Karnataka II PUC Mathematics (KSEAB) study plan

State and apply matrix operations (addition, scalar multiplication, multiplication, transpose) and verify properties such as (AB)^T = B^T A^T on small matrices

Compute 2x2 and 3x3 determinants by cofactor expansion and use row/column reduction to simplify before expanding

Solve systems of linear equations in two and three variables using Cramer's rule and the inverse-matrix method, and classify solutions as unique, infinite or none

Recall standard antiderivatives (power, exponential, trigonometric, 1/x, 1/(1+x^2), 1/sqrt(1-x^2)) and integrate by substitution

Set up and evaluate definite integrals using the fundamental theorem of calculus and the substitution rule

Integrate using integration by parts, including choosing u by the ILATE preference order and repeating the method for products like x^2 e^x

Evaluate integrals of rational functions using partial fractions for distinct linear, repeated linear and irreducible quadratic factors

Apply special reduction formulas and evaluate definite integrals with symmetry properties (even/odd functions, 0 to 2a substitutions)

Find the area under simple curves and between two curves by setting up definite integrals with correct limits and sketch the region

Re-derive determinant properties (row swap sign change, identical rows give zero, scalar multiplication) and use them to evaluate determinants without full expansion

Perform vector addition, scalar multiplication, dot product and cross product, and compute magnitudes, unit vectors and projections

Use the scalar triple product to test coplanarity and compute the volume of a parallelepiped

Write equations of lines in vector and Cartesian form (point-direction, two-point) and of planes in normal and intercept form

Compute shortest distance from a point to a plane and between skew lines using the cross-product formula

Verify whether a given relation is reflexive, symmetric and transitive, and decide equivalence class membership on small finite sets

Find angles between lines and planes and between two planes using direction vectors and normals, and test perpendicularity and parallelism

Determine whether a function is one-one, onto or bijective, and compute the inverse of a bijection on a small domain

Compose two functions and verify or disprove f(g(x)) = g(f(x)) with a counterexample

Classify binary operations by closure, commutativity and associativity, and identify identity and inverse elements

Solve simple problems on the number of relations and functions between two finite sets using 2^(mn) and n^m

Test continuity of piecewise functions at a point using left-hand limit, right-hand limit and function value, and classify discontinuities

Differentiate using chain rule, product rule, quotient rule, implicit differentiation and logarithmic differentiation

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

Verify Rolle's theorem and the mean value theorem for a stated function on a stated interval and find the guaranteed c

Find rates of change, increasing/decreasing intervals and local maxima/minima using the first and second derivative tests

Classify and solve first-order differential equations by separation of variables and by homogeneous substitution y = vx

Solve linear differential equations of form dy/dx + Py = Q using the integrating factor e^(integral P dx)

Form a differential equation from a family of curves by eliminating arbitrary constants

Evaluate principal values of inverse trigonometric functions and simplify expressions using standard identities and substitution

Solve equations involving inverse trigonometric functions by converting to algebraic relations and rejecting extraneous roots

Apply conditional probability, multiplication theorem and Bayes' theorem to multi-stage problems stated in words

Use the binomial distribution to compute probabilities of exactly, at least and at most r successes, and find its mean and variance

Distinguish independent events from mutually exclusive events and test independence numerically

Formulate a linear programming problem from a word problem by defining decision variables, objective function and non-negativity constraints

Solve two-variable LPPs graphically by finding the feasible region and testing corner points, and identify infeasible or unbounded cases

Work through three full-length timed papers under exam conditions, allocating time per section as in the actual paper

Re-solve every previously logged error and confirm the fix without looking at the original solution

Drill high-frequency short-answer items (formula recall, one-step evaluations) to build speed on the low-mark questions

Consolidate a single condensed revision sheet covering formulas across all domains