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MATHEMATICS-I-A · Common Test for University Admissions (大学入学共通テスト)

MATHEMATICS-I-A/11

Mathematics I and Mathematics A

Mathematics I & A · 2024 · Variant 1

Relative difficulty

Demanding · 4.2/5

Analysis source: National Center for University Entrance Examinations (DNC)

Analysis aligned to the official syllabus and assessment design.

Relative difficulty

4.2 / 5

Total marks

100

Duration

70 min

Most tested topic

Probability, quadratic functions, data analysis and geometry conditions are frequent high-yield areas, especially when embedded in a real-world or dialogue-style setting.

Cohort performance

Session statistics from official examination reports

Total marks

100

Duration

70 min

Session difficulty

4.2 / 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

1

数学I・数学A is based on Mathematics I and Mathematics A, including numbers and expressions, quadratic functions, figures and measurement, data analysis, cases and probability, integer properties and geometric properties. R7 Common Test mathematics emphasizes mathematical activity:…

2

R7 mathematics follows the Common Test pattern of guided mathematical activity: read the situation, infer the relation, then compute.

3

The 70-minute, 100-point paper gives 0.7 minutes per mark; long dialogues must be skimmed for mathematical conditions before detailed reading.

4

For quadratic max/min, the reliable calculation is: convert to vertex form, check axis, evaluate endpoints if the domain is restricted.

5

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

Model everyday or mathematical situations using expressions, functions, figures and probability.
Carry out algebraic, geometric and statistical procedures accurately.
Choose efficient solution strategies and connect multiple representations.
Interpret results in the context of a problem and judge reasonableness.
Use diagrams, tables and conditions to support multi-step reasoning.

Skill weighting

Cognitive skills emphasised in official test design.

Algebraic manipulationAlgebraicmanipulationMathematical modelingMathematicalmodelingGeometric and probabilistic reasoningGeometric andprobabilisticData interpretationDatainterpretation
SkillWeightShare
  • Geometric and probabilistic reasoning

    Weight: 30100%
  • Algebraic manipulation

    Weight: 2583%
  • Mathematical modeling

    Weight: 2583%
  • Data interpretation

    Weight: 2067%

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

Probability: Multiplying probabilities as if events were independent when sampling without replacement. — Update numerator and denominato…

2023 20232022 20222021 20212020 20204 sessions

Quadratic functions: Finding the vertex but ignoring the restricted domain for maximum/minimum. — Evaluate vertex and endpoints whenever …

2023 20232022 20222021 20212020 20204 sessions

Data analysis: Confusing correlation with causation or standard deviation with range. — State what each statistic measures before matchin…

2023 20232022 20222021 20212020 20204 sessions

Geometry: Assuming a diagram is to scale. — Use only marked equalities, parallel lines, angles and given lengths as evidence.

2023 20232022 20222021 20212020 20204 sessions

Integer properties: Testing too few cases and missing parity or divisibility constraints. — Factor first, then apply parity/modular condi…

2023 20232022 20222021 20212020 20204 sessions

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

Use the first minute to classify

Identify the domain of each major question before calculating: quadratic, trigonometric ratio, data, probability, integer or geometry. Classification prevents using a familiar formula in the wrong context.

Write formulas with conditions

For quadratics, note domain restrictions; for probability, note whether events are independent; for geometry, note congruence/similarity conditions before calculation.

Draw full probability trees

The Common Test often uses dependent events. Show changing denominators after each draw or condition, then simplify only at the end.

Turn data into numbers

For box plots, scatter plots and standard deviation, estimate center, spread and correlation direction. Compute deviations when values are provided rather than relying on visual impression.

Exploit answer format

Fill-in numeric boxes reward exact arithmetic. Keep fractions exact until the final box and check sign, digit count and simplification.

Reserve review time

Aim to finish the first pass in 62 minutes. Use the final 8 minutes to revisit probability conditions and algebra signs, where avoidable errors cluster.

