OFFICIAL SYLLABUS

Unit – I Sets

Sets and their representations. Empty set. Finite and Infinite sets. Equal sets, Subsets, Subsets of a 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.

Unit – II Relations and Functions

Ordered pairs, Cartesian product of sets, Number of elements in the Cartesian product of two finite sets. Cartesian product of the set of reals with itself (up to R x R x R). Definition of Relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special type of relation, Pictorial representation of a function, domain, co-domain and range of A function. Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, Signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotients of functions.

Unit – III 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 unit circle. Truth of the identity sin²x + cos²x = 1, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications. Deducing identities like the following:

tan (x±y) = tanx ± tany/ 1 -+ tanx tany

cot (x±y) = cotx coty -+1 / coty ± cotx

sin alpha (±) sin beta = 2sin(1/2) (alpha ± beta) cos(1/2) (alpha -+ beta)

cos alpha + cos beta = 2cos(1/2) (alpha + beta) cos(1/2) (alpha - beta)

cos alpha - cos beta = - 2sin(1/2) (alpha + beta) sin(1/2) (alpha - beta)

Identities related to sin2x, cos2x, tan2x, sin3x, cos3xand tan3x. General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a.

Unit – IV Principle of Mathematical Induction

The Principle of Mathematical induction and Simple applications.

Unit – V Permutation and Combinations

The fundamental principle of counting. Factorial n, Permutations and combinations, derivation of formulae and their connections, simple applications.

Unit – VI Complex Numbers and Linear Inequalities

Need for complex numbers, especially root of (-1) to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equation in the complex number system.

Linear inequalities: Algebraic solution of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variable. Solution of a system of linear inequalities in two variables- graphically.

Unit – VII Limits and Derivates

Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

Unit – VIII Straight Lines

Brief recall of 2D from earlier classes. 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. Distance of a point from a line.

Unit – IX Conic Sections

Sections of a cone: Circles, Ellipse, Parabola, Hyperbola, 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.

Unit – X Probability

Random experiments: Outcomes, Simple spaces (set representation). Events: Occurrence of events ‘not,’ ‘and’ ‘or’ events, mutually exclusive events. Axiomatic (set theoretic) probability, connections with the theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’ & ‘or’ events.

Unit – XI Statistics

Measure of dispersion: mean deviation, variance and standard deviation of ungrouped/ grouped data. Analysis of frequency distributions with equal means but different variances.

Unit – XII 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.

Unit – XIII 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 if a G.P. Geometric mean (G.M), relation between A.M. and G.M. Sum to n terms of the special series.

Unit – XIV Introduction to Three Dimensional Geometry

Coordinates axes and coordinate planes in three dimensions. Coordinates of a point Distance between two points and section formula.

Unit - XV Mathematical Reasoning

Mathematically acceptable statements. Connecting words/ phrases- consolidating the understanding of “if and only if (necessary and sufficient) conditions”, “implies,” “and/or”, “Implied by,” “and,” “or”, “there exists” and their use through variety of examples related to real life and Mathematics. Validating the statements involving the connecting words – difference between contradiction, converse and contrapositive.

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