Bihar Board Class 11th 12th Syllabus Maths

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-e-: -~ lfi~fit?.n (XI-XII) Qiq_lloilf- 2007•
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q1w~q; (XI-XII) Ql4_4<fiq-2007-09
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Gd4e•
& XII )
(Cl ass -XI
L.lnttodvc{lon •·
rihe~ a visio n in whic h ahe purpo ses nre emb'Cdded 10 J
The high er seco ndary ~cho ol ma1hema1ics dc"lc · 1od •. so<:r·e ,Y: "'10 dc 11elop, he
conte. xt that is· b0 ~h• broa der and more consi s1en1 with accel eratin g c ha nges ,n · ay s 1
re . all s ruden rs. T he ms1ruc11on mu s1 rcn
broad er goals for
qu1s 11e ada ptabi lity, the instru ction musa adop t s,n~ t
ci tly recog niz ing that they will spend their adult lives in a socie ty incrca
the ~eed s of all s tuden ts, expli gr
ods.
domi nated by tec hnolo gy and quan titati ve meth
ical ideas acces s ible to all .stude nts in spite of L
It is inten ded to prov ide a comm on body of Math emat . . i f urther educaft,,c
or
'
exist ' d ispan .. . the incre asing neces sity
·• mg t,es 1n educ ation al oppo rtuni ty in Mathematics and ton
well taken that the stude nts enter ing highe r secon dary stage
and alter nativ e caree rs.. It ic; well unde rs tood and . st
d·rn · nt, but these diffe re nces a re be addressed b
1 _er m many ways , inclu ding math emat ical achie veme Y
nts rathe r than by delet ions.
ennc hme nt_and exten sions of the purp osed conte e
room dyna mic in wh ich teach ers and stude nts becom
Ther e is a visio n of the emer genc e of a new class of studen
and solvi ng math emat ical probl ems. Asse ssme nt
natur al partn ers in deve lopin g math emat ical ideas ed with key aspec ts 0 ;
of instru ction and shou ld be align
learn ing shou ld be view ed as an integ ral part
instr uctio n.
sion of
ics curri culum inclu des the re finem ent and exten
In class es XI and XII espec ially, the Math emat
that all stude nts can-
meth ods of math emat ical prob lem solvi ng so
g appro ache s to inves tigat e and understand
* use, with incre asing confi denc e, probl em-s olvin
math emat ical conte nt;
g strate gies to solve prob lems from within and
* appl y integ rated math emat ical probl em-s olvin
outsi de math emat ics;
outsi de Math emat ics;
gnise and form ulate probl ems from situa tions withi n and
* Reco
to real-w orld prob lems s ituati on.
* Appl y the proc ess of Math emat ical mode lling
* move towa rds abstr actio ns.
ematica l ideas and relat ionsh ip.
* refle ct upon and clari fy their think ing abou t math
gener alisat ions disco vered throu gh investigations;
* form ulate math emat ical defin itions and expre ss
ng.
* expr ess math emat ical ideas orall y and in writi
sharp
analy tical abilit y logic al inter preta tion skill and
In short , at this stage stude nts shou ld deve lop
think ing pow er.
ics are recommended.
The foJlowing instructional practices in Mathemat
ng and apply ing math emat ical ideas .
* The activ e invo lvem ent of stude nts in const ructi
a goal of instr uctio n .
* Trea ting prob lem solvi ng as a mean s as well as
stude nt inter actio n.
* Effec tive ques tioni ng techn iques that prom ote
as, smal l grou ps, indiv idual explo ration s, peer
* The use of a varie ty of instru ction al form ats such
rk, use of Math emat ical Labo rator ies, etc.
instr uctio n, whol e-cla ss discu ssion s, proje ct-wo
orall y and in writi ng.
* Stud ent comm unlca tion of Math emat ical ideas
n of the inter relat edne ss of Math emat ical topics.
* The estab lishm ent, unde rstan ding and appli catio
of instr uctio n .
* The asses smen t of learn ing as an integ ral part
as possible :
. The foJlowing prac tices need to be avoided as far
es of know ledge .
* Assu ming teach er and text as exclu sive sourc
* Rote mem oriza tion of facts and proce dures.
* Pape r-and -pen cil mani pulat ive skill work .
* Instr uctio n by teach er expo sition .

007-09
~ tf..,1~-4=~D-- 2
lITT1-ffw.n (XI-XII) ....

