• ·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.

Relations & 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 (upto 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.

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.

·         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

Complex Numbers and Quadratic Equations

Need  for  complex  numbers,  especially √−1 ,  to  be  motivated  by  inability  to  solve  some  of  the

Quardratic   equations.   Algebraic   properties   of   complex   numbers.Argand   plane   and   polar

representation  of  complex  numbers.Statement  of  Fundamental  Theorem of Algebra,  solution  of

quadratic  equations  (with  real  coefficients)  in  the  complex  number  system.Square  root  of  a

complex number.

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.Graphical method of finding a solution of system of linear inequalities in two variables

Permutations and Combinations

·Fundamental  principle  of  counting.Factorialn.  (n!)  Permutations  and  combinations,  derivation of Formulae for n
h and their connections, simple applications.

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.

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., infinite G.P. and its sum,

geometric  mean  (G.M.),  relation  between  A.M.  and  G.M

·         Brief  recall  of  two  dimensional  geometry  from  earlier  classes.  Shifting  of  origin.  Slope  of a  line

and angle between two lines. Various forms of equations of a line: parallel to axis, point -slope

form, slope-intercept form, two-point form, intercept form and normal form. General equation of a

line.Equation of family of lines passing through the point of intersection of two lines.Distance of a

point from a line.

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.

Introduction to Three-dimensional Geometry

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

·         Derivative    introduced    as    rate    of    change    both    as    that    of    distance    function    and

geometrically.Intuitive  idea  of  limit.Limits  of  polynomials  and  rational  functions  trigonometric,

exponential  and  logarithmic functions.Definition  of  derivative  relate  it to scope  of  tangent  of  the

curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial

and trigonometric functions.

·         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 variety of examples related to real life and

Mathematics.  Validating  the  statements  involving  the  connecting  words,  difference  among

contradiction, converse and contra positive.

·         Measures   of   Dispersion:   Range,   Mean   deviation,   variance   and   standard   deviation   of

un grouped/grouped  data.  Analysis  of  frequency  distributions  with  equal  means  but  different

variances.

Probability     

·         Random  experiments;  outcomes,  sample  spaces  (set  representation).  Events;  occurrence  of

events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set

theoretic)  probability,  connections with  other  theories  of  earlier  classes. Probability  of  an  event,

probability of ‘not’, ‘and’ and ‘or’ events.