Sets, operations on sets, Venn diagrams, De Morgan laws, Cartesian product, relations and equivalence relations. Real numbers on a line. Complex numbers — modulus, argument, cube roots of unity. Binary number system and conversions. Arithmetic, Geometric and Harmonic progressions. Quadratic equations. Linear inequations in two variables (graphs). Permutations and combinations. Binomial theorem. Logarithms and applications.

Types of matrices and operations on matrices. Determinant of a matrix and its properties. Adjoint and inverse of a square matrix. Solution of a system of linear equations in two or three unknowns by Cramer's rule and the Matrix method.

Angles and their measures in degrees and radians. Trigonometric ratios and identities. Sum and difference formulae. Multiple and sub-multiple angles. Inverse trigonometric functions. Applications — heights and distances, properties of triangles.

Rectangular Cartesian coordinates, distance formula. Equation of a line in various forms, angle between lines, distance of a point from a line. Equation of a circle. Parabola, ellipse and hyperbola — standard forms, eccentricity and axis. Points in 3D space, direction cosines and ratios. Equations of a plane, line and sphere.

Real-valued functions — domain, range and graph. Composite, one-one, onto and inverse functions. Limits and standard limits. Continuity and algebraic operations on continuous functions. Derivative at a point — geometric and physical meaning. Derivatives of sum, product, quotient and composite functions. Second-order derivatives. Increasing/decreasing functions and maxima & minima.

Integration as the inverse of differentiation, by substitution and by parts. Standard integrals. Definite integrals and areas of plane regions. Order and degree of a differential equation; general and particular solutions; first-order, first-degree equations with applications to growth and decay.

Vectors in two and three dimensions; magnitude and direction. Unit and null vectors. Addition, scalar multiplication, dot product and cross product. Applications — work done by a force, moment of a force and geometric problems.

Statistics: classification of data, frequency and cumulative frequency distributions, histograms, pie charts, frequency polygons. Measures of central tendency — mean, median, mode. Variance, standard deviation, correlation and regression. Probability: sample space and events; mutually exclusive, exhaustive, complementary events; classical and statistical definitions; addition and multiplication; conditional probability and Bayes' theorem; random variables and Binomial distribution.