2011 mathematical methods (cas) exam 1
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7/27/2019 2011 Mathematical Methods (CAS) Exam 1
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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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Instructions
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Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic
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Question 1
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Instructions
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Question 2
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Question 3
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Question 5
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Question 9FRQWLQXHG
Question 8
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Question 9
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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
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