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1 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 Course Nuer: MAT110 Course Title: Alger for Preclculus. Descriptio: This course i iteredite lger is desiged to help prepre studets for Preclculus courses. Topics iclude: fctorig, rtiol epressios, rtiol epoets d roots, qudrtic equtios d iequlities, vritio, coic sectios, reltios d fuctios, trscedetl fuctios, sequeces d series, d the developet of word prole lysis d solutio. 4 clss hours. 3. Studet Lerig Outcoes (istructiol ojectives: itellectul skills: Upo successful copletio of course studets will e le to: fctor polyoils d solve polyoil equtios y fctorig. siplify d perfor opertios o rtiol epressios. pply properties to siplify rtiol epoets. siplify d perfor opertios with rdicl epressios. solve rdicl equtios, qudrtic equtios d iequlities. siplify d perfor opertios o fuctios d coposite fuctios. grph qudrtic, rtiol, rdicl, solute vlue d epoetil fuctios. grph lier equtios d iequlities. grph coic sectios. solve syste of equtios. grph d ipulte iverse fuctios d logrithic fuctios. use sic trigooetric defiitios to evlutio right trigle proles. solve pplictio proles. 4. Credits: 4 credits 5. Stisfies Geerl Eductio Requireet: No 6. Prerequisite: MAT030 Eleetry lger or pproprite thetics plceet score 7. Seester(s Offered: Fll, Sprig 8. Suggested Geerl Guidelies for Evlutio: Coprehesive fil eitio, hour tests, proles, cses, d quiz ppers. 9. Geerl Topicl Outlie (Optiol: Plese see the ttched course outlie. MAT110. Alger for Preclculus Pge 1 of 5
2 MAT110. Alger for Preclculus Outlie I. Fctorig. Fctorig trioils. Solvig qudrtic equtios y fctorig c. Applictios of qudrtic equtios II. Rtiol Epressios. The fudetl property of rtiol epressios. Multiplictio d divisio of rtiol epressios c. Additio d sutrctio of rtiol epressios d. Cople frctios e. Equtios ivolvig rtiol epressios f. Applictio of rtiol epressios g. Direct d iverse vritio pplictios III. Roots d Rdicls. Fidig roots. Multiplictio d divisio of rdicls c. Additio d sutrctio of rdicls d. Rtiolizig the deoitor e. Siplifyig rdicl epressios f. Equtios with rdicls g. Cople uers IV. Qudrtic Equtios d Iequlities. Solvig qudrtic equtios y the squre root property. Solvig qudrtic equtios y copletig the squre c. Solvig qudrtic equtios y the qudrtic forul d. Equtios qudrtic i for e. Foruls d pplictios ivolvig qudrtic equtios f. Nolier d frctiol iequlities V. Additiol Fuctio Topics. Grphs of fuctios d reltios. Trsfortios of grphs c. Coiig fuctios d. Iverse fuctios VI. Solvig systes of equtios. Solvig systes of lier equtios usig grphig. Solvig systes of lier equtios usig sustitutio c. Solvig systes of lier equtios usig dditio ethod d. Systes of lier equtios i three vriles e. Solvig lier systes usig trices f. Deterits d Crer s rule g. Nolier systes of equtios VII. Grphs of Nolier Fuctios d Coic Sectios. Grphs of qudrtic fuctios. Grphs of eleetry fuctios d circles c. Grphs of ellipses d erols d. Grphs of solute vlue fuctios d iequlities e. Grphs of olier d frctiol iequlities f. Grphs of rtiol fuctios VIII. Trscedetl Fuctios. Epoetil fuctios d pplictios. Logrithic fuctios d pplictios c. Siple trigooetric fuctios d pplictios IX. Sequeces d series. Sequeces. Series c. Arithetic sequeces d series MAT110. Alger for Preclculus Pge of 5
