Yamaguchi Prefectural Public High School Entrance Examination - Mathematics study plan

Expand and simplify 30 expressions involving monomials, polynomials, and the distributive law without a calculator, checking each answer by substitution.

Factor 25 quadratic expressions of the forms x²+(a+b)x+ab and a²−b², and explain in writing why each factorization is correct.

Solve 20 linear equations and 10 simultaneous systems in two variables by both substitution and elimination, recording which method was faster and why.

Compute with square roots: simplify 15 radical expressions and rationalize 10 denominators, stating the rule used at each step.

Solve 15 linear inequalities and represent each solution set on a number line, including cases that flip the inequality sign.

Translate 10 short word problems into equations or inequalities and solve them, labeling the unknown clearly before writing the equation.

Solve 8 simultaneous equations with fractional or decimal coefficients by first clearing denominators.

State and apply the conditions for a system of two linear equations to have one solution, no solution, or infinitely many solutions.

Sketch the graphs of y=ax² for five values of a and describe in writing how the sign and magnitude of a affect width and direction.

Convert 12 quadratic functions between standard form and vertex form by completing the square, and read off the vertex and axis of symmetry.

Determine the maximum or minimum value of 10 quadratic functions on a stated interval, distinguishing the vertex case from the endpoint case.

Solve 10 problems combining proportional and inverse proportional relations, including determining the constant of proportionality from given data.

Model and solve 8 rate, mixture, and motion problems that reduce to quadratic equations, rejecting extraneous roots with a written reason.

Solve 10 quadratic equations by factoring, completing the square, and the quadratic formula, and verify which method suits each form.

Interpret the discriminant for 10 equations and state the number of real solutions without fully solving.

Connect the intersection points of a line and a parabola to the solution of the corresponding simultaneous equations in 6 worked examples.

Apply the Pythagorean theorem and similar-triangle ratios to 15 right-triangle problems, drawing and labeling each figure before calculating.

Compute areas and volumes of 10 composite figures built from triangles, circles, prisms, and pyramids, showing each decomposition step.

State and use the inscribed-angle and tangent-chord relationships to find 10 unknown angles, justifying each step by naming the theorem.

Write full two-column or paragraph proofs for 5 congruence and similarity claims, citing the exact condition used (side-angle-side, angle-angle, and so on).

Solve 10 problems on circle properties, including chord, tangent, and arc relationships, and write the theorem used beside each answer.

Use similarity ratios to compute unknown lengths and areas in 8 figures, distinguishing length ratio from area ratio.

Identify and correct 5 flawed proofs by locating the missing condition or unjustified step.

Construct 3 accurate scale drawings with compass and straightedge procedures described in words, then verify a claimed property by measurement.

Compute relative frequencies and means from 5 data sets, and choose and justify an appropriate representative value for each.

Solve 12 probability problems using counting of equally likely outcomes, including cases with and without replacement, listing the sample space explicitly.

Read and interpret 5 tables and graphs, writing one sentence on a misleading feature or limitation of each.

Apply number and expression skills to 10 data-handling items involving ratios, percentages, and averages.

Write 6 explanation-type answers in which you state the strategy, show the reasoning, and give the conclusion in complete sentences within a set time limit.

Complete two full mock papers under exam timing and score them against a marking scheme, recording time spent per section.

Classify every mock error by domain and by cause (concept, calculation, misreading, time), then list your three weakest items.

Re-solve the 10 most frequent error types from your log and confirm each is now correct without notes.