Mie Entrance Mathematics study plan

Compute fluently with integers, fractions, decimals, and powers, and simplify expressions containing radicals and absolute values without a calculator

Factor and expand polynomials, and manipulate algebraic fractions, stating the domain restriction at each step

State and apply the triangle angle-sum, exterior-angle, and parallel-line angle relationships, and classify quadrilaterals by their angle and side properties

Write a two-column or paragraph justification for each angle result rather than only giving the numeric answer

Prove two triangles congruent using SSS, SAS, ASA, and AAS, and identify when SSA fails to determine a triangle

Apply similarity criteria (AA, SAS similarity, SSS similarity) to set up and solve proportional side-length equations

Use the Pythagorean theorem and its converse to classify triangles and to find unknown lengths in composite figures

Convert between exact radical form and decimal approximation, and decide when an exact answer is required

Sketch and interpret linear functions, extracting slope and intercepts from equations, tables, and two points

Solve linear equations and inequalities, including those with fractional coefficients, and represent solution sets on a number line

Solve systems of two linear equations by substitution and elimination, and interpret the solution as an intersection point

Translate a short word problem into an equation or system, then check whether the answer is reasonable in context

Convert a quadratic function between standard, factored, and vertex forms, and read off the vertex, axis of symmetry, and intercepts

Solve quadratic equations by factoring, completing the square, and the quadratic formula, and use the discriminant to count real roots

Analyze proportional and inverse-proportional relationships and distinguish their graphs, tables, and constant-rate statements

Apply circle theorems on inscribed angles, central angles, tangents, and chords to find unknown angles and lengths

Compute the area and perimeter of triangles, parallelograms, trapezoids, and sectors, and of composite figures built from them

Compute the volume and surface area of prisms, cylinders, pyramids, cones, and spheres, and solve for a missing dimension given the volume

Use similarity ratios to relate the scale factor of two solids to their area ratio and volume ratio

Sketch a net for a given solid and check that the net's area matches the computed surface area

Compute mean, median, mode, and range from raw data and from a frequency table, and explain how an outlier shifts each measure

Read and construct histograms, box plots, and scatter plots, and describe the shape and spread of a distribution in words

Calculate probabilities for single and two-stage events using lists, tables, and tree diagrams, and distinguish experimental from theoretical probability

Combine measurement and data by computing a rate or density from a table of measurements and interpreting the result

Distinguish a conjecture from a proof, and produce a counterexample to disprove a false general statement

Write a direct proof and a proof by contradiction on short algebraic or geometric claims, with each step justified

Identify the logical error in a flawed argument, such as circular reasoning or treating the converse as true

Explain your reasoning in clear written sentences that a classmate could follow without asking a question

Solve multi-step problems that chain algebra, geometry, and measurement, and identify the sub-goal at each stage

Model a real-world situation with a function, solve it, and justify why the model's domain is restricted

Complete two full timed practice papers under exam conditions and mark every uncertain item for review

Build a personal error log grouped by domain and schedule a final pass over the two weakest domains