Tamil Nadu HSE First Year Mathematics study plan

Classify real numbers and apply the laws of exponents and radicals to simplify expressions involving surds and rational exponents

State and apply the remainder and factor theorems to factor cubic and quartic polynomials completely

Form quadratic equations from given roots and analyse the nature of roots using the discriminant without solving

Resolve proper rational functions into partial fractions for distinct linear, repeated linear and irreducible quadratic factors

Solve word problems that reduce to quadratic equations and verify that each root satisfies the original condition

Derive the slope, intercept and normal forms of a straight line and convert one form into another

Compute distances, angles between lines and perpendicular distances from a point to a line using standard formulae

Find the equation of a circle given centre and radius, three points, or the endpoints of a diameter

Determine the centre and radius of a general second-degree circle equation by completing the square and check whether a given line is a tangent, secant or neither

Apply the condition for a pair of straight lines through the origin to be real, coincident or imaginary

Derive the standard equations, focus, directrix, vertex and latus rectum of parabola, ellipse and hyperbola and identify each conic from its equation

Solve problems on tangents and normals to conics at a given point using the parametric form

Convert between degrees and radians and evaluate trigonometric ratios for allied, compound and multiple angles

Prove trigonometric identities involving sum, difference and transformation formulae (product to sum and sum to product)

Solve general trigonometric equations and express the full solution set in the required interval

Apply the fundamental principle of counting to arrange and select objects with and without repetition and with restrictions

Compute permutations and combinations of restricted selections, including circular permutations and distribution problems

Prove statements for all natural numbers by the principle of mathematical induction, writing the basis step, induction hypothesis and induction step explicitly

Expand binomials with positive integral index and find a specified general term, middle term or particular coefficient

Compute sums of finite arithmetic, geometric and special series and find the sum to infinity of a convergent geometric series

Evaluate limits of algebraic, trigonometric and exponential-type functions using standard limits, rationalisation and the squeeze idea

Test continuity of a piecewise function at a point by comparing left-hand limit, right-hand limit and function value

Differentiate from first principles and apply the product, quotient and chain rules to composite functions

Differentiate implicit, parametric, inverse trigonometric and logarithmic functions, and compute second derivatives

Apply differentiation to find gradients, tangents, normals and simple rates of change

Describe sets in roster and set-builder form and perform union, intersection, difference and complement operations on finite sets

Verify set identities using Venn diagrams and membership tables, and count elements using the inclusion-exclusion formula

Determine whether a relation is reflexive, symmetric, transitive or an equivalence relation, and classify functions as one-one, onto or bijective

Compute determinants of orders two and three and apply properties of determinants to simplify evaluation

Classify matrices, perform matrix multiplication and find inverses using the adjugate or row reduction

Perform vector addition, scalar multiplication, dot product and cross product, and interpret each geometrically

Apply vectors to prove collinearity, coplanarity and perpendicularity, and compute areas of triangles and parallelograms

Integrate standard algebraic, trigonometric, exponential and reciprocal functions using the basic rules

Evaluate definite integrals and apply substitution and integration by parts to standard composite integrands

Compute areas bounded by simple curves and lines using definite integrals

Define sample space and events and compute probabilities using the classical and axiomatic approaches

Apply addition and multiplication theorems, including conditional probability, to combined events

Solve probability problems using permutations and combinations to count favourable outcomes

Re-attempt one full-length mixed paper under timed conditions and log every unresolved doubt against its domain

Revise the formula sheets from weeks 1 to 7 and drill the highest-weight domains for accuracy under time pressure