Rectangle Square Triangle Parallelogram Trapezoid Circle P = 2l + 2w P = 4s P = a + b + c P = 2a + 2b P = a + b + c + d C = 2pr = pd
|
|
- Sharleen Washington
- 5 years ago
- Views:
Transcription
1 Geoet eiete d Ae = eiete, A = Ae, C = Cicufeece, V = Volue ectgle Sque Tigle llelog Tpezoid Cicle = l + w = 4s = + + c = + = + + c + d C = p = pd A = lw A = s A= A = A= ( + c) A = p c w s c d d l Volue ectgul Solid ectgul id igt Cicul Coe igt Cicul Clide Spee V = lw V lw = 3 V = p V = p V = 4 p w l l w Agles Clssified Mesue Acute igt Otuse Stigt 0 < A< 90 A= < A< 80 A= 80 A A A A Tigles Clssified Sides Sclee Isosceles Equiltel No two sides e equl. At lest two sides e equl. All tee sides e equl. C Z A B X Y Tigles Clssified Agles Acute igt Otuse All tee gles e cute. Oe gle is igt gle. Oe gle is otuse. C Z A B X Y
2 US Custo Sste of Mesueet Metic Sste of Mesueet Legt ices (i.) = foot (ft) 3 feet = d (d) Legt illiete () = 0.00 ete cetiete (c) = 0.0 ete = 000 = 00 c 36 ices = d 580 feet = ile (i) deciete (d) ete () = 0. ete =.0 ete = 0 d Cpcit dekete (d) = 0 etes cup (c) = 8 fluid ouces (fl oz) ectoete () = 00 etes pits = qut (qt) cups = pit (pt) = 6 fluid ouces kiloete (k) = 000 etes 4 quts = gllo (gl) Cpcit (Liquid Volue) Weigt 6 ouces (oz) = poud (l) 000 pouds = to (T) Tie 60 secods (sec) = iute (i) 60 iutes = ou () 4 ous = d 7 ds = week illilite (L) lite (L) ectolite (L) kilolite (kl) Weigt illig (g) cetig (cg) decig (dg) = 0.00 lite =.0 lite = 00 lites = 000 lites = 0.00 g = 0.0 g = 0. g L = 000 L kl = 0 L g = 000 g Tepetue Celsius (C) to Feeit (F) 9 F = C+ 3 5 Feeit (F) to Celsius (C) 5 F - 3 C = 9 g (g) =.0 g dekg (dg) = 0 gs ectog (g) = 00 gs kilog (kg) = 000 gs g = 0.00 kg etic to (t) = 000 kilogs kg = 0.00 t t = 000 kg =,000,000 g =,000,000,000 g US Custo d Metic Equivlets Legt Volue i.. 54 c ect = ft 305 d 94 i. 6 k Ae i c ft 093 d 836 c 394 i ft. 09 d k 6 i c 055. i ft. 96 d ce ces i c 3 3 ft c 06 i ft 3 3 qt 946 L L. 06 qt gl L L 64 gl Mss oz 835. g g 035 oz l kg kg 05. l
3 Nottio d Teiolog Epoets... = fctos Fctios epoet se ueto deoito Lest Coo Multiple (LCM) Give set of wole ues, te sllest ue tt is ultiple of ec of tese wole ues. tios o : o to A copiso of two qutities divisio. opotios c = A stteet tt two tios e equl. d Getest Coo Fcto (GCF) Give set of iteges, te lgest itege tt is fcto (o diviso) of ll of te iteges. Tpes of Nues Equlit d Iequlit Sols = is equl to is ot equl to < is less t > is gete t Sets is less t o equl to is gete t o equl to Te ept set o ull set (solized o { }): A set wit o eleets. Te uio of two (o oe) sets (solized ): Te set of ll eleets tt elog to eite oe set o te ote set o to ot sets. Te itesectio of two (o oe) sets (solized ): Te set of ll eleets tt elog to ot sets. Te wod o is used to idicte uio d te wod d is used to idicte itesectio. Algeic d Itevl Nottio fo Itevls Tpe of Itevl Algeic Nottio Itevl Nottio Ope Itevl < < (, ) Gp Closed Itevl, Ntul Nues (Coutig Nues): N = {,, 3, 4, 5, 6,... } Hlf-ope Itevl < <, ) (, Wole Nues: W = { 0,,, 3, 4, 5, 6,... } Iteges: Z = {..., 4, 3,,, 0,,, 3, 4,... } tiol Nues: A ue tt c e witte i te fo wee d e iteges d 0. Itiol Nues: A ue tt c e witte s ifiite oepetig decil. el Nues: All tiol d itiol ues. Cople Nues: All el ues d te eve oots of egtive ues. Te stdd fo of cople ue is + i, wee d e el ues, is clled te el pt d is clled te igi pt. Asolute Vlue Te distce el ue is fo 0. > Ope Itevl < Hlf-ope Itevl (, ) -,, ) (-, dicls Te sol is clled dicl sig. Te ue ude te dicl sig is clled te dicd. Te coplete epessio, suc s 64, is clled dicl o dicl epessio. I cue oot epessio 3, te ue 3 is clled te ide. I sque oot epessio suc s, te ide is udestood to e d is ot witte. Te Igi Nue i i = - d i = ( -) =-
4 Fouls d Teoes ecet A = (te pecet popotio), 00 B wee = pecet (witte s te tio 00 ) B = se (ue we e fidig te pecet of) A = out ( pt of te se) B = A (te sic pecet equtio), wee = te o pecet (s decil o fctio) B = se (ue we e fidig te pecet of) A = out ( pt of te se) ofit ofit: Te diffeece etwee sellig pice d cost. ecet of ofit: pofit = sellig pice - cost. ecet of pofit sed o cost: pofit cost. ecet of pofit sed o sellig pice: Iteest Siple Iteest: I = t Copoud Iteest: A= + Cotiuousl Copouded Iteest: A= wee I = iteest (eed o pid) A = out ccuulted t pofit sellig pice e t = picipl (te out ivested o oowed) = ul iteest te i decil o fctio fo t = tie (oe e o fctio of e) = te ue of ties pe e iteest is copouded e = Te tgoe Teoe I igt tigle, te sque of te legt of te poteuse is equl to te su of te sques of te legts of te two legs: c = + oilit of Evet poilit of evet ue of outcoes i evet = ue of outcoes i sple spce Distce-te-Tie d = t Te distce tveled d equls te poduct of te te of speed d te tie t. Specil oducts. - = ( + ) ( - ): Diffeece of two sques. + + = = - : Sque of ioil su : Sque of ioil diffeece = ( + ) ( - + ): Su of two cues = ( - ) ( + + ): Diffeece of two cues Cge-of-Bse Foul fo Logits Fo,,, > 0 d,, log log = log Distce Betwee Two oits Te distce d etwee poits, ( ) + ( - ) is d = - Midpoit Foul Te idpoit etwee poits, is + +,.. c. 90 ( ) d (, ) ( ) d (, )
