MCT 4C Exam Review: 1. Simplify each of the following: a) b) c)

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1 MCT4C EamReview: A)EponentialandLogarithmicFunctions: 1. Simplifyeachofthefollowing: a) b) c) 2. Changetologarithmicform: a)4 =64 b)2048=2 +5. Changetoeponentialform: a)log 24=4 b)2 1=log Evaluate: a)log 2 2 b)log 2 2 c)log 270 log 10 d) 1 log5 e) log f)log 2 2 log 9 2 g) log 2 + log h)log 4 log 4 6+log 4 8 i) 2 log log16 5. Solvefor: a)5 2 =625 b) +2 =200 c)4(6) 5+ = Solvefor: a)log4+log=2 b)log 2 4+log 2 ( 2)=0 7. Describethetransformationsand a)f()=2 + 4 b)g()= 2( )+5 sketcheachfunction: 8. In2001,Jordanboughtanantiquesliderulefor$25.Itisestimatedthatthesliderulewillincreaseinvalueby%/year. a)findthevalueofthesliderulein2015. b)whenwillthesliderulebeworth$50? c)ifjordankeepstherulefor50years,howmuchwillithaveincreasedinvalue? 9. Asampleof500cellsinamedicalresearchlabdoublesevery20min. a)determineaformulaforthenumberofcellsattimet,wheretismeasuredinminutes. b)howlongwillittakeforthepopulationtoreach18000?answercorrectto2decimalplaces. 10.Anewcardepreciatesinvalueby4.5%everyyear.Whenwillthecarbeworthhalfitsoriginalvalue? 11.MostofCanada searthquakesoccuralongthewestcoast.in1949,therewasanearthquakeinthequeencharlotte Islandsthathadamagnitudeof8.1ontheRichterScale.In1997therewasanearthquakeinsouthwesternB.C.witha magnitudeof4.6ontherichterscale.howmanytimesmoreintensewasthe1949earthquake? 12.Theloudnesslevelofaheavysnoreis69dB.HowmanytimesmoreintenseIsasnorethanaconversationat60dB? 1.AliquidhasapHof4.5.Whatisthehydrogenionconcentration(mol/L)intheliquid? Answers: 1. a) y 48 b)mn 4 c)4 2.a)log 4 64= b)log =+5.a) 4 =24 b) = a)5 b)1/5 c) d) e)2/ f) g) h)1 i)2 5.a)2 b)2.82 c) a)25 b)9/4 8.a)7.81 b)2025 c)$84.60increase 9.a)n(t)=500(2) t/20 b)10.4min years mol/l

2 B)PolynomialFunctions: 1. Factoreachofthefollowingepressionsfully: a)5 2 y 15 4 y 2 b)t +6t 2 27t c)6m 2 m 2 d)625a 4 81b 4 2. Factoreachofthepolynomialsbelowanduseittofillinthechartanddrawasketchofthefunction: Function: intercepts: y intercept: As,y As,y Sketch: a)f()= (+1)( 1) b)g()= c)p()= a)findafamilyofcurvesequationofaquarticfunctionwithzeroesat 2and0. b)findaspecificequationforafunctionthatistangenttothe aisat 1,and f() 0 for 2 4. Findtheequationthatmodelsthegraphbelow: a) b) 5. Theareaofarectangleisgivenbytheepression Findtheperimeteroftherectangle.

3 C)PolynomialEquations: 1. Solveeachofthefollowingequations: a) =0 b)6a 5a 2 6a=0 c)12t 2 = 5t 2. Thebaseofatriangleis4cmmorethan2timesitsheight.Findthedimensionsofthetriangleifitsareais5cm 2.. Thevolumeofastoragechestismodeledbytheepression a)findthedimensionsofthebo. b)findthevolumeoftheboifthesmallestdimensionis12cm. 4. ThepopulationofatownismodeledbythefunctionP(t)=t 4 5t +80t+15000,wheretisthetimeinyearsfromthe presenttimeandpisthepopulation. a)whattypeoffunctionisp(t)? b)whichfinitedifferencesareconstantforthispolynomialfunction? c)whatisthecurrentpopulationofthetown? d)whatwillthepopulationbein8years? 5. Avideogamecompanycansell1500videogamesforapriceof$45each.Researchsuggeststhatforevery$5increase inprice,thecompanywillsell100lessgames. a)whatpricewillmaimizethecompany srevenue? b)whatisthemaimumrevenue? 6. Apieceofcardboard0cm20cmisusedtomakeabobycuttingoutasquareofequaldimensionsfromeachcorner. Findthesimplifiedepressionthatrepresentsthevolumeofthebo. D)TrigonometryofTriangles: 1. Drawthetwospecialtriangles. 2. DescribewhentouseSOHCAHTOA,SineLawandCosineLaw.. Solveforineachofthefollowing: Triangle: Answer: Triangle: Answer: o

