Transcription of Recurrence Rel. Past Papers Unit 1 Outcome 4 - …
1 Outcome4 MultipleChoiceQuestionsEachcorrectanswer inthissectionis de nedbytherecurrencerelationun+1=14un+8wit hu0= de nedbytherecurrencerelationun+1=25un+6wit hu0= thelimitofthesequence? 225D. 30[ENDOFMULTIPLECHOICEQUESTIONS]WrittenQ uestions3.[SQA]PSfragreplacementsOxy4.[S QA]Asequenceis de nedbytherecurrencerelationun=0 9un 1+2 ,u1=3 .(a) (b) Whatis thesmallestvalueofnforwhichun>10?1(c) Findthelimitofthissequenceasn! .25.[SQA]Asequenceis de nedbytherecurrencerelationun+1=0 3un+5 with rsttermu1.(a) Explainwhythissequencehasa limitasntendstoin (b) PSfragreplacementsOxyPage 1 Questionsmarked `[SQA]'c SQAAll othersc HigherStill NotesHigherMathematicsPSfragreplacements Oxy6.[SQA]Twosequencesare generatedbytherecurrencerelationsun+1=au n+10andvn+1=a2vn+ ! . [SQA]PSfragreplacementsOxy8.[SQA]PSfragr eplacementsOxy9.[SQA] PSfragreplacementsOxyPage2 Questionsmarked `[SQA]'c SQAA llothersc HigherStillNotesHigherMathematicsPSfragr eplacementsOxy10.
2 [SQA]PSfragreplacementsOxy11.[SQA] PSfragreplacementsOxyPage3 Questionsmarked `[SQA]'c SQAA llothersc HigherStillNotesHigherMathematicsPSfragr eplacementsOxy12.[SQA]PSfragreplacements Oxy13.[SQA] PSfragreplacementsOxyPage4 Questionsmarked `[SQA]'c SQAA llothersc HigherStillNotesHigherMathematicsPSfragr eplacementsOxy14.[SQA]PSfragreplacements Oxy15.[SQA]Onthe rstdayofMarch,a bankloansa man 2500ata 300exceptforthesmaller nalamountwhichwillpayoff theloan.(a) Theamountthatheowesatthestartofeachmonth is + recurrencerelationinvolvingun+ (b) Findthedateandtheamountofthe PSfragreplacementsOxyPage5 Questionsmarked `[SQA]'c SQAA llothersc HigherStillNotesHigherMathematicsPSfragr eplacementsOxy16.[SQA]Amandecidestoplant a numberoffast-growingtreesasa boundarybetweenhispropertyandtheproperty ofhisnextdoorneighbour. Hehasbeenwarned,however, bythelocalgardencentre that,duringanyyear, thetreesare expectedtoincreaseinheightby0 5 theheightofthetreesatthestartofanyyear.
3 (a) If headoptsthe 20%pruningpolicy ,towhatheightwillheexpectthetreestogrowi nthelongrun?3(b) Hisneighbouris concernedthatthetreesare growingatanalarmingrateandwantsassurance sthatthetreeswillgrownotallerthan2 [SQA] PSfragreplacementsOxyPage6 Questionsmarked `[SQA]'c SQAA llothersc HigherStillNotesHigherMathematicsPSfragr eplacementsOxy18.[SQA]PSfragreplacements Oxy[ENDOFWRITTENQUESTIONS] PSfragreplacementsOxyPage7 Questionsmarked `[SQA]'c SQAA llothersc HigherStillNotes
