GuidetoUsingtheTi-nspire
Solve,Factor&Expand
Thesearethebasicfunctionsyouwillneedtoknow.
OpenCalculate(A)
Solve:[Menu][3][1]–(equation,variable)|Domain
Factor:[Menu][3][2]–(terms)
Expand:[Menu][3][3]–(terms)
Matrices
Matricescanbeusedasaneasywaytosolvethe‘findthevaluesofmforwhichthereiszeroorinfinitely
manysolutions’questions.Whentheequationsax+by=canddx+ey=fareexpressedasamatrix
,lettingthedeterminantequalto0willallowyoutosolveform.
E.g.Findthevaluesofmforwhichthereisnosolutionsorinfinitelymanysolutionsfortheequations
2x+3y=4andmx+y=1
Determinant:[Menu][7][3]Enterinmatrixrepresentingthecoefficients,solvefordet()=0.
Remembertoplugbackinto
differentiatebetweenthesolutionsfor
nosolutionsandinfinitelymany
solutions.
ModulusFunctions
Whilebeingwrittenas||onpaper,thefunctionforthemodulusfunctionisabs()(orabsolutefunction).
i.e.justaddinabs(function)
DefiningDomains
Whilegraphingorsolving,domainscanbedefinedbytheadditionof|lowerbound<x<upperbound
Thelessthanorequaltoandgreaterthanorequaltosignscanbeobtainedbypressingctrl+<or>
Thisisparticularyusefulforfogandgoffunctions,whenadomainisrestriced,theresultingfunction’s
domainwillalsoberestricted.
2.Openagraphpageandtype,f(g(x))intothegraphbar
Thetracefeaturecanbeusedtofindouttherangeanddomain.Trace:[Menu][5][1]
CompletingtheSquare
Theeasywaytofindtheturningpointquickly.TheTi-nspirehasabuiltinfunctionforcompletingthesquare.
[Menu][3][5]-(function,variable)
e.g.Findtheturningpointof
Sofromthattheturningpointwillbeat(-2,1)
EasyMaximumandMinimums
InthenewerversionoftheTi-nspireOS,therearefunctionstofindmaximum,minimums,tangentlinesand
normallineswithacoupleofclicks,goodformultiplechoice,otherwiseworkingwouldneedtobeshown.
Youcandosomeofthesevisuallyonthegraphingscreenoralgebraicallyinthecalculatewindow.
Maximums:[Menu][4][7]–(terms,variable)|domain
Minimums:[Menu][4][8]–(terms,variable)|domain
Tangentsatapoint:[Menu][4][9]–(terms,variable,point)
Normalsatapoint:[Menu][4][A]-(terms,variable,point)
FindingVerticalAsymptotes
VerticalAsymptotesoccurwhenthefunctionisundefinedatagivenvalueofx,i.e.whenanythingisdivided
by0.Wecanmanipulatethisfacttofindverticalasymptotesbylettingthefunctionequalandsolvingfor
x.
Thex-yFunctionTest
Everynowandthenyouwillcomeacrossthiskindofquestioninamultiplechoice
section.
Youcoulddoitbyhandordoitbycalculator.Theeasiestwayistodefinethefunctionsandsolvethe
conditionforx,thentestwhethertheoptionistrue.Iftrueisgiven,itistrueotherwiseitisfalse.
SooptionBiscorrect.
TheTimeSaverforDerivatives
Thesamethingcanbedoneforthedoublederivative.
Justremembertoredefinetheequationsoruseadifferentletter,e.g.g(x)anddg(x)
SolvingForCoefficientsUsingDefinitionsofFunctions
DerivingUsingtheRightMode
RADIANMODE
DEGREESMODE
GettingExactValuesOntheGraphScreen
UsingtCollecttosimplifyawkwardexpressions
Sometimesthecalculatorwon’tsimplifysomethingthewaywewantitto.tCollectsimplifiesexpressions
thatinvolvestrigonometricpowershigherthan1orlowerthan-1tolineartrigonometricexpressions.
StreamlinedMarkovChains
BinomialDistributions
Forasinglevalueofxe.g.Pr(X=2)=[Menu][5][5][D](Pdf)
Formultiplevaluesofxe.g.Pr(X<2)=[Menu][5][5][E](Cdf)
e.g.ProbabilityofSuccess=0.4,Numberoftrials=10,i.e.X~Bi(10,0.4)
Findtheprobabilityoftwosuccessesandlessthantwosuccesses
Pr(X=2)=0.1209,Pr(X<2)=0.0464
NormalDistributions
Pr(X<1)=0.2420,Pr(0<X<1)=0.3413
Integrals
ShortcutKeys
Copy:Ctrlleftorrighttohighlight,[Ctrl]+[c]
Paste:[Ctrl]+[v]
InsertDerivative:[CAPS]+[-]
InsertIntegral:[CAPS]+[+]
UsingTiInspirewithVectors.
Vectorsmayalsobeenteredascolumnvectorsratherthanrow
vectors.(i.e.onerowfori,onerowforjandonerowforkif
needed.)Usingcolumnsispreferred.
Trytheseusingyourcalculator:
Definevectorsa=3i+2j+4kandb=-3i+5j+2kusing2column
vectors.
1.Finda.b
Ans:9
2.Findaunitvectorinthedirectionofa
Ans:√29/29(3i+2j+4k)
3.Findtheanglebetweenaandb
Ans:1.296radians
Nowtrythis:
Ifr(m,n)=cos(m)sin(n)i +sin(m)cos(n)j
Definer(m,n)usinga2by1matrix.
1.Evaluater(π/4,π/3)
Ans:¼(√6i+√2j)
Youmaywishtostoreanswersusingsomeothervariableifthe
problemlookslikeyouaregoingtoneedtheseresultsagain.
Don’tforgettoclearvariablesa-zusingMenu1-4ifnecessary.