4 5. Determinethenumberoftrianglesthatcanbecreatedundereachofthefollowingrestrictions: a)a=55 o,a=12,b=9 b)a=40 o,a=7m,b=10m c)p=72 o,p=5.5cm,q=6cm 6.Findtheheightofthegiventower: 7. Findtheperimeterofapentagonthatisinscribedinsideacircleof25cm. 8. Findtheperimeterandareaofthegiventriangle.Becareful! ># =# &9M! KLM! 9. Mattisrepairingthewiringonaradiobroadcasttower.Heisinthebasketofarepairtruck40mfromthetower.Hecan seethetopofthetoweratanangleofelevationof42 o.hecanseethebaseofthetowerifhelooksdownatanangleof 2 o. a)drawadiagramtorepresentthissituation. b)howhighisthetower? E)TrigonometricFunctionsandPeriodicMotion: 1. Fillinthechartbelowforeachofthefollowingangles: Sketch: StandardAngle: RAA: Principle Angle: Positive Co terminal: Negative Co terminal: a) 140 o b) 50 c) 520 o d) 800 o 2. UsingSpecialAngleTrianglesandthegraphsofthesineandcosinefunctions,findtheeactvalue: a)cos45 o b)tan0 o c)sin60 o d)cos180 o e)sin 90 o. UsetheCASTRuleandSpecialAngleTrianglestofindtheeactvalueof: a)sin15 o b)cos15 o c)tan210 o d)tan( 210 o ) e)cos( 0 o )

5 4. Solveforallvaluesofthetainthedomain foreachofthefollowing: a) tanθ = 0.76 b) cosθ = c) sinθ = 2 d) tanθ = 1 5.Completethechartbelow: Function Amplitude Period PhaseShift (withdirection) AisofFunction (Asanequation) Maimum Minimum a) y = 2 cos(θ ) +1 ( ) b) 1 y = sin 2 θ 90o 4 6.Usethechartabovetosketchthegraphforeachequationbelow: a) y = 2 cos(θ ) +1 b) 1 y = sin 2 θ ( 90o) 4 4 y 2 1!1!2!!4 7.Determinethefunctionforthefollowingusingthegivensinusoidalfunction: a)period120 o,amplitude2andma(0 0,1)giveny=sin b)themaimumisandtheminimumis.theperiodis180 o andthegraphbeginsat(0,0)giveng()=cos 8. Findtheequationthatbestmodelseachgraphbelow: 4 y 2 1!1!2!!4 a) b) 9. AFerriswheelhasadiameterof18mandalowestpointat2mabovetheground.CatherineboardstheFerriswheelat thebottomandfindsthatshereachesthetopoftheferriswheel16secondslater. a)findtheequationthatmodelscatherine sheightontheferriswheel. b)findcatherine sheightafter2minutesontheride.

6 F)Vectors 1. Forthegivendiagram,findavectorequivalentto a) AB b) DF c) AE + AC d) BE + CD e) CH CG f) GF CB g) BD + CG + FA h) AG DH FD 2. Forthegivendiagram,findavectorequivalentto a) AD + AH b) BC + FH c) CH DB d) HB CD. Findthehorizontalandverticalcomponentsofavectorwitheachgivenmagnitudeandbearing: a) m = 20N,[N40 o W] b) m = 5.8N,[220 o ] c) m = 100N,[S o E] 4. A0kgmassisonarampinclinedat5 o. a)whatistheforceofgravityactinguponthemass? b)findthehorizontalandverticalforcesacting uponthemass. 5. TwoATV sareusedtopullacrate.ropesareattachedtothecratesoftheatvasshown.findthemagnitude anddirectionoftheresultantforce. %,06)(1+#0 6. Aplanetravelsat200km/honaheadingof[S0 o W].Findtheresultantvelocityoftheplaneasitfliesintoa windwithavelocityof50km/h[s70 o E]. 7. Aboattravelsonaheadingofnorthwestat10km/h.Becauseofthecurrent,theboatisactuallytravellingat 8km/h[N0 o W].Findthehorizontalandverticalcomponentsofthecurrent.

