2002 Quarter 1 Math 172 Final Exam. Review

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1 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 Empty Set (φ) Sectios.,.5 &.6. Rel Numes d thei Popeties Ntul Numes (N), Whole Numes (W), Iteges (J), Rtiol Numes (Q), Itiol Numes (I), Rel Numes (R) Miscelleous Popeties Commuttive popety of dditio/multiplictio Associtive popety of dditio/multiplictio Distiutive popety Additive/Multiplictive idetity popety Additive/Multiplictive Ivese Popety Multiplictio Popety of Zeo Sectio.3. Opetios o the Set of Rel Numes if is positive o zeo Asolute Vlue = if is egtive Opposite of opposite: ( ) = Additio: Additive Ivese Popety + (-) = - + = 0 Sutctio: = + (-) Multiplictio: The poduct is positive/egtive if the umes hve the sme/ulike sigs Divisio : Multiplic tive Ivese Popety = = = The quotiet is positive/egtive if the umes hve the sme/ulike sigs Divisio y zeo is ot defied Sectio.4. Evlutig Expessios Ode of Opetios: Evlute iside y goupig symols fist. Whee goupig symols is missig, use the followig ode. Evlute ech expoetil expessio (i ode fom left to ight). Pefom multiplictio d divisio (i ode fom left to ight) 3. Pefom dditio d sutctio (i ode fom left to ight)

2 00 Qute Mth 7 Fil Exm. Review Sectios. &.3. Lie equlity d Polem Solvig Use of the Additio/Multiplictio Popety of Equlity to solve lie equtio i oe vile 3 types of equtios: Idetity, Coditiol Equtio, Icosistet Equtio Applictios: Nume Polem Ivestmet Polem Mixtue Polem Uifom Motio Polem Geometic Polem Sectio.. Fomuls Solvig fo vile Geometic Fomuls: Tigle: Ae = ½ h; Peimete P = + + c Rectgle: Ae A = LW; Peimete P = L + W Sque: Specil cse of ectgle Cicle: Ae A = π ; Cicumfeece C = π; Dimete d = Rectgul Solid: V = LWH Simple Iteest A = P + Pt Compoud Iteest (Sectio 5.): Amout Fomul A = P( + ) Uifom Motio Polem: Distce = Speed Time Sectios.4 &.5. Iequlities d thei Gphs Use of Additio/Multiplictio Popety of Iequlity to solve iequlity (multiplyig oth sides of iequlity y the sme egtive ume eveses the iequlity) Solvig compoud iequlity usig the coective d / o Repesettio of solutio set: Itevl Nottio d Gph Sectio 3.. Gphig Lies i the Rectgul Coodite System Sketchig lies y usig give poits y itecepts Sketchig veticl lies Sectio 3.. Slope of Lie y y chge i y - coodite Slope : m = = x x chge i x - coodite Slope of hoizotl d veticl lies Slope of pllel lies: m = m Slope of pepedicul lies : m = m = ise u

3 00 Qute Mth 7 Fil Exm. Review Sectio 3.3. Thee Foms fo the Equtio of Lie Poit-slope fom: y y = m(x x) Slope-itecept fom: y = mx + Stdd Fom: Ax + By = C Sectio 3.4. (System of) Lie Iequlities Gphig lie iequlity usig the method descied o pge 5 the Test Poit Method Sectios 4. & 4.. Systems of Lie Equtios Uique solutio (idepedet system), o solutio (icosistet system), ulimited ume of solutios (depedet system) Solvig systems of two equtios i two ukows Gphiclly By Sustitutio By the Additio method Sectio 5.. Itegl Expoets, Scietific Nottio = = ; Negtive Expoets : = Zeo Expoet: 0 = (fo 0) Poduct Rule: m = m+ m m Quotiet Rule : = Covesio etwee Stdd Nottio d Scietific Nottio Sectio 5.. Expoets: Powe Rules Powe of Powe Rule: ( m ) = m Powe of Poduct Rule: () = Powe of Quotiet Rule : = Sectios 5.3, 5.4 & 5.5. Fudmetl Opetios with Polyomils Evlutig Polyomil Fuctios Additio, Sutctio d Multiplictio of Polyomils Multiplyig Biomils: Sque of sum: ( + ) = + + Sque of diffeece: ( ) = + Poduct of sum d diffeece: ( + )( ) = the FOIL Method Divisio of Polyomils: Odiy (Log) Divisio divided = (diviso)(quotiet) + (emide) divided emide = quotiet + diviso diviso

