Math 060/ Final Exam Review Guide/ / College of the Canyons

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1 Mth 060/ Fil Exm Review Guide/ 00-0/ College of the Cyos Geerl Iformtio: The fil exm is -hour timed exm. There will be pproximtely 40 questios. There will be o clcultors or otes llowed. You will be give the formuls for how to fctor the sum d differece of cubes. b ( b)( b b ) d b ( b)( b b ) Topics: Solve lier iequlities. (Sectio.8) Write d grph equtios of lies, icludig fidig slope. (Sectios.-.6) Solve systems of lier equtios. (Sectios 4.-4.) Multiply d divide polyomils. (Sectios ) Simplify expressios with zero d egtive expoets. (Sectio 5.4) Fctor polyomils. (Sectios ) Add, subtrct, multiply, divide rtiol expressios. (Sectios 7., 7., 7.5, 7.6) Solve equtios. (Sectios.,.4, 6.6, 7.7) Solve word problems. (Sectios.6,.7, 4.4, 4.5, 6.7, 7.8) Study Tip: Write oe mth questio (from the smple fil, your pst exms, d the book) per x5 crd. O the bck of the x5 crd write where you foud the problem d the swer. Mix the crds up whe you prctice solvig the problems. Write otes to yourself o the bck of the crds if you eed to remember formuls or other steps. Formuls to Remember: y y Slope betwee two poits: m x x Slope of prllel lies: m m Slope of perpediculr lies: m m or m m Slope-Itercept Form of Lie: y mx b A x-itercept is ( x, 0). I other words, let y 0. Poit-Slope Form of Lie: y y m( x x ) A y-itercept is (0, y). I other words, let x 0. Verticl lies hve the equtio x with udefied slope. Horizotl lies hve the equtio y b with slope of zero. The grph of the lies y mx d Ax By 0 go through the origi.

2 Formuls to Remember, cotiued: Expoet Rules (See pge 48.) Product m m Power m ( ) m Quotiet m m if 0 Product to Power ( b) b Quotiet to Power b b if b 0 Zero Expoet 0 if 0 Negtive Expoet if 0 if 0 Quotiet to Negtive Power b b if 0, b 0 Polyomils: Specil Forms ( A B)( A B) A B ( A B) A AB B ( A B) A AB B Uiform Motio: (Rte)(Time) Distce OR (Distce) / (Rte) Time If wid or curret ffects the rte, use x y for trvelig with d use x y for trvelig gist. The object s speed is represeted by x, d the wid (or curret) speed is represeted by y. Simple Iterest: (Pricipl$)(Rte%) Iterest$ [This formul is good over legth of time yer.] [Remember to chge % ito deciml form.] Mixture: (Qutity)(Cocetrtio%) Amout [Remember to chge % ito deciml form.] Work: idividul time idividul time t where t represets time together. Complemetry gles dd up to 90. Supplemetry gles dd up to 80. Are of rectgle: A LW Are of trigle: bh A bh Pythgore Theorem: b c

3 Smple Problems for the Mth 060 Fil Exm, 00-0 (Sulliv, Struve, Mzzrell combo book). Solve the iequlities. Grph the solutio set o umber lie d write the solutio set i itervl ottio.. x (.8 #7) ( x 4) x 8 (.8 #77) 4( x ) ( x ) x (.8 #79) d. 4(w ) ( w ) 5( w ) (.8 #85). Grph ech lier equtio by fidig its itercepts. Write the coordites of the x-itercept: (, ). Write the coordites of the y-itercept: (, ).. x 6y 8 (. #67) x 5y 5 (. #69) 9x y 0 (. #7). Grph the followig lies.. x 5 (. #8) y 6 (. #85) 4. Grph the lie tht cotis the give poit d hs the give slope.. (, ); m 0 (. #5) (,); m (. #5) 5 (,4); m (. #55) d. (0,0); m is udefied (. #57) 5. Use the slope d y-itercept to grph ech lie.. y x (.4 #9) 5 y x (.4 #45) x y 0 (.4 #5) d. x y (.4 #8)