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 quadratic functions

Official topic weighting

Figures, measurement and geometric properties

Official topic weighting

Data analysis

Official topic weighting

Cases, probability and integer properties

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

LowHigh
Topic
2020
2021
2022
2023
2024
Σ

Cases, probability and integer properties

32
32
32
32
32
160

Numbers, expressions and quadratic functions

28
28
28
28
28
140

Figures, measurement and geometric properties

22
22
22
22
22
110

Data analysis

18
18
18
18
18
90

Difficulty trend

How session difficulty has shifted across recent years

20202021202220232024
2020 2020 · 4.0/52021 2021 · 4.0/52022 2022 · 4.0/52023 2023 · 4.0/52024 2024 · 4.2/5

Paper comparison

Marks and duration breakdown across papers in this session

Mathematics I and Mathematics A: Algebra, functions, geometry, data, probability, integers and guided multi-step tasks

100 marks70 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

    数学I・数学A is based on Mathematics I and Mathematics A, including numbers and expressions, quadratic functions, figures and measurement, data analysis, cases and probability, integer properties and geometric properties. R7 Common Test mathematics emphasizes mathematical activity:…

  • 2Message

    R7 mathematics follows the Common Test pattern of guided mathematical activity: read the situation, infer the relation, then compute.

  • 3Message

    The 70-minute, 100-point paper gives 0.7 minutes per mark; long dialogues must be skimmed for mathematical conditions before detailed reading.

  • 4Message

    For quadratic max/min, the reliable calculation is: convert to vertex form, check axis, evaluate endpoints if the domain is restricted.

  • 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

    Probability: Multiplying probabilities as if events were independent when sampling without replacement. — Update numerator and denominato…

  • 7Pitfall

    Quadratic functions: Finding the vertex but ignoring the restricted domain for maximum/minimum. — Evaluate vertex and endpoints whenever …

  • 8Pitfall

    Data analysis: Confusing correlation with causation or standard deviation with range. — State what each statistic measures before matchin…

  • 9Pitfall

    Geometry: Assuming a diagram is to scale. — Use only marked equalities, parallel lines, angles and given lengths as evidence.

  • 10Pitfall

    Integer properties: Testing too few cases and missing parity or divisibility constraints. — Factor first, then apply parity/modular condi…

  • 11Strength

    Use the first minute to classify: Identify the domain of each major question before calculating: quadratic, trigonometric ratio, data,

  • 12Strength

    Write formulas with conditions: For quadratics, note domain restrictions; for probability, note whether events are independent; for

  • 13Strength

    Draw full probability trees: The Common Test often uses dependent events. Show changing denominators after each draw or condition

Teacher briefing pack

One-page session summary for tutors and classroom review

2024 2024

Mathematics I & A

数学I・数学A is based on Mathematics I and Mathematics A, including numbers and expressions, quadratic functions, figures and measurement, data analysis, cases and probability, integer properties and geometric properties. R7 Common Test mathematics emphasizes mathematical activity: re

  • 数学I・数学A is based on Mathematics I and Mathematics A, including numbers and expressions, quadratic functions, figures and measurement, data analysis, cases and probability, integer properties and geometric properties. R7 Common Test mathematics emphasizes mathematical activity:…

  • R7 mathematics follows the Common Test pattern of guided mathematical activity: read the situation, infer the relation, then compute.

  • The 70-minute, 100-point paper gives 0.7 minutes per mark; long dialogues must be skimmed for mathematical conditions before detailed reading.

  • Probability: Multiplying probabilities as if events were independent when sampling without replacement. — Update numerator and denominato…

  • Quadratic functions: Finding the vertex but ignoring the restricted domain for maximum/minimum. — Evaluate vertex and endpoints whenever …

Total marks
100
Duration
70 min
Session difficulty
4.2 / 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・数学A is based on Mathematics I and Mathematics A, including numbers and expressions, quadratic functions, figures and measurement, data analysis, cases and probability, integer properties and geometric properties. R7 Common Test mathematics emphasizes mathematical activity: reading situations, formulating relationships, choosing methods and interpreting results. National Center for University Entrance Examinations (DNC) emphasises probability, quadratic functions, data analysis and geometry conditions are frequent high-yield areas, especially when embedded in a real-world or dialogue-style setting.. Priority revision: Numbers, expressions and quadratic functions, Figures, measurement and geometric properties, Data analysis, Cases, probability and integer properties. Identify the domain of each major question before calculating: quadratic, trigonometric ratio, data, probability, integer or geometry. Classification prevents using a familiar formula in the wrong context.

