Tamil Nadu SSLC Mathematics study plan

Factorise cubic and quartic polynomials using the factor theorem and synthetic division, then find the GCD and LCM of two polynomials by factorisation.

Solve quadratic equations by factorisation, completing the square and the quadratic formula, and classify the roots using the discriminant.

Sketch the graph of a quadratic function and read off its vertex, axis of symmetry and zeros, linking the sign of the discriminant to the number of x-intercepts.

Find the square root of a polynomial by the long-division method and verify each answer by squaring it back.

Add, multiply and transpose matrices up to order 3x3, and evaluate 2x2 and 3x3 determinants.

Solve two-variable simultaneous linear equations by elimination, substitution, cross-multiplication and Cramer's rule, and state whether each system is consistent.

Generate terms of an AP and a GP, find the nth term and the sum of n terms, and solve 'which term' and 'how many terms' problems.

Apply Euclid's division lemma and the fundamental theorem of arithmetic to find HCF and LCM and to test divisibility.

State and prove Thales' theorem and its converse, and apply them to divide a segment in a given ratio and to prove lines parallel.

State and prove the Pythagoras theorem and its converse, and use them to compute unknown sides and to recognise right triangles.

Prove two triangles similar using the AA, SSS and SAS criteria, writing the vertex correspondence correctly at every step.

Solve 2-mark and 5-mark similarity problems involving nested triangles, midpoints and parallel lines inside a triangle.

Apply circle theorems: angle in a semicircle, cyclic quadrilateral, alternate segment, and equal chords subtending equal arcs.

Construct tangents to a circle from an external point and a tangent at a point on the circle, recording the construction steps in order.

Prove the two-tangent theorem and use it to calculate lengths, perimeters and angles in tangent configurations.

Solve concurrency problems involving medians, altitudes, perpendicular bisectors and angle bisectors of a triangle.

Compute range, variance and standard deviation for raw and grouped data using both the direct method and the assumed-mean shortcut.

Interpret standard deviation and variance by comparing two distributions and predicting the effect of shifting and scaling the data.

Calculate probabilities of simple events from the classical definition and of compound events using the addition and multiplication rules for mutually exclusive and independent cases.

Solve complementary-event problems and standard experiments: two dice, a deck of cards and drawing balls from a bag.

Compute curved surface area, total surface area and volume of cylinders, cones, spheres and hemispheres from given dimensions.

Use the frustum formulae for curved surface area, total surface area and volume in real objects such as buckets, glasses and lamp shades.

Solve combined-solid problems (cylinder with hemisphere, cone on cylinder, sphere inside cylinder) by adding or subtracting volumes and surface areas.

Convert units correctly between centimetres, metres, litres and cubic centimetres, and keep exact answers in terms of pi where the question requires it.

Use the trigonometric ratios, the identities sin^2 + cos^2 = 1 and its relatives, and complementary-angle relations to simplify and prove expressions.

Solve heights-and-distances problems with one and with two angles of elevation or depression, drawing a labelled diagram before every calculation.

Apply the distance, section and midpoint formulae and find the coordinates of a point dividing a segment in a given ratio, internal or external.

Find the slope of a line, the angle between two lines, and the equation of a line in slope-intercept, point-slope, two-point and intercept form.

Write relations as sets of ordered pairs, arrow diagrams and Cartesian products, and classify them as reflexive, symmetric, transitive or equivalence relations.

Identify one-one, onto and bijective functions and compute the composition of two given functions.

Complete two full-length timed mock papers under exam conditions and self-mark them against the official marking pattern.

Rebuild a personal error log and re-solve every question previously answered wrongly across all eight domains.