Tokyo Metropolitan Public High School Entrance Examination - Mathematics study guide
Tokyo Metropolitan Public High School Entrance Examination - Mathematics · Work through your exam, one topic at a time.
The Tokyo Metropolitan Public High School Entrance Examination in Mathematics (東京都立高等学校入学者選抜学力検査 数学) is the mathematics paper used by Tokyo's metropolitan public high schools to decide admission, usually alongside Japanese, English, social studies and science, plus an interview or essay depending on the school and selection method. It is taken by students finishing compulsory education, mainly third-year junior high students, and by some applicants with equivalent qualifications. The Tokyo Metropolitan Public High School Entrance Examination - Mathematics study guide has 6 sections and about 1,683 words.
01Numbers and Algebraic Expressions
Numbers and Algebraic Expressions is the fluency domain: the Tokyo Metropolitan examination uses it to check whether you can handle integers, square roots, and symbolic manipulation quickly and accurately before the longer problems later in the paper. Expand with the distributive law: a(b+c)=ab+ac.
230 words, about 1 min02Linear Equations and Functions
Linear Equations and Functions tests whether you can translate a relationship into an equation, solve it exactly, and read the same relationship from a graph. Expect simultaneous equations, linear functions y=ax+b, intersections, and short word problems about rates or costs.
277 words, about 1 min03Quadratic Functions and Equations
Quadratic Functions and Equations connects the graph of y=ax² with solving equations and finding intersections. The exam tests transformations of the parabola, factoring and formula methods, the discriminant, and the link between roots and x-intercepts.
279 words, about 1 min04Geometry: Plane Figures and Angles
Plane Figures and Angles checks angle-chasing: applying parallel-line facts, triangle and polygon angle sums, and circle angle theorems in a clear order. Diagrams are usually not to scale, so mark only what is given or proved.
315 words, about 2 min05Geometry: Congruence and Similarity
Congruence and Similarity is proof-and-ratio territory. You need to select a valid congruence or similarity condition, match corresponding vertices correctly, and use side, area, and parallel-line ratios without mixing them up.
285 words, about 1 min06Data Handling and Probability
Data Handling and Probability tests interpretation as much as calculation: reading tables and graphs correctly, choosing the right average, and counting equally likely outcomes. Tokyo-style questions often combine a small data set with a probability or expected-frequency question.
297 words, about 1 min