~ c objectives of teaching math .
The
• .
. I b'I' d I . . e ma11cs at lhe ~nio:- ~ctondar)' i.lnge ,.,, to de,el~p .irn,-.ng ~1udenl.
~~
With sharp thinking and apphu1,on or m,11hcmJ,,cs rnr ~ ° ,
nalyttca a I lly, eep og1cal mterp t01100 . .
50unda . · re
a riollS other branch~s of sc1enc~ and humani1 ics C010-Mathcmot1ci;. En v,ronmenm l Mat hema11cs.
113
t'cal Econom1cs). Developing probl I · ..
t,(athe!Jl'l I cm-so vmg ab1l11y and 10 be a ble 10 formulate real-1,rc •awac,oo,. I~
3
thematically. /J1P
J11 Th
. em athematization
. of the concepts
. h, b . ·rh
· as een stressed upon rather than role learning. at 1h1s sluge. e l .i:i!
proposed sylla~us 15 ~n am~lgamation of the present Bihar Syllabus and new NCERT-syllabus in n wny that ~
the broad heading~ given 10 th e ne~ N~ER:-syllabus have been retained while the conten ts of both the
syllabi have b~~n incorporated keepi_ng .:" mmd. For_example "chord of contact equations of tangents ~nd
normals, condition of t~ngency of a line , have been included in the co-ordinate gi ve a better understand ing
ioiether with a tool to mcrease problem solving ability.
The present NCERT syllabus has been retained with few additions but no deletion . presum ing the Class-
XL Examination will be internal assessment of the school and questions in the Board Examination would be
asked from Class-XII portion of the syllabi. It may be proposed that twenty per cent (20%) of the total
weightage be given on objective type questions and rest on "short answer" questi ons fully based on the
syllabus with main focus being given on the application of mathematical concepts and ideas.
The teachers need to use more figures, sketches of various curves while deliverin g their lectures in the
cl~sses. This helps the students visualise the abstract ideas, thereby making the transition to abstraction
easier. For the sake of convenience of teachers and students, the syllabus is presented in an explicit form.
COURSE-STRUCTURE
Class-XI
One Paper Three Hours Max. Marks : 100

Units Marks
I. Mathematical Logic, Sets and Functions 26
2. Algebra 30
3. Trigonometry IO
4. Co-ordinate Geometry 14
5. Elements of Calculus 08
6. Statistics and Probability 12
100

3. Outlines of the Syllabus (For Class-XI):
UNIT-I: MATHEMATICAL LOGIC, SETS & FUNCTIONS: (Periods-12)
1. Sets : Sets and their representations, Finite & infi nite sets, Empty sets, Equal sets,
Subsets, Power sets, Universal sets, Venn diagrams, Operations on sets (Union,
Intersection, Difference of sets), Complement of a set, Application of sets. De Morgan's
Law, Intervals in the set of real numbers.
2.. Relations and Functions : Ordered pairs, cartesian product of two sets, Number of
el~ments in the cartesian product of two finite sets. Definition of a relation, fun ction as
a special kind of relation between two sets. ~ictorial rep~esentation o~ a relation and
function, Real-valued functions of a real variable. Domain, Co-domain and range of
such functions, Different types of function s and their basic properties (Constant, identity,
Polynomial, Modulus, Signum, Greatest-integer fu~ction), lnject~ve, surjective_ and
bijective functions Sum, Difference, Product o~functions, Gra~hs of all such functions.
Symmetry and transformation of graph of functions, unde~standmg the g~aphs of f\x+a),
f(x)+a, f(ax), a,f(x), - f(x) , f(Jxl) , Jf(~)I if th~ graph f(x) 1s known. Basic prop:rt1es of
modulus, exponential and logarithmic functions. (Beriods-15)

--- ~ q1Wf'icfi (XI-XII) Qlq_lli;Fiq-2007-09

J. Math emat ical Logic : Stat ement. basic logic al conn
ec tives (words/phruses) . u,,
I
Venn diagrams in logic. Nega tive operation, Comp ound
statem ents and their negat, r,t
Conc epts and under stand ing of quant ifiers (• If and only
ir'. '" impli es·. ~implied : ·: ,
"and/ or". "and" , "or", "for all ". "ther e exists ") Valid
ation of statem ents, Differe)
betwe en contr adicti on. conve rse and contr aposi tive statem
ents. (Periods.~ ,
Truth tables , tauto logy. Duali ty, Algebra of statem ents,
Appl icatio ns of logic in sotv,~•'
simp le probl ems. Kind of proof s; direc t, contr aposi tive,
by contr adict ion by counic' 1

exam ple. Cond itiona l and bicon dition al statem ents, valid 1
argum ents.
4. Boolean Algebra : Boole an algeb ra as an algeb raic struc
ture. Princ iple of dualit ·
Boole an funct ions, Appli cation of Boolean Algeb ra in
Switc hing Circu it.(Pe riods -~

