1. C(2L0A1S4S –-1X5I)I
One Paper MaxT Mimarek: s3. 1h0rs0.
Units No. of Periods Marks
I. Relations and Functions 30 10
II. Algebra 50 13
III. Calculus 80 44
IV. Vectors and Three - Dimensional Geometry 30 17
V. Linear Programming 20 16 VI. Probability 30
Total 240 100
Unit - I: Relations and Functions
1. Relations and Functions: 15 Periods
fTuynpcetsio onfs ,r ceolamtiponossi:t er effulenxcitvieo,n ss,y minmveertsrei co,f tar afunnsictitvioen a. nBdi neaqruy iovpaleernactieo nresl.a tions. Functions: One to one and onto
2. Inverse Trigonometric Functions: 15 Periods
pDreofpinerittiioesn ,o f riannvgeer,s ed torimgoanino,m pertirnicc ifpuanlc tvioalnuse. branch. Graphs of inverse trigonometric functions. Elementary
Unit-II: Algebra
1. Matrices: 25 Periods
aCnodn cskepewt, snyomtamtioetnr,i co mrdaetrr,i ceeqsu. aAlidtyd,i ttiyopne, sm ouf lmtipaltirciacteiso, nz earnod a sncda laidr emntuitltyi pmlicaatrtiixo,n t roafn mspaotsreic eosf, as immaptlrei xp,r osypmermtieest roicf oadf dnitoinon-z,e mrou lmtipatlricicaetiso nw hanosde scparloadr umcut ltisip ltihcea tizoenro. Nmoant-rcixo m(rmesutrtiactti vtitoy soqf umaruel timplaitcraitcieosn ooff omrdaterri c2es) .a nCdo enxciesptetn coef (eHlemereen atlal rmy artorwic easn wdi lcl ohlauvme nre aolp eenratrtiieosn).s . Invertible matrices and proof of the uniqueness of inverse, if it exists;
2. Determinants: 25 Periods
aDpeptleircmatiinoanns to fo df eat ersmquinaraen tms iantr fiixn d(uinpg ttoh e3 a rxe a 3o fm a attrriiacnegs)le, . pArdojpoeirnttie asn odf indveetresrem oifn aan stqsu, amrei nmoartsr, ixc.o C-foacntsoisrtse nacnyd, einqcuoantisoisntse ninc yt waon do r nthurmeeb evra roiafb lseosl u(htiaovnins go uf nsiyqsutee mso louft iolinn)e uars inegq uinatvieornses obfy a emxaamtripxl.e s, solving system of linear
Unit-III: Calculus
1. Continuity and Differentiability: 20 Periods
Cfuonncttiinonusit,y d aenridv adtiivffee roefn itmiapbliilcitiyt ,f udnercitviaotnivs.eC oofn ccoemptp oofs ietxep founnecntitoianls ,a nchda liong raurilteh, mdeicri vfuanticvteiso nofs .i nverse trigonometric
97
2. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative expressed in parametric forms. Second order derivatives. Rolle's and Lagrange's Mean Value Theo reomf s f(uwnictthioounst proof) and their geometric interpretation.
2. Applications of Derivatives: 10 Periods
dAeprpivliactaivtieosn isn o fa dpeprriovxaitmiveast:i ornat,e mofa xchimanag ea nodf bmodinieims, ain (cfrierasts indge/rdiveactrievaes integs tf umncottiiovnast,e dta nggeeonmtse tarnicda lnlyo ramnadl s,s eucsoen odf dsuebrijveactti vaes wteesltl gaisv reena la-sli fae psritouvaatbiolen tso).o l). Simple problems (that illustrate basic principles and understanding of the
3. Integrals: 20 Periods
fIrnatcetgiorantsi oann da sb yin pvaerrtsse. pErvoacluesast ioofn doiff fseirmenptliea itniotner.g Irnaltse gorfa tthioen f oolflo aw ivnagri etytyp eo af nfdu npcrtoiobnlesm bsy b sausebdst oitnu ttihoenm, :b y partial
d d d d d
x x x x x
∫ , ∫ , ∫ , ∫ ,
∫
2 2
± a ± a a - a + b + c a + b + c
p + q p + q
x 2 2 x x 2
x x x x
x x
∫ ∫ ∫ ∫
∫ ∫
d , d , a ± d , - a d
98
2 2 2
2 2
a + b + c a 2
+ b + c
a + b + c d , (p + q) a 2
+ b + c d .
