Japan

Kyotsu Test Mathematics

Japanese Common Test for University Admissions mathematics section. Two parts covering algebra through calculus.

Exam Format

Questions

Math I (multiple topics, mark-sheet) + Math II (multiple topics, mark-sheet). Fill-in-the-digit style where you mark each digit of your answer.

Duration

Math I: 70 minutes, Math II: 60 minutes (130 minutes total)

Scoring

100 points per section, 200 points total.

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 Math I, prioritize trigonometry and quadratic functions, as these topics appear almost every year and carry substantial point value.
  • 3For Math II, focus on calculus (differentiation and integration) and coordinate geometry, which are consistently the highest-weighted sections.
  • 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, paying attention to the structured, guided problem format where each sub-question builds on the previous one.

How Math Zen Helps

Math Zen covers the foundational topics tested in both Math I and Math II, including algebra, trigonometry, geometry, 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

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