Okayama Public High School Entrance Examination - Mathematics study plan

Expand and factorise algebraic expressions (単項式・多項式の計算、因数分解) accurately, including expressions with two variables, and write down each step of the working rather than skipping lines.

Solve linear equations and simultaneous equations in two unknowns, then verify each answer by substituting back into the original equations.

Translate short word problems into equations, stating clearly what the variable represents before solving.

Explain in writing why a chosen transformation step is valid (等式の性質、分配法則), using correct Japanese mathematical terminology.

Manipulate square roots (平方根) confidently: simplify, rationalise denominators, and estimate values without a calculator.

Solve quadratic equations (二次方程式) by factoring, by completing the square, and by the quadratic formula, and choose the most efficient method for each problem.

Use the discriminant to decide how many real solutions an equation has before solving it.

Justify in writing why a solution you rejected (e.g. a negative length) is invalid in the problem's context.

Read values from and sketch linear functions (一次関数) from tables, equations, and graphs, including finding the gradient and intercept directly from a graph.

Set up and solve problems about linear functions in context (rate, distance-time, cost) by first identifying the two variables and their units.

Determine the equation of a line from two points, from a point and a gradient, and from a parallel or perpendicular condition.

Explain how changing the constants in y = ax + b changes the graph, and predict the change before drawing it.

Connect proportional and inverse-proportional relationships (比例・反比例) to their graphs and equations, and state the domain restrictions in context.

Interpret the intersection point of two graphs as the solution of a pair of simultaneous equations, and explain this link in writing.

Solve 'rate of change' (変化の割合) questions using both the formula and the graph, and check that the sign of the answer makes sense.

Describe the relationship between an equation, a table, and a graph in a single written explanation of about 120 words.

Prove triangle congruence (三角形の合同) using the correct conditions, writing given information, what is to be proved, and the reasoning chain in the standard format.

Apply properties of parallel lines, angles in polygons, and the inscribed angle theorem (円周角の定理) to find unknown angles, showing each step.

Use similarity (相似) to find lengths and areas, and state the similarity condition you used.

Construct a proof of Pythagoras' theorem or a related length result using congruent triangles.

Solve combined geometry problems that require an auxiliary line (補助線), and write a sentence explaining why that line was drawn.

Calculate areas and volumes of composite figures, including cones, spheres, and similar solids, keeping units consistent.

Explain a proof strategy to someone else in writing, in the order: what is given, what is needed, what bridge connects them.

Identify the weakest step in a flawed proof supplied by your own notes and rewrite it correctly.

Organise raw data into frequency tables and histograms, and choose an appropriate representative value (平均値・中央値・最頻値) with a written reason for the choice.

Read and compare box plots (箱ひげ図), stating what the interquartile range shows about spread.

Compute probabilities of compound events using tables and tree diagrams, and distinguish 'at least one' from 'exactly one'.

Critique a misleading graph or statistic and explain in writing how it distorts the data.

Complete two full-length mock papers under timed conditions and record the time spent per section.

Classify every error as knowledge, calculation, misreading, or time pressure, and rank the categories by frequency.

Re-solve every error from weeks 1-8 without notes, and confirm which ones now succeed on the first attempt.

Write a one-page exam-day plan covering section order, time allocation, and a check routine for each domain.