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SUPERVISOR TO ATTACH PROCESSING LABEL HERE
Victorian Certificate of Education
2014
Letter
STUDENT NUMBER
FURTHER MATHEMATICS
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Written examination 2
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Monday 3 November 2014
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Reading time: 9.00 am to 9.15 am (15 minutes)
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Writing time: 9.15 am to 10.45 am (1 hour 30 minutes)
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QUESTION AND ANSWER
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Structure
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Core
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15
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Module
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Nu ay v 6
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45
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Number of
questions
Number of questions
to be answered
Number of
marks
Number of
modules
Number of modules
to be answered
Number of
marks
Total 60
• Students are permitted to bring into the examination room: pens, pencils, highlighters, erasers,
sharpeners, rulers, one bound reference, one approved graphics calculator or approved CAS
calculator or CAS software and, if desired, one scientific calculator. Calculator memory DOES NOT
need to be cleared.
• 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 38 pages, with a detachable sheet of miscellaneous formulas in the
centrefold.
• Working space is provided throughout the book.
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.
• All written responses must be in English.
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 FURMATH EXAM 2
Instructions
This examination consists of a core and six modules. Students should answer all questions in the core
and then select three modules and answer all questions within the modules selected.
You need not give numerical answers as decimals unless instructed to do so. Alternative forms may
involve, for example, ›, surds or fractions.
Diagrams are not to scale unless specified otherwise.
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FURTHER MATHEMATICS
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
FURMATH EXAM 1 & 2
2
Further Mathematics formulas
Core: Data analysis
x−x
sx
standardised score:
z=
least squares regression line:
y = a + bx, where b = r
residual value:
residual value = actual value – predicted value
seasonal index:
seasonal index =
sy
sx
and a = y − bx
actual figure
deseasonalised figure
Module 1: Number patterns
arithmetic series:
a + (a + d ) + … + (a + (n – 1)d ) = geometric series:
a + ar + ar2 + … + ar n – 1 =
infinite geometric series:
a + ar + ar2 + ar3 + … =
n
n
[ 2a + (n − 1)d ] = (a + l )
2
2
a (1 − r n )
,r≠1
1− r
a
, r <1
1− r
Module 2: Geometry and trigonometry
area of a triangle:
1
bc sin A
2
Heron’s formula:
A=
circumference of a circle:
2π r
area of a circle:
π r 2
volume of a sphere:
4 3
π r 3
surface area of a sphere:
4π r 2
volume of a cone:
1 2
π r h
3
volume of a cylinder:
π r 2h
volume of a prism:
area of base × height
volume of a pyramid:
1
area of base × height
3
1
s ( s − a )( s − b)( s − c) , where s = (a + b + c)
2
3
Pythagoras’ theorem:
c2 = a2 + b2
sine rule:
a
b
c
= =
sin A sin B sin C
cosine rule:
c2 = a2 + b2 – 2ab cos C
Module 3: Graphs and relations
Straight-line graphs
y2 − y1
x2 − x1
gradient (slope):
m=
equation:
y = mx + c
Module 4: Business-related mathematics
PrT
100
simple interest:
I=
compound interest:
A = PRn, where R = 1 +
hire-purchase:
r
100
2n
effective rate of interest ≈
× flat rate
n +1
Module 5: Networks and decision mathematics
Euler’s formula:
v+f=e+2
Module 6: Matrices
determinant of a 2 × 2 matrix:
a b
a b 
; det A =
A=
= ad − bc

c d
c d 
inverse of a 2 × 2 matrix:
A−1 =
1  d −b 
where det A ≠ 0
det A  −c a 
END OF FORMULA SHEET
FURMATH EXAM 1 & 2