Gaokao Mathematics study plan

Determine domains, ranges, and parity for polynomial, rational, radical, exponential, logarithmic, piecewise, and absolute-value functions, writing out the restriction behind each answer.

Apply the power, product, quotient, and chain rules to differentiate composite expressions and write tangent-line equations at a specified point.

Classify monotonic intervals from the sign of the derivative and locate local and endpoint extrema on closed intervals.

Negate quantified statements and distinguish necessary from sufficient conditions inside short algebraic settings.

Solve parameterized monotonicity and extremum problems, discussing each parameter case explicitly before concluding.

Prove inequalities by constructing an auxiliary function and analyzing its monotonicity or minimum value.

Count and locate zeros of a function by combining monotonicity with sign checks at interval endpoints.

Solve quadratic, rational, and absolute-value inequalities and report solution sets in interval notation.

Derive standard equations of lines, circles, and ellipses from stated geometric conditions rather than from memory.

Convert between equations and geometric features such as center, radius, foci, and eccentricity, and sketch each figure accurately.

Solve line-circle intersection problems using distance-to-line conditions and discriminants, computing chord lengths and midpoints.

Translate point-locus conditions into equations and solve the resulting locus problems.

Derive and use standard equations, foci, asymptotes, and directrices of hyperbolas and parabolas from their definitions.

Set up conic-line systems, apply Vieta's relations, and extract chord lengths, midpoints, and slope products.

Solve parameter-range and fixed-point problems on conics by combining geometric constraints with algebraic inequalities.

Verify each conic answer geometrically by checking that the computed features match the stated figure.

Compute classical and conditional probabilities using tree diagrams together with the addition and multiplication rules.

Build discrete distributions and compute expectation and variance, stating each distribution's parameters first.

Apply binomial and hypergeometric models and use normal-curve symmetry to obtain requested probabilities.

Interpret sampling, regression coefficients, and independence-test outputs in context, and count arrangements and selections and expand binomial powers via the general term.

Prove line-line, line-plane, and plane-plane parallelism and perpendicularity, justifying each step with a named theorem.

Build right-handed coordinate frames and compute plane normal vectors from three points or two direction vectors.

Compute dihedral angles, line-plane angles, and point-to-plane distances by vector methods, keeping exact values until the final step.

Compute volumes and surface areas of prisms, pyramids, and spheres embedded in composite solids.

Simplify trigonometric expressions using sum, difference, double-angle, and auxiliary-angle formulas.

Solve triangles with the sine rule, cosine rule, and area formula, deciding correctly when two valid triangles exist.

Compute dot products, projections, and vector coordinates, and use them to prove perpendicularity and parallelism.

Carry out complex-number arithmetic in algebraic and trigonometric form, computing modulus and argument.

Solve arithmetic and geometric sequence problems, including conversions between the general term and the partial-sum formula.

Apply grouping, telescoping, and multiply-and-subtract summation techniques to composite sequences.

Solve sequence inequality and existence problems by combining sequence structure with derivative or inequality tools.

Complete a full-length timed mock and revise every entry in the accumulated error log.