Tokyo Metropolitan Public High School Entrance Examination - Mathematics study plan

Expand and simplify algebraic expressions involving parentheses and negative signs without errors in 20 mixed problems.

Factor quadratic expressions of the form x² + (a+b)x + ab and a² - b² using the distributive law in reverse.

Solve linear equations with one variable, including those with fractions and decimals, and verify solutions by substitution.

Translate five short Japanese word problems into algebraic expressions and solve them, checking units and conditions.

Simplify radical expressions (√) and rationalize denominators in 15 problems, including √(a²b) forms.

Solve simultaneous linear equations in two variables using both substitution and elimination, and interpret the solution as an intersection point.

Graph linear functions y = ax + b from equations and derive equations from given graphs, including negative and fractional slopes.

Set up and solve two-variable word problems (e.g., mixture, speed, and age problems) by defining variables clearly.

Determine the equation of a line given two points, a point and slope, or a point and a parallel/perpendicular line.

Solve problems involving the intersection of two lines and the area of triangles formed by lines and axes.

Interpret and solve rate, ratio, and proportion problems using linear function models, including unit conversions.

Explain in writing how changes in slope and intercept affect the graph and the meaning in context.

Apply angle properties of parallel lines, triangles, and polygons (including exterior angles) to find unknown angles in 20 diagrams.

Prove triangle congruence using SSS, SAS, ASA, and RHS, and identify corresponding parts correctly.

Use properties of isosceles triangles, parallelograms, and circles (inscribed angle theorem, tangent-radius perpendicularity) to solve problems.

Construct clear geometric arguments in Japanese, stating given information, properties used, and conclusion.

Identify and apply similarity conditions for triangles (AA, SAS, SSS) to find unknown lengths and ratios.

Use the midpoint theorem, parallel lines and segment ratios, and area ratios of similar figures in multi-step problems.

Solve problems combining congruence and similarity, such as proving two triangles are similar and then using the ratio to find a length.

Draw auxiliary lines (e.g., parallel lines, diagonals) to reveal congruent or similar triangles in complex figures.

Solve quadratic equations by factoring, completing the square, and the quadratic formula, and choose the most efficient method.

Graph quadratic functions y = ax² + bx + c, identifying vertex, axis of symmetry, intercepts, and maximum/minimum values.

Solve quadratic word problems involving area, projectile motion, and optimization, and interpret the domain restrictions.

Relate the discriminant to the number of real solutions and to the graph's x-intercepts.

Compute probabilities using equally likely outcomes, including combinations and permutations where appropriate.

Interpret and create frequency tables, histograms, and box plots, and calculate mean, median, mode, and range.

Solve problems involving conditional probability and expected value in simple contexts.

Critically evaluate statistical claims and identify misleading graphs or sampling issues.

Complete two full-length timed practice exams (50 minutes each) under exam conditions, allocating time per section.

Review all errors from the practice exams and categorize them by domain and error type (conceptual, procedural, careless).

Re-solve the highest-priority error types from weeks 1–7 using a personalized error log.

Create a one-page formula and strategy sheet covering all six domains for final review.