CBSE SYLLABUS NCERT CLASS 11TH
UNIT I: SETS AND FUNCTIONS
1. Sets
Sets and their representations. Empty set. Finite and Infinite Sets. Equal sets. Subsets. Subsets of the set of real numbers, especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and intersection of sets. Difference of sets. Complement of a Set, Properties of Complement Sets.
2. Relations and Functions
Ordered pairs, Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the reals with itself (up to R × R × R). Definition of relation, pictorial diagrams, domain, co-domain, and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain, and range of a function. Real-valued function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, and greatest integer functions with their graphs. Sum, difference, product, and quotients of functions.
3. Trigonometric Functions
Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of the unit circle. The truth of the identity sin²x + cos²x = 1 for all x. Signs of trigonometric functions and sketches of their graphs. Expressing sin (x + y) and cos (x + y) in terms of sin x, sin y, cos x, and cos y. Identities related to sin2x, cos2x, tan2x, sin3x, cos3x, and tan3x. General solution of trigonometric equations of the type sin θ = sin α, cos θ = cos α, and tan θ = tan α. Proofs and simple applications of sine and cosine formulas.
UNIT II : ALGEBRA
1. Principle of Mathematical Induction
Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications.
2. Complex Numbers and Quadratic Equations
The need for complex numbers, especially −1, to be motivated by the inability to solve every quadratic
equation. Brief description of algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of the Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system, and square root of a complex number.
3. Linear Inequalities
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. Solution of a system of linear inequalities in two variables—graphically.
4. Permutations and Combinations
Fundamental principle of counting. Factorial n. Permutations and combinations: derivation of formulas and their connections, simple applications.
5. Binomial Theorem
History, statement, and proof of the binomial theorem for positive integral indices. Pascal’s triangle, general and middle term in binomial expansion, simple applications.
6. Sequence and Series
Sequence and Series. Arithmetic Progression (A.P.), Arithmetic Mean (A.M.), Geometric Progression (G.P.), general term of a G.P., sum of n terms of a G.P. Arithmetic and geometric series, infinite G.P. and its sum, geometric mean (G.M.).
UNIT III : COORDINATE GEOMETRY
1. Straight Lines
Brief recall of 2-D from earlier classes, shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axes, point-slope form, slope-intercept form, two-point form, intercepts form, and normal form. General equation of a line. Equation of a family of lines passing through the point of intersection of two lines. Distance of a point from a line.
2. Conic Sections
Sections of a cone: circles, ellipses, parabolas, hyperbolas, a point, a straight line, and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse, and hyperbola. Standard equation of a circle.
3. Introduction to Three-Dimensional Geometry
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.
UNIT IV : CALCULUS
Limits and Derivatives Derivatives introduced as rate of change both as that of distance function and geometrically, Definition of derivative, relate it to the slope of the tangent of the curve, derivative of sum, difference, product, and quotient of functions. Derivatives of polynomial and trigonometric functions.
UNIT V: MATHEMATICAL REASONING
Mathematically acceptable statements. Connecting words/phrases—consolidating the understanding of “if and only if (necessary and sufficient) condition,” “implies,” “and/or,” “implied by,” “and,” “or,” “there exists,” and their use through a variety of examples related to real life and mathematics. Validating the statements involving the connecting words—difference between contradiction, converse, and contrapositive.
UNIT VI : STATISTICS AND PROBABILITY
1. Statistics
Measure of dispersion: mean deviation, variance, and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.
2. Probability
Random experiments: outcomes, sample spaces (set representation). Events: Occurrence of events, ‘not,’ ‘and,’ & ‘or’ events, exhaustive events, and mutually exclusive events. Axiomatic (set theoretic) probability, connections with the theories of earlier classes. Probability of an event, probability of ‘not,’ ‘and,’ & ‘or’ events.