UNIT -II: ALGEBRA
l. Sequ ence and Series : Definition of a seque nce as
a funct ion, Exam ple of finite and
infini te seque nces, general terms of an A.P., GP. and
H.P. Prope rties of A.P. and Qp_
and their appli cation . Conc ept of A.M., G.M. and H.M
. and relati on between thell\.
Diffe rence betwe en a seque nce and a series. Sum of the
first n terms of an A.P., Qp_
Sum of an infinite G.P. Sum of an Arith metic ogeom etric
series . Evalu ation :En, l:n1 and
:En3 • Simp le application of means, Inequalities.
(Periods-12)
2. Complex numbers : Need for complex numbers to be
motiv ated by inabi lity to solve
every quadr atic equation. Brief description of algeb raic
prope rties of comp lex numbers.
Repre senta tion of comp lex numb ers as point s on Arga
nd plane , polar representation.
State ment of Fund amen tal theorem of Algebra, solut ion
of Fund amen tal theorem of
Algeb ra, soluti on of quadr atic equat ions in the comp lex
numb er syste m. Modulus and
argum ents of comp lex numbers. Trian gle inequality, Squa
re root of a comp lex number,
cube root of unity.
(Periods-JO)
3. Quad ratic equa tions and expr essio ns : Quad ratic
equa tions and expressions.
Symmetric functions of roots, formation of quadratic equat
ions with given roots , common
roots , Extre me values of quadr atic expre ssion s.
(Periods-O8)
4. Permutation & Combination: Fundamental Principle
of count ing. Conc ept of Factorial
of non-n egati ve integ ers. Perm utatio ns and comb inatio
ns, Deriv ative of formulae and
their conne ction s, simpl e appli catio ns (inclu ding, perm
utatio ns in group s and cyclic
perm utatio ns).
(Periods-JO)
5. Principle of Mathematical Induction : The need
for math emat ical induc tion. The
princ iple of mathe matic al induc tion and simp le appli catio
ns. (Periods-O4)
6. Binomial Theo rem: History, statem ent and proof of
the bioni mal theor em for positive
integ ral indic es. Pasca l's triang les, gener al and midd
le term in binom ial expansion.
simp le appli catio ns.
(Periods-O8)
7. Loga rithm : Defin ition with respe ct to a given base
and natur al base, properties and
appli catio n to simp le probl ems.
(Periods-O4)
8. Some important Infinite Serie s: Binom ial Theo rem
for negat ive and fracti onal indices.
expo nenti al and logar ithmi c serie s with prope r cond itions
on the varia ble and without
proof , simp le appli catio ns.
(Periods-O6)
~UN IT- III: TRIGONOMETRY
(Periods-JS)
Posit ive and nega tive angle , Meas uring angle s in
radia ns & in degre es and
conv ersio n from one meas ure to anoth er. Defin ition
of trigo nome tric functions,
Trigo nome tric ratios of gener al angle s. Effec t of addin
g one or more right angle s to the
argum ent. Perio dic funct ions, Perio ds of trigon omet ric
funct ions, signs of trigonometric
funct ions, Grap hs of sine, cosin e, tange nt and their

----
recip rocal funct ions. General

~ intttflo(cfi (XI-XII) Qlq__i4<fiq- 2007-09

· l , n)'tles li:e
ca .., " cflF'

