L E P M A

Victorian Certificate of Education
2014
SUPERVISOR TO ATTACH PROCESSING LABEL HERE
Letter
STUDENT NUMBER
MATHEMATICAL METHODS (CAS)
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Written examination 2
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Thursday 6 November 2014
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Reading time: 3.00 pm to 3.15 pm (15 minutes)
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Writing time: 3.15 pm to 5.15 pm (2 hours)
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QUESTION AND ANSWER
BOOKn
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Structure
of book rm
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22
22
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2
5
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58
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Total
80
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ato bring into the examination room: pens, pencils, highlighters, erasers,
Students
are
permitted
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v
N rulers,
sharpeners,
y a protractor, set-squares, aids for curve sketching, one bound reference, one
a
approved CAS
calculator (memory DOES NOT need to be cleared) and, if desired, one scientific
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S
Section
•
M
Number of
questions
P
Number of questions
to be answered
Number of
marks
calculator. For approved computer-based CAS, their full functionality may be used.
• Students are NOT permitted to bring into the examination room: blank sheets of paper and/or white
out liquid/tape.
Materials supplied
• Question and answer book of 22 pages with a detachable sheet of miscellaneous formulas in the
centrefold.
• Answer sheet for multiple-choice questions.
Instructions
• Detach the formula sheet from the centre of this book during reading time.
• Write your student number in the space provided above on this page.
• Check that your name and student number as printed on your answer sheet for multiple-choice
questions are correct, and sign your name in the space provided to verify this.
• All written responses must be in English.
At the end of the examination
• Place the answer sheet for multiple-choice questions inside the front cover of this book.
Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic
devices into the examination room.
© VICTORIAN CURRICULUM AND ASSESSMENT AUTHORITY 2014
2014 MATH METHODS (CAS) EXAM 2
SECTION 1
Instructions for Section 1
Answer all questions in pencil on the answer sheet provided for multiple-choice questions.
Choose the response that is correct for the question.
A correct answer scores 1, an incorrect answer scores 0.
Marks will not be deducted for incorrect answers.
No marks will be given if more than one answer is completed for any question.
SECTION 2
Instructions for Section 2
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Answer all questions in the spaces provided.
In all questions where a numerical answer is required, an exact value must be given unless otherwise
specified.
In questions where more than one mark is available, appropriate working must be shown.
Unless otherwise indicated, the diagrams in this book are not drawn to scale.
A
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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 2014
MATHMETH (CAS)
2
THIS PAGE IS BLANK
3
MATHMETH (CAS)
Mathematical Methods (CAS)
Formulas
Mensuration
area of a trapezium:
1 a+b h
(
) 2
volume of a pyramid:
curved surface area of a cylinder:
2π rh
volume of a sphere:
volume of a cylinder:
π r 2h
area of a triangle:
volume of a cone:
1 2
πr h
3
Calculus
d n
x = nx n − 1
dx
d ax
e = ae ax
dx
1
d
( log e ( x) ) = x
dx
d
( sin(ax) ) = a cos(ax)
dx
d
( cos(ax) ) = − a sin(ax)
dx
d
a
= a sec 2 (ax) ( tan(ax) ) = 2
dx
cos (ax)
( )
∫ x dx = n + 1 x + c, n ≠ −1
1
∫ e dx = a e + c
1
∫ x dx = log x + c
1
∫ sin(ax)dx = − a cos(ax) + c
1
∫ cos(ax)dx = a sin(ax) + c
n
( )
ax
n +1
ax
e
du
dv
v
−u
d u
dx
dx
quotient rule:  =
2
dx  v 
v
dv
du
d
( uv ) = u + v dx
dx
dx
product rule: 1
1
Ah
3
4 3
πr
3
1
bc sin A
2
dy dy du
f ( x + h) ≈ f ( x) + h f ′( x)
approximation: =
dx du dx
chain rule: Probability
Pr(A) = 1 – Pr(A′)Pr(A ∪ B) = Pr(A) + Pr(B) – Pr(A ∩ B)
Pr(A|B) =
Pr ( A ∩ B )
Pr ( B )
transition matrices: Sn = T n × S0
variance: var(X) = σ 2 = E((X – µ)2) = E(X 2) – µ2
mean: µ = E(X)
Probability distribution
discrete
continuous
Mean
Pr(X = x) = p(x)
Pr(a < X < b) =
∫
b
a
f ( x)dx
µ = ∑ x p(x)
µ=
∫
∞
−∞
x f ( x)dx
END OF FORMULA SHEET
Variance
σ 2 = ∑ (x – µ)2 p(x)
σ2 =
∫
∞
( x − µ ) 2 f ( x)dx
−∞
09999 : VICTORIAN SECONDARY COLLEGE
VCE MATHEMATICAL METHODS (CAS)
Written Examination 2
ANSWER SHEET – 2014
STUDENT
NAME:
STUDENT NUMBER
JOHN STUDENT
INSTRUCTIONS:
99123456A
USE PENCIL ONLY
SIGN HERE IF YOUR NAME AND NUMBER ARE PRINTED CORRECTLY.
SIGNATURE:
If your name or number on this sheet is incorrect, notify the Supervisor.
Use a PENCIL for ALL entries. For each question, shade the box which indicates your answer.
All answers must be completed like THIS example:
A
B
C
D
E
Marks will NOT be deducted for incorrect answers.
NO MARK will be given if more than ONE answer is completed for any question.
If you make a mistake, ERASE the incorrect answer – DO NOT cross it out.
SUPERVISOR
USE ONLY
ONE ANSWER PER LINE
ONE ANSWER PER LINE
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ONE ANSWER PER LINE
Shade the “ABSENT” box
if the student was absent
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SUPERVISOR’S
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OFFICE USE
ONLY
Please DO NOT fold, bend or staple this form.
© NCS Pearson 18313
USE PENCIL ONLY