4 6. Write the equtio of the lie. Your swer should be i slope-itercept form y mx. Through the poits (,) d (, 4) (.5 #4) Through the poits (, ) d (, ) (.5 #4) Through the poits (,) d (4, 6) (.5 #67) d. Through the poit (0, ) d prllel to the lie x y 5 (.6 #5) e. Through the poit (, 0) d prllel to the lie x y 4 (.6 #5) f. Through the poit ( 4, ) d perpediculr to the lie y 4x (.6 #57) g. Through the poit (7,5) d perpediculr to the y-xis. (.6 #6) 7. Solve the followig systems of lier equtios. If there is oe solutio, write the solutio s ordered pir (x,y). Otherwise if there re ifiitely my solutios or o solutio, stte so. x y. Solve by grphig: (4. #) 6x y 4 x y 7 Solve by substitutio or elimitio: (4. #7) x y Solve by substitutio or elimitio: x y 6x y d. Solve by substitutio or elimitio: x 4 y 0 5x y 6 (4. #) (4. #9) 8. Fid the product.. d. e. f. ( x y) ( xy ) (5. #85) ( x )( x ) (5. #55) ( x ) (5. #7) (5k ) (5. #75) ( x y ) (5. #77) ( x )( x x ) (5. #8)

5 9. Simplify. Write swers with positive expoets. (If you hve umber rised to positive expoet, fid its vlue.). 0 (4 b ) (5.4 #55) 5 (5.4 #69) m (5.4 #7) d. 4 5 e. m f. yz y z (5.4 #75) (5.4 #79) (5.4 #87) 0. Divide d simplify.. d. e. 4x x x x x x x 0 4 x 7x 0x 5 x x x 8 x (5.5 #) (5.5 #5) (5.5 #7) (5.5 #47) (5.5 #5)

6 . Fctor completely. If the polyomil cot be fctored, sy tht it is prime. (I Sectio 6. the uthor sks studets to fctor by tril d error or by groupig. This will ot be the cse o the fil exm. You my choose method tht works for you.). d. e. f. g. h. i. j. k. l. m.. o. p. q. r. s. t. u. v. w. x. y. z. x x x (6.5 #47) x 00 (6.5 #9) 9 (6.5 #) x x x (6.5 #7) 8x 7 y (6.4 #5) x 0x 5 (6.4 #9) 6x 4x 9 (6.4 #) 4z z 9 (6.4 #7) 7 x (6.4 #49) 9x y (6.4 #85) x 5x (6. #) 4 p p (6. #9) (6. #5) 5w w 6 (6. #49) 6x 7x (6. #85) 0x x 4x (6. #9) 6 x ( x ) 5 x ( x ) 4( x ) (6. #95) m 9m 8 (6. #) z z 45 (6. #) x 5xy 6y (6. #5) y 8y 8 (6. #5) 4 4x x x (6. #5) g 4g (6. #7) 4 5 b 60b 45 b (6. #6) x ( x ) y ( x ) (6. #67) t t 4t (6. #77)

7 . Perform the idicted opertio. y 4y 8 y y 6 9y. (7. #7) p p p 6 p p p 9 x x x x 5x 4 x 4x (7. #9) (7. #59) d. c 4 8 c 0 0 e. f. x x x x x x x y x y y x g. h x 9 i. x x 9x 4 6 j. m 0 k. m m m 4 l. m b b b 6 b 4 b b 6 b 4 x x 9 x (7. #47) (7. #) (7. #5) (7. #55) (7.5 #4) (7.5 #6) (7.5 #67) (7.5 #77) (7.6 #5) (7.6 #4) (7.6 #45)

