Class XI MATHS NOTES[1], Cheat Sheet of Mathematics

Download Class XI MATHS NOTES[1] and more Cheat Sheet Mathematics in PDF only on Docsity! - b 0 Date : 9 Pgs B__| (asby> sory uy aaplaas) = —;—lo-b)! S_o?~ be Bab (orb) pt tt = (ann) Cateabab') © (aad) Gab(aak > 5 a oa ee ay - (a-b) Ca*tab+b™) = (a-b)*4 2ab(o-s) p——j Cosbee)* = otabtacts rab s Qhea ea | a Pj Ore bPeed- dbs (ashse) (otertact-ab- be - a) Po FE lane) (o-b)™ 4 (b-) 4 C0)? ] a a ’ => >0 py bx 5 coe ga OI 7 AS +04 Sesame fe ET ER eC) “Vo, 4 . : — :  Dato [us 5 < 0 Bee dn, (59 TTT F/ + PAA care mu a 5 oy ) we » w«)u €% alu (5:0 By re Aju [osu (6) - Kom B27. “ oo | ie Sean nH a as: — 5 wi TK 7} ee Sm ae a mm mm aadasc saree? —_ f& Ss prisiut mie Magen salut 0k ofihag a= Gne= F740 aud 94 | ao u- & -s ® 4 O-3 < "get. Gx-77 £0 Se [ ; i 1: 7 = 1420 - eS MX 4 4%= 4 a fo- Ww) Gt) 2 0 ay “YE A= WE Zh 5 4 a ee cone oe REO é ——_ S05 Oo pet ea Be ok tu . a Fey Tha solulou sor ef 2" # 2 ¢ 3x x FY o | -© @ @® [27 Se T+ W a A+ _¢ 7. Bn SRS eG =T 1 + Wee = FP Oe )OHD9 [> Comergo =* hm ¢ 7 Te watts ty te owe 2 OF oh + En (2x +2) (n~2 ® > 6O- =~ AS @ a ot - . fe TE Dg baa «6 ES, Tye fo aca ‘ | Were s TE power even Hun sign of tuthrel pl wail wat c | Use in uber ing” aa  Trap evuht prepeuky of. aq: Se OD Fe wo. ant bare bet, ane either (my dian Alan qrasku Ham Ay Hoan the wale of log i tye. Ea Ug, 10 > 0 : (og 5 010170 ; ae _ {® Me vas end fa On@ on rere 4 oh | He Wwe arene ara ny —_| & ~ve. te oi eq, 1 C6 * toe <0 [© etn Ven & eaahak (eg) whan bang vaatable (be x-toms) - | Ware @. wit ban_of Sree —-| Ent leg. (x-ad > - Study ge alge ar] ak en bone” of a ed —| fe: yy (x-a) > 0 ~ Bi gin 4 Hits hamges mista a) ¢ <a) | = ix Prue: Klay find Lewaln end belie JE — ewe Ug, on 75) >4- iNRygdhton with, Lo ouswen So a ese a ture tf Sone 2 : ==eE Sen 7 2 2xm>a . ~ Ode 24 + 2 er Beet > oO ~ 4 =P > / I — we tesy Ge2y>0— | caf eee % — % “Phy Ty Or A Dowel | OO) esac] OME SKE 1) af x Lp beoObvso | = ees wz * bow ~ ao} wa Les) be + ag ZZ _ <> : re “ « 6 = — | et tie Fed tee vel HE Qe lone a] sa 4 eee eet ae = Al oes ee ze Stet pg es Md wit #2) eC eo | PS Ron ned PRE ree ' aah A iW KL sth HAL ee “welt be tng ted 4 (109) N. eo Sek of ah Nakuwh ves = Ru. 34, nf | we Sot of wher was = RO, 2, 3,4 ZoaD = Sok of Wh iyo w = Re 33 0542,3,.2, Zr = Soret ath tve fatagorny = 12/9, 44 -IN- wz = Sebo alk -va dengout = £423; 4 Q= Sek of Ul Retinal wise fs MUED 20h R = Sek f ath Rash ues ‘ G- A= Ser of eth eruttonal we, § RS = AU ava “Resh uae cea 0 ye fie ® Evephy Sor /nath ser/veid SUT honing ue ehtranee ta huh try hw wv a Sabsek of. tH yer, Reprmemred oh 2 4 ; Siugte ton 7 A ser Mani ng eun ean @) Frare Sok} SME, Bs S02 i ef SU tolrosa, wo, of eal are def ne ga . © %e, V