5 iciples d opeties opeties of Additio d Multiplictio opet Additio Multiplictio Couttive opet Associtive opet + = + ( + )+ c = + + c = c = ( c ) Idetit + 0 = 0 + = = = Ivese + (-)= 0 = 0 Zeo-Fcto Lw: 0 = 0 = 0 Distiutive opet: ( + c)= + c Additio (o Sutctio) iciple of Equlit A = B, A + C = B + C, d A - C = B - C ve te se solutios (wee A, B, d C e lgeic epessios). Multiplictio (o Divisio) iciple of Equlit A = B, AC = BC, d A B = ve te se solutios C C (wee A d B e lgeic epessios d C is ozeo costt, C 0). opeties of Epoets Fo ozeo el ues d d iteges d : Te epoet = Te epoet 0 0 = Te poduct ule = Te quotiet ule Negtive epoets + - = - = owe ule = owe of poduct = owe of quotiet Zeo-Fcto opet = If d e el ues, d = 0, te = 0 o = 0 o ot. opeties of tiol Nues (o Fctios) If is tiol epessio d,,, d K e poloils wee,, S 0, te Te Fudetl iciple Multiplictio Divisio Additio Sutctio opeties of dicls K = K = S S S = S + + = - If d e positive el ues, is positive itege, is itege, d. =. = 3. = opeties of Logits is el ue te = = 4. o, i dicl ottio, = = Fo > 0,,, > 0, d el ue,. log = 0 3. = log. log = 4. log = 5. log = log + log Te poduct ule 6. log = log - log Te quotiet ule 7. log = log Te powe ule opeties of Equtios wit Epoets d Logits Fo > 0,,. If =, te =.. If =, te =. 3. If log = log, te = ( > 0 d > 0). 4. If =, te log = log ( > 0 d > 0).
6 Equtios d Iequlities Lie Equtio i (Fist-Degee Equtio i ) + = c, wee,, d c e el ues d 0. Tpes of Equtios d tei Solutios Coditiol: Fiite Nue of Solutios Idetit: Ifiite Nue of Solutios Cotdictio: No Solutio Lie Iequlities Lie Iequlities ve te followig fos wee,, d c e el ues d 0: + < c d + c + > c d + c Copoud Iequlities Te iequlities c < + < d d c + d e clled copoud lie iequlities. (Tis icludes c< + d d c + < d s well.) Asolute Vlue Equtios Fo stteets d, c > 0:. If = c, te = c o = c.. If + = c, te + = c o + = c. 3. If =, te eite = o =. Asolute Vlue Iequlities Fo c > 0:. If < c, te - c< < c.. If + < c, te - c< + < c. 3. If > c, te < - c o > c. 4. If + > c, te + < - c o + > c. (Tese stteets old tue fo d s well.) udtic Equtio A equtio tt c e witte i te fo + + c = 0, wee,, d c e el ues d 0. udtic Foul Te solutios of te geel qudtic equtio c + + c = 0, wee 0, e = - ± - 4. Te Disciit Te epessio 4c, te pt of te qudtic foul tt lies ude te dicl sig, is clled te disciit. If 4c > 0, tee e two el solutios. If 4c = 0, tee is oe el solutio, If 4c < 0, tee e two oel solutios. =-. 4. If + = c+ d, te eite + = c + d o + = -( c+ d). Sstes of Lie Equtios Sstes of Lie Equtios (Two Viles) Te sste is... cosistet, d te equtios e idepedet. (Oe solutio) icosistet, d te equtios e idepedet. (No solutio) cosistet, d te equtios e depedet. (Ifiite ue of solutios)
7 Fuctios Fuctio, eltio, Doi, d ge A eltio is set of odeed pis of el ues. Te doi D of eltio is te set of ll fist coodites i te eltio. Algeic Opetios wit Fuctios f f. ( f + g)= f + g 4. g ( )= g. ( f - g)= f - g 5. f g f g = Te ge of eltio is te set of ll secod coodites i te eltio. 3. ( f g)= f g A fuctio is eltio i wic ec doi eleet s ectl oe coespodig ge eleet. Oe-to-Oe Fuctios A fuctio is oe-to-oe fuctio if fo ec vlue of i te ge tee is ol oe coespodig vlue of i te doi. Ivese Fuctios If f is oe-to-oe fuctio wit odeed pis of te fo (, ), te its ivese fuctio, deoted s f -, is lso oe-to-oe fuctio wit odeed pis of te fo,. If f d g e oe-to-oe fuctios d f ( g )= fo ll i Dg d g( f )= fo ll i Df, te f d g e ivese fuctios. Gps of Fuctios Te Ctesi Coodite Sste udt II ( egtive, positive) (-, +) udt III ( egtive, egtive) (-, -) -is Lie Fuctios (Lies) udt I ( positive, positive) (+, +) (0, 0) Oigi -is udt IV ( positive, egtive) (+, -) Stdd fo: A + B = C Wee A d B do ot ot equl 0 Slope of lie: - = Wee - Slope-itecept fo: = + Wit slope d -itecept (0, ) oit-slope fo: - = - Wit slope d poit, lie ( ) o te Hoizotl lie, slope 0: = Veticl lie, udefied slope: llel lies ve te se slope. = epedicul lies ve slopes tt e egtive ecipocls of ec ote. udtic Fuctios (ols) ols of te fo = + + c:. Vete: - - f,.. Lie of Set: ols of te fo : = - + k. Vete: ( k, ). Lie of Set: = =- 3. Te gp is oizotl sift of uits d veticl sift of k uits of te gp of =. I ot cses:. If > 0, te pol opes upwd. Lie of Set Vete. If < 0, te pol opes dowwd.
