Toyama Prefectural Public High School Entrance Examination - Mathematics study plan
Toyama Prefectural Public High School Entrance Examination - Mathematics · Give each week a clear focus.
8 weeks · About 7 hours per week
Numbers and Algebraic Expressions & Geometry (Plane and Solid Figures)
Compute fluently with signed numbers, fractions, and mixed operations without a calculator
Expand and factor quadratic and linear expressions, including difference of squares
State and apply the Pythagorean theorem to find missing sides in right triangles
Classify triangles and quadrilaterals by their defining properties
Your checkpoint
A 40-item timed drill (30 minutes) on expressions and triangle/quadrilateral properties, scored with all errors corrected in writing
Geometry (Plane and Solid Figures) & Numbers and Algebraic Expressions
Prove congruence and similarity of triangles using the standard criteria
Use similarity ratios to compute unknown lengths and areas
Simplify radical expressions and rationalize denominators
Solve problems combining Pythagorean lengths with radical simplification
Your checkpoint
Five fully written similarity/congruence proofs plus a 10-item radical-simplification set, all self-graded against a checklist
Geometry (Plane and Solid Figures)
Compute areas and volumes of prisms, pyramids, cylinders, cones, and spheres
Solve problems involving surface area and cross-sections of solids
Apply inscribed-angle and circle-chord relationships to find angles and lengths
Draw accurate auxiliary lines to convert unfamiliar figures into known shapes
Your checkpoint
A one-page formula sheet you wrote yourself plus 12 mixed solid-geometry and circle problems solved with diagrams shown
Equations and Inequalities & Numbers and Algebraic Expressions
Solve linear equations and simultaneous equations in two variables by elimination and substitution
Solve quadratic equations by factoring, completing the square, and the quadratic formula
Translate word problems into equations and verify solutions against the original conditions
Manipulate expressions so that a target variable is isolated
Your checkpoint
A 25-item equation set with a written translation (sentence to equation) for every word problem, scored and reviewed
Equations and Inequalities & Functions and Graphs
Solve linear inequalities and represent solution sets on a number line
Solve systems mixing an equation and an inequality
Interpret slope and intercept from a linear function in context
Sketch linear and quadratic graphs from their equations and read key features off a graph
Your checkpoint
A two-part worksheet: 10 inequality problems with number-line solutions and 6 graphs sketched by hand with intercepts and vertices labeled
Functions and Graphs & Data Handling and Probability
Determine domain, range, and rate of change from tables, graphs, and equations
Model a real situation with a linear or quadratic function and answer a question from the model
Compute mean, median, mode, and range and choose the appropriate measure for a context
Read and construct histograms and box plots and compare two data sets
Your checkpoint
A short modeling report: one real scenario modeled by a function and one data set analyzed with summary statistics and a hand-drawn box plot
Data Handling and Probability & Mathematical Reasoning and Problem Solving
Compute classical and experimental probabilities for single and compound events
Use tree diagrams and tables to enumerate outcomes systematically
Justify a multi-step solution with clear reasoning at each step
Identify and correct a flawed argument in a worked solution
Your checkpoint
A 15-item probability set plus two written critiques of deliberately flawed solutions, each naming the error and giving the correct reasoning
Geometry (Plane and Solid Figures) & Mathematical Reasoning and Problem Solving & Numbers and Algebraic Expressions
Solve full-length mixed problems under timed conditions
Diagnose and re-drill your three weakest error categories from earlier weeks
Write complete, logically ordered solutions for multi-step geometry problems
Verify answers by an independent method (estimation, substitution, or reverse check)
Your checkpoint
Two timed 50-minute mock sections scored, with an error log listing each mistake, its cause, and the re-drill completed
Milestones
Week 2: Score at least 80% on the Week 1-2 expression and geometry drill without notes; all similarity proofs judged complete
Week 4: Solve 20 of 25 equation items correctly, including at least 4 of 5 word problems translated correctly
Week 6: Correctly graph all 6 functions with labeled intercepts and answer all modeling questions with units stated
Week 8: Achieve 75% or higher on both timed mock sections and show a closed error log with every category re-drilled