Pomel ot wysatets)= Fa, e;i,0,u% hte, = PAP Bury A sey, ; wees to, of Choma ens tin! : cx, . Uatrthed a dfiiye OF €x. OT = fio, oT “eo eo oe” PPPPOROFCeeeneeeeaeaaseaneseas: v? ® Fyhonk S07 t Ty Sur old R= 81,93, 484 Mare aah 99s of elton, dom, Oo : o © fe wa, Hors w(ad > nla) SG: ae = fe: S 2 4,2,34 The UT wlusg CUmmadi wee epeak Capa ID= 21, 2,3,4% Hare Ar, & an equal seb 14, 3,194 YD be wet equal sat bret.  ® Uriveual gab (U) 1 A se ebidh uvtelug alt elemaule a obo ele \ we 7 » 4 olen SUG) iucbad uy (we ew eho aly U: b 1 34, 5) = a’ cap wand C ALU 3,54, KrK 244 ® Super: Sek Sub- Seb ‘ MH kh A ental Mw ser B, How SOFA & said to be Ho Subse of Band seh 6 in thd de be Hee supa of A. Raproremtohion $ A CB bes B-Riurs, 4,5) pA ft 36% ow ACB Proper Subssh: K yeu ne <4 CSuntr = 2°) au sy A Resse Subsek } % tet, Prteiaae “Flore ba cg | Ween) 12, #, Rave a iF deey ein tele be, gs Oty YUr whl eontaimy all rabsols— Seis Subsele . * Sk . 2,3 # Rada bathe neo ax © N (A) = RM Wan botoR we, of subeat— b= £1,2,5,4)52 —> we of Sues 95 . Bos wo. of Paapén subeh —» o%4 wa of Prapey subselr a B04 se 5 net Fe ee J of Aw 2%  RELATION AND FUNCTIONS 2 The connectinn berueon 2 sety ealled a Retotion. y Be: A= 8-8,-260, 1,2, 8 ke B= £123,594 : Relotion ‘ A(R) = ROxy): are ¥y wlhoxe x EAs JE BY Cm west Far os) Re BOSD, 6U9, 609, 011), C19, 9G # Also, A notahow w A Subse of AxB a & Co-dowalu : z £12 Syne AY wn a Torah wo. of Relations prom sek A *p setB = 2 ( tare fme nay ne nceyy , = Dowaln of HA Relation These elemeteof (hiv sek) A which Lmel DMAGS Available im set B cy called Douro Ser. Co Demain : Conplere: sab B Cdeend set) a alld Cs-brwae Ser, B Rese i These elements of B lik anc image of soma ehementy tw ser A 4 ealled Rouge seh, En. EASE 1 2,8, 4/56] Defies « Rabin R’ Grou Ath ty 9 R= Pea, 4) tg see] . Bowrsly 2 B1/2) 3,454 a Co-bomein £4,253, 4,5,64 — Rawae. a 2, 3,4, S64 © 1335 Wh \ 1 TUS SEE 4 Function | K natatton RK prom a sur A te ager Boo eled fnctlou. t: © Erry etemamb of Ser A hay on iuaye in toro Se te damsel by He © ro Cima $:A38 iw seb B. t ser A hey wanna, tain ae eg ue Eveny fm Hou ty a saloon bur ven salshinn may wah be on Als ta eats fenebion , © Convers “g wor ors oWaued bul ae boy, Ad vd oblawed, © Complore set A wus ba downin , Comverging alls weg _" Find te Donaty, fe (cm): Sa SS 7 “4330 ot Seed. se TeBT | SCAN, we PLLA 7, Sneeny ee WLLL ALLL | Some S>- 3 3 -o ca 1 & 5 eae ! ©3,00)—§-2,- 1% a te Ree + 4G) eee R-2 ® “2x44 pS R- fay, x8 a OR-§£ EAL © nor - Jaad 7) d Qaeda xy ty = 4-3 oc (2y- 12 9 => om = ECStyy ryt oy ; ITE FO ry wy Sm GH M-8+y ». b Pokenwtua, Hoa t (nage of 2 ond da par TRS ac ye ~ co 2910 C2 13 =4420-I9 aCD=6 CX) > 0048 = getinetietil 5... DP AEHID oh ayuna-h ban ‘ ys Y Ete aoe % BD, 19%  pt Fou daten wining pres wage, cs “ eS tect = mone Han 1 value, So, or instanea tahow to find out a Phe ator value with Hue given ome. 7 @ Line Teat fon Function : wh. a ayn Cael dasa Ah te Yoonin cuits Ha gersple oF weave, Hawn dL , : ihe ‘ Phe Han th it wee a frmmting function , - * i ~ . ~ ‘ ey ' bo, Thus wn / C=@) ns vi : . s ey ~ ere oie, ih aa fometion ® ghd A 1 © me e ossible, if Wa ion. = P fom Dowdy Eyomplest been nt on ’ 1 1 ’ ' ‘ ’ 1 1 eo a &) ete? ® Exe §(%) = og, i) Om , OR b cease every real ON ®& Ger nara wy Op ns Fa i Om © [o, «') ® at rr) , ®zZ power. by: @Saat hu MR ) Bf (md = 9C ®) ey, t : et d= Tra Q®N- Ow POs ea ® Con) Ln) Olam) Orne © Cem) © Rt ty ba OF To,n') TTS) here e~3 0 y : ye ESB Boe) Pe rqure vx WA wos have i) Ea (m« Loy ( cs ne Sqond prot and (Rt © to, yz (%"3) decyu'h beane 0, © lam) OG) Orne SO 0) vaso gee T 3,0) 7 ee Date : Oi (gets Famer * bank (0) 4. oto - | - | aes f fo = /S0% 7 = ‘9 fiat Ry — _— aia ” See es @ re X20, To ee LR eR | = ® yet NOT : ® 44 i res wee bern: P~ Lo - x A NN , Renge 1 ~ $0} z rl a © fy seat * Th x>0 ras 4 s % X<0 Hayy © su(%) =-4 TR x=0 Huda = sgrlx'}) = O Donal CER 5 Raogeige £1019) 4 § f 4 4 4 4 4 4 $ f  Ens - Sgn (x-3) = A. Solve fo 2 | < Ss). 0-9 wer Vo tVQ 7 < N-B>O =D KX>a, . — i KE Cae . . - : Sg (ot Baa 0) = 4 Ys ° > C= Bee C6 a => (9) (-3) C0 ; - 6 : SORE Cs En Plot Mo gop of OLX) Ie Find Hae re Ho= Dewan se ER-Lo er Ra,-1% 4 v  : ° Ex, Pl He guoph t foc) ond eee tO = M8 #400: ee Myce ee “Rea M-frey Ges) = +5] oy =o4y = RSsenes —_____ Grusieat= Tye funtion! © [x], HOprbreue grate: J gat te aoa 0 te, OD Vor OR *xED Eye [x]-0 => xe€Lo2) )o-[x]-1 > x efs, 2) )4-[%* 1-3 >xeL3, rt) ) = [x] = -1 xe [-1,0) 2 ie Woe een aay -1) oy Goap 3h mn III ee se  RIGONOMETRIC THENTITIES Anglo OS \ Amok of subation from midi sida tarwinok sido, © Senagerianh J sea y ex. [ nee ae 360) font of a complebe angle Le 6K! Cohutta) FARR anaaneaeggeegeseeeeeeeagcaacaaneanaceannaann BNL Sive Taw Cos Caste suite) Ent Gwent =04°30! ths nadion \ a ae ; | w 4430's Gee (22) | * Geay = (95\° =) a ; = (rte xod - 4a = SR ad TE SWB =O yen Bene pnez Ee wig Fesd=o Han 9 = buat) 5nez odd wauldiple of & eo) Ext Gs toh = cos @:20"~ 39") =-O%S 30° 8 = 2 © ao Can ene . i 45 870)" = oy az) [0500) 0] 74S (1ARo_ 36) cos 40° = 3 mae . . “8 csag ? & 4 nj NEF 3H . “S® = oa » 8 Fbnil) * snez MTT daa 2 "7 o © Sept pag Hae Yrodrard™ ta valuta (uitot @) on (ne +6) Coy Step? g ved dg Big of sho porhtoulon fumeion wring AST. be Step> Dh nw & even Wega, 9 with nemann seg ele, fw & ou Fran Ha ponkutan flgoguarde ? SS tt Wye will chouge Sim ——> eof 5 See e__, see ; darn —u piser: TM A+B = 130° Mor, anA= Sm abe, esA +usR = 9 SHSCCEUUUUD AUS daada  © ws (A ~B) = esp: USB + SMA ING AES Compowid= bugis. Rnwuhar: © Sin( Aas) = amb asB + esa + sing © Sin (KR -8) = SNK + CIB- SK ginQ © as (A+B) = wSAruB ~ sinnvanB | ( “ eo eo oo is © trn( pag) — taht tug ~ (as8) = AF a a8 © ut CQx@)~ ubnete ea LA & ea © sm (ase). sin (q- 8) = MOA -weB © = tos™B -coi7 A OS (ALB ( s "ces (A ~8),, C8" ~ sity HM Some (ined sound 9 os Se ea war fw ® sin 13°. - ain Hee Oe as BY © as e. Viera _ e SOS FD" = ogy 2 eat a es pe ~ On Se — _ e © tony 29.5° 2 fon Ly Qt ise ee e ON ORS' = or ae ON FST ake ° © ttn can Nt ea, © te 5 WER = 04 |© tea a6h eee Dy - _ Se 22.67 = wh Re = JT44 toh 18"= ah = ay ® in 18s Gm ae) eo ie ae ® sin \& din Be L — + toy 46° = —— — 2 1 * er Be = . © SM 45° isn a ~~ Ss e sy a a ——. WS 15 = ug aL VB : ee _ Ia — OT —~ ~~» ® gi ee me . + | no Ss aa + den3} a o eos 53 ao Sm53 24 €  Rone of f =O Stuy bess @ The Rouge of Y= a ua eb HK wilh ba [- fars® , [ase] Ex 4 = 4 +b Bri Bes Y= Sax sense Vates® = Sisters = Jay "¢L 27] ye [-va, vi) © hrm, value € ottatg + Bet 29 = dab vive 060 | © (ie nua oe qu ae olin of a “see t pus = (as)* whee af >0 Ow Rage kag AMA GM Basque Dasguality Y_ (tom 2 & be us Vv se br Quek apd <1 Atb o RM = seb, aMayee SERS ae a Ane % eruideriug Bun arb, co “RM 4M] bet = = 24 e Atb+e + GM=%ae _+ . Bey The wiWivebeg 9: im a \Suxtoxzap (AM & OM ®) eta 2 Ae oy 9 BK BAK osx ek pie PS 7 > a @) 2 ‘9D a > afro rae mi ote | "Gs a ee ae -a\h . > 2 > 2G "JE [n--6] ark ? — “> oe Bes d= Ds 2x- Suiwn th for qu (16% 2%)” aah Pty 7 d* 20% 44 > ‘tf = ue Me +Q ‘, . o ice > ae (t-%)*- 42 for duaye (20x My) wef > Wr = (e- %) 4 apn = 4 Buoy = 20-1)? 361044 =) Ms ve [2 ever]  fo \ Dewain 2 OCEDL ra yeLit) eubd } 2aV Re NOTE! Pert 9 diy tve vali X afer widely yet ayo itself - a Graph of Triqonematiue Funchiew>? f=] | + w = ow - _- i >  () Be sin HW | @® gaora | Sh eee oto sina @) gz ten wm : Yo) y= dee % dy 2 dy = = soe“ =\ = ? = SOK cas ™ dx dx ee ’ | © — g = Cosee H @) Otte i sy Se = —eosee x ian ey = career roe dx dx :  Date : Poe ‘ at = y ; : — @| matted vp EE . | ——————— 1 : 4 = = d = (tw) Bat — 2 tas 2¢ qv ae 7 HA=-Q own KRe-3 i DE a a BO [i Fm beng seco] - eo : ees | sian nee . 5. ez — te “Le -y OL t= -3 CO 2 28 ~OD4+8 | SMe. (ps) es SS eS ee >) aa S| Maw wor | - Mot uaa. © -  wm! Tr & dee seawerse proce of diffarombatron _:) — Defeatre tategration © Dedoftte jwregvad an” SPE ee yee ae ee (se bata) a) Se . ae eee, = f = BSS — Og x pt Poe oluex hve Ol | ide = | A de = deg [PT] | ee ‘ . iN : . § fet dx = eM & ® wee Ext (3ax = 3 fane oe © | cos Hd = ‘snxte ! &) Seca de = tomate © tin Xd = —coexte | @) [essetcdie = <eoha +e | N y 7 i = 4 | ® . “[iseen: tonn de = Seem +e ©) caer tata dv = ~Lasee x + ¢ Q © | Pen oe = doy Tree Fong Tone] C2) ee sy