3 MAT 110 ALGEBRA FOR PRECALCULUS OUTCOMES BASED LEARNING MATRIX COURSE OUTCOMES At the ed of this course, studets will e le to: Fctorig polyoils d solve polyoils y Fctorig. Siplify d perfor opertios o rtiol epressios Apply the properties of rtiol epoets Siplify d perfor opertios with rdicls, d Solve rdicl equtios Solve qudrtic equtios d iequlities OUTCOMES ACTIVITIES 1. Fctor ooil fro polyoil.. Fctor y groupig. 3. Fctor trioil of the for + + c 4. Fctor trioil of the for + + c 5. Fctor the differece of two perfect squres. = ( + ( 6. Fctor perfect squre trioil. 7. Fctor the su of two cues. 3 3 = ( ( + + Fctor the differece of two cues = ( + ( = ( + + = ( 8. Use ultiple fctorig techiques to fctor copletely y epressio. 9. Solve equtios y fctorig. + + c = Solve pplied proles usig fctorig. 1. Siplify rtiol epressios (reduce to lowest ters. Multiply d divide rtiol epressios. 3. Add d sutrct rtiol epressios with like deoitors d with ulike deoitors. 4. Solve rtiol equtios. 5. Siplify cople frctios. 6. Solve pplied proles. 1. Siplify epoetil epressios usig:. = +. ( = = c. ( d. = whe 0 e. = whe 0 f. 0 = 1 whe 0 g. 1 = whe 0. Trslte etwee epoetil d rdicl fors usig:. 1 = whe is positive iteger greter th 1. ( = = whe is positive iteger greter th 1 d is y iteger. 1. Siplify rdicl epressios.. Add, sutrct, d ultiply rdicl epressios. 3. Rtiolize deoitors (ooil squre root deoitors d ioil squre root deoitors. 4. Solve rdicl equtios. 5. Solve pplied proles. Solve qudrtic equtios + + c = 0, 0 MAT110. Alger for Preclculus Pge 3 of 5
4 Siplify d perfor opertios d copositio of fuctios. Grphs of qudrtic fuctios Grphs of rtiol, rdicls, solute vlue d epoetil fuctios. Grph Coic Sectios 1. By fctorig.. By qudrtic forul. ± = 4c 3. Discriit, D = 4c 4. Solve y the squre root ethod: = the = ± 5. Solve y copletig the squre. 6. Solve pplied proles. 7. Solve qudrtic iequlities: + + c > 0, 0 1. Opertios fuctios: Su ( f + g ( = f ( + g( Differece g ( = f ( g( ( f Product ( fg ( = f ( g( f f ( ( = g g( f o g ( = f g( ] d g o f ( = g f ( Quotiet. copositio of fuctios: ( [ ( [ ] 3. Fid doi d rge of fuctio. Qudrtic fuctios: f ( = + + c, 0 If > 0, the prol opes upwrd. If < 0, the prol opes dowwrd 1. Grph fro: f ( = ( h + k Where verte = ( h, k d is of syetry = k (. Grph fro: f = + + c d is of syetry = Where verte ( f (, 1. Grph rtiol fuctios: y = 1, 0. Grph rdicl fuctios: y = where 0 3. Grph solute vlues fuctios: y = 4. Grph epoetil fuctios: 5. Solvig Epoetil equtios y = 1. Grph circle:,where ceter ( h, k = & r = rdius ( h + ( y k = r y. Grph ellipse: + = 1, where -it. = d y-it. = ( 0, ± y 3. Grph erol: = 1 y = 1 ( ±,0, where -it. = ( ±,0 d, where y-it. = ( 0, ± MAT110. Alger for Preclculus Pge 4 of 5
5 Solvig systes of equtios 1. Solvig systes of lier equtios i three vriles. Solvig systes of lier equtios usig trices 3. Deterits 4. Solvig systes of lier equtios usig Crer s rule 5. Solvig olier systes equtios Iverse fuctio, Logrith d properties of logriths 1. Fid iverse fuctio : f 1 (. Fid Logrith: y = log es the se s y = Use the sic defiitios to fid the trigooetric fuctio vlues of give cute gle i right trigle 1. Clculte si trigooetric fuctio vlues of give cute gle i right trigle si θ = cos θ = dj t θ = dj csc θ = sec θ = dj cot θ = dj. Use scietific clcultor or trigooetric tles correctly. 3. Solve right trigles. 4. Solve pplied proles. MAT110. Alger for Preclculus Pge 5 of 5
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