8 Coic Sectios Equtios of Hoizotl ol Equtio of Cicle = + + c + o = -k wee 0. Te pol opes left if < 0 d igt if > 0. Te vete is t ( k, ). Te equtio of cicle wit dius d cete k, + ( - ) =. - k is (, k) (, ) Te lie = k is te lie of set. Equtio of Ellipse Te stdd fo fo te equtio of ellipse wit its cete t te oigi is d (- ) Te poits,0,0 e te -itecepts (clled vetices). d ( 0, - ) Te poits 0, e te -itecepts (clled vetices). We > : + =. Te seget of legt joiig te -itecepts is clled te jo is. Te seget of legt joiig te -itecepts is clled te io is. We > : k + Te seget of legt joiig te -itecepts is clled te jo is. Te seget of legt joiig te -itecepts is clled te io is. Te stdd fo fo te equtio of ellipse wit its ( - ) ( - k) cete t (, k) is + =. k k - - (, k) + Equtio of Hpeol I geel, tee e two stdd fos fo equtios of peols wit tei cetes t te oigi... -itecepts (vetices) t,0 -,0 No -itecepts d Asptotes: = d =- Te cuves ope left d igt. -itecepts (vetices) t 0, 0, - No -itecepts d Asptotes: = d =- Te cuves ope up d dow. = (, 0) is Te equtio of peol wit its cete t k, ( - ) ( - k) ( - k) ( - ) o (0, ) (0, ) = (, 0) = =
Properties of Addition and Multiplication. For Addition Name of Property For Multiplication
Nottio d Sols Tpes of Nues Ntul Nues (Coutig Nues): N = {,, 3, 4, 5, 6,...} Wole Nues: W = { 0,,, 3, 4, 5, 6,...} Iteges: Z = {..., 4, 3,,, 0,,, 3, 4,...} Rtiol Nues: tiol ue is ue tt e witte i te fo of
More information2002 Quarter 1 Math 172 Final Exam. Review
00 Qute Mth 7 Fil Exm. Review Sectio.. Sets Repesettio of Sets:. Listig the elemets. Set-uilde Nottio Checkig fo Memeship (, ) Compiso of Sets: Equlity (=, ), Susets (, ) Uio ( ) d Itesectio ( ) of Sets
More informationBINOMIAL THEOREM SOLUTION. 1. (D) n. = (C 0 + C 1 x +C 2 x C n x n ) (1+ x+ x 2 +.)
BINOMIAL THEOREM SOLUTION. (D) ( + + +... + ) (+ + +.) The coefficiet of + + + +... + fo. Moeove coefficiet of is + + + +... + if >. So. (B)... e!!!! The equied coefficiet coefficiet of i e -.!...!. (A),
More informationEinstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,
MSS SEQUENCE AND SERIES CA SEQUENCE A sequece is fuctio of tul ubes with codoi is the set of el ubes (Coplex ubes. If Rge is subset of el ubes (Coplex ubes the it is clled el sequece (Coplex sequece. Exple
More informationChapter Real Numbers
Chpter. - Rel Numbers Itegers: coutig umbers, zero, d the egtive of the coutig umbers. ex: {,-3, -, -,,,, 3, } Rtiol Numbers: quotiets of two itegers with ozero deomitor; termitig or repetig decimls. ex:
More informationNegative Exponent a n = 1 a n, where a 0. Power of a Power Property ( a m ) n = a mn. Rational Exponents =
Refeece Popetie Popetie of Expoet Let a ad b be eal umbe ad let m ad be atioal umbe. Zeo Expoet a 0 = 1, wee a 0 Quotiet of Powe Popety a m a = am, wee a 0 Powe of a Quotiet Popety ( a b m, wee b 0 b)
More informationPROGRESSION AND SERIES
INTRODUCTION PROGRESSION AND SERIES A gemet of umbes {,,,,, } ccodig to some well defied ule o set of ules is clled sequece Moe pecisely, we my defie sequece s fuctio whose domi is some subset of set of
More informationMath 153: Lecture Notes For Chapter 1
Mth : Lecture Notes For Chpter Sectio.: Rel Nubers Additio d subtrctios : Se Sigs: Add Eples: = - - = - Diff. Sigs: Subtrct d put the sig of the uber with lrger bsolute vlue Eples: - = - = - Multiplictio
More informationALGEBRA. ( ) is a point on the line ( ) + ( ) = + ( ) + + ) + ( Distance Formula The distance d between two points x, y
ALGEBRA Popeties of Asoute Vue Fo e umes : 0, 0 + + Tige Iequity Popeties of Itege Epoets Ris Assume tt m e positive iteges, tt e oegtive, tt eomitos e ozeo. See Appeies B D fo gps fute isussio. + ( )
More informationBaltimore County ARML Team Formula Sheet, v2.1 (08 Apr 2008) By Raymond Cheong. Difference of squares Difference of cubes Sum of cubes.
Bltimoe Couty ARML Tem Fomul Seet, v. (08 Ap 008) By Rymo Ceog POLYNOMIALS Ftoig Diffeee of sques Diffeee of ues Sum of ues Ay itege O iteges ( )( ) 3 3 ( )( ) 3 3 ( )( ) ( )(... ) ( )(... ) Biomil expsio
More informationAppendix A Examples for Labs 1, 2, 3 1. FACTORING POLYNOMIALS
Appedi A Emples for Ls,,. FACTORING POLYNOMIALS Tere re m stdrd metods of fctorig tt ou ve lered i previous courses. You will uild o tese fctorig metods i our preclculus course to ele ou to fctor epressios
More informationImportant Facts You Need To Know/Review:
Importt Fcts You Need To Kow/Review: Clculus: If fuctio is cotiuous o itervl I, the its grph is coected o I If f is cotiuous, d lim g Emple: lim eists, the lim lim f g f g d lim cos cos lim 3 si lim, t
More information* power rule: * fraction raised to negative exponent: * expanded power rule:
Mth 15 Iteredite Alger Stud Guide for E 3 (Chpters 7, 8, d 9) You use 3 5 ote crd (oth sides) d scietific clcultor. You re epected to kow (or hve writte o our ote crd) foruls ou eed. Thik out rules d procedures
More informationSULIT 3472/2. Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan.
