Class 12 Mathematics Part 2

Antiderivatives and standard integrals, substitution, trigonometric identities and partial fractions, integration by parts and special integrals, definite integrals with their properties and the limit of a sum.

Areas under simple curves, areas between two curves, horizontal strips, symmetry, and worked board-style area problems with parameters.

Order and degree, formation of differential equations, variable separable and homogeneous methods, first order linear equations and their applications.

Scalars and vectors, the types of vectors, addition and scalar multiplication, components and direction cosines, the section formula, the dot product with projections, and the cross product with areas.

Direction cosines and direction ratios, the vector and cartesian equations of a line, the angle between two lines, and the shortest distance between skew and parallel lines.

Formulating a linear programming problem, the feasible region, the corner point method, bounded and unbounded regions, and graphical solutions with real-life constraints.

Conditional probability and its properties, the multiplication theorem, independent events, the theorem of total probability and Bayes' theorem, random variables with mean and variance, and Bernoulli trials leading to the binomial distribution.