Class XI Mathematics

Sets and their representations, empty set, finite and infinite sets, subsets, power set, universal set, Venn diagrams, union and intersection of sets, difference of sets, complement of a set, and De Morgan's laws.

Cartesian product of sets, relations, domain, co-domain, and range of a relation, functions as special types of relations, real-valued functions, domain and range, graphs of standard functions, and algebra of functions.

Measurement of angles in degrees and radians, definition of trigonometric functions using unit circle, signs, domains, ranges, graphs, periodicity, associated angles, and trigonometric functions of sum and difference of angles.

Formulae for multiple angles (2A, 3A) and submultiple angles (A/2), general solutions of basic and quadratic trigonometric equations, sine and cosine rules in triangles, and area formulae.

Complex numbers as ordered pairs of reals, algebraic operations, modulus and conjugate of a complex number, Argand plane and polar representation, square root of complex numbers, and solutions of quadratic equations with negative discriminant.

Linear inequalities, algebraic solutions of linear inequalities in one variable and their representation on the number line, graphical solution of linear inequalities in two variables, and graphical solution of system of linear inequalities in two variables.

Slope of a line, angle between two lines, conditions for parallelism and perpendicularity, forms of equations of a line: slope-intercept, point-slope, two-point, intercept, normal form, general equation, distance of a point from a line, and concurrent lines.

Definition of a circle, standard equation with centre and radius, general second-degree equation representing a circle, circle passing through given points, parametric equations, and condition of tangency.

Fundamental principle of counting, factorial n (n!), permutations as arrangements, derivations of formula for nPr, restricted permutations, permutations of objects not all distinct, combinations as selections, derivation of nCr, relation between nPr and nCr, and practical counting problems.

History and statement of Binomial Theorem for positive integral indices, Pascal's triangle, expansion of (x + y)^n, general term, middle term(s), numerically greatest term, and applications to divisibility and approximations.

Sequence and Series, Arithmetic Progression (AP), Arithmetic Mean (AM), Geometric Progression (GP), general term of a GP, sum of n terms of a GP, infinite GP and its sum, geometric mean (GM), relation between AM and GM, and sum to n terms of special series.

Conic sections as intersections of a plane with a double-napped right circular cone, eccentricity e, parabola (e = 1), ellipse (e < 1), hyperbola (e > 1), standard equations, foci, vertices, directrices, axes, latus rectum, and focal distances.

Coordinate axes and coordinate planes in three dimensions, coordinates of a point in space, signs in eight octants, distance between two points in 3D, section formula for internal and external division, and centroid of a triangle.

Intuitive concept of limit, left-hand and right-hand limits, condition for existence of limit, algebra of limits, evaluation of algebraic limits by factorization and rationalization, standard trigonometric limits, and exponential and logarithmic limits.

Derivative introduced as rate of change, definition of derivative at a point and as a function, differentiation from first principles (ab initio), derivatives of polynomials and trigonometric functions, product and quotient rules of differentiation.

Limitations of measures of central tendency, range, mean deviation about mean and median for raw, discrete, and continuous frequency distributions, variance and standard deviation, and coefficient of variation for comparing stability.

Random experiments, outcomes and sample space, events: occurrence of events, types of events: impossible and sure events, mutually exclusive and exhaustive events, axiomatic approach to probability, and addition theorem of probability.