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Section
Number of
questions
Number of questions
to be answered
A
B
13
54
13
27
Number of
modules
6
Number of modules
to be answered
3
Number of
marks
13
27
Total 40
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10
Module 1: Number patterns
Before answering these questions you must shade the Number patterns box on the answer sheet for
multiple-choice questions and write the name of the module in the box provided.
Question 1
Stefan swam laps of his pool each day last week.
The number of laps he swam each day followed a geometric sequence.
He swam 1 lap on Monday, 2 laps on Tuesday and 4 laps on Wednesday.
The number of laps that he swam on Thursday was
A.
5
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6
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D. 12
E. 16
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C. tn =±±n
D. tn =±+ 4n
E. tn =±+ 4n
SECTION B – Module 1: Number patterns – continued
11
2011 FURMATH EXAM 1
Question 3
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8
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5
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1
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Use the following information to answer Questions 7, 8 and 9.
Craig plays sport and computer games every Saturday.
Let x be the number of hours that he spends playing sport.
Let y be the number of hours that he spends playing computer games.
Craig has placed some constraints on the amount of time that he spends playing sport and computer games.
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Question 8
By spending Saturday playing sport and computer games, Craig believes he can improve his health.
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)RUWKHIHDVLEOHUHJLRQVKRZQLQWKHJUDSKDERYHWKHPD[LPXPYDOXHRIW occurs at
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785129(5
2011 FURMATH EXAM 1
24
Module 4: Business-related mathematics
Before answering these questions you must shade the Business-related mathematics box on the answer
sheet for multiple-choice questions and write the name of the module in the box provided.
Question 1
An electrician charges $68 per hour to complete a job.
A Goods and Services Tax (GST) of 10% is added to the charge.
Including GST, the cost of a job that takes three hours is
A.
$6.80
B.
$20.40
C. $204.00
D. $210.80
E. $224.40
Question 2
An amount of $22 000 is invested for three years at an interest rate of 3.5% per annum, compounding annually.
The value of the investment at the end of three years is closest to
A.
$2 310
B.
$9 433
C. $24 040
D. $24 392
E. $31 433
Question 3
A van is purchased for $56 000.
Its value depreciates at a rate of 42 cents for each kilometre that it travels.
The value of the van after it has travelled 32 000 km is
A. $13 440
B. $26 880
C. $29 120
D. $32 480
E. $42 560
Question 4
Nathan bought a $2 500 bedroom suite on a contract that involves no deposit and an interest-free loan for a
period of 48 months.
He has to pay an initial set-up fee of $25.
In addition, he pays an administration fee of $3.95 per month.
The total amount that Nathan will have to pay in fees for the entire 48 months, as a percentage of the original
price of $2 500, is closest to
A. 1.6%
B. 4.0%
C. 7.6%
D. 8.5%
E. 8.6%
SECTION B – Module 4: Business-related mathematics – continued
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785129(5
2011 FURMATH EXAM 1
30
Question 6
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785129(5
2011 FURMATH EXAM 1
32
Module 6: Matrices
Before answering these questions you must shade the Matrices box on the answer sheet for
multiple-choice questions and write the name of the module in the box provided.
Question 1
The matrix below shows the airfares (in dollars) that are charged by Zeniff Airlines to fly between
Adelaide (A), Melbourne (M) and Sydney (S).
from
A
M
S
0
85
89 A
85
0
99 M
97 101
to
0 S
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A.
$85
B.
$89
C.
$97
D.
$99
E. $101
Question 2
⎡0 1 ⎤
⎡1 ⎤
, B = ⎢ ⎥ and C =
If A = ⎢
⎥
⎣1 0 ⎦
⎣0 ⎦
A.
⎡0 ⎤
⎢3 ⎥
⎣ ⎦
B.
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⎣ ⎦
C.
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⎣ ⎦
D.
⎡2⎤
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⎣ ⎦
E.
⎡2⎤
⎢3 ⎥
⎣ ⎦
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⎣ ⎦
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785129(5
2011 FURMATH EXAM 1
34
Use the following information to answer Questions 5 and 6.
Two politicians, Rob and Anna, are the only candidates for a forthcoming election. At the beginning of the
election campaign, people were asked for whom they planned to vote. The numbers were as follows.
Candidate
Number of people who plan
to vote for the candidate
Rob
5692
Anna
3450
During the election campaign, it is expected that people may change the candidate that they plan to vote for
each week according to the following transition diagram.
24%
75%
Rob
Anna
76%
25%
Question 5
The total number of people who are expected to change the candidate that they plan to vote for one week after
the election campaign begins is
A.
828
B. 1423
C. 2251
D. 4269
E. 6891
Question 6
The election campaign will run for ten weeks.
If people continue to follow this pattern of changing the candidate they plan to vote for, the expected winner
after ten weeks will be
A. Rob by about 50 votes.
B. Rob by about 100 votes.
C. Rob by fewer than 10 votes.
D. Anna by about 100 votes.
E. Anna by about 200 votes.
SECTION B – Module 6: Matrices – continued
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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 2011
FURMATH EX 1 & 2
2
Further Mathematics Formulas
Core: Data analysis
x−x
sx
standardised score:
z=
least squares 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:
n
n
a + (a + d ) + … + (a + (n – 1)d ) =  2a + ( n − 1) d  = ( a + l )
2
2
geometric series:
a + ar + ar2 + … + arn–1 =
infinite geometric series:
a + ar + ar2 + ar3 + … =
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
FURMATH EX 1 & 2
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:
effective rate of interest ≈
r
100
2n
× 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