SULT 347/ Rumus-umus eikut oleh memtu d mejw sol. Simol-simol yg diei dlh yg is diguk. LGER. 4c x 5. log m log m log 9. T d. m m m 6. log = log m log 0. S d m m 3. 7. log m log m. S, m m logc 4. 8. log.
More informationPerimeter: P = 2l + 2w. Area: A = lw. Parallelogram. Perimeter: P = 2a + 2b. Area: A= h( b+ 3. Obtuse
Geoetry Perieter d re Trigle Retgle Squre h Perieter: P = + + re: = h l Perieter: P = l + w w re: = lw s Perieter: P = 4s re: = s Trpezoid h d Prllelogr Perieter: P = + + + d h re: = h( + ) Perieter: P
More informationPhysicsAndMathsTutor.com
PhsicsAMthsTuto.com 6. The hpeol H hs equtio, whee e costts. The lie L hs equtio m c, whee m c e costts. Leve lk () Give tht L H meet, show tht the -cooites of the poits of itesectio e the oots of the
More informationWeek 13 Notes: 1) Riemann Sum. Aim: Compute Area Under a Graph. Suppose we want to find out the area of a graph, like the one on the right:
Week 1 Notes: 1) Riem Sum Aim: Compute Are Uder Grph Suppose we wt to fid out the re of grph, like the oe o the right: We wt to kow the re of the red re. Here re some wys to pproximte the re: We cut the
More informationPLANCESS RANK ACCELERATOR
PLANCESS RANK ACCELERATOR MATHEMATICS FOR JEE MAIN & ADVANCED Sequeces d Seies 000questios with topic wise execises 000 polems of IIT-JEE & AIEEE exms of lst yes Levels of Execises ctegoized ito JEE Mi
More informationD Properties and Measurement
APPENDIX D. Review of Alge, Geomet, nd Tigonomet A D Popetie nd Meuement D. Review of Alge, Geomet, nd Tigonomet Alge Popetie of Logitm Geomet Plne Anltic Geomet Solid Anltic Geomet Tigonomet Li of Function
More informationAppendix D: Formulas, Properties and Measurements
Appendi D: Fomul, Popetie nd Meuement Review of Alge, Geomet, nd Tigonomet Unit of Meuement D. REVIEW OF ALGEBRA, GEOMETRY, AND TRIGONOMETRY Alge Popetie of Logitm Geomet Plne Anltic Geomet Solid Anltic
More informationNATIONAL SENIOR CERTIFICATE NASIONALE SENIOR SERTIFIKAAT GRADE 12/GRAAD 12
NAIONAL ENIOR CERIFICAE NAIONALE ENIOR ERIFIKAA GRADE /GRAAD MAHEMAIC P/WIKUNDE V NOVEMBER 7 MARKING GUIDELINE/NAIENRIGLYNE MARK/PUNE: 5 is memodum cosists o pges. Hiedie memodum best uit bldsye. Copyigt
More informationGraphing Review Part 3: Polynomials
Grphig Review Prt : Polomils Prbols Recll, tht the grph of f ( ) is prbol. It is eve fuctio, hece it is smmetric bout the bout the -is. This mes tht f ( ) f ( ). Its grph is show below. The poit ( 0,0)
More informationSummary: Binomial Expansion...! r. where
Summy: Biomil Epsio 009 M Teo www.techmejcmth-sg.wes.com ) Re-cp of Additiol Mthemtics Biomil Theoem... whee )!!(! () The fomul is ville i MF so studets do ot eed to memoise it. () The fomul pplies oly
More informationMath 152 Intermediate Algebra
Mth 15 Iteredite Alger Stud Guide for the Fil E You use 46 otecrd (oth sides) d scietific clcultor. You re epected to kow (or hve writte o our ote crd) foruls ou eed. Thik out rules d procedures ou eeded
More informationIntermediate Arithmetic
Git Lerig Guides Iteredite Arithetic Nuer Syste, Surds d Idices Author: Rghu M.D. NUMBER SYSTEM Nuer syste: Nuer systes re clssified s Nturl, Whole, Itegers, Rtiol d Irrtiol uers. The syste hs ee digrticlly
More informationAlgebra 2 Important Things to Know Chapters bx c can be factored into... y x 5x. 2 8x. x = a then the solutions to the equation are given by
Alger Iportt Thigs to Kow Chpters 8. Chpter - Qudrtic fuctios: The stdrd for of qudrtic fuctio is f ( ) c, where 0. c This c lso e writte s (if did equl zero, we would e left with The grph of qudrtic fuctio
More informationChapter Real Numbers
Chpter. - Rel Numbers Itegers: coutig umbers, zero, d the egtive of the coutig umbers. ex: {,-3, -, -, 0,,, 3, } Rtiol Numbers: quotiets of two itegers with ozero deomitor; termitig or repetig decimls.
