Japan

Kyotsu Test Mathematics

Japanese Common Test for University Admissions mathematics sections: Mathematics I·A and Mathematics II·B·C, in the format introduced with the new curriculum in 2025.

Exam Format

Questions

Mathematics I·A: 4 compulsory multi-part questions (30 + 30 + 20 + 20 points). Mathematics II·B·C: 3 compulsory Mathematics II questions (15 + 15 + 22 points) plus 3 chosen from 4 selection questions worth 16 points each (sequences, statistical inference, vectors, curves and the complex plane). Mark-sheet format where you fill in each digit of your answer.

Duration

Mathematics I·A: 70 minutes, Mathematics II·B·C: 70 minutes, in separate sessions on the second exam day.

Scoring

100 points per section, 200 points total. No partial credit: each digit box is either right or wrong.

Calculator

No calculator allowed.

Study Strategies

  • 1Practice the fill-in-the-digit answer format until it feels natural: you must compute exact numerical values, and there is no partial credit for close answers.
  • 2In Mathematics I·A, all four questions are compulsory, so there is no escape route: quadratic functions, figure measurement with trigonometric ratios, data analysis, combinatorics and probability, and figure properties all have to be solid.
  • 3In Mathematics II·B·C, decide your three selection questions (from sequences, statistical inference, vectors, and curves with the complex plane) months before the exam, and drill only those three; the compulsory questions lean on trigonometric functions, exponentials and logarithms, and differentiation and integration.
  • 4Build mental arithmetic speed: without a calculator, you need to handle fractions, square roots, and trigonometric values quickly and accurately.
  • 5Work through past Kyotsu exams under timed conditions: the problems are long, often wrapped in dialogue or real-world settings, and 70 minutes per section makes reading speed and skip-and-return discipline as decisive as the mathematics.

How Math Zen Helps

Math Zen covers the foundational topics tested in both Mathematics I·A and Mathematics II·B·C, including algebra, trigonometry, geometry, sequences, probability, statistics, and calculus. As Kyotsu-specific templates are added, you will be able to practice the guided, multi-step problem style unique to this exam.

Topics Covered

Arithmetic

7 subtopics, 19 templates

FractionsDecimals & PercentagesOrder of OperationsRounding & EstimationRatios & ProportionsPowers & RootsModular Arithmetic

Algebra

10 subtopics, 29 templates

Simplifying ExpressionsFactoringSolving EquationsInequalitiesBinomial TheoremPartial FractionsLinear SystemsPolynomial DivisionAbsolute ValueWord Problems

Functions

5 subtopics, 10 templates

Domain & RangeCompositionInverse FunctionsExponential FunctionsPiecewise Functions

Trigonometry

5 subtopics, 12 templates

Basic RatiosIdentitiesEquationsInverse TrigLaw of Sines/Cosines

Geometry

12 subtopics, 29 templates

AreaPerimeterVolumeSurface AreaAnglesTrianglesCirclesCoordinate GeometryCongruence & SimilarityTransformations3D GeometryConstructions

Sequences & Series

7 subtopics, 17 templates

Arithmetic SequencesGeometric SequencesSeries SumsConvergence TestsPower SeriesTaylor SeriesRecursive Sequences

Derivatives

12 subtopics, 24 templates

Power RuleProduct RuleQuotient RuleChain RuleTrigonometricImplicit DifferentiationHigher-OrderLogarithmicRelated RatesOptimizationLinearizationMean Value Theorem

Integrals

19 subtopics, 22 templates

Power RuleDefinite IntegralsTrigonometricu-SubstitutionConstant RuleIntegration by PartsPartial FractionsArea Between CurvesVolume (Disk/Washer)Volume (Shell)Arc LengthTrig SubstitutionImproper IntegralsTrapezoidal RuleSimpson's RuleSurface AreaWork & ForceReduction FormulasAdvanced Rational

Probability

7 subtopics, 16 templates

Basic ProbabilityConditional ProbabilityBayes' TheoremCombinationsPermutationsDistributionsExpected Value

Statistics

8 subtopics, 16 templates

Descriptive StatisticsRegressionCorrelationConfidence IntervalsHypothesis TestingChi-Square TestsNormal DistributionSampling