4 00 Qute Mth 7 Fil Exm. Review Sectios 5.6, 5.7 & 5.8. Fctoig Polyomils Fctoig out the Getest Commo Fcto Fctoig Diffeece of Two Sque: = ( + )( ) Fctoig Diffeece o Sum of Two Cues: 3 3 = ( )( + + ); = ( + )( + ) Fctoig Pefect Sque Tiomils: + + = ( + ) ; + = ( ) Fctoig x + x + c: the c Method; d Til d Eo Fctoig Polyomils with Fou Tems: ty fctoig y goupig Fctoig y Sustitutio Sectio 5.9. Solvig Equtios y Fctoig Zeo Fcto Popety: = 0 = 0 o = 0 Pythgoe Theoem: Fo ight tigle with legs, d hypoteuse c, + = c Sectio 6.. Rtiol Expessios: Popeties Domi of Rtiol Expessio Reducig to Lowest Tems/Buildig Up the Deomito: c Bsic Piciple of Rtiol Numes : = c Sectio 6.. Rtiol Expessios: Multiplictio & Divisio c c Multiplic tio : = d d c d Divisio : = d c Sectio 6.3. Rtiol Expessios: Additio & Sutctio Additio & Sutctio: Build up ech tiol expessio to equivlet foms with ideticl deomitos (pefely the LCD Lest Commo Deomito) Sectio 6.4. Rtiol Expessios: Complex Fctios Method A: Pefom the computtios of the umeto d deomito septely d the divide Method B: Simplifyig Complex Fctio: Multiply the umeto d deomito y the LCD fo ll of the fctios i the complex fctio Negtive Expoets Sectio 6.5. Solvig Equtios ivolvig Rtiol Expessios Multiply ech side of the equtio y the LCD of the tiol expessios to elimite ll deomitos Bewe of exteous oots (divisio y zeo): check ll swes Usig the Extemes - Mes c Popety t o solve Popotio : = d = c d (Coss Multiply)

5 00 Qute Mth 7 Fil Exm. Review Sectio 6.6. Rtiol Expessios: Applictios Solvig Fomul / Solvig fo Vile Uifom Motio Polems Wok Polems Miscelleous Polems Sectio 7.. Rtiol Expoets th oot vs. Picipl th oot 0 / = 0 m/ = ( / ) m = ( m ) / m Negtive Rtiol Expoet : = m Poduct Rule: s = +s s Quotiet Rule : = s Powe of Powe Rule: ( ) s = s Powe of Poduct Rule: () = Powe of Quotiet Rule : = Sque oot of x : (x ) / = x fo y el ume x Sectios 7., 7.3 & 7.4. Rdicls d Opetios o Rdicls m m = ; = = Poduct Rule : Quotiet Rule : = = ( ) m Simplified Rdicl: No pefect th powe s fctos of the dicd No fctios iside the dicl No dicls i the deomito (tiolizig the deomito) Additio/Sutctio: Comie like dicls Multiplictio : cses (sme idex vs. diffeet idices) p m mp ( ) = Powes of Rdicl Expessio s Powes of Rdicl Expessios Divisio: tiolizig the deomito (usig cojugte)

6 00 Qute Mth 7 Fil Exm. Review Sectio 7.5. Solvig Equtios with Rdicls d Expoets Equtios with Itegl Expoets: Usig the odd-oot popety o the eve-oot popety Equtios with Rdicls: Risig ech side to powe (check fo exteous oots) Equtios with Rtiol Expoets: Comiig the two methods ove (elimite oot fist d the powe secod) x + x y + y Mid - poit Fomul : M =, Distce Fomul : d = Sectio 7.6. Complex Numes ( x x ) + ( y y ) 3 i = i = i = i i 4 = Sque Root of Negtive Nume : Fo > 0, - = i Stdd Fom + i Additio/Sutctio lgeiclly usig stdd fom pefom opetios s with iomils (collect el pts d collect imgiy pts) Multiplictio: FOIL & simplify usig i = - Divisio: Multiply oth umeto d deomito y complex cojugte of the deomito Sectios 8., 8. & 8.3. Qudtic Equtios Solvig Qudtic Equtio y Fctoig Completig the Sque Qudtic Fomul ± 4c x + x + c = 0 x = Usig the detemit to decide the tue of the solutios of qudtic equtio Witig qudtic equtio with give solutios Solvig equtios qudtic i fom

BINOMIAL THEOREM SOLUTION. 1. (D) n. = (C 0 + C 1 x +C 2 x C n x n ) (1+ x+ x 2 +.)

BINOMIAL 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),