Updated 2026-07-03

Paper breakdown

Mathematics I and Mathematics A: Algebra, functions, geometry, data, probability, integers and guided multi-step tasks

100 marks70 min

Top chapters

Numbers, expressions and quadratic functions28 marks
Figures, measurement and geometric properties22 marks
Data analysis18 marks
Cases, probability and integer properties32 marks

Exam structure insights

Marks by syllabus topic

Revision priority from official test-design weighting.

Numbers, expressions and quadratic f28 marks
Figures, measurement and geometric p22 marks
Data analysis18 marks
Cases, probability and integer prope32 marks

Mark accessibility

Estimated difficulty spread based on official design.

Probability, quadratic functions, data analysis and geometry conditions are freq

23
46
31
Easy: 23 marksMedium: 46 marksHard: 31 marks

Paper structure

Official paper breakdown for this subject.

100Marks
  • Mathematics I and Mathematic

    100·10·100%

Official syllabus scope

数学I・数学A is based on Mathematics I and Mathematics A, including numbers and expressions, quadratic functions, figures and measurement, data analysis, cases and probability, integer properties and geometric properties. R7 Common Test mathematics emphasizes mathematical activity: reading situations, formulating relationships, choosing methods and interpreting results.

Difficulty verdict

Rated 4/5 for January sessions. Probability, quadratic functions, data analysis and geometry conditions are frequent high-yield areas, especially when embedded in a real-world or dialogue-style setting.

What examiners measure

1. Model everyday or mathematical situations using expressions, functions, figures and probability. 2. Carry out algebraic, geometric and statistical procedures accurately. 3. Choose efficient solution strategies and connect multiple representations. 4. Interpret results in the context of a problem and judge reasonableness. 5. Use diagrams, tables and conditions to support multi-step reasoning.

Where the marks are

Highest-weight syllabus areas: Numbers, expressions and quadratic functions; Figures, measurement and geometric properties; Data analysis; Cases, probability and integer properties.

Examiner notes & key calculations

  • R7 mathematics follows the Common Test pattern of guided mathematical activity: read the situation, infer the relation, then compute.
  • The 70-minute, 100-point paper gives 0.7 minutes per mark; long dialogues must be skimmed for mathematical conditions before detailed reading.
  • For quadratic max/min, the reliable calculation is: convert to vertex form, check axis, evaluate endpoints if the domain is restricted.
  • Probability items commonly require P(A and B) = P(A) x P(B|A), not P(A) x P(B). Write the conditional event explicitly.
  • For data, standard deviation changes with spread, not with every value increasing by the same constant.
  • Geometry partial reasoning often depends on naming the theorem: similarity, cyclic quadrilateral, angle bisector, power of a point or sine/cosine rule.
  • Integer problems become faster when rewritten as factor pairs or congruences instead of brute-force enumeration.
  • Paper 1: Mathematics I and Mathematics A · 100 marks · 70 min · Algebra, functions, geometry, data, probability, integers and guided multi-step tasks.

Exam tips

Paper format

Duration
70 min
Total marks
100
Weighting
100%
Question types
Algebra, functions, geometry, data, probability, integers and guided multi-step tasks
  • Identify the domain of each major question before calculating: quadratic, trigonometric ratio, data, probability, integer or geometry. Classification prevents using a familiar formula in the wrong context.
  • For quadratics, note domain restrictions; for probability, note whether events are independent; for geometry, note congruence/similarity conditions before calculation.
  • The Common Test often uses dependent events. Show changing denominators after each draw or condition, then simplify only at the end.

Common mistakes

  • Probability

    Multiplying probabilities as if events were independent when sampling without replacement.

    How to avoid: Update numerator and denominator on every branch and label conditional probabilities.

  • Quadratic functions

    Finding the vertex but ignoring the restricted domain for maximum/minimum.

    How to avoid: Evaluate vertex and endpoints whenever the domain is bounded.

  • Data analysis

    Confusing correlation with causation or standard deviation with range.

    How to avoid: State what each statistic measures before matching to the scenario.

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

MATHEMATICS-I-A/11 — Common Test for University Admissions (大学入学共通テスト) Mathematics I & A (2024) | Revui