More informationRahul Chacko. IB Mathematics HL Revision Step One
IB Mthemtics HL Revisio Step Oe Rhul Chcko Chpte. Aithmetic sequeces d seies; sum of fiite ithmetic seies; geometic sequeces d seies; sum of fiite d ifiite geometic seies. Sigm ottio. Aithmetic Sequeces
More informationM5. LTI Systems Described by Linear Constant Coefficient Difference Equations
5. LTI Systes Descied y Lie Costt Coefficiet Diffeece Equtios Redig teil: p.34-4, 245-253 3/22/2 I. Discete-Tie Sigls d Systes Up til ow we itoduced the Fouie d -tsfos d thei popeties with oly ief peview
More informationGEOMETRY Properties of lines
www.sscexmtuto.com GEOMETRY Popeties of lines Intesecting Lines nd ngles If two lines intesect t point, ten opposite ngles e clled veticl ngles nd tey ve te sme mesue. Pependicul Lines n ngle tt mesues
More informationME 501A Seminar in Engineering Analysis Page 1
Fobeius ethod pplied to Bessel s Equtio Octobe, 7 Fobeius ethod pplied to Bessel s Equtio L Cetto Mechicl Egieeig 5B Sei i Egieeig lsis Octobe, 7 Outlie Review idte Review lst lectue Powe seies solutios/fobeius
More informationI. Exponential Function
MATH & STAT Ch. Eoetil Fuctios JCCSS I. Eoetil Fuctio A. Defiitio f () =, whee ( > 0 ) d is the bse d the ideedet vible is the eoet. [ = 1 4 4 4L 4 ] ties (Resf () = is owe fuctio i which the bse is the
More informationProperties and Formulas
Popeties nd Fomuls Cpte 1 Ode of Opetions 1. Pefom ny opetion(s) inside gouping symols. 2. Simplify powes. 3. Multiply nd divide in ode fom left to igt. 4. Add nd sutt in ode fom left to igt. Identity
More informationAdvanced Higher Maths: Formulae
Advced Highe Mths: Fomule Advced Highe Mthemtics Gee (G): Fomule you solutely must memoise i ode to pss Advced Highe mths. Rememe you get o fomul sheet t ll i the em! Ame (A): You do t hve to memoise these
More informationName: Period: Date: 2.1 Rules of Exponents
SM NOTES Ne: Period: Dte:.1 Rules of Epoets The followig properties re true for ll rel ubers d b d ll itegers d, provided tht o deoitors re 0 d tht 0 0 is ot cosidered. 1 s epoet: 1 1 1 = e.g.) 7 = 7,
More informationANSWER KEY PHYSICS. Workdone X
ANSWER KEY PHYSICS 6 6 6 7 7 7 9 9 9 0 0 0 CHEMISTRY 6 6 6 7 7 7 9 9 9 0 0 60 MATHEMATICS 6 66 7 76 6 6 67 7 77 7 6 6 7 7 6 69 7 79 9 6 70 7 0 90 PHYSICS F L l. l A Y l A ;( A R L L A. W = (/ lod etesio
More informationUNIT 4 EXTENDING THE NUMBER SYSTEM Lesson 1: Working with the Number System Instruction
Lesso : Workig with the Nuber Syste Istructio Prerequisite Skills This lesso requires the use of the followig skills: evlutig expressios usig the order of opertios evlutig expoetil expressios ivolvig iteger
More informationFor students entering Honors Precalculus Summer Packet
Hoors PreClculus Summer Review For studets eterig Hoors Preclculus Summer Pcket The prolems i this pcket re desiged to help ou review topics from previous mthemtics courses tht re importt to our success
More informationPhysicsAndMathsTutor.com
PhysicsAdMthsTuto.com PhysicsAdMthsTuto.com Jue 009 3. Fid the geel solutio of the diffeetil equtio blk d si y ycos si si, d givig you swe i the fom y = f(). (8) 6 *M3544A068* PhysicsAdMthsTuto.com Jue
More informationALGEBRA. Set of Equations. have no solution 1 b1. Dependent system has infinitely many solutions
Qudrtic Equtios ALGEBRA Remider theorem: If f() is divided b( ), the remider is f(). Fctor theorem: If ( ) is fctor of f(), the f() = 0. Ivolutio d Evlutio ( + b) = + b + b ( b) = + b b ( + b) 3 = 3 +
More information[Q. Booklet Number]
6 [Q. Booklet Numer] KOLKATA WB- B-J J E E - 9 MATHEMATICS QUESTIONS & ANSWERS. If C is the reflecto of A (, ) i -is d B is the reflectio of C i y-is, the AB is As : Hits : A (,); C (, ) ; B (, ) y A (,
More informationCape Cod Community College
Cpe Cod Couity College Deprtetl Syllus Prepred y the Deprtet of Mthetics Dte of Deprtetl Approvl: Noveer, 006 Dte pproved y Curriculu d Progrs: Jury 9, 007 Effective: Fll 007 1. Course Nuer: MAT110 Course
More informationLecture 2. Rational Exponents and Radicals. 36 y. b can be expressed using the. Rational Exponent, thus b. b can be expressed using the
Lecture. Rtiol Epoets d Rdicls Rtiol Epoets d Rdicls Lier Equtios d Iequlities i Oe Vrile Qudrtic Equtios Appedi A6 Nth Root - Defiitio Rtiol Epoets d Rdicls For turl umer, c e epressed usig the r is th
More information82A Engineering Mathematics
Clss Notes 9: Power Series /) 8A Egieerig Mthetics Secod Order Differetil Equtios Series Solutio Solutio Ato Differetil Equtio =, Hoogeeous =gt), No-hoogeeous Solutio: = c + p Hoogeeous No-hoogeeous Fudetl
More informationGRAPHING LINEAR EQUATIONS. Linear Equations. x l ( 3,1 ) _x-axis. Origin ( 0, 0 ) Slope = change in y change in x. Equation for l 1.
