Karnataka II PUC Basic Mathematics (KSEAB) study plan

Derive slope-intercept, point-slope and two-point forms, and convert 10 general-form line equations into slope form.

Solve problems on perpendicular distance, angle between two lines, and lines through the intersection of two given lines.

Write the equation of a circle from centre-radius, diameter endpoints and three points, and recover centre and radius by completing the square.

Classify parabola, ellipse and hyperbola from eccentricity and directrix data, and sketch six conics marking focus, vertex and latus rectum.

Evaluate limits of algebraic, trigonometric and exponential expressions using standard limits, rationalisation and substitution.

Test continuity of piecewise functions at a point and find the unknown constant that makes a function continuous.

Differentiate products, quotients, composites and implicit relations using the chain rule, and do three first-principles derivatives.

Redo five mixed conic and circle problems so Domain 5 stays active.

Find intervals of monotonicity and classify local maxima and minima using the first and second derivative tests.

Compute equations of tangent and normal to a curve at a given point.

Evaluate indefinite integrals using standard forms, substitution and integration by parts.

Evaluate definite integrals and use them to find the area under a curve and between a line and a parabola.

Compute mean, median, mode, range, quartile deviation, mean deviation and standard deviation for grouped and ungrouped data.

Apply the addition and multiplication theorems of probability to 15 mixed problems, including complementary events.

Solve conditional-probability problems with two-stage tree diagrams and check answers for consistency.

Interpret a computed standard deviation or probability in one sentence of context.

Finish Domain 8 by solving 10 word problems that combine descriptive statistics with probability rules.

Perform union, intersection, difference and complement operations on sets, and verify De Morgan's laws on two concrete examples.

Test relations for reflexive, symmetric and transitive properties, and identify equivalence relations from a given list.

Classify functions as injective, surjective or bijective, find inverse functions where they exist, and compute domains, ranges and composites.

Carry out matrix addition, multiplication and transpose, and identify symmetric and skew-symmetric matrices.

Expand 2x2 and 3x3 determinants, apply their properties, and find adjoint and inverse where it exists.

Solve a three-variable system by Cramer's rule and by the matrix-inverse method, and verify the solution.

Compute nPr and nCr, count arrangements with restrictions and circular permutations, and find the general, middle and constant terms in a binomial expansion.

Identify AP and GP from given terms, compute the nth term and sum to n terms, insert arithmetic and geometric means, and sum an infinite GP with |r|<1.

Compute sums of the first n natural numbers, their squares and their cubes and apply them to short word problems.

Calculate simple interest, compound interest, effective rate and present value for at least six realistic loan and deposit cases.

Find the present and future value of ordinary annuities, and compute true discount, banker's discount and banker's gain on a bill.

Formulate linear programming problems from word problems, graph the feasible region, and optimise by the corner-point method, noting unbounded or infeasible cases.

Sit two full-length timed mock papers of three hours each under exam conditions.

Rework every item in the error log from Weeks 1 to 7 until each is solved without notes.

Condense all ten domains into a single revision sheet of formulas, standard results and common traps.