»
.c.olutjon s of Lrig . d ~ni te. Mul tiple and sutim ulllp
poun
Tran sfor m . OllOrnclnc CQU;thons,_Com .
\.
RcJ r atton formula. Conditional 1dcn1,1ic glc. drc um· rud 'us,
0
d. a ' " between side~ and ~nglcs of a
u ianofo Arcll or triim. . o
· c ·
m-ra 1us and . rela tion bc1~ccn 1hClm . App hc1w on to s11nph: problems. e
M . , ex n•dii and
01vre s theorem and r . l,e
CO-ORDINATv app icauon 10 si mpl e problems . (P,riods-09) 6f '
UNIT-IV: a;,, GE OM ETR Y
. • f 1·
I. Stra ight line s ·. 'Stan d.ard gene ral equation or a s1raigh1 line , lnu:rsec11on o ines,
.
two s1rnighl lines . Slope of a line and angl ~
e I~
Equation of bisectors of angle between
· us ,,orms of equations of a line. concurrency or t rec ines.h 1·
between two lines · vano
nire )
e-biseclors (incentre), altitudes (ortho-ce
concurrency of medians (cenlroid), angl
and pc rpen d",cu Iar-bisec · tors (circum-centre).
a cone :
2 ~on lc Se~tions : Definition of a conic by focus directrix properly, s~ctions of
•
t. a straight line and pair of in1ersec1ing Imes
circle, ellipse. parabola, hyperbola, a poin s of
Standard equations and simple propertie
a~ a degenerated case of a conic section. of a
Equation of tangent and normal. Locus
c,r~le, ~arabola ellipse and hyperbola. (Periods-12)
point, simple problems.
and dimensional
3• Intr odu ctio n of three dimensional geometry, cordinate axis
ts and
on plane, distance between two poin
coord:nate, coordinates of a point -
sect ion formula.
(Periods-18)
UNIT-V: ELEMENTS OF CALCULUS
tions of a single variable and their graphs).
Recall Unit- I, Sections 3 (Real-valued func of -
e introduced as rate of change both as that
Concepts of limit & continuity. Derivativ on
itive idea of limit and continuity. Definiti
distance functions and geometrically, intu and
of the curve, Relation between continuity
of derivative, relate it to slope of tangent a func tion ,
rence, product and quotient of
differentiability. Derivative of sum, diffe
functions.
Derivative of polynomial and trigonometric (Periods-08)
UNIT-VI: STATISTICS & PROBABILITY ation and
ency and dispersion, variance, mean devi
1. Stat istic s : Measure of central tend ions
ped data. Analysis of frequency distribut
standard deviation of ungrouped / grou
and variance of combined distribution.
with equal means but different variances
n).
omes, sample spaces (set representatio
2. Probability : Random experiments, outc ually
' & 'or events, exhaustive events, mut
Events : occurence of events, 'not', 'and
probability) Connections with the theories
exclusive events. Axiomatic (set theorotic
t, probability of 'not', 'and' & 'or' events.
of earlier classes. Probabilit~, of an even (Periods-JO)
s (like environments,
ofproblems related to real-life situation
Note: Focus shou ld be Laid on formulation
r subjects of study.
travel etc.) and con nect ions with othe
+

crf- XII

~- 1 : ~ ~ ~ (Relation and Function)
metric), ~,: ft (Transitive),
1.1 ~ 31 h'~ - ~ ~ wm (~ (R efl ex ive ),~ (Sym
~ ~, i:t,ffi)' cfiT W"ITTR, ~ "Qiff i, m-"'<R ~ ) I
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1.2
f-;1cn)o1f1-Jfd<I i:t,ffi)' cfiT 311& 3m: ~ m'U'lcti TJI

~ 9
~ qpu~fqq:; (XI-XII) 4icl'-i&itf-2007-0

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Matrix). ~ (Transpose). mm ~ ~ U1fTftft'I l ~ (Symmetric and Skew Symmetric of
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f
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dx
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--G-
~ ~,'4f~i:fi (XI-XII} QIQ_i4i!fiq-2007-09

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+
COURSE-STRUCTURE
Class-XII
One Paper Three Hours Max. Marks : I 00
Units Marks
1. Relations and functions 10
2. Algebra 13
3. Calculus 40
4. Vectors and Three-dimensioJJal geometry 18
5. Linear programming 09
6. Probability 10
100

UNIT-I: RELATIONS AND FUNCTIONS: (Periods-12)
1. Relations and Functions: Types of relations : Reflexive, Symmetric and Transitive,
Equivalence relations, Composite functions , Inverse of a function , Binary Operations.

2. Inverse trigonometric Functions : (Periods-12)
Elementary conce pts and properties of inverse trigonometric functions , Definition,
Range, domain, general and principle value branches. Graphs of inverse trigonometric
function s. Elementary properties of inverse trigonometric functions.
0

UNIT-II : ALGEBRA:
1. Matrices : , (Periods-IS)
Concept of a matrix, Notation, order, equality, types of matrices, zero matrix, transpose
of a matrix, Symmetric and Skew-symmetric matrices. Addition, Multiplication and
scalar multiplication of matrices, Addition, Multiplication and scalar multiplication of
matrices and their simple properties, Non-commutativity of matri x-multiplication and
concepts of zero-divisors in product of matrices. Concept of elemei:itary row and column
operations. Adjoint of a matrix and invertible matrices. Proof of uniuences of inverse,
if it exists.

