ЦТ Mathematics study plan

Simplify and evaluate 60 expressions built from powers, roots and absolute values, including rationalising denominators and combining radicals.

Factor, expand and recognise the standard polynomial patterns (difference of squares, perfect square, sum and difference of cubes) until each is reproduced from memory in under 30 seconds.

Reduce, add, multiply and divide rational expressions, stating the admissible values of the variable for every result.

Solve linear and quadratic equations by factoring, by completing the square and by the discriminant, then verify each root by substitution.

Translate 15 short verbal statements into algebraic expressions or equations and check each translation numerically.

Solve 2x2 and 3x3 linear systems by substitution, elimination and determinants, and label each system as consistent, dependent or inconsistent.

Solve rational, radical and absolute-value equations, rejecting extraneous roots by explicit checking.

Solve linear, quadratic, rational and absolute-value inequalities and write each answer set in interval notation and on a number line.

Sketch the solution region of systems of two inequalities and justify the choice of test points.

State and apply Vieta's relations to recover sums and products of roots without solving.

Apply triangle congruence and similarity criteria to compute unknown sides, angles and ratios, and write the similarity proportion explicitly before substituting.

Compute the area of triangles and quadrilaterals using at least four distinct tools: base-height, Heron's formula, the sine formula and diagonals.

Use the Pythagorean theorem, median and angle-bisector properties and the sine and cosine rules in combined problems.

Prove three standard planimetry statements from scratch (sum of angles, midline theorem, Thales proportionality).

Apply inscribed-angle, tangent-chord and cyclic-quadrilateral theorems to find arcs, angles, chords and tangent lengths in circle configurations.

Compute distances, midpoints, slopes and vector components in the coordinate plane, and use the dot product to test perpendicularity and find angles.

Convert freely between degrees and radians and evaluate sine, cosine and tangent at standard and quadrantal angles without a table.

Derive the Pythagorean identity and use it, with the sign-by-quadrant rule, to recover all trigonometric functions from a single given value.

Derive and apply the sum, difference, double-angle and half-angle formulas and the reduction formulas to simplify compound trigonometric expressions.

Solve trigonometric equations of the forms sin x = a, cos kx = b and quadratic-in-sine type, writing the full general solution before restricting to the requested interval.

Solve trigonometric inequalities on a stated interval and shade the solution set on the unit circle.

Evaluate inverse trigonometric functions and their compositions while respecting principal ranges, and identify where an inverse does not exist.

Determine domain, range, parity, zeros and asymptotes of rational, radical, exponential and logarithmic functions.

Sketch graphs from a parent function using shifts, stretches, reflections and absolute values, then read off monotonicity intervals and extrema.

Find inverse functions where they exist and state the domain restriction that makes the inverse valid.

Compute terms and partial sums of arithmetic and geometric progressions, including infinite geometric sums with ratio of modulus below one.

Model and solve growth, decay and simple interest situations with linear, exponential and logarithmic equations.

Determine the relative position of lines and planes in space and compute angles between lines and planes and distances from a point to a plane.

Compute volumes and total and lateral surface areas of prisms, pyramids, cylinders, cones, spheres and frustums, including composite solids.

Draw and use cross-sections of polyhedra and solids of revolution to set up a volume calculation before computing it.

Count outcomes with the multiplication rule, permutations and combinations, and decide correctly whether order matters in a given selection.

Compute classical and complementary probabilities and interpret the mean, median and spread of a small data set.

Set up and solve motion, work, mixture and percentage-change word problems by defining variables and writing one equation per unknown before solving.

Solve optimization and estimation problems by testing boundary cases, comparing candidate values and rounding answers sensibly.

Re-solve without notes every item recorded in the error log from weeks 1 to 7 and retire each entry only after two clean attempts.

Complete two full-length timed mock tests under exam conditions and compute a domain-by-domain score profile from the results.