JJ Prelim 2011 Paper 2 Marking Scheme
Section A: Pure Mathematics
1
(i)
dy
1
=
.
Let y = 1 + x , then
dx 2 x
4
1
1
dx =
1+ x
= 2
3
1
2 ( y 1) dy
y
2
1
1 dy
y
3
2
3
= 2 y ln y
2
= 2 [3 ln 3] 2 [ 2 ln 2]
2
= 2 + 2 ln
3
(ii)
dv
1
=
dx
x
Let u = ln(1 + x
Class:
Register No:
Name:
CRESCENT GIRLS' SCHOOL
SECONDARY FOUR
PRELIMINARY EXAMINATION
ADDITIONAL MATHEMATICS
Paper 1
4038/01
2 Sep 2010
Additional materials: Answer Paper
Graph Paper
2 hours
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Candidate Name : _
CT Group : _
Index no : _
PIONEER JUNIOR COLLEGE
JC 2 Midyear Examination
MATHEMATICS
Higher 2 Paper 1
Tuesday
( 9740 / 1 )
28 June 2011
Additional material: Answer paper, List of Formulae MF15
TIME 3 hours
INSTRUCTIONS TO CANDIDATES
Do
3
1
The function f is defined for all real values of x by f ( x) x 3e x + x .
=
2
Prove, by differentiation, that f is strictly increasing for all real values of x .
2
)
(
d
1 + x2
ln 3 3 x + x 3 = 3 .
dx
3x + x
Show that
(ii)
3
(i)
Hence or otherwise, fi
1
2011 JC2 H2 Math Midyear Exam Paper 2 Suggested Solution
1
Objective : To formulate a system of linear equations from a problem situation and solve the
system using a graphic calculator.
Solution
Let $x, $y, $z be the cost of a DVD, HTS and HDTV respect
Candidate Name : _
CT Group : _
Index no : _
PIONEER JUNIOR COLLEGE
JC 2 Midyear Examination
MATHEMATICS
Higher 2 Paper 2
Wednesday
( 9740 / 2 )
29 June 2011
Additional material: Answer paper, List of Formulae MF15
TIME 3 hours
INSTRUCTIONS TO CANDIDATES
Innova Junior College/H2 Mathematics/Mid Year Examinations/Paper 1/Solutions
1(i)
x ( x 5)
x 3
x ( x 5)
x 3
5( x 5)
x 3
5( x 5)
x 3
( x 5 )2
0
x 3
JC2 2011
+
3
0
5
+
x < 3 or x =
5
(ii)
x ( x 5)
x 3
x < 3 or
5( x 5)
x 3
x=
5
0 x < 9 or x =
25
2(i)
Alt:
l
Innova Junior College/H2 Mathematics/Mid Year Examinations/Paper 2/Solutions
1(i)
Let g (= x ( x a )
x)
JC2 2011
2
g ( x) g ( x a) b g ( x a)
f ( x ) =( x a )( x 2a )
b
2
(
Coordinates of axial intercepts are ( a, 0 ) , ( 2a, 0 ) , and 0, 4a 3b
)
y
4a 3b
Raffles Institution
2011 Year 6 Term 3 Common Test
H2 Mathematics 9740
SOLUTIONS
1
f ( x) x e + x
=
3 x2
f = 3 x 2 e x + x 3 (2 xe x )= x 2 e x (3 + 2 x 2 ) + 1
'( x)
+1
2
[3]
2
2
For all values of x , we have
x 2 0, e x > 0, (3 + 2 x 2 ) > 0 , and so x
2011 JC 2 JCT MA 9740
Section A: Pure Mathematics [49 marks]
1
Terry wishes to buy a certain number of guppies, mollies, goldfish and neon tetras for
his new aquarium. Three fish shops offer the following prices per fish:
Fish
shop
Unit price ($)
Guppies
Name
(
)
Class
RIVER VALLEY HIGH SCHOOL
2011 Year 6 Common Test
Higher 2
MATHEMATICS
9740/01
29 June 2011
Paper 1
3 hours
Additional Materials:
Answer Paper
List of Formulae (MF15)
Cover Page
READ THESE INSTRUCTIONS FIRST
Do not open this booklet until yo
2011 RVHS Year 6 H2 Maths Common Test
Solutions
1
1
6e 2t
dt =
dx
6 ( 3e 2t )2 4
1 1
3e 2t 2
ln 2t
= x+c
6 2 ( 2 ) 3e + 2
1
3e 2t 2
x+c
ln 2t
=
24 3e + 2
When t = 0,
1
1 1
ln 5 + c
ln =
24 5 12
c=0
1
3e 2t 2
x = ln 2t
24 3e + 2
( )
When t , x 0.
