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2018-DSE
MATH CP
PAPER
1
HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY
HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2018
Candidate Number
MATHEMATICS CompulsoryPart
PAPER
1
Question-Answer Book
8:30 am - 10:45 am (2% hours)
This paper must be answered in English
INSTRUCTIONS
(1)
After the announcement of the start of the
examination, you should first write your
Candidate Number in the space provided on
Page 1 and stick barcode labels in the spaces
provided on Pages 1, 3, 5, 7, 9 and 11.
(2)
This paper consists of THREE sections, A(1),
A(2) and B.
(3)
Attempt ALL questions in this paper. Write your
answers in the spaces provided in this Question-
Answer Book. Do not write in the margins.
Answers written in the margins will not be
marked.
(4)
Graph paper and supplementary answer sheets
will be supplied on request. Write your
Candidate Number, mark the question number
box and stick
a barcode label on each
sheet,
and fasten them with string INSIDE this book.
(5)
Unless otherwise specified, all working must be
clearly shown.
(6)
Unless otherwise specified, numerical answers
should be either exact or correct to 3 significant
figures.
(7)
The diagrams in this paper are not necessarily
drawn to scale.
(8)
No extra time will be given to candidates for
sticking on the barcode labels or filling in the
question number boxes after the 'Time is up'
announcement.
@6)8+';{eiYthffi
{,RWn[.rc
Hong Kong Examinations and Assessment Authority
All Rights Reserved 2018
2018-DSE.MATH-CP I_I
I
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SECTION
I
A(t)
(35 marks)
Make b the subject of the formul
u o:4 = bl I
32
(3 marks)
o
.v
L
o
+{
6
o
c)
'o
I
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a
b0
d
o
q.)
2
Simplify
#f
and express your answer with positive indices.
(3 marks)
-q
o
c)
p
k
L
F
a
|<
'
c)
o
ko
q
q
Answers written in the margins
20I8-DSE.MATH-CP I_2
will not be marked.
2
.-)
Please stick the barcode label here
3
up 265.473 to the nearest integer.
(a)
Round
(b)
Round down 265,4'73 to
(c)
Round
l
decimalplace.
off 265.473 to 2 significant figures
(3 marks)
{.)
€o
d
cd
JZ
J4
k
()
C)
3
-o
o
B
(
'
4.
C)
A box contains
n
white balls,
5 black balls and 8
then the probability of drawing a red ball
red balls.
If a ball is randomly drawn from
i" ? .Find the value of n .
5
bo
the box,
(3 marks)
H
cn
C)
-a
F
C)
c)
L
B
o
k
a
L
o
a
a
q
a
Answers written in the margins
20I8.DSE-MATH.CP I-3
will not
be marked.
J
Goontohe
next
5
Factorize
(a)
9r3
-l8r2s
(b)
gr3
-l8r2s-rs2
,
+2s3
(4 marks)
ldLi
6
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pC)
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C)
(B
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()
(.)
6.
(a)
(b)
Findtherangeofvaluesof
x whichsatis$both
3-t >2x+7
2
oo
and
k(d
x+8>0.
c)
Write down the greatest integer satisfying both inequalities in (a).
(4 marks)
L(
6)
P
Lr
o
kq)
C)
o
d
'
I
Answers written in the margins will not be marked,
2018-DSE-MATH-CP
I-4
4
.)
Please stick the barcode label here
7
The marked price of a vase
discount
of
is 30%
above its
of $ 88 is made by selling
price of the vase.
cost. A loss
40% on its marked price. Find the marked
the vase at
a
(5 marks)
t,C)
o
J4
J4
!
k
d
(d
po
c)
-o
0
b0
E
d
o
c)
€
o
k
c)
I
k
k
H
;
o
C)
a
T
I
Answers written in the margins will not be marked.
20I8-DSE.MATH-CP I_5
5
Go on to
he next
8.
In Figure
l,
ABCDE is a circle. It is given that
AB /l
ED . AD and .BE
intersect at the point
F
B
A
C
E
D
Figure I
Eo
Express
x and y
in terms
of
d
(5 marks)
€
C)
lzk
+r
(.)
€
€q)
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o
F
tr
bo
L
(d
ts
()
(.)
o
C)
9
k
L
o
L
q)
L
o
F
o
Answers written in the margins will not be marked.