8 . Solve the equtios. Check your solutio.. check: 4 4 (. #5) p 0.05 p 57.5 check: p 0.05 p 57.5 (. #5) 0.0(c 4) 0.4( c ) check: 0.0(c 4) 0.4( c ) (. #59) 4. Solve the equtios.. Solve for r: A P Prt (.4 #5) Solve for b: Solve for y: A h ( B b ) (.4 #55) x y z (7.7 #5) d. Solve for S: R S T (7.7 #55) 5. Solve the equtios.. d. e. f (6.6 #7) 4x x 0 (6.6 #9) 6 (6.6 #47) x x x 0 (6.6 #59) y y 4y 0 (6.6 #6) ( ) 8 (6.6 #7)

9 6. Solve the equtios. Remember to check for vlues of the vrible which mke the expressios i ech rtiol equtio udefied.. 7 x x 6 x x x 8 (7.7 #) (7.7 #5) (7.7 #5) Wrig: The bold prited words show below t the begiig of the word problems will ot lwys pper with the word problems listed o the fil. 7. Bd Ivestmet. (.6 #4) After Mrs. Fisher lost 9% of her ivestmet, she hd $,750. Wht ws Mrs. Fisher s origil ivestmet? Vrible d wht it represets: Equtio: Origil Ivestmet: 8. Commissio. (.6 #5) Melie receives % commissio o every house she sells. If she received commissio of $857, wht ws the vlue of the house she sold? Vrible d wht it represets: Equtio: Vlue of House Sold: 9. Agles. (.7 #) Fid two supplemetry gles such tht the mesure of the first gle is 0 less th three times the mesure of the secod. Vrible d wht it represets: Equtio: Mesures of both gles: 0. Uiform Motio. (.7 #9) Two bots leve port t the sme time, oe goig orth d the other trvelig south. The orth-boud bot trvels 6 mph fster th the south-boud bot. If the southboud bot is trvelig t 7 mph, how log will it be before they re 40 miles prt? (You my use the tble below to help set up your equtio d solve the problem.) Equtio: Legth of time:

10 . Uiform Motio. (.7 #4) A 60-mile trip beg o freewy i cr trvelig t 6 mph. Oce the rod becme -le highwy, the cr slowed to 54 mph. If the totl trip took 6 hours, fid the time spet o ech type of rod. (You my use the tble below to help set up your equtio d solve the problem.) Equtio: Time spet o freewy: Time spet o -le highwy:. Uiform Motio. (.7 #45) Crol kows tht whe she jogs log her eighborhood greewy, she c complete the route i 0 miutes. It tkes 0 miutes to cover the sme distce whe she wlks. If her joggig rte is 4 mph fster th her wlkig rte, fid the speed t which she jogs. (You my use the tble below to help set up your equtio d solve the problem.) Equtio: Joggig speed:. Uiform Motio. (4.4 #7) Vess d Richie re ridig their bikes dow tril to the ext cmpgroud. Vess rides t 0 mph while Richie rides t 7 mph. Sice Vess is little speedier, she stys behid d cles up cmp for 0 miutes before levig. How log hs Richie bee ridig whe Vess is 7 miles hed of Richie? (You my use the tble below to help set up your equtio d solve the problem.) Equtio: Legth of time:

11 4. Uiform Motio. (4.4 #) Suppose tht Jose bikes ito the wid for 60 miles d it tkes him 6 hours. After log rest, he returs (with the wid t his bck) i 5 hours. Determie the speed t which Jose c ride his bike i still ir d determie the effect tht the wid hd o his speed. (You my use the tble below to help set up your system of equtios d solve the problem.) System of Equtios: Jose s speed: Wid speed: 5. Uiform Motio. (4.4 #9) With tilwid, smll Piper ircrft c fly 600 miles i hours. Agist this sme wid, the Piper c fly the sme distce i 4 hours. Fid the effect of the wid d the verge irspeed of the Piper. (You my use the tble below to help set up your system of equtios d solve the problem.) System of Equtios: Piper s speed: Wid speed: 6. Okld Bsebll. (4.4 #9) The ttedce t the gmes o two successive ights of Okld A s bsebll ws 44,000. The ttedce o Thursdy s gme ws 7000 more th two-thirds of the ttedce t Fridy ight s gme. How my people tteded the bsebll gme ech ight? Vribles d wht they represet: System of Equtios: Attedce o Thursdy: Attedce o Fridy: 7. Agles. (4.4 #7) The mesure of oe gle is 5 more th hlf the mesure of its complemet. Fid the mesures of the two gles. Vribles d wht they represet: System of Equtios: Mesure of oe gle: Mesure of the other gle:

