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MATHEMATICAL METHODS (CAS)

Written examination 1

Tuesday 8 November 2011

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 book

Number of

questions

Number of questions

to be answered

Number of

marks

10 10 40

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Materials supplied

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Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic

devices into the examination room.

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Question 1

a. 'LIIHUHQWLDWH 4 x ZLWKUHVSHFWWRx

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b. ,IgxxVLQxQG

g

6

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Instructions

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Question 2

a. )LQGDQDQWLGHULYDWLYHRI1

3 4x ZLWKUHVSHFWWRx

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b. 6ROYHWKHHTXDWLRQxxIRUx

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Question 3

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b. 6ROYHWKHHTXDWLRQ

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for

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Question 4

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Question 5

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Question 6

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Question 7

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Question 9FRQWLQXHG

Question 8

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Question 9

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fRRfxx ax a > 0

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y = f(x)

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Question 10FRQWLQXHG

Question 10

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END OF QUESTION AND ANSWER BOOK

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MATHEMATICAL METHODS (CAS)

Written examinations 1 and 2

FORMULA SHEET

Directions to students

Detach this formula sheet during reading time.

This formula sheet is provided for your reference.

VICTORIAN CURRICULUM AND ASSESSMENT AUTHORITY 2011

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MATH METH (CAS) 2

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3 MATH METH (CAS)

END OF FORMULA SHEET

Mathematical Methods (CAS)

Formulas

Mensuration

area of a trapezium:1

2 a b h+( ) volume of a pyramid:

1

3Ah

curved surface area of a cylinder: 2Srh volume of a sphere:4

33

Sr

volume of a cylinder: Sr2h area of a triangle:1

2bc Asin

volume of a cone:1

32

Sr h

Calculus

d

dxx nxn n

( )=

-1

x dx

nx c nn n=

+

+ +

1

111 ,

d

dxe aeax ax( )= e dx a e c

ax ax= +1

d

dxx

xelog ( )( )=

1

1

xdx x ce= + log

d

dxax a axsin( ) cos( )( )= sin( ) cos( )ax dx a

ax c= +1

d

dxax a axcos( )( ) -= sin( )

cos( ) sin( )ax dx

aax c= +

1

d

dxax

a

ax

a axtan( )

( )

( ) ==

cos

sec ( )2

2

product rule:d

dxuv u

dv

dxv

du

dx( )= + quotient rule:

d

dx

u

v

vdu

dxu

dv

dx

v

=

2

chain rule:dy

dx

dy

du

du

dx= approximation: f x h f x h f x+( ) ( ) + ( )

Probability

Pr(A) = 1 Pr(Ac) Pr(AB) = Pr(A) + Pr(B) Pr(AB)

Pr(A|B) =Pr

Pr

A B

B

( )( )

transition matrices: Sn = Tn uS0

mean: = E(X) variance: var(X) = V2 = E((X)2) = E(X2) 2

probability distribution mean variance

discrete Pr(X=x) =p(x) = xp(x) V2 = (x )2p(x)

continuous Pr(a< X < b) = f x dxa

b( ) =

x f x dx( ) 2 2=

( ) ( )x f x dx