2018.DSE-MATH.CP I-6
6
-)
Please stick the barcode label here
9
Acartravelsfromcity P tocity Q atanaveragespeedof T2kJnlh andthenthecartravelsfromcity p
tocity R atanaveragespeedof 90km/h Itisgiventhatthecartravels 210km in 161 minutes
(5 marks)
for the whole joumey. How long does the car take to travel from city P to cily Q ?
j'
o
o
.v
+/
(q
tr
E
o
q)
-o
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c
B
a
bo
H
(d
tr
C)
()
C)
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c
t<
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L
'
q
L
c)
a
F
o
a
tr
Answers written in the margins will not be marked.
20I8-DSE.MATH-CP 1_7
7
Goontohe
next
SECTION A(2) (35 marks)
10
The box-and-whisker diagram below shows the distribution of the ages of the clerks in team X of a
company. It is given that the range and the inter-quartile range of this distribution are 43 and 21
respectively.
l9
Age
27
38
a
b
(a)
Find a and b
(b)
There are five clerks in team l' of the company and three of them are of age 3 8 . It is given that
the range of the ages of the clerks in team Y is 20 . Team X and team / are now combined to
form a section. The manager of the company claims that the range of the ages of the clerks in the
section and the range of the ages of the clerks in team X must be the same. Do you agree?
Explain your answer.
(2 marks)
(3 marks)
'1,
Jog
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k
()
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C)
c.)
o
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bo
b0
(d
(€
o
c)
c)
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k
k
q
kq)
o
q
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2018.DSE-MATH.CP 1_8
8
I
Please stick the barcode label here
I
1
.
The following table shows the distribution of the numbers of children of some families:
Number of children
0
I
2
J
4
Number of families
k
2
9
6
7
It is given that
(a)
k
is a positive integer.
If the mode of the distribution is 2 , write down
(i)
the least possible value
(ii)
the greatest possible value
of
ft
;
of
ft
.
(2 marks)
ro
()
+r
(€
(b)
()
o
JI
k
If the median of the distribution is 2 , write down
(D
(ii)
.o
the least possible value
of t
the greatest possible value
(€
()
-o
;
of
,t
.
(2 marks)
(c)
'oo
If the mean of the distribution is 2 , findthe value of ,t
(2 marks)
(.)
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bo
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C)
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C)
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k
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L
C)
C)
Answers written in the margins
2018.DSE-MATH-CP 1-9
will not be marked.
9
Go on
totre next
12
Let f(x)=4y1r+l)2 + ax+b , where a and D are constants. It is given that x-3
of f(x) When f(x) is dividedby x+2 , the remainder is 2b+165
(a)
Find
(b)
Someone claims that the equation f(x) =
Explain your answer.
a
and b
.
is a factor
(3 marks)
g
has at least one irrational
root. Do you agree?
(4 marks)
0)
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()
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(d
J4
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JA
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C)
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a
b0
bo
(€
(€
c)
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tr
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C)
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!
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H
k
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c.)
a
Answers written in the margins
20I8-DSE-MATH.CP 1_IO
will not be marked.
10
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C)
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L
d
k
d
()
c)
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C)
i
4
Answers written in the margins will not be marked.
20I8-DSE-MATH-CP I_I
I
11
Go on to
he next
l3
In Figure 2, ABCD is a trapezium
with IABC
=
90o and AB // DC
that IAED = 90o
E
is a point lying
on .BC such
D
A
B
C
E
Figure 2
!()
*(!
o
,o
o
(a)
Prove
(b)
It is given that AB = 15 cm
that AABE - LECD
(i)
Find the length
(iD
Find the area
(iiD
Is there a point
of
(2 marks)
,
CD
AE = 25
cm and
!q)
lzk
CE =36 cm
q)
,o
.
of LADE
o
.
.F lying on AD
such that the distance between
E and F
is
less
(6 marks)
()
bo
L
than 23 cm ? Explain your answer.
C)
C)
C)
k
L
q
L
k
()
o
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2018-DSE-MATH-CP 1-I2
will not be marked
I2
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.o
!()
()
*
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6J
q)
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()
(.)
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C)
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k
L
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(.)
C)
q
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2018-DSE-MATH-CP I_I3
13
Go on
tohe next
14.
A right circular cylindrical container of base radius 8 cm and height 64 cm and an inverted right
circular conical vessel of base radius 20 cm and height 60 cm are held vertically. The container is
fully filled with water. The water in the container
is now poured into the vessel.