2 2
2
2
x x x x x x
x x x x
x x x x x x x
dDeefifninititee i ninteteggraralsl sa nasd ae vlaimluaitt ioonf ao fs udmefi,n Fitue nindtaemgreanlst.a l Theorem of Calculus (without proof). Basic properties of
4. Applications of the Integrals: 15 Periods
oAnplpyl)i,c Aatrieoan sb eitnw feiennd ianngy tohfe t haree taw uon adbeor vsei msapidle ccuurrvveess (, tehsep reecgiaiollny slhinoeus,ld c ibrec lcelse/apralrya ibdoelnasti/feilalibplese).s (in standard form
5. Differential Equations: 15 Periods
Deqeufaintiiotino nw, hoordsee rg aennde rdael gsroeleu. tGioenn eisr agl iavnedn .p Sarotliuctuiloanr soofl udtiioffnesr eonft iaa ld iefqfeuraetniotinals eoqfu afitrisotn .o rFdoerrm aantido nf iorsft ddifefgerreeen tbiayl omf etthheo dfo romf s. eparation of variables of homogeneous differential equations. Solutions of linear differential equation
+ py = q, where p and q are functions of x or constants
+ px = q, where p and q are functions of y or constants
Unit-IV: Vectors and Three-Dimensional Geometry
1. Vectors: 15 Periods
oVfe cvteocrtso arsn d( esqcualaalr, s,u mniat,g nzietruod, ep aanrdal ldeilr eacntdio nc oolfli na evaerc tvoerc. tDorisr)e, ctpioosni tcioonsi nveesc atonrd odfi reac tpioonin rt,a tnioesg aotfi vae v eocft oar . vTecytpoers, cdoivmidpionng ean ltisn eo fs eag mveecntot ri,n aad gdiivteionn r aotfio v. ectors, multiplication of a vector by a scalar, position vector of a point
(Dcreofisns)it piorno,d uGcet oomf veertcrtiocrasl, sIcnatlearrp trreitpaltei opnr,o dpuroctp eorft iveesc taonrds parpopjelcictaiotino nosf ao vf escctaolra ro n(d aolitn) ep.roduct of vectors, vector
3. 2. Three - dimensional Geometry: 15 Periods
Direction cosines and direction ratios of a line joining two points. Cartesian and vector equation coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a pla noef . aA lningele, between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.
Unit-V: Linear Programming
1. Linear Programming: 20 Periods
pInrotrgordaumcmtioinng, r(eLla.Pte.d) pterromblienmolso, gmy asuthcehm aast iccoanl sftorarminutsl,a toiobnje cotifv eL .fPu.n cptrioobnl,e mopst,i mgriazpathioicna.l Dmiefftehroedn t otfy psoeslu otifo lnin efoarr sporloubtlieomnss (uinp ttow oth rveaer inaobnle-st,r ivfeiaals icbolne starnadin tisn).f easible regions, feasible and infeasible solutions, optimal feasible
Unit-VI: Probability
1. Probability: 30 Periods
tChoenodreimtio, nRala npdroomba bvialirtiya,b lme uanltdip liitcsa ptiroonb atbhieliotrye mdi stornib uptrioobna, bmilietayn, ianndde pveanridaenncte eovfe na tsr,a ntdootaml pvraorbiaabbliel.i tRy,e pBeaaytee'ds independent (Bernoulli) trials and Binomial distribution.
Prescribed Books:
1) Mathematics Part I - Textbook for Class XI, NCERT Publication
2) Mathematics Part II - Textbook for Class XII, NCERT Publication
99
4. MATHEMATICS QUESTION PA P(CERod De ENSoI.G 0N41 ) CLASS - XII (2014-15)
Time 3 Hours Max. Marks: 100
NSo. . Typology of Questions OuLtceoarmneins ga nd VeArnys Swheor rt ComTepsettienngc ies
(1 marks)
100
AnLsownegr 1 (4 marks)
AnLsownegr II (6 marks)
Marks Weig%h tage
1. (RKenmoewmlebdegrein bga-sed tSoim knploew r escpaelcl iqfiuce fsatciotsn,s , tperrimncsi,p cleosn, coerp tths,e ories, Iredceintet,if iyn, fdoermfinaet,i oonr )
• Reasoning
• ASknialllsy tical
• tChriintckainl g
• Derivative
2 3 1 20 20%
2. (UCnodmerpsrteahnedninsigo-n -to be faanmd itlioa ru wnditehr smtaenadn ing ccoonmcpeaprteu,a clloyn, tirnatsetr, pret, ienxfpolramina, tpioanra)phrase
2 2 1 16 16%
3. aAbpsptrlaiccat tiinofno r(mUaseti on in caopnplcyr ektne osiwtuleadtigoen t,o t on ew csiotunatetinotn tso, Uinstee rgpirveetn a seixtaumatpiolen,, oprr osovlivdee aa n problem)
1 3 2 25 25%
4. HSkiigllhs O( Ardnearl yTsihs i&nk ing Scoymntphaerseis, -c Conlatsrsaisfty,, or ddiiffffeerreenntti aptiee cbeest owfe en iannfdo/romr aitnitoeng,r aOter guanniiqzue e fprioemce sa o vfa irnieftoyr mofa tion sources)
1 2 2 21 21%
5. 101
5- Evaluation Disciplinar ya-n (dA Mppurlatiis-e , jvualduge eo,r wanodrt/ho orf jau dsetcifisyio tnh oe r oouuttccoommee,s obra steod p orend ict values)
(v2a+lu1e s based)
1 18 18%
TOTAL 6x1=6 13x4=52 7x6=42 100 100%
QUESTION WISE BREAK UP
Type of Question MQuaerkst ipoenr TQotuael sNtioon. sof MToartakls
VSA 1 6 06
LA-I 4 13 52
LA-II 6 7 42
Total 26 100
1. No chapter wise weightage. Care to be taken to cover all the chapters.
2. Tthhe eo vaebroavlel wteemigphltaatgee itso o dnilfyf ear esnatm foprlme. oSfu qituaebslteio innst earnnda lt yvpaorlioagtyi oonf sq mueastyi obnes msaamdee. for generating similar templates keeping