2
6
Tampines Junior College (JC 2 H2 Mathematics 9740/2 - Semestral Assessment Two)
1.
x
4
The region enclosed by the curve y = xe , the line x = 2 and the x-axis is denoted by
R. Find the volume of revolution formed when R is rotated completely about the
TEMASEK JUNIOR COLLEGE, SINGAPORE
JC 2
June Common Test 2011
9740
MATHEMATICS
Higher 2
29 June 2011
Additional Materials:
Answer paper
List of Formulae (MF15)
2 hour 30 minutes
READ THESE INSTRUCTIONS FIRST
Write your Civics group and name on all the work
Section A: Pure Mathematics [69 marks]
1
The diagram above shows a water funnel in the shape of an inverted cone with base radius
1.5 cm and height 3 cm. Water drips out of the funnel through a small hole at the tip of the
cone at a constant rate of 0.01
1
SERANGOON JUNIOR COLLEGE
2010 JC2 PRELIMINARY EXAMINATION
MATHEMATICS
Higher 2
Wednesday
9740/1
18 August 2010
Additional materials: Writing paper
List of Formulae (MF15)
TIME : 3 hours
READ THESE INSTRUCTIONS FIRST
Write your name and class on the cove
1
INNOVA JUNIOR COLLEGE
JC 2 PRELIMINARY EXAMINATION 1
in preparation for General Certificate of Education Advanced Level
Higher 2
CANDIDATE
NAME
Civics Group
INDEX NUMBER
Mathematics
9740/02
Paper 2
01 July 2011
Additional materials:
Answer Paper
Graph p
INNOVA JUNIOR COLLEGE
JC 2 PRELIMINARY EXAMINATION 1
in preparation for General Certificate of Education Advanced Level
Higher 2
CANDIDATE
NAME
CLASS
INDEX NUMBER
MATHEMATICS
9740/01
Paper 1
27 June 2011
3 hours
Additional Materials:
Answer Paper
Graph Pa
Class:
Register No:
Name:
CRESCENT GIRLS SCHOOL
SECONDARY FOUR
PRELIMINARY EXAMINATION
ADDITIONAL MATHEMATICS
Paper 2
4038/02
13 Sept 2010
Additional materials: Answer Paper
2 hours 30 minutes
READ THESE INSTRUCTIONS FIRST
Write your name, register number
MERIDIAN JUNIOR COLLEGE
JC2 Mid Year Examination
Higher 2
_
H2 Mathematics
Paper 1
9740/01
29 June 2011
3 hours
Additional Materials: Writing paper
List of Formulae (MF15)
_
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Write your name and civics group on all the work yo
MJC 2011 H2 MATHS JC2 MID YEAR EXAMINATION PAPER 1
Qn
Q1
(i)
Solution
Inequalities
Method 1
Since x 2 + 1 1 ,
Therefore ln x 2 + 1 0
(
)
Method 2
y
x
O
(
)
From graph ln x 2 + 1 0
(ii)
(
)
From (i) since ln x 2 + 1 0 therefore need to solve
(3 x )
2 x 2 x
NJC_JC_2_H2_Maths_2011_Mid_Year_Exam_Questions
1
A local town council of National Town wanted to survey residents of a block of
flats with 72 units to determine if they would like to have lift-upgrading to have
the lifts serve every floor of the block. It
MERIDIAN JUNIOR COLLEGE
JC 2 Mid Year Examination
Higher 2
_
H2 Mathematics
9740/02
Paper 2
01 July 2011
3 hours
Additional Materials: Writing paper
List of Formulae (MF15)
_
READ THESE INSTRUCTIONS FIRST
Write your name and civics group on all the work y
NANYANG JUNIOR COLLEGE
JC2 MID-YEAR EXAMINATION
Higher 2
MATHEMATICS
9740/01
Paper 1
30 June 2011
3 hours
Additional Materials:
Answer Papers
List of Formulae(MF15)
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Write your name and class on every script you hand in.
Write
MJC 2011 H2 MATHS JC2 MID YEAR EXAMINATION PAPER 2
Qn
1
Solution
System of Linear Equation
f (2) = 7 4a + 2b3 + c = 7 - (1)
f (1) = 2 2a + b3 = 2 - (2)
At x = 3 , f (3)= 2 ( 3) + 10= 16
f (3) = 16 9a + 3b3 + c = 16 -(3)
4 2 1 7
Using GC on the augmented
1
Let x, y and z be the number of adult, children and senior citizen tickets sold respectively.
x + y + z = 500
7.50x + 4.00y + 3.50z = 3025
x = 2y
x + y + z = 500
7.50x + 4.00y + 3.50z = 3025
x 2y = 0
Using GC, we get
i.e. x = 300, y = 150, z = 50
Hence,
NANYANG JUNIOR COLLEGE
JC2 MID-YEAR EXAMINATION
Higher 2
MATHEMATICS
9740/02
Paper 2
6 July 2011
2 hours
Additional Materials:
Answer Papers
List of Formulae(MF15)
Graph Paper
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Write your name and class on every script you han
1(i)
Solution:
Every horizontal line, y k , k + cuts the graph of f at most once, hence f is a one-one function
=
and f 1 exists.
x ln
ln y =3
Let y = 3 ,
ln y
x=
ln 3
ln x
, x>0
f 1 :
ln 3
R= ( 0, ) Df =
f
x
(ii)
Since R f Df , f 2 exists.
f 2 : x 33