~
. .~ ¥:UUlf'icfi (XI-XII) Giq_il9iq-2007-09

( Ptriods- l S)
2. Determinants : , r dcierm·,nants rr •
rl ) Properues o · , .. ,inors
Determinanl of a square mal.rix (uplo 3 11 J mar c~ · h . a of a triangle. Consistency.
. . f d I • nt.s in finding t e arc .
cofactors and apphcat,ons o c enmna of linear equations in rw
inconsistency and number of possible solu1ions of a sySlem 0

or three variables (using matrix inversion me1hod).
UNIT-Ill: CALCULUS:
(Ptriods-18)
1. Dlfferentlablllty: . .
. • · Of a composite function , Cham rule
Derivative of a function at a point, Denvat,ve • d . h .·
.
Derivatives of implicit functions, inverse • I f nctions exponent,a 1an 1ogant m1c
circu ar u '. . .
. •
functions. Logarithmic differentiation. Denvauve o · f functions expressed m paramet1c
forms. Derivatives upto order three. f)
Rolle's and Lagrange's mean value theorems / th eo rem (without proo and their
geometric interpretations.
2. Applications of Derivatives : . (Periods-JS)
.
· · ·
dy I dx as a rate-measurer, geometric interpretation o f dy/dy , increasing
. . and decr~asing
.
·
functions, tangents and normals, approx1ma · t·10n, s·gns
1 of derivatives • maxima and
minima
3. Indefinite Integrals: (Periods-JS)
d
4. Definite integrals : (Periods-JO)
Definite Integrals as limit of a sum and its simple properties. Fundamental theorem of
calculus (without proof), Evaluation of definite integrals. Properties of definite integrals.

5. Application of the integrals: (Periods-JO)
Application in finding the area enclosed by simple curves, especially lines, areas of
circles/ Parabolas/ ellipses (in standard form), area between the two above said curves
(clearly identifiable regions).
6. Differential Equations : (Periods-JO)
Definition, order degree. Formation of differential equation whose general solution is
given, general and particular solutions of a differential equations. Solution of differential
·equations by method of separtion of variables, homogenous differential equations of
first order and first degree. Linear differential equation of order one (or the type : dy/
dx + p(x)y = q(x). Applications of differential equations to problem related to the
environment and to Dynamics (simple cases only).
UNIT-IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY :
1. Vectors:
(Periods-JO)
Vectors and scalars, magnitude, and direction of a vector. Direction consines / ratios of
a vector, types of vectors (equal, unit'. zero, parallel and collinear vectors), position
vector of a point, negative of a vector, local and free vectors, components of a vector,
addition of vectors, multiplication by scalars. Position vector of a point dividing a line
segment in a given ratio. Scalar and vector product of two vectors with their geometrical
meaning. Projection of a vector on a line. Scalar and vector triple product.
2. Introduction to Three-dimensional Geometry: (Periods-JS)
Co-ordinate axes and co-ordinate planes in three dimensions. Co-ordinates of a point,
Distance between two points and section formula.
Direction cosines/ ratios of a line joining two points Cart · • f 1· e and
• esian equation o a in
plane. Angles between (a) two lines, (b) two planes (c) al·
,
d o· t ce
me an a pIane. 1s an of

~ lil&-4flnt; (XI-XII) ql<l4tJiq- 2007-09

a point from a line Colli . ~
. t bet · . neanty of three points. Coplanar and skew lines. Shor1e5l
d 1s ance ween two hnes c d' • . d
. d · on Ilion of m1crsec1ion of two tines and two planes an a
1
1me an a pane.
Condition of coplanarityof t
.
1• • · t
wo mes m vector and cartesian form length of perpendicu ar ~
I~
of a pomt from a plane by both vectors an d cartes1an
. met hod . ~
LINEAR INEQUATIONS AND LINEAR PROGRAMMING:
JNl'f·V:
1. Linear ineq_uati9nS, Algebraic solutions of linear inequation~ in one variable and their I~
rep~esentatton ~n the number line. Graphical solutions of linear inequations in two~
vanables. Solution of system of linear inequations in two variables (graphically).
Introduction, definition of related terminology such as constraints, objective function ,
optimization, different types of linear programming problems (LPP), mathematical
formulation of LPP, graphical method of solution for problems in two variables, feasible
and infeasible regions, feasible and infeasible solutions, optimal and feasible solutions
(up to three non-trivial constraints)

JNJT-VI: PROBABILITY : (Periods-12)
t. Probability : Multiplication theorem on probability. Conditional probability,
independent events, total probability, Bay'es theorem. Random variable and its
probability distribution, mean and variance of haphazard variable. Repeated independent
(Bernoulli) trials and Binomial distribution.
Note: Attempt should be made to discuss real life problems as far as practicable. Techniques ofmatrices,
:alculus and linear programming should be used to solve such problems.
+

- - -~ frifi (XI-XII) Qtq_4c;fiq-2007-09
tflW.,.