7 G)GeometryandMeasurement Length Area Mass Capacity Volume 1in=2.54cm 1ft=0.048m 1yd=0.9144m 1mile=1.609km 1in 2 =6.45cm 2 1ft 2 =0.0929m 2 1yd 2 =0.84m 2 Iacre=4047m 2 1oz=28.6g 1lb=0.454kg 1T=0.91t 1floz=29.6m 1qt=0.947L 1gal=4.546L 1in =16.9cm 1ft =0.028m 1. Findtheareaandperimeterofthedeckdesignedattheright, a)infeet b)inmetres 2. Acubeandaspherebothhaveasurfaceareaof400cm 2.Whatarethevolumesof eachshape?. Agolfballhasadiameterof4.cm.Howmuchemptyspaceisthere,ininches,inacylindricalcanthatfits eactly4golfballs? 4. Describethedifferencebetweeneachsetofterms: a)secantandtangent b)secantandchord c)arcandsector e)sectorandsegment 5. a)acirclewitharadiusof12incheshasanarclengthof2feet.whatisthecentralangleofthearc? b)thecentralangleofasectoris200 o.findtheradiusofthecircleiftheareaofthesectoris40cm Thedistancefromthecentreofacircletoapointoutsidethecircleis0cm.Thelengthofthetangentdrawn fromthispointtothecircleis20cm.whatistheradiusofthecircle? 7. a)findtheareaofthesectorboundbychordsacandbc. b)findtheareaofthesegmentbelowchordab. %K#4C# ####?# <<;=# %K#4C# #=# #####>#

8 MCT4C EamReview Answers: A)EponentialandLogarithmicFunctions: 1. a) y 48 b)mn 4 c)4 2.a)log 4 64= b)log =+5.a) 4 =24 b) = a)5 b)1/5 c) d) e)2/ f) g) h)1 i)2 5.a)2 b)2.82 c) a)25 b)9/4 8.a)7.81 b)2025 c)$84.60increase 9.a)n(t)=500(2) t/20 b)10.4min years mol/l B)PolynomialFunctions: 1. a)5 2 y 2 (y 2 ) b)t(t+9)(t ) c)(2m+1)(m 2) d)(25a 2 +9b 2 )(5a+b)(5a b) 2. a)f()= (+1)( 1),1& 1,,, b)g()= 2 ( 2)( ),0&2&,0,, c)p()= ( 1)( 2),0&1&2,0,,. a)various b)various(f()=a(+1) 2 ( 2),a<0 4.a)f()= 1/12( 2) (+1) 2 (+) 2 b)f()= 1/8( 1)(+1) (+4) C)PolynomialEquations: 1. a) 2, 5 b)/2, 2/,0 c)1/, /4 2.b=14cm,h=5cm a),+2,+ b)2520cm 4. a)quartic b)4 th c)15000 d) a)$60 b)$ (0 2)(20 2) D)TrigonometryofTriangles:. i)9.66 ii)17.46 o iii)44.68 iv) o 5.a)1 b)2 c) m P=96.14,A=41.44cm m E)TrigonometricFunctionsandPeriodicMotion: 1.a)40,140,500, 220 b)50,10,10, 410 c)20,160,880, 200 d)80,280,280, a) 1 b) 1 c) b) c) 1 2 d) 1 e) 2 4.a)20.61 o, o b) o, o c)240 o,00 o d)15 o,15 o 5. a)2,60 o, 90 o (Left),y=1,, 1 b)¼,180 o,90 o (right),y=0,¼, ¼ 7. a)y=2sin() 1 b)g()=cos2( 45 o ) 8.a)f()= 2.5cos½+2.5 b)h(t)=2cos6t+1 9. a)h(t)= 9cos(11.25t)+11 b)11m

9 F)Vectors: 1.a) CD,GH,EF b) FD,EC c) AG,BH d) BF,DH e) CD,AB f) 0 g) BC,FGh) AE 2.a) AE b) GH,DC c) CF d) FC.a)12.86N[W],15.2N[N] b).72n[w],4.44n[s] c)5.2n[e],99.86n[s] 4.a)294N b)292.88n[horiz.],25.6n[vert.] N,[65.2 o ] km/h[S15.57 o W] km/h[S],.07km/h[E] G)GeometryandMeasurement: 1.a)P=26.61ft,A=45ft 2 b)p=8.11m,a=4.18m 2 2.Volume=54.4cm,Sphere=751.49cm.8.26cm,5.08in 4.a)Secantintersectsattwopoints,whiletangentsintersectsatone b)endpointsofachordlieonthecircle,whilethesecantintersectsandetendsthroughthecircle. c)anarcisaportionofthecircumferenceofacirclewhileasectorisaportionoftheareaofacircle. d)sectoristheareaofacirclesubtendedbyacentralangle,whileasegmentisaportionofthatareasubtended byachord. 5.a) o b)4.79cm cm 7.a)188.15cm 2 b)96.05cm 2

Parts Manual. EPIC II Critical Care Bed REF 2031

Parts Manual. EPIC II Critical Care Bed REF 2031 EPIC II Critical Care Bed REF 2031 Parts Manual For parts or technical assistance call: USA: 1-800-327-0770 2013/05 B.0 2031-109-006 REV B www.stryker.com Table of Contents English Product Labels... 4