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f) a” -q™= am * 5 ho /at=a" pa” = Yo" aya")’= a" Pe na!” ="fa_ @ (a2 far naz otta_ =( ai) PROPERTIES OF LCGARITHM “Logarithms : ax — loqq X =m * Special types+ 4) common log (4 =10) —* logic x = logx 5% b) natural log (a=e) —» logex= Inx | 2) logex + logay = loga (xy) #) loga x? = nlogax 8) loge x -logay = toga (4) 4) logam : !OGr0 m logue e | 9) a'°%P= bh m aha? ab McTIPLiCNTON pvision OF So oniaus 4) Svbs. volves m enlev (econ © or 1) -» perform ‘he 2) Mvthiplicotion. system of equations or like muliplyma, 3) Divisione o) 2s division (common method) _ SPECIAL. TS 4) by substition 2) elimmartion _s) by eakukakr (mode 5) »_ Gey)x-y) = x?-y* Peat: = x22 3x *%y 4 Pay? ay wy. Ash et Te. Vi om DivryY= xteByty? erbay)= (xty)Oerony ty) j REMAINDER, DER THEOR EM Ea A ER oo 2) (-y)*= x? - Bey sy* A Uys (ey)(x? xy ty) “if a__polynsmal fG) is divided by x-r, *he remander alsin x sis Oa a : 4 (R) a POCOY UARAT ANPEOT NO ISG: = tea ‘a te AG siti Sebi aitit Sy Down nance [Serier |) S- MMMMBATOR Torey Domain= x volves for f() __ Range - -y valves from» (¢e ~1f £0) is @ polynomial ard cis aq real number, “Peal nos. only speidie “3 pom then x-r_is a factor of flx) if and only if f)=0. _ _Byalves not defined s eves = we *fraction- denominator is O ll ig oa: Soe rk om eb reteset 2 eS eiiee ee oe 5 a soli cerirek fn is) Mice “5 eat Ge WARS Sip 4 <0 i ae pera: § Lp. ee bed ad Sito | eee i ae 9776 TAT jy SUS” ee ail real nes except 3 CARDINAL NOTES CARDINAL NOTES {d= 2-0, =As-%=¢ £An= a, + (ned | pee So ee . es posed tay Lan Sg EE ol osama Loo] _ 23 er Si STAT _2tASBX TE, ENG “helt n- (n=even) SMe ers atet s 2 sum Of flesh 50 terms. —- _ : . BM ca {015 Se -”-) Aa me coefficent_of the term? _ get r atic. (or-rny(be | j app tio inka ety Mle mw term is aime when exponent of x48 zero a Rif g & b ore \meor, each term hos a Combined sleqree of h % ifa&b are non-lregr, the iy the _empansion will form an Paria ee at ~Ogi-farb)*= a* + Zab ¥b* Begg +) = 2h te 776m cies ‘ XSL ee et le let ALL_vonibles = 4 1 oe colle a © wien there are coneiants ¢ constant to oonstowth ~ mthiply © Qn, n of term, Sn some with AsP PROPORTIONS AND VARIATIONS *Direct 8 y= kx — CARDINAL NOTES CARDINAL NOTES TRIGONOMETRY... ADDITONAL r nCr= nl NIT OF ANGLES msccou, —SC—~=~—~CS CENTENSUMAL- we Nay eg rl (n-nt 4 rev = 260 cen Arey : yroas Arey =6400m)s 4 degme = 60min €60 1 grod 4 minvle = GOsec lEC 4.cent. min ANGLE RELATIONS iS "complementary + ZA4ZB = go" *expementory : 4A+2B=360" + supplementary + 4A+ Zp =13¢° * co-terminal : [A+ 4B]=360(n) AETRIC IDENTITIES % TIPE ~¥ complimentory angle identities (A+B = 90") Pion some + Sinr6 =025 (90-6) sxt+ y~ m= Tor 'CA) “x=rcost [ows t | ] *y=rsine [sine =e TRIGCONCMETRIC FORM CF _A POINT 2z=rcos Of spe (xt ©4007 (Y4) COMPLEX NUMBERS srectanquior forms Z=2a+b 2207 +b? ‘ 4 2 rag mal IMAG NOY ton6= "4 solar form ‘ z=rle@) pees b=rsin& ¥remenber : us [= — NANGLES — "rent Circe - circle on the surfoce of g sbhere, whose pane posces throuyn the center of the spher >pheriaa) Angle - on angle formed by the intersection of Awo real circles spherical “Triangle. - a triangle on “the surfoce of +the sphere formec!_ by ‘the mtersechm of three great circles ~) PROPERTIES OF SPHERICAL TRIANGE: 120 CABSC <5404 AziRE | }e0 i E =A+B+C -180" * Spherical Defect :]o=3¢0 ~ (At B+C)” Ie fics le coker arele *Sum_of interior angles + «Area, ° *Spherical Excess 4 then 186° + te Burd vo “Bight Spheriaa/ Triangle A=90'-A B= 9'-B E240%-c “Napier 's Rok! 3NCO) The cine of any middle port is equal +o tne produ Of the cosines of ts cppestie parts “in ~.