Assam HSLC Class 10 Elective Advanced Mathematics study plan

State and prove the key triangle theorems (angle sum, Pythagoras and its converse, mid-point theorem, similarity criteria) from memory in writing

Apply congruence and similarity criteria to solve at least 15 two-column proof problems, writing each reason explicitly

Factorise and divide polynomials using the factor and remainder theorems, including the factorisation of cubic expressions

Solve at least 10 problems combining polynomial division with the factor theorem, checking each remainder by substitution

Solve circle theorem problems involving tangent properties, cyclic quadrilaterals, angles in the same segment, and the alternate segment theorem

Construct triangles, angle bisectors, perpendicular bisectors, and circles through given points using ruler and compass, with construction steps written out

Derive and apply the trigonometric ratios for 0, 30, 45, 60, and 90 degrees without consulting a table

Prove standard trigonometric identities and simplify at least 12 identity-based expressions

Solve linear equations in two variables by elimination, substitution, and cross-multiplication, including word problems

Solve quadratic equations by factorisation, completing the square, and the quadratic formula, and interpret the discriminant

Form and solve at least 8 word problems that translate into linear or quadratic equations

Apply trigonometric ratios to heights-and-distances problems involving single and double observation points, drawing a correct diagram for each

Identify the common difference or ratio of a sequence and write its general term for both AP and GP

Compute sums of AP and GP series, including the sum to n terms and the infinite GP sum where the ratio is less than one

Prove and use the laws of indices and surds, including rationalising denominators and simplifying nested radicals

Classify numbers as rational or irrational and prove irrationality of standard cases such as the square root of 2 by contradiction

Derive and apply the distance, section, and mid-point formulas, and find the slope of a line from two points

Write equations of lines in slope-intercept, point-slope, and general form, and test conditions for parallel and perpendicular lines

Solve problems on area, volume, and surface area of cylinders, cones, spheres, hemispheres, and combinations of solids

Convert between units of length, area, and volume in mensuration problems and interpret results in context

Compute mean, median, and mode for grouped and ungrouped data, including the use of assumed-mean and step-deviation methods

Calculate range, variance, and standard deviation for raw data and interpret each measure of spread

Apply the classical definition of probability to simple events and use the addition rule for mutually exclusive events

Solve at least 10 probability problems involving dice, coins, cards, and simple combined events, stating the sample space explicitly

Write sets in roster and set-builder form and perform union, intersection, difference, and complement operations

Use Venn diagrams to solve counting problems, including the inclusion-exclusion rule for two and three sets

Identify relations and functions, determine domain and range from a given rule, and test whether a relation is a function

Revise number-system concepts by solving 15 mixed objective questions on rational and irrational numbers and surds

Attempt three full-length mock papers under exam timing, covering the highest-weight domains

Review every error from the mocks and re-solve the underlying problem type until it is correct without notes

Re-derive the 20 most-used formulas from geometry, trigonometry, algebra, and mensuration from memory

Consolidate a one-page revision sheet of theorems, identities, and formulas for final review