Mie Entrance Mathematics study guide
Mie Entrance Mathematics · Work through your exam, one topic at a time.
The Mie Prefectural High School Entrance Examination in Mathematics (三重県立高等学校入学者選抜 数学) is the mathematics paper taken by students applying to prefectural high schools in Mie Prefecture, Japan. It is a written, short-answer examination: candidates write numerical answers, expressions, and multi-step reasoning rather than choosing from options, and later parts of a question often build on an earlier result. The Mie Entrance Mathematics study guide has 8 sections and about 2,290 words.
01Numbers and Algebraic Expressions
Short-answer items on signed arithmetic, order of operations, expansion, factorisation and square-root simplification. Marks are lost on the intermediate lines rather than on the final answer, so the exam rewards clean, justified steps.
286 words, about 1 min02Equations and Inequalities
Linear equations, simultaneous pairs, simple quadratics and linear inequalities, plus short word problems that must first be translated into one of these forms. Do the same operation to both sides.
305 words, about 2 min03Functions and Graphs
Reading and drawing proportional (y = ax), linear (y = ax + b), inverse-proportion (y = a/x) and quadratic (y = ax²) graphs, and using a graph to solve an equation. In y = ax + b, a is the slope and b the y-intercept.
331 words, about 2 min04Plane Geometry
Angle chasing with parallel lines, triangle congruence and similarity, and circle angle facts, normally fitted into a two- or three-step calculation. Angles on a straight line sum to 180°, around a point to 360°.
308 words, about 2 min05Measurement and Spatial Figures
Area and perimeter of plane figures and surface area and volume of prisms, cylinders, cones and spheres, including the effect of enlarging a solid. Area: triangle ½bh; trapezium ½(a+b)h; circle πr², circumference 2πr.
240 words, about 1 min06Data Handling and Probability
Summarising a small data set and computing probabilities from lists, tables or simple experiments. Mean = sum of values ÷ number of values.
259 words, about 1 min07Mathematical Reasoning, Explanation, and Proof
Short written justifications: explaining why a statement is true, spotting the flaw in someone else's reasoning, producing a counterexample, and setting out a two- or three-line proof. Separate what is given from what must be shown, and write the target at the top.
250 words, about 1 min08Integrated and Cross-Topic Problem Solving
Multi-step problems that combine two or more domains: rates with algebra, ratios with geometry, functions read from a table, or a diagram that must be modelled by an equation. The mathematics is familiar; the difficulty is choosing the order of steps.
311 words, about 2 min