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### Transcript of MATHEMATICAL METHODS (CAS) Methods (CAS) Formulas Mensuration area of a trapezium: 1 2 ()ab+ h...

• MATHEMATICAL METHODS (CAS)Written examination 1

Wednesday 4 November 2015 Reading time: 9.00 am to 9.15 am (15 minutes) Writing time: 9.15 am to 10.15 am (1 hour)

QUESTION AND ANSWER BOOK

Structure of bookNumber of questions

Number of questions to be answered

Number of marks

10 10 40

Studentsarepermittedtobringintotheexaminationroom:pens,pencils,highlighters,erasers,sharpeners,rulers.

StudentsareNOTpermittedtobringintotheexaminationroom:notesofanykind,blanksheetsofpaper,correctionfluid/tapeoracalculatorofanytype.

centrefold. Workingspaceisprovidedthroughoutthebook.

Instructions Detachtheformulasheetfromthecentreofthisbookduringreadingtime. Writeyourstudent numberinthespaceprovidedaboveonthispage.

AllwrittenresponsesmustbeinEnglish.

Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic devices into the examination room.

VICTORIANCURRICULUMANDASSESSMENTAUTHORITY2015

SUPERVISOR TO ATTACH PROCESSING LABEL HEREVictorian Certificate of Education 2015

STUDENT NUMBER

Letter

• 2015MATHMETH(CAS)EXAM1 2

• 3 2015MATHMETH(CAS)EXAM1

TURN OVER

Question 1 (4marks)a. Lety=(5x+1)7.

Find dydx. 1mark

b. Let f x xxe( ) log ( ) .= 2

i. Findf(x). 2marks

ii. Evaluatef(1). 1mark

• 2015MATHMETH(CAS)EXAM1 4

Question 2 (3marks)

Let = f xx

( ) ,1 3 wherex0.

Giventhatf (e)=2,find f (x).

• 5 2015MATHMETH(CAS)EXAM1

TURN OVER

Question 3 (2marks)

Evaluate 11

4

xdx

.

• 2015MATHMETH(CAS)EXAM1 6

Question 4continued

Question 4 (6marks)Considerthefunction f R f x x x: , , ( ) .[ ] = + ( )3 2 12 3 4

3 2

a. Findthecoordinatesofthestationarypointsofthefunction. 2marks

• 7 2015MATHMETH(CAS)EXAM1

TURN OVER

Theruleforfcanalsobeexpressedas f x x x( ) .= ( ) +( )12

1 2 2

b. Ontheaxesbelow,sketchthegraphoff, clearlyindicatingaxisinterceptsandturningpoints. Labeltheendpointswiththeircoordinates. 2marks

y

x8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8

87654321

1

O

2345678

c. Findtheaveragevalueoffovertheinterval0x2. 2marks

• 2015 MATHMETH (CAS) EXAM 1 8

Question 5 (3 marks)On any given day, the depth of water in a river is modelled by the function

h t t t( ) sin ,= +

14 8 12

0 24

where h is the depth of water, in metres, and t is the time, in hours, after 6 am.

a. Find the minimum depth of the water in the river. 1 mark

b. Find the values of t for which h(t) = 10. 2 marks

• 9 2015MATHMETH(CAS)EXAM1

TURN OVER

Question 6 (3marks)LettherandomvariableXbenormallydistributedwithmean2.5andstandarddeviation0.3LetZbethestandardnormalrandomvariable,suchthatZ~N(0,1).

a. FindbsuchthatPr(X>3.1)=Pr(Z