«+) TA) 2) The sine of amy middie port is +¢*- 2be cosh _ aw Tangent low abs iol G+ - ie Ate) _ARABEA of At La (eerscors). me Peeton de A= en *A=1 ph -Azzabsin@ as mw Gouare 37 A*S to Mn a Pit rah i : ‘ela Sex. f Nelegrams sel zi 2 at A wah eS ee ea eee AS&ba A=sdid sin $ n (ee velar stress SS SP acy, ree tae A= ab sind. - “Altitudes A= Be, tle ele eWeek oT * MS | = ve Laer Te base ee at SSeS ks 4 “ i) alla ile, emggst ii 2 : ale : \ 4 = 4 (S-a)(S-b)(S-c)(S-d)_ «$= asbre +o are ° Circe,” @radivs is always toa tangent lire PASS @diameter is a 1 bisector to a Chord _ @ Cross Chord “Theorem + AE(EB)=CE(oE) eal ig ‘4 ABC, B+LSA ol gre Ph osahedmn triangle — 29 20 12 “rareo of base Lopenimeter oe Cylinder Awcube . = V- meh sf W263 0 -e23"P where, C= no. of edges wz) LSA= Zirh SPT LSA = 452 ; $ 3 *v=e-p+2 N= no. of sides Tsh= 65° *TSA* ns?p P= 0. Of faces ‘ d=s513 es vr ne. of vertices a ; e Volume = ops? tan ( /2) $= edge tengtn In] 244an* ('2%h) d= ciinedral angle stale ; Pisstel gt = Zar Ct) a (2 vet bios ai [sin('#%)] ecto \ CARDINAL NOTES as WL distance between bass Ye TROUXCATED PRIS) &. portion of a Pp fying & +Wo honi-paralje! poianes: Which ot Naini ard eye their Nine of jntesectin outside the prem ; K : aan : 4 nts 1S. Vz Anhove aye = %y | An fRism4ToiD ‘ @ Poly having +wo poraiie! bases which are Poyg = Jos Ore lateral faces wre ore Nes ard quadr lat erals wy, eice tying in ome base ond a orp vertex. eras “Expamas /cone ‘polyhedron Containing riangior latera| faces with commen vertex and a polygon base. ac Eas ASA ete al 2 hPL) _T3A= LSA 48 fy ‘he Other base & (A +A, +4Am) RS Se Eee ee Ah ae | | ; | a CARDINAL NOTES CPHERICAL Poly GON: tes y A= frct . a Sg Oe — Ps roel ao - = 120" i “ nil E= Anges - (n-2)120° z RERICAL PYRAMID ; 8 Ve PPE id i A ies: BuO" at IRNATAS, r | Cc ____E= 2Anges =(n-2yizo") S % — abscissa -DISTANCES __IN_SEGMENTS DIVIDED EQvaLLy y.~ oralinate Xa nt i) +x, pens diving, rt yo2 (yey) +, no, vied cenaty AREA OF FPOLYEON BY COORDINATES Beng Bete Me tai LINE EXTENSION 610pE 21% Ya ys Ya A X= A(X2-x,) +x, m= tan@ = y2-M Aet [G&y, +XeY> 4+ Xs Yq +%q Yn) — (¥ix2 +Y2 Xa +Ya%y tam) Yn2 N(y2-y) *¥, hoe, % Vertices Shyicl be in CW op CW mamer ond ada Giny EQUATION oF A Le Set A _LINE 40 @a0/K other General fim: AxrByC+O Stored Fam AxsBy=C sic +3 W=mxtb Point- Slope 3 oy =yi= m(x-»,) R= Oy Two- Point form ° n 26 - Intercer “¥Centroid C9) DISTACE BET. TwO POINTS / LENETHH CP A LINE Le aa Al PaO) d= [oa-? +(ys-y)? whet: M2 YeVnwA as-Cps-¢ Th 30: ax OB A B “yin . d-1 0-4 *Cy-y) G,-2° PML) AND PERPENDICULAR LINES WRoralie\ (//) : mMi=m2 SS > wFerpendiovior + mymz= -J m= 4 { 4 = 2m = ¥%2-% ‘ im. 3 u #y=* (45° \ine) M2 — 3 mM, CARDINAL NOTES (y-k)? 4a (x-h) (x-n)*= = 4a (y-ik) R/L? Ay*+Bx +Cy+ D0 vid, Ax? +By +Cx 4020 ea ae aa Gt Pa as Square Property of Rapokoln AS Zi i 2S bay Sa y,* i mw % s Or Focus +o vertex, vertex 4p olirectriy a *Lalws Rechm: LR=4a q *F to directrix: Ba it __hecentrotyi ea 7 CARDINAL NOTES ELLIPSE ~* Genera) Form: Ax? +By*+ Cx +Dy +E =D Stondard Fern. Se ON ee = 1 <> ey = MNO KS ¥. Pury) b ‘ ‘ iB t7 <7 mapr Axis. 3 = U } L di oe d : me —#— a Ss Q- semi-major axis EY b- 6emi-minor axis " ~wEements a ¢ “Distance of center to foe oe fa*-o* | ‘Length of Major oxis + 2a "Length of Mircr avis’ 2 oe ec Al * Eccentricity : Io! @= Sa Ay fod eo “Det of directrin from Cs las Ye | poses - *Area! [Asi ab » Rerimeter 3 P= 2i fa*+b? | \ =e L ‘bet 2400:3:2¢ | fo
