Complex Math - Math practice questions PDF

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Complex/DorisTurnerMedMathQuestions   1. Problemtype:IVinfusionrate+infusionpump Medication:azithromycin  PROBLEM  SupposeMrs.Turner’sorderscallfor500mgofazithromycintobeadministered intravenouslyforcommunityacquiredpneumonia.Thesolutionhasbeendilutedtoa concentrationof2mg/mLandneedstobeadministeredover1hour.  Atwhatrateshouldtheinfusionpumpbeset?  HINT  Startbyfiguringouthowmanymilliliterswillbeneededtoadministertheordereddose.  SAMPLESOLUTION  1. Determinehowmanymillilitersoftheconcentrationwillbedeliveredtoadminister theordereddose.  500mg x1mL=250mL  2mg  2. DividethetotalnumberofmLneededtodeliverthe500mgbytheexpected durationof1hour.  250mL=250mL/hr  1hr  ANSWER  Number:250 Units/Rate:mL/hr  

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2. Problemtype:Dosagecalculation+Stockonhand Medication:venlafaxine   PROBLEM  Mrs.Turner’sdailymedicationsincludevenlafaxineextendedrelease,150mg,by mouth,onceaday.However,thehospitalpharmacyonlycarries75mg extendedreleasetablets.  Howmanytabletsofvenlafaxineextendedreleaseshouldbeadministeredtoher?  HINT  Youcanusetheequationbelow,whereXisthenumberoftabletsthatshouldbe administered.  D(ordereddose)xQuantity=X  H(doseonhand)  SAMPLESOLUTION  1.Determinewhatinformationyouhave. D(ordereddose)=150mg H(doseonhand)=75mg Q(quantity)=1tablet

 2.Plugintotheequationandsolve.  D(150mg)x1tablet=X  H(75mg)  X=2tablets  ANSWER  Number:2 Units:tablets   

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 3.Problemtype:Totaldailydosage Medication:Acetaminophen@hospital   hypothetical    SupposeMrs.Turner’sproviderupdatedherorderfor325mg,2tabs,bymouthq6h PRNtemp.>100.5Fto325mg,2tabs,bymouthq4hPRNtemp.>100.5F.The  Davis’sDrugGuidereportsthatacetaminophenhasamaximumrecommendeddosage  of4g/day.  HowmanydosescanMrs.Turnertakewithoutexceedingtherecommendedmaximum dosage?   HINT  Thereare1000mginonegram.   SAMPLESOLUTION  1.Determinehowmanymilligramsarein4grams.  4gx1000mg=4000mg   1g  2.Determinehowmany325mgtabletsgointo4000mg. 4000mgx1tablet=12.3tablets     325mg  3.Rounddowntothenearestwholetablet=12tablets  4.Dividethetotalnumberoftabletsbythenumbertabletsinadose.  12tabletstotalx1dose=6doses   2tablets   ANSWER  Number:6 Units:doses 

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4.Problemtype:Totaldailydosecalculation Medication:acetaminophen@hospital  PROBLEM  SupposeMrs.Turner’scurrenttemperatureis100.8F.Fortemperaturesgreaterthan100.5 F,theprescriber’sorderallowsacetaminophen,325mg,2tabs,bymouth,every6hours. Assumethatonherfirstdayofhospitalization,Mrs.Turner’stemperatureisgreaterthan 100.5Fthreetimes.  Howmanygramsofacetaminophenwillshehaveingestedonherfirstdayof hospitalization?Roundyouranswertohundredths.  HINT  Multiplythenumberoftakendosesbythenumberoftablets.  SAMPLESOLUTION  1.Multiplythenumberofdosestakenbythenumberoftabletsperdose.  3dosesx2tablets=6tablets   1dose  2.Multiplythedosageofacetaminophenbythenumberoftablets.    6tabletsx325mg=1950mg   1tablet  3.Convertthetotaldailymilligramstograms.  1950mgx1g=1.95g   1000mg   ANSWER  Number:1.95 Units:g  

5.Problemtype:Dosagecalculation+Stockonhand  Medication:potassiumchloride  PROBLEM  Mrs.Turner’sdailymedicationsincludepotassiumchloride,10mEqtabletbymouth oncedaily.Thehospitalpharmacywilldispensepotassiumchlorideliquid10%(1.5gram or20mEqper15mL).TheKClliquidwillbefurtherdilutedina6ozglassofwateror juiceforadministration.  WhatvolumeoftheKCl10%liquidshouldbeusedforMrs.Turner’susualdailydose?  HINT  Multiplythedesireddosebytheconcentration.  SAMPLESOLUTION   1.Multiplythedesireddosebytheconcentration.  10mEqx15mL=7.5mLofKCl10%liquid      day20mEqday   ANSWER  Number:7.5 Units:mL/day   

