating D, check whether intersections lie inside the given domain.
Inequalities
Forgetting to reverse the inequality sign when multiplying or dividing by a negative.
How to avoid: Mark negative operations with an arrow before rewriting the inequality.
Trigonometry
Using the wrong side for sine, cosine or tangent.
How to avoid: Label sides relative to the given angle, not relative to the drawing orientation.
Analysis is paraphrased for study purposes. Always verify against the official examiner report and mark scheme.