12 8. Iterest. (4.5 #9) Hrry hs $0,000 to ivest. He ivests i two differet ccouts, oe expected to retur 5% d the other expected to retur 8%. If he wts to er $575 for the yer, how much should he ivest t ech rte? (You my use the tble below if you wish.) System of Equtios or Equtio: Amout ivested t 5%: Amout ivested t 8%: 9. Mixture. (4.5 #9) A lb techici eeds 60 ml of 50% slie solutio. How my ml of 0% slie solutio should she dd to 60% slie solutio to obti the required mixture? (You my use the tble below if you wish.) System of Equtios or Equtio: Qutity of 0% solutio: 0. Mixture. (4.5 #4) How my liters of 0% silver must be dded to 70 liters of 50% silver to mke lloy tht is 0% silver? You my use the tble below if you wish.) System of Equtios or Equtio: Qutity of 0% solutio:

13 . Are of Trigle. (6.7 #9) The sil o silbot is i the shpe of trigle. If the height of the sil is times the legth of the bse d the re is 54 squre feet, fid the dimesios of the sil. Equtio: Bse of sil: Height:. Pythgore Theorem. (6.7 #) Your big-scree TV mesures 50 iches o the digol. If the frot of the TV mesures 40 iches cross the bottom, fid the height of the TV. Equtio: Height of TV:. Are of Rectgle. (6.7 #) The legth of rectgle is mm more th twice the width. If the re is 00 squre mm, fid the dimesios of the rectgle. Equtio: Legth: Width: 4. Uiform Motio. (7.8 #75) While triig for iro m competitio, Toy bikes for 60 miles d rus for 5 miles. If his bikig speed is 8 times his ruig speed d it tkes 5 hours to complete the triig, how log did he sped o his bike? Equtio: Legth of time: 5. Uiform Motio. (7.8 #79) You hve 0-mile commute ito work. Sice you leve very erly, the trip goig to work is esier th the trip home. You c trvel to work i the sme time tht it tkes for you to mke it 6 miles o the trip bck home. Your verge speed comig home is 7 miles per hour slower th your verge speed goig to work. Wht is your verge speed goig to work? Equtio: Averge speed to work:

14 6. Uiform Motio. (7.8 #7) A bot c trvel km dow the river i the sme time it c go 4 km up the river. If the curret i the river is km per hour, how fst c the bot trvel i still wter? Equtio: Bot s speed: 7. Work. (7.8 #65) After hittig prctice for the Log Bech Stte volleybll tem, Dye c retrieve ll of the blls i the gym i 8 miutes. It tkes Mkii 6 miutes to retrieve ll the blls. If they work together, to the erest teth of miute, how log will it tke these two plyers to retur the volleyblls d be redy to strt the ext roud of hittig prctice? Equtio: Time together: 8. Work. (7.8 #69) It tkes ppretice twice s log s the experieced plumber to replce the pipes uder old house. If it tkes them 5 hours whe they work together, how log would it tke the ppretice loe? Equtio: Time for ppretice loe: 9. Work. (7.8 #7) Usig sigle hose, Jet c fill pool i 6 hours. The sme pool c be dried i 8 hours by opeig dripipe. If Jet forgets to close the dripipe, how log would it tke her to till the pool? Equtio: Time to fill pool: