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

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)



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




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




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




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




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




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


Suppose the total water imported can exceed 38 m 106.1 at thn

year

871-n7277 106.1101.50.9...101.50.9101.50.9101.5

81-n27 106.1)0.9...0.90.91(101.5

3

32

0.91

0.91 n

impossible is which

15

19.0 n





17. (a) Required probability

19

5

15

1

4

4

C

CC

5

415

15

16

1

17

2

18

3

19

4C

3876

5

r.t. 0.00129

(b) Required probability

19

5

15

2

4

3

C

CC

5

315

14

16

15

17

2

18

3

19

4C

969

35

r.t. 0.0361

(c) Required probability

969

35

3876

51

5

2

5

1

5

0

15

13

16

14

17

15

18

3

19

4

15

12

16

13

17

14

18

15

19

4

15

11

16

12

17

13

18

14

19

15

C

CC

3876

3731

r.t. 0.963




18. (a)

83222

192 kxkxxy

y

8322219 2 kxkxx

0113222 2 kxkxx

)113)(2(4)22( 2 kk

92164 2 kk

76)2(4 2 k

76 , for all real values of k

0 , for all real values of k

L and Γ intersect at two distinct points.

(b) (i) a ,b are the roots of 0113222 2 kxkxx

ab

2

113

k

2

113

k

ba

2

22

k

1 k

2)( ba

abba 222

abba 4)( 2

)

2

113(4)1( 2

kk

226122 kkk

2342 kk

(ii) AB

2)( ba

2342 kk

19)2( 2 k

358898944.419 , for all real values of k

No, it is impossible.




19. (a)

30sin

24

)4230180sin(

AC

65071278.45AC

cm 7.45AC (corr to 3 sig fig)

The length of AC is 45.7 cm

(b) (i)

10

2

ACCF

CF

ACCF

4

1

65071278.45

4

1CF

4126782.11CF

cm 4.11CF (corr to 3 sig fig)

(ii) 30sin))((

2

1 of Area AFABABF

06339098.57 ACCFAF

42cos))((2222 BCACBCACAB

42cos)65071278.45)(24(224)65071278.45( 222AB

11826911.32AB

ABF of Area

30sin)06339098.57)(11826911.32(

2

1

2cm 1943369.458

2cm 458 (corr to 3 sig fig)




(iii) 30cos))((2222 ABAFABAFBF

30cos)11826911.32)(06339098.57(2)11826911.32()06339098.57( 222BF

36690449.33BF

Let h be the height of ABF with base BF

ABFBFh of Area))((

2

1

1943369.458))((

2

1BFh

1943369.458)36690449.33)((

2

1h

46400026.27h

Let the inclination of the thin metal sheet ABC to

horizontal ground be

h

10sin

46400026.27

10sin

35300646.21

The inclination of the thin metal sheet ABC to horizontal

ground = 4.21

(iv) 36690449.33BF

22 10 ABBD

52184808.30BD

22 10 CFDF

18033989.56DF

03454623.60

2Let

DFBDBFs

BDF of Area

460

741482.426

))()((

DFsBDsBFss




Paper 2

Question No. Key Question No. Key

1. A 26. A

2. D 27. B

3. A 28. C

4. D 29. B

5. D 30. B

6. A 31. D

7. B 32. D

8. A 33. C

9. C 34. D

10. C 35. B

11. B 36. C

12. C 37. C

13. B 38. A

14. B 39. A

15. C 40. B

16. D 41. D

17. D 42. B

18. A 43. C

19. D 44. B

20. D 45. A

21. C

22. D

23. A

24. A

25. C

Note: Figures in brackets indicate the percentages of candidates choosing the correct answers.

Documents

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