(a)
Find the volume of water in the vessel in terms
(b)
Find the depth of water in the vessel
(c)
If
of
(2 marks)
zr
(4 marks)
a solid metal sphere of radius 14 cm is then put into the vessel and the sphere is totally
(3 marks)
immersed in the water, will the water overflow? Explain your
answer.
13
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c)
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(d
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(.)
C)
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k
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q
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-d
6)
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2018-DSE.MATH-CP 1_I4
will not be marked.
t4
.f
(l)
C)
Jk
(d
+r
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C)
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C)
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P
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k
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L
o
a
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20I8.DSE-MATH-CP 1-15
15
Go on
tohe next
SECTION
l5
B
(35 marks)
,3, 4, 5, 6,7 ,8
eight-digit phone numbers can be formed?
Aneight-digitphonenumberisformedbyapermutationof
(a)
How many different
(b)
If
2
and
9.
(1 mark)
the first digit and the last digit of an eight-digit phone number are odd numbers, how many
(2 marks)
different eight-digit phone numbers can be
formed?
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€o
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q
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C)
c)
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C)
o
Answers written in the margins
20I8.DSE-MATH.CP 1-I6
will not be marked
I6
.l
l6
The 3rd term and the 4th term ofa geometric sequence are 720 and 864 respectively.
(a)
Find the lst term of the
sequence.
(b)
Find the greatest value
of n
lessthan 5x1014
(2 marks)
such that the sum of the (n
+l)th term and the (2n+l)th term is
.
(3 marks)
.--.i
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a
b0
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(.)
d)
0)
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k
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a
C)
q)
q
o
Answers written in the margins
2018-DSE-MATH.CP I_I7
will not be marked.
I7
Go on
tohe next
t'7
(a) In Figure 3(a), ABCD is a paper card in the shape of a parallelogram. It is given that
AB = 60 cm , IABD =20" and IBAD =120o
C
D
A
Figure 3(a)
Find the length
(b)
of AD
.
(2 marks)
The paper card in Figure 3(a) is folded along
is 40 cm ( see Figure 3(b) ).
BD
such that the distance between
A
and' C
A
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tr
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B
k
a
k
(i)
Find IABC
(ii)
Find the angle between the plane ABD and the plane BCD
o
kc)
C)
(5 marks)
Answers written in the margins will not be marked.
20I8.DSE-MATH.CP I_I8
18
.l
-.:
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tlc)k
.v
k
(g
(d
po
C)
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(d
0.)
d)
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()
c)
a
k
ko
a
0)
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2018-DSE-MATH-CP I_19
T9
Go on to
he next
I
18
It is given that
f(3)
=
99
f(")
partly varies as
*2
and partly varies
as
x
Suppose
that f(2) = 66
and
.
(a)
Find f(x)
(b)
LetQbethevertexofthegraph of
(3 marks)
.
y=f(x)
and R bethevertexofthegraphof
(i)
Using the method of completing the square, find the coordinates
(ii)
Write down the coordinates
(iii)
The coordinates of the point
of
R
of p
/=27 -f(x).
.
.
S are (56,0) . Let P be the circumcentre of AQRS
Describe the geometric relationship between P , Q and R . Explain your answer.
,
(5 marks)
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p()
pq)
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k
k
()
0)
I
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2018.DSE-MATH.CP 1_20
will not be marked.
20
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c.)
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C)
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(,)
(,)
a
a
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20I8-DSE-MATH-CP 1-2I
21
Go on
tofre next
19
Thecoordinatesof thecentreofthecircle C are (8,2) . Denotetheradiusof C by r. Let
straightline kx-5y-21=0, where ft isaconstant. Itisgiventhat Z isatangentto C.
(a)
Find the equation
(b)
Z
of C
passes through the
in terms
of r .
point D(18,39)
(i)
Find
(iD
It is given that
Hence, express
12
in terms
of
k
.
Z bethe
(4 marks)
.
r.
inscribed circle
L
cuts the y-axis at the
of LDEF . Is ADEF
.
F
Let be a point such that C is the
an obtuse-angled triangle? Explain your answer.
point E
(8 marks)
o
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c)
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20I8-DSE-MATH-CP 1-22
will not be marked.
22
a
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()
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0)
0)
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()
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k
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ko
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k
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20I8-DSE.MATH-CP I-23
23
Go on to
tre
next
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END OF PAPER
Answers written in the margins
2018-DSE.MATH-CP I-24
will not be marked.
24