GRAPHING LINEAR EQUATIONS Qudrt II Qudrt I ORDERED PAIR: The first umer i the ordered pir is the -coordite d the secod umer i the ordered pir is the y-coordite. (, ) Origi ( 0, 0 ) _-is Lier Equtios Qudrt
More informationUNIT V: Z-TRANSFORMS AND DIFFERENCE EQUATIONS. Dr. V. Valliammal Department of Applied Mathematics Sri Venkateswara College of Engineering
UNIT V: -TRANSFORMS AND DIFFERENCE EQUATIONS D. V. Vllimml Deptmet of Applied Mthemtics Si Vektesw College of Egieeig TOPICS:. -Tsfoms Elemet popeties.. Ivese -Tsfom usig ptil fctios d esidues. Covolutio
More informationDRAFT. Formulae and Statistical Tables for A-level Mathematics SPECIMEN MATERIAL. First Issued September 2017
Fist Issued Septembe 07 Fo the ew specifictios fo fist techig fom Septembe 07 SPECIMEN MATERIAL Fomule d Sttisticl Tbles fo A-level Mthemtics AS MATHEMATICS (7356) A-LEVEL MATHEMATICS (7357) AS FURTHER
More informationMathematical Statistics
7 75 Ode Sttistics The ode sttistics e the items o the dom smple ed o odeed i mitude om the smllest to the lest Recetl the impotce o ode sttistics hs icesed owi to the moe equet use o opmetic ieeces d
More information2.Decision Theory of Dependence
.Deciio Theoy of Depedece Theoy :I et of vecto if thee i uet which i liely depedet the whole et i liely depedet too. Coolly :If the et i liely idepedet y oepty uet of it i liely idepedet. Theoy : Give
More informationPearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE Mathematics and Further Mathematics
Peso Edecel Level 3 Advced Subsidiy d Advced GCE Mthemtics d Futhe Mthemtics Mthemticl fomule d sttisticl tbles Fo fist cetifictio fom Jue 08 fo: Advced Subsidiy GCE i Mthemtics (8MA0) Advced GCE i Mthemtics
More informationContent: Essential Calculus, Early Transcendentals, James Stewart, 2007 Chapter 1: Functions and Limits., in a set B.
Review Sheet: Chpter Cotet: Essetil Clculus, Erly Trscedetls, Jmes Stewrt, 007 Chpter : Fuctios d Limits Cocepts, Defiitios, Lws, Theorems: A fuctio, f, is rule tht ssigs to ech elemet i set A ectly oe
More informationLaws of Integral Indices
A Lws of Itegrl Idices A. Positive Itegrl Idices I, is clled the se, is clled the idex lso clled the expoet. mes times.... Exmple Simplify 5 6 c Solutio 8 5 6 c 6 Exmple Simplify Solutio The results i
More informationLEVEL I. ,... if it is known that a 1
LEVEL I Fid the sum of first terms of the AP, if it is kow tht + 5 + 0 + 5 + 0 + = 5 The iterior gles of polygo re i rithmetic progressio The smllest gle is 0 d the commo differece is 5 Fid the umber of
More information,... are the terms of the sequence. If the domain consists of the first n positive integers only, the sequence is a finite sequence.
Chpter 9 & 0 FITZGERALD MAT 50/5 SECTION 9. Sequece Defiitio A ifiite sequece is fuctio whose domi is the set of positive itegers. The fuctio vlues,,, 4,...,,... re the terms of the sequece. If the domi
More informationNumerical integration
Numeicl itegtio Alyticl itegtio = ( ( t)) ( t) Dt : Result ( s) s [0, t] : ( t) st ode odiy diffeetil equtio Alyticl solutio ot lwys vilble d( ) q( ) = σ = ( d ) : t 0 t = Numeicl itegtio 0 t t 2. t. t
More information«A first lesson on Mathematical Induction»
Bcgou ifotio: «A fist lesso o Mtheticl Iuctio» Mtheticl iuctio is topic i H level Mthetics It is useful i Mtheticl copetitios t ll levels It hs bee coo sight tht stuets c out the poof b theticl iuctio,
More informationFormula List for College Algebra Sullivan 10 th ed. DO NOT WRITE ON THIS COPY.
Forula List for College Algera Sulliva 10 th ed. DO NOT WRITE ON THIS COPY. Itercepts: Lear how to fid the x ad y itercepts. Syetry: Lear how test for syetry with respect to the x-axis, y-axis ad origi.
More informationFor this purpose, we need the following result:
9 Lectue Sigulities of omplex Fuctio A poit is clled sigulity of fuctio f ( z ) if f ( z ) is ot lytic t the poit. A sigulity is clled isolted sigulity of f ( z ), if f ( z ) is lytic i some puctued disk
More informationMth 95 Notes Module 1 Spring Section 4.1- Solving Systems of Linear Equations in Two Variables by Graphing, Substitution, and Elimination
Mth 9 Notes Module Sprig 4 Sectio 4.- Solvig Sstems of Liear Equatios i Two Variales Graphig, Sustitutio, ad Elimiatio A Solutio to a Sstem of Two (or more) Liear Equatios is the commo poit(s) of itersectio
More informationCHAPTER 5 : SERIES. 5.2 The Sum of a Series Sum of Power of n Positive Integers Sum of Series of Partial Fraction Difference Method
CHAPTER 5 : SERIES 5.1 Seies 5. The Sum of a Seies 5..1 Sum of Powe of Positive Iteges 5.. Sum of Seies of Patial Factio 5..3 Diffeece Method 5.3 Test of covegece 5.3.1 Divegece Test 5.3. Itegal Test 5.3.3
More informationA GENERAL METHOD FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS: THE FROBENIUS (OR SERIES) METHOD
Diol Bgoo () A GENERAL METHOD FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS: THE FROBENIUS (OR SERIES) METHOD I. Itroductio The first seprtio of vribles (see pplictios to Newto s equtios) is ver useful method
More information10.3 The Quadratic Formula
. Te Qudti Fomul We mentioned in te lst setion tt ompleting te sque n e used to solve ny qudti eqution. So we n use it to solve 0. We poeed s follows 0 0 Te lst line of tis we ll te qudti fomul. Te Qudti
More informationSemiconductors materials
Semicoductos mteils Elemetl: Goup IV, Si, Ge Biy compouds: III-V (GAs,GSb, ISb, IP,...) IV-VI (PbS, PbSe, PbTe,...) II-VI (CdSe, CdTe,...) Tey d Qutey compouds: G x Al -x As, G x Al -x As y P -y III IV
More informationx x x a b) Math 233B Intermediate Algebra Fall 2012 Final Exam Study Guide
Mth B Iteredite Alger Fll 0 Fil E Stud Guide The fil e is o Thursd, Deceer th fro :00p :00p. You re llowed scietific clcultor d 4" 6" ide crd for otes. O our ide crd e sure to write foruls ou eeded for
More informationPearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE Mathematics and Further Mathematics
Peso Edecel Level Advced Subsidiy d Advced GCE Mthemtics d Futhe Mthemtics Mthemticl fomule d sttisticl tbles Fo fist cetifictio fom Jue 08 fo: Advced Subsidiy GCE i Mthemtics (8MA0) Advced GCE i Mthemtics
More informationALGEBRA II CHAPTER 7 NOTES. Name
ALGEBRA II CHAPTER 7 NOTES Ne Algebr II 7. th Roots d Rtiol Expoets Tody I evlutig th roots of rel ubers usig both rdicl d rtiol expoet ottio. I successful tody whe I c evlute th roots. It is iportt for
More informationWe show that every analytic function can be expanded into a power series, called the Taylor series of the function.