6.Problemtype:IVflow+allergicreaction   hypothetical Medication:ceftriaxone   PROBLEM  Mrs.Turner’soriginalorderscalledforceftriaxone,1g,tobeadministeredintravenously daily.Thesolutionhasbeendilutedtoaconcentrationof1g/50mLtobeadministered over30minutes.Twentyminutesintothefirstinfusion,Mrs.Turnerreportsanadverse reactiontotheantibioticandtheinfusionisstopped.  HowmanymLofconcentrationwereadministeredbeforetheinfusionwasstopped? Roundyouranswertothenearestwholenumber.   HINT  Dividethetimeelapsedbytheinfusionratetodeterminethecompletionpercentageof theinfusion.   SAMPLESOLUTION   1.Determinethecompletionpercentageoftheinfusion.  20min(timeelapsed)=0.667(or66.7%)  30min(totalinfusiontime)  2.Multiplytheinfusionvolumebythepercentage.  50mLx0.667=X  X=33mL  ANSWER  Number:33 Units:mL  

7.Problemtype:Dosagecalculation+weightbaseddosage  Medication:azithromycin@hospitalhypothetical  AccordingtotheDavis’sDrugGuide,childrensixmonthsoldoryoungerwith communityacquiredpneumoniacanbeadministeredazithromycinorallyusinga weightbaseddosage.Childreninthisagegroupcanreceive10mg/kgonthefirstday, then5mg/kgforfourmoredays.Assumeyouneedtoadministerthistoachildweighing 20.3lbs.  Whatisthetotaldoseofazithromycinthechildwillreceiveoverfivedays?Round youranswertothenearestwholenumber.  HINT  Convertpoundstokilograms,andmultiplytheweightbythedosage.  SAMPLESOLUTION  1.Convertpounds(lbs)tokilograms(kg).  20.3lbsx1kg=9.227kg   2.20lb  2.Multiplythefirstday’sdosagebyweightinkg.  10mgx9.227kg=92.27mg  kg  3.Multiplythedosagegivenfordays25byweightinkg,andmultiplybythenumberof daysadministered(4).  9.227kgx5mgx4=184.54mg    kg  4.Addtheresultsfromsteps2and3.  92.27mg+184.54mg=276.81mg,roundedto277mg  ANSWER  Number:277mg  Units:mg 

 8.Problemtype:Unitconversation+stockonhand Medication:levothyroxine@hospital  Mrs.Turner’sorderscalledfor50mcgoflevothyroxine,bymouth,daily.Thepharmacy stocksthemedicationin0.025mgtablets.  Howmanytabletsareneededtoadministertheordereddose?  HINT  Startbyconverting50mcgtomg.Thenusetheequationbelow,whereXisthenumber oftabletsthatshouldbeadministered.  D(ordereddose)xQuantity=X  H(doseonhand)  SAMPLESOLUTION  1.Convertmicrograms(mcg)tomilligrams(mg).  50mcgx1mg=0.05mg   1000mcg  2.Determinewhatinformationyouhave.  D=0.05mg H=0.025mg Q=1tablet  3.Plugintotheequationandsolve.  D(0.05mg)x1tablet=X  H(0.025mg)  X=2tablets  ANSWER  Number:2  Units:tablets  

9.Problemtype:Totaldailydosecalculation Medication:Unitsofinsulin@home  Athome,Mrs.Turnertakes16unitsofinsulinaspart,twiceadaywithmeals.Shealso takes45unitsoflongactinginsulinglargine,daily.  HowmanytotalunitsofinsulindoesMrs.Turnertakedaily?   HINT  StartbymultiplyingthedosageofinsulinaspartbyhowoftenMrs.Turnertakesit.  SAMPLESOLUTION  1.Multiplythedosagebythenumberofunitsperdose.    16unitsx2=32units    2.Addthetotalnumberofinsulinaspartunitsandthetotalnumberofinsulinglargine units.  32units+45units=77units    ANSWER  Number:77 Units:units  

10.Problemtype:Dosagecalculation  hypothetical Medication:Insulinaspart@hospital   Theproviderorderedinsulinaspartonaslidingscalefor1unit/10gCHOsubcutaneous +1unit/50pointsabove150BG.Mrs.Turnerwilleatamealthatcontains40gCHOand hasapremealBGlevelof160.  Howmanyunitsofinsulinshouldbeadministered?  HINT  Addtheunitscalculatedfromtheslidingscaletotheunitsnecessaryforthepatient’s currentBGlevel.  SAMPLESOLUTION  1.Performtheslidingscalecalculation(1unit/10gCHO).  40gCHOx1unit =4units  10gCHO   2.Subtract150fromMrs.Turner’spremealBG.  160BG150BG=10points  3.Multiply10pointsbythenumberofunitsper50points.  10pointsx1unit =0.2units   50points   Rounddowntothenextwholeunit=0unit  4.Addtheunitsfromtheslidingscaletotheadditionalunitsneededforevery50points above150BG.  4units+0unit=4units   ANSWER  Number:4 Units:units

