2017 HKDSE Math CP CTL(20170419) 2017-DSE-MATH-CP 1-1 Mathematics Compulsory Part Paper 1 Solution Marks Remarks 1. y y x k 3 y x yk 3 1 3 k x y 2. 5 2 3 1 4 ) ( ) ( m n m 10 3 12 m n m 3 22 n m 3. (a) ) )( 3 ( 3 4 2 2 y x y x y xy x (b) y x y xy x 33 11 3 4 2 2 ) 3 ( 11 ) )( 3 ( y x y x y x ) )( 11 3 ( y x y x 4. Let x, y be the number of regular tickets and concessionary tickets sold respectively 50976 78 126 5 y x y x 50976 5 78 126 x x 72 360 y x The number of admission tickets sold that day 432 5. (a) 5 6 and 3 8 11 ) 2 ( 7 x x x 1 and 8 11 ) 2 ( 21 x x x 1 and 5 x x 5 1 x (b) 2, 3, 4, 5 are the only integers satisfying (a) So, there are 4 integers satisfying both inequalities in (a)
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New 2017 HKDSE Math CP CTL(20170419) Mathematics … · 2018. 10. 26. · 2017 HKDSE Math CP CTL(20170419) 2017-DSE-MATH-CP 1-3 Solution Marks Remarks 9. (a) Let x mL be the actual
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2017 HKDSE Math CP CTL(20170419)
2017-DSE-MATH-CP 1-1
Mathematics Compulsory Part Paper 1 Solution Marks Remarks
1.
y
yxk
3
yxyk 3
1
3
k
xy
2.
52
314
)(
)(
m
nm
10
312
m
nm
3
22
n
m
3. (a) ))(3(34 22 yxyxyxyx
(b) yxyxyx 331134 22
)3(11))(3( yxyxyx
))(113( yxyx
4. Let x, y be the number of regular tickets and concessionary tickets sold
respectively
5097678126
5
yx
yx
50976
578126
xx
72
360
y
x
The number of admission tickets sold that day
432
5. (a) 56 and
3
811)2(7
x
xx
1 and 811)2(21 xxx
1 and 5 xx
51 x
(b) 2, 3, 4, 5 are the only integers satisfying (a)
So, there are 4 integers satisfying both inequalities in (a)
2017 HKDSE Math CP CTL(20170419)
2017-DSE-MATH-CP 1-2
Solution Marks Remarks
6. (a) The coordinates of 3)4,(' A
The coordinates of 9) (9,'B
(b) AB of Slope
)3(9
49
-
12
13
B'A' of Slope
94
93
13
12
B'A' of Slope AB of Slope
13
12
12
13
1
''BAAB
7. (a)
9
1
360
x
40x
(b) Let N be the number of students in the school
360
1584090360180
N
900N
The number of students in the school
900
8. (a)
x
ky
When 81y , 144x
14481
k
972k
xy
972
(b) y of in value Change
144
972
324
972
27
2017 HKDSE Math CP CTL(20170419)
2017-DSE-MATH-CP 1-3
Solution Marks Remarks
9. (a) Let x mL be the actual capacity of a standard bottle
2
10200
2
10200 x
205 195 x
The least possible capacity is 195 mL
(b) 2460012023400 x
LxL 6.241204.23
Least total capacity L4.23
No, I don’t agree the claim.
10. (a)
)(
)(
)(
)OR(OP
SSSORSOPS
commonOSOS
givenRSPS
given
(b) 10POQ
10QORPOQ
20POR
Area of the sector OPQR
26360
20
2cm 2
11. (a) 70
15
8070895
ba
5ba
3
226180
b
b
2a
69$median
deviation standard
fig) sig 3 (corr to $7.33
04$7.3303024
2017 HKDSE Math CP CTL(20170419)
2017-DSE-MATH-CP 1-4
Solution Marks Remarks
12. (a) Let 1V cm3 and 2V cm3 be the volume of smaller right pyramid
and larger right pyramid respectively
2
1
V
V
3
9
4
27
8
21 VV
)20)(84(
1680
2V
827
271680
1296
The volume of the larger pyramid
3cm 1296
(b) Volume of smaller pyramid 384 cm3
Height of smaller pyramid
12
3
2
8
384Area)(8) (Base
3
1
144Area Base cm2
basein square ofLength
12
144
area surface Total
14448
2
12)12(
2
1 2
2
2cm 384
2017 HKDSE Math CP CTL(20170419)
2017-DSE-MATH-CP 1-5
Solution Marks Remarks
13. (a) Let the equation of C be ryx 22 )1()4( , where r is a real
constant
Since C passes through )5,6( ,
So, we have r 22 )15()26(
001r
The equation of C : 100)1()4( 22 yx
(b) Radius of C 10
GF
22 )111())3(2(
13
10
F lies outside C
(c) (i) F ,G , H are collinear
(ii) The equation of straight line which passes through F and
H :
23
)1(11
3
11
x
y
5
19
5
12 xy
019512 yx
2017 HKDSE Math CP CTL(20170419)
2017-DSE-MATH-CP 1-6
Solution Marks Remarks
14. (a) )f( x
cbxaxxx )42)(73( 2
cxbaxax 28)712()143(6 23
3446136 23 xxx
31143 a
9a
(b) (i) Since )g( x is a quadratic polynomial, degree of quotient
when )g( x is divided by 42 2 axx is 0
cbxxxAx )492()g( 2 , where A is a constant
)g()f( xx
))492(()42)(73( 22 cbxxxAcbxaxxx
)42)(73( 2 axxAx
)g()f( xx is divisible by 42 2 axx
(b) (ii) 0)g()f( xx
0)492)(73( 2 xxAx
3
7
Ax or 4x or
2
1x
Since
2
1 is not an integer, I don’t agree the claim
2017 HKDSE Math CP CTL(20170419)
2017-DSE-MATH-CP 1-7
Solution Marks Remarks
15.
243log3
9log0
b
b
a
a
9log243log3 bb
9
243log3 b
273 b
3b
2a
xy 3log2
xy 3log2
23 yx
16. (a) The total volume of water imported
7197277 101.50.9...101.50.9101.50.9101.5
)0.9...0.90.9(1101.5 1927
0.91
0.91101.5
207
8101.31763501
fig) sig 3 (corr tom 101.32 38
(b) Since the water imported every year is positive,
imported water of volume totalThe
...101.50.9101.50.9101.5 7277
...)0.90.9(1101.5 27
0.91
1101.5 7
8101.5
8101.6
No, I don’t agree the claim.
Suppose the total water imported can exceed 38 m 106.1 at thn