10 Lectue 8 We show tht evey lytic fuctio c be expded ito powe seies, clled the Tylo seies of the fuctio. Tylo s Theoem: Let f be lytic i domi D & D. The, f(z) c be expessed s the powe seies f( z) b (
More informationChapter 23. Geometric Optics
Cpter 23 Geometric Optic Ligt Wt i ligt? Wve or prticle? ot Geometric optic: ligt trvel i trigt-lie pt clled ry Ti i true if typicl ditce re muc lrger t te wvelegt Geometric Optic 2 Wt it i out eome ddreed
More informationPre-Calculus - Chapter 3 Sections Notes
Pre-Clculus - Chpter 3 Sectios 3.1-3.4- Notes Properties o Epoets (Review) 1. ( )( ) = + 2. ( ) =, (c) = 3. 0 = 1 4. - = 1/( ) 5. 6. c Epoetil Fuctios (Sectio 3.1) Deiitio o Epoetil Fuctios The uctio deied
More informationCHAPTERS 5-7 BOOKLET-2
MATHEMATIS XI HAPTERS -7 BOOKLET- otets: Pge No hpte Bioil Theoe 7-8 hpte Stight Lies 8- hpte 7 Sequees Seies - Bioil Epessio A lgei epessio osistig of two tes with ve o ve sig etwee the is lle ioil epessio
More informationThings I Should Know In Calculus Class
Thigs I Should Kow I Clculus Clss Qudrtic Formul = 4 ± c Pythgore Idetities si cos t sec cot csc + = + = + = Agle sum d differece formuls ( ) ( ) si ± y = si cos y± cos si y cos ± y = cos cos ym si si
More informationSection 3.6: Rational Exponents
CHAPTER Sectio.6: Rtiol Epoets Sectio.6: Rtiol Epoets Objectives: Covert betwee rdicl ottio d epoetil ottio. Siplif epressios with rtiol epoets usig the properties of epoets. Multipl d divide rdicl epressios
More informationCrushed Notes on MATH132: Calculus
Mth 13, Fll 011 Siyg Yg s Outlie Crushed Notes o MATH13: Clculus The otes elow re crushed d my ot e ect This is oly my ow cocise overview of the clss mterils The otes I put elow should ot e used to justify
More information( ) dx ; f ( x ) is height and Δx is
Mth : 6.3 Defiite Itegrls from Riem Sums We just sw tht the exct re ouded y cotiuous fuctio f d the x xis o the itervl x, ws give s A = lim A exct RAM, where is the umer of rectgles i the Rectgulr Approximtio
More informationInduction. Induction and Recursion. Induction is a very useful proof technique
Iductio Iductio is vey useul poo techique Iductio d Recusio CSC-59 Discete Stuctues I compute sciece, iductio is used to pove popeties o lgoithms Iductio d ecusio e closely elted Recusio is desciptio method
More informationAdd Maths Formulae List: Form 4 (Update 18/9/08)
Add Mths Formule List: Form 4 (Updte 8/9/08) 0 Fuctios Asolute Vlue Fuctio f ( ) f( ), if f( ) 0 f( ), if f( ) < 0 Iverse Fuctio If y f( ), the Rememer: Oject the vlue of Imge the vlue of y or f() f()
More informationAdvanced Higher Maths: Formulae
: Fomule Gee (G): Fomule you bsolutely must memoise i ode to pss Advced Highe mths. Remembe you get o fomul sheet t ll i the em! Ambe (A): You do t hve to memoise these fomule, s it is possible to deive
More informationCalendar of first week of the school year. Monday, August 26 Full Day get books & begin Chapter 1
Gettig Strted Pcket Hoors Pre-Clculus Welcoe to Hoors Pre-Clculus. Hoors Pre-Clculus will refresh your Algebr skills, review polyoil fuctios d grphs, eplore trigooetry i depth, d give you brief itroductio
More informationThe Handbook of Essential Mathematics
Fo Pulic Relese: Distiutio Ulimited The Ai Foce Resech Lotoy The Hdook of Essetil Mthemtics Fomuls, Pocesses, d Tles Plus Applictios i Pesol Fice X Y Y XY Y X X XY X Y X XY Y Compiltio d Epltios: Joh C.
More informationBITSAT MATHEMATICS PAPER. If log 0.0( ) log 0.( ) the elogs to the itervl (, ] () (, ] [,+ ). The poit of itersectio of the lie joiig the poits i j k d i+ j+ k with the ple through the poits i+ j k, i
More informationjfpr% ekuo /kez iz.ksrk ln~xq# Jh j.knksm+nklth egkjkt ( )( ) n n + 1 b c d e a a b c d e = + a + b c
Dwld FREE Study Pckge fm www.tekclsses.cm & Le Vide www.mthsbysuhg.cm Phe : 0 90 90 7779, 9890 888 WhtsApp 9009 60 9 SEQUENCE & SERIES PART OF f/u fpkj Hkh# tu] ugh vkjehks dke] fif s[k NksMs qj e/;e eu
More informationSTATICS. CENTROIDS OF MASSES, AREAS, LENGTHS, AND VOLUMES The following formulas are for discrete masses, areas, lengths, and volumes: r c
STTS FORE foe is veto qutit. t is defied we its () mgitude, () oit of litio, d () dietio e kow. Te veto fom of foe is F F i F j RESULTNT (TWO DMENSONS) Te esultt, F, of foes wit omoets F,i d F,i s te mgitude
More informationPhysicsAndMathsTutor.com
PhysicsAdMthsTuto.com PhysicsAdMthsTuto.com Jue 009 7. () Sketch the gph of y, whee >, showig the coodites of the poits whee the gph meets the es. () Leve lk () Solve, >. (c) Fid the set of vlues of fo
More informationA Level Further Mathematics A (H245) Formulae Booklet. Specimen. OCR 2017 H245 Turn over QN 603/1325/0
A Level Futhe Mthemtics A (H45) Fomule Booklet Specime OCR 07 H45 Tu ove QN 603/35/0 Pue Mthemtics Aithmetic seies S ( l) { ( ) d} Geometic seies S S ( ) fo Biomil seies ( b) C b C b C b b ( ),! whee C!(
More informationNumerical Integration - (4.3)
Numericl Itegrtio - (.). Te Degree of Accurcy of Qudrture Formul: Te degree of ccurcy of qudrture formul Qf is te lrgest positive iteger suc tt x k dx Qx k, k,,,...,. Exmple fxdx 9 f f,,. Fid te degree
More informationPROGRESSIONS AND SERIES
PROGRESSIONS AND SERIES A sequece is lso clled progressio. We ow study three importt types of sequeces: () The Arithmetic Progressio, () The Geometric Progressio, () The Hrmoic Progressio. Arithmetic Progressio.
