Mathematics
Class XI
Syllabus for Half Yearly Exam 2015-16
S.NO
Distribution of Syllabus
1
Sets:
Sets and their representations. Emptyset. Finite and infinite set. Equal sets. Subsets
of the set of real numbers especially intervals (with notations).Powerset.
Universalset. Venndiagrams.Union and intersection of sets. Difference of sets.
Complement of a set.
Relations & Functions:
Ordered pairs ,Cartesian product of sets.Number of elements in thecartesian
product of two finite sets.Cartesians products of their real with itself(upto R
xRxR).Defination of relation,pictorialdigrams,domain.codomain andrange of
relation.Functionas special kind of relation from one set to another.Pictorial
representation of a function,domain,co domain & 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 function with their graphs.Sum,difference,product and quotients of
functions.
Trigonometric Functions:
Positive and negative angles.Measuring angles in radians and indegrees and
conversion from one measure to another.Definition of trigonometric functionswith
the help of unitcircle.Truth of the identity sin2x + cos 2 x = 1,forall x.Signs of
trigonometric functions and sketch of their graphs..Expressingsin(x + y) and cos(x+y)
in terms of sin x,siny,cosx&cosy.Deducing the identities like the following:
Tan(x + y)= tan x + tan y ,cot(x+y)= cot x coty+1
1+ tanx tany
cot y + cot x
Sin x –sin y = 2 sin x+y cos x-y ,cos x + cos y =2 cos x+y cos x-y
2
2
2
2
Sin x –sin y = 2 cos x+y sin x-y ,cos x + cos y =-2 sin x+y sin x-y
2
2
2
2
2
Trigonometric Functions contd-----Identities related to sin2x,cos2x,tan2x,sin3x,cos3x and tan3x.General solution of
trigonometricequtations of the type sin0=sin
Principle of Mathematical Induction:
Processes of the proof by induction.motivating the application of the methodby looking at
natural numbers as the least inductive subset of real numbers.The principle of mathematical
induction and simple applications.
(Unit Test 1)
Complex Numbersand quadratic equations:
Need for complex numbers,especially,to be motivated by inability to solve every quadratic
equation.Brief description of algeberic properties of complex numbers.Argandplan and polar
representation of complex numbers.Statement of fundamental theorem
of algebra solution of quadratic equation in the complex number system.
3
4
Linear inequalities:
Linear inequalities.Algeberic solution of linear inequalities in one variable their
representation on the number line.Graphical solution of linear inequalities in two
variable.Solution of system of linear inequalities in two variables-graphically.
Permutation&combinations:
Fundamental principal of counting.Factorialn(n.)
Permutation&combination,derivation of formula and their connection simple application.
Binomial theorem:
History,statement and proof of the binomial theorem for positive
integralindices.Pascal’Striangle general and middle term in binomial expansion,simple
applications. (2nd term Unit test)
Sequence Series:
Sequence and series.Arthematicprogession(A.P)
Arthemetic mean(A.M)Geomatricprogession(G.P)
General term of a G.P sum ofntermsofaG.P,geometric mean(G.M) relation between A.M and
G.M.Sumton terms of the special series:
n
nn
∑ K , ∑ K2 and∑ K3
k=1
k=1
k=1
Straight Lines:
Brief recall of 2D from earlier classes.Slope of a line and angle between to two lines.Various
form so equations of a line :parallel to axes,point-slope form,slope-intercept form,two point
form,intercept form and normal form.General equation of a line.Distance of a point from a
line.