Tamil Nadu HSE Second Year Mathematics study plan

Derive and apply the standard forms of the circle, parabola, ellipse and hyperbola, then classify a conic from its general second-degree equation by computing the discriminant

Compute centre, foci, eccentricity, directrix and latus rectum for all four conics and sketch each from its equation without a graphing aid

Solve 15 mixed conic problems (tangency, chord of contact, condition for a line to touch a conic) and log each error type in a mistake notebook

State the mean value theorems (Rolle and Lagrange) precisely with their hypotheses and verify each hypothesis for five given functions on a stated interval

Apply the first and second derivative tests to classify stationary points and sketch monotonic and concavity behaviour for ten rational and trigonometric functions

Solve problems on asymptotes, rectangular hyperbola and the parametric forms of each conic using t-parameters

Apply the mean value theorem to prove inequalities and to locate intervals containing roots

Compute maxima and minima of applied word problems (area, volume, cost) and justify global versus local extrema on a closed interval

Use the derivative to determine intervals of increase/decrease and points of inflection for polynomial and exponential functions

Time yourself on a 25-mark mixed set covering conics and calculus applications and record the minutes spent per question

Build a complete table of standard integrals (algebraic, trigonometric, exponential, logarithmic forms) and reproduce it from memory in under ten minutes

Evaluate definite integrals using substitution, integration by parts and partial fractions, solving at least 25 problems across the three techniques

Apply definite integrals to compute area under curves, area between two curves, and volume of solids of revolution about the x-axis

Classify first-order differential equations by order, degree and type, then solve variable-separable and homogeneous equations

Solve linear differential equations using the integrating factor and verify each solution by back-substitution

Solve Bernoulli-form and exact differential equations and identify when the integrating factor is a function of x alone or y alone

Compute areas and volumes in applied settings (bounded regions, rotated curves) and set up the integral before evaluating it

Revisit maxima-minima and mean value theorem problems under timed conditions to confirm retention from weeks 1 and 2

Complete a full-length timed paper section combining integration, differential equations and calculus applications

Rank your five weakest question types from the timed section and write a targeted drill list for week 5