More informationReference. Reference. Properties of Equality. Properties of Segment and Angle Congruence. Other Properties. Triangle Inequalities
Refeene opeties opeties of qulity ddition opety of qulity If =, ten + = +. Multiplition opety of qulity If =, ten =, 0. Reflexive opety of qulity = Tnsitive opety of qulity If = nd =, ten =. Suttion opety
More informationUnit 1 Chapter-3 Partial Fractions, Algebraic Relationships, Surds, Indices, Logarithms
Uit Chpter- Prtil Frctios, Algeric Reltioships, Surds, Idices, Logriths. Prtil Frctios: A frctio of the for 7 where the degree of the uertor is less th the degree of the deoitor is referred to s proper
More informationMATHEMATICIA GENERALLI
MATHEMATICIA GENERALLI (y Mhmmed Abbs) Lgithmi Reltis lgb ) lg lg ) b b) lg lg lg m lg m d) lg m. lg m lg m e) lg lg m lg g) lg lg h) f) lg lg f ( ) f ( ). Eetil Reltis ). lge. lge.... lge...!! b) e......
More informationMathematics. Trigonometrical Ratio, Functions & Identities
Mthemtics Tigmeticl Rti, Fuctis & Idetities Tble f tet Defiitis stems f Mesuemet f gles Relti betwee Thee stems f Mesuemet f gle Relti betwee c d gle 5 Tigmeticl Rtis Fuctis 6 Tigmeticl Rtis f llied gles
More informationx a y n + b = 1 0<b a, n > 0 (1.1) x 1 - a y = b 0<b a, n > 0 (1.1') b n sin 2 + cos 2 = 1 x n = = cos 2 6 Superellipse (Lamé curve)
6 Supeellipse (Lmé cuve) 6. Equtios of supeellipse A supeellipse (hoizotlly log) is epessed s follows. Implicit Equtio y + b 0 0 (.) Eplicit Equtio y b - 0 0 (.') Whe 3, b, the supeellipses fo
More informationGEOMETRY. Rectangle Circle Triangle Parallelogram Trapezoid. 1 A = lh A= h b+ Rectangular Prism Sphere Rectangular Pyramid.
ALGEBA Popeties of Asote Ve Fo e mes :, + + Tige Ieqit Popeties of Itege Epoets is Assme tt m e positive iteges, tt e oegtive, tt eomitos e ozeo. See Appeies B D fo gps fte isssio. + ( ) m m m m m m m
More informationMATHEMATICS IV 2 MARKS. 5 2 = e 3, 4
MATHEMATICS IV MARKS. If + + 6 + c epesents cicle with dius 6, find the vlue of c. R 9 f c ; g, f 6 9 c 6 c c. Find the eccenticit of the hpeol Eqution of the hpeol Hee, nd + e + e 5 e 5 e. Find the distnce
More informationPlane Kinetics of Rigid Bodies 동역학 및 응용
Ple Kietics of igid odies 동역학 및 응용 EQUTONS O PLNE OTON esultt of the pplied etel foces : esultt foce (pss though ss cete) + ouple oets of the etel foces gul otio z ouple : sste of foces with esultt oet
More informationEinstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,
MB BINOMIAL THEOREM Biomial Epessio : A algebaic epessio which cotais two dissimila tems is called biomial epessio Fo eample :,,, etc / ( ) Statemet of Biomial theoem : If, R ad N, the : ( + ) = a b +
More informationPhysics 232 Exam I Feb. 13, 2006
Phsics I Fe. 6 oc. ec # Ne..5 g ss is ched o hoizol spig d is eecuig siple hoic oio. The oio hs peiod o.59 secods. iiil ie i is oud o e 8.66 c o he igh o he equiliiu posiio d oig o he le wih eloci o sec.
More informationName: A2RCC Midterm Review Unit 1: Functions and Relations Know your parent functions!
Nme: ARCC Midterm Review Uit 1: Fuctios d Reltios Kow your pret fuctios! 1. The ccompyig grph shows the mout of rdio-ctivity over time. Defiitio of fuctio. Defiitio of 1-1. Which digrm represets oe-to-oe
More informationSummer MA Lesson 4 Section P.3. such that =, denoted by =, is the principal square root
Suer MA 00 Lesso Sectio P. I Squre Roots If b, the b is squre root of. If is oegtive rel uber, the oegtive uber b b b such tht, deoted by, is the pricipl squre root of. rdicl sig rdicl expressio rdicd
More informationMATH Midterm Solutions
MATH 2113 - Midtem Solutios Febuay 18 1. A bag of mables cotais 4 which ae ed, 4 which ae blue ad 4 which ae gee. a How may mables must be chose fom the bag to guaatee that thee ae the same colou? We ca
More informationEXERCISE a a a 5. + a 15 NEETIIT.COM
- Dowlod our droid App. Sigle choice Type Questios EXERCISE -. The first term of A.P. of cosecutive iteger is p +. The sum of (p + ) terms of this series c be expressed s () (p + ) () (p + ) (p + ) ()
More information