Miyazaki Entrance Mathematics study plan

Expand and simplify expressions containing parentheses, negative signs, and nested brackets with zero sign errors on a 20-item set

Factor quadratic expressions of the form x^2 + bx + c and ax^2 + bx + c by inspection, and verify each factorization by re-expansion

Compute with square roots: simplify radicals, rationalize denominators, and combine like radical terms

Convert between decimals and fractions and apply rounding rules to a stated number of significant figures

Solve linear equations including those with fractional coefficients and variables on both sides

Solve simultaneous linear equations in two variables by both elimination and substitution, and choose the faster method per problem

Solve quadratic equations by factoring, completing the square, and the quadratic formula, and state why a chosen method is efficient

Set up and solve word problems that translate into linear or quadratic equations, defining the variable explicitly before solving

Solve linear inequalities and represent solution sets on a number line, handling multiplication or division by a negative correctly

Solve simultaneous inequalities and express the combined solution set in interval notation

Solve quadratic inequalities by sketching the corresponding parabola and reading off the sign regions

Distinguish conditions that require an inequality from those that require an equation when reading a problem statement

Identify domain and range for linear, inverse proportion (y = a/x), and quadratic functions, including restricted domains

Sketch the graph of y = ax^2 + bx + c by finding the vertex, axis of symmetry, and intercepts without plotting many points

Determine the equation of a line or parabola from given conditions such as two points, a vertex and a point, or a gradient and intercept

Interpret the constant of proportionality a in y = a/x in context, including its sign and what happens as x approaches zero

Solve maximum/minimum problems by completing the square and justify why the vertex gives the extremum

State and apply the congruence conditions for triangles and write a two-column proof of triangle congruence

Use similarity to find unknown lengths, and justify each step by naming the similarity condition used

Apply circle theorems: inscribed angle, angle in a semicircle, tangent perpendicular to radius, and the alternate segment idea

Compute areas and volumes of composite figures by decomposing them into known shapes

Translate a geometric statement into a labelled diagram before attempting a proof

Write a proof-based explanation of a circle theorem in continuous prose, stating assumptions before the argument

Critique a flawed sample proof, name the specific logical gap, and rewrite the corrected version

Explain in writing why a geometric construction works, referencing the relevant theorem by name

Produce a diagram-free written description of a figure precise enough for another student to redraw it

Compute mean, median, mode, and range from raw data and from a frequency table, and explain which measure best represents a given dataset

Calculate relative frequency and use it to estimate probability, distinguishing experimental from theoretical probability

Solve probability problems with two-stage events using tables or tree diagrams, including without-replacement cases

Justify a conclusion drawn from data in writing, naming the statistic used and one limitation of the data

Explain the reasoning behind a probability answer in full sentences rather than only giving a fraction

Complete two full timed mock papers under exam conditions and record per-domain accuracy

Write full worked explanations for every mock question answered incorrectly, not just the corrected answer

Re-drill the two weakest domains identified by mock results until accuracy exceeds 80 percent

Practise allocating time across sections so no question is left blank in the final ten minutes