11.Problemtype:Unitconversion+orderscorrection  hypothetical Medication:levothyroxine@hospital   SupposeMrs.Turner’sproviderwritesarevisedorderof25mgofherdaily levothyroxine.Giventhatheroriginalorderwasinmicrograms,yoususpectthisnew ordercontainsanerror.Youtaketheappropriatemeasurestogettheorderscorrected inordertoavoidadministeringanoverdose.  Iftheerrorhadnotbeencaught,howmanytimesmorelevothyroxinewouldhavebeen given?  HINT  Startbyconverting25mgtomicrograms.  SAMPLESOLUTION  1.Convertmilligrams(mg)tomicrograms(mcg).  25mgx1000mcg=25,000mcg   1mg  2.Dividetheincorrectmcgdosagebycorrectmcgdosage.   25,000mcg=1000  25mcg   ANSWER  Number:1000 Units:timesoverdose  

12.Problemtype:IVflowrate+dropfactor  hypothetical Medication:azithromycin@hospital   SupposeMrs.Turner’sproviderorders500mgofazithromycintobedeliveredina250 mLIVsolutionover3hours.ThedosewillbedeliveredusingIVtubingwithadropfactor of15(15gtt(drops)=1mL)  WhatistheappropriaterateofflowfortheIV,indropsperminute?Roundyour answertothenearestwholenumber.  HINT  StartbydetermininghowmanymLwillbedeliveredperminute.   SAMPLESOLUTION  1.DividethetotalnumberofmLneededtodeliverthe500mgdilutionbytheexpected durationinminutes,convertinghourstominutes.  250mLx1hr   = 1.389mL/min 3hr60min    2.MultiplythemL/minbythedropfactorandroundtothenearestwholenumber.  1.389mLx15gtt=20.8gtt/min     1min 1mL  3.Roundyouranswertothenearestwholenumber.  =21gtt/min  ANSWER  Number:21 Units:gtt/min  

13.Problemtype:IVflowrate+dropfactor   hypothetical Medication:azithromycin@hospital   Ontheseconddayofhospitalization,Mrs.Turner’sorderscallfor500mgof azithromycintobedeliveredina250mLIVsolutionover3hours.Thedosewillbe deliveredusingIVtubingwithadropfactorof10(10gtt(drops)=1mL).  WhatistheappropriaterateofflowfortheIVindropsperminute?Roundyour answertothenearestwholenumber.  HINT  StartbydetermininghowmanymLwillbedeliveredperminute.   SAMPLESOLUTION  1.DividethetotalnumberofmLneededtodeliverthe500mgdilutionbytheexpected duration,convertinghourstominutes.  250mLx  1hr =1.389mL/min 3hr 60min  2.MultiplythemL/minbythedropfactorandroundtothenearestwholenumber.  1.389mLx10gtt=13.89gtt/min     1min 1mL  Roundyouranswertothenearestwholenumber=14gtt/min   ANSWER  Number:14 Units:gtt/min  

14.Problemtype:Correctdays’supply  Medication:Insulin@primarycarehypothetical   Mrs.Turnerisprescribedinsulinaspart,16units,SCTIDatmealtimes.WhenMrs. Turnerreturnshome,theproviderwouldliketoswitchhermealtimeinsulin  administrationtoapendeliverydeviceinsteadofinsulinsyringes.Theproviderwillkeep thesamedose.AssumethatMrs.Turnereatsthreemealsaday.  Ifthepencartridgescontain3mLofU100insulinaspart,howoftenwillDorisneedto replacethecartridge?Roundyouranswerdowntothenearestwholeday.  HINT  U100insulincontains100units/1mL.   SAMPLESOLUTION   1. Multiplythenumberofunitsbythenumberofmealseachday.  16unitsx3meals=48unitsofinsulinaspart      mealdayday  2.MultiplytheconcentrationofU100insulinbythevolumeofacartridge.  100unitsx3mL=300units     mLcartridgecartridge  3.Multiplytheresultfromstep2bythenumberofunitsperday,sothattheunitscancel.  300unitsx1day=6.25days/cartridge,roundedto6days    cartridge48units   ANSWER  Number:6 Units:days     

15.Problemtype:Correctdays’supply  Medication:Insulin@primarycarehypothetical    AssumethatMrs.Turner’sproviderdecidestoprescribeinsulinaspart,16unitsSCTID atmealtimes,andMrs.TurnerreceivesaU100,10mLvialofinsulinaspart.Assume  thatMrs.Turnereatsthreemealsaday.  HowlongwouldaU100,10mLvialofinsulinaspartlastatthisdosage?Roundyour downanswertothenearestwholeday.  HINT  U100insulincontains100units/1mL.  SAMPLESOLUTION  1.Multiplythenumberofunitsbythenumberofmealseachday.   16unitsx3meals=48unitsofinsulinaspart      mealdayday   2.MultiplytheconcentrationofU100insulinbythevolumeofthevial.  100unitsx10mL=1000units     1mLvialvial  3.Multiplytheresultfromstep2bythenumberofunitsperday,sothattheunitscancel.  1000unitsx1day=20.8days/vial,roundeddownto20days    Vial48units   ANSWER  Number:20 Units:days...