mt 2008 zon c kuching k1

8/14/2019 MT 2008 zon C Kuching k1

1/19

5

SULIT

Nombor Kad Pengenalan

Angka GiliranNama:

_______________________________________________

Jawatankuasa Kurikulum Zon C Kuching, Sarawak

PERCUBAAN SIJIL PERLAJARAN MALAYSIA 2008ADDITIONAL MATHEMATICS

Kertas 1

Sept 2008

2 jam

3472/1

Dua jam

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Tuliskan angka giliran dan nombor

kad pengenalan anda pada ruang

yang disediakan.

2. Kertas soalan ini adalah dalam

bahasa Inggeris sahaja.

3. Calon dikehendaki membaca arahan

di halaman belakang kertas soalan

ini

Untuk kegunaan Pemeriksa

Kod Pemeriksa:

Soalan Markah Pernuh Markah Diperoleh1

2

3

4

56

7

8

9

10

11

12

13

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18

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20

21

22

23

24

25

Jumlah 80

Kertas soalan ini mengandungi 18 halaman bercetak

3472/1 2008 Hak Cipta Jawatankuasa Kurikulum Zon C, Pelajaran Gabungan Kuching [SMKTAR]

[lihat sebelah

SULIT


2/19

SULIT 3472/1

Important Formulae

The following formulae may be helpful in answering the questions. The symbols given are the onescommonly used.

Algabra

1.2 4

2

b b acx

a

2. m n m na a a

3. m n m na a a

4.

nm mn

a a5. log log loga a amn m n

6. log log loga a am

m nn

7. log logn

a am n m

8.log

loglog

ca

c

bb

a

9. ( 1)nT a n d

10. 2 ( 1)2

n

nS a n d

11.1n

nT ar

12.)( 1) (1, 1

1 1

n n

n

a r a r s r

r r

13. 11 ,

aS r

r

Statistics

1.x

xN

2.fx

xf

3.2

2( ) x x xx

N N

4.

22( ) f x x fx

xf f

5.12

m

N Fm L c

f

6.1

0

100Q

IQ

7.i i

i

W II

W

8.!

( )!

n

r

np

n r

9.!

( )! !

n

r

nC

n r r

10. ( ) ( ) ( ) ( )p A B P A P B P A B

11. ( ) , 1n r n r

rP X r C P q p q

12. mean, np

13 npq

14.X

Z

3472/1 2008 Hak Cipta Jawatankuasa Kurikulum Zon C, Pelajaran Gabungan Kuching [SMKTAR] SULIT

SULIT 3472/1

2


3/19


4/19

5

Probability of upper tail Q(z) for normal distribution N(0, 1)

z 0 1 2 3 4 5 6 7 8 91 2 3 4 5 6 7 8 9

SUBTRACT0.

0 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4661 .4641 4 81

2

1

6

2

0

2

4

2

8

3

2 36

0.1

.4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247 4 8 12

16

20

24

28

32

36

0.

2

.4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .3859 4 8 1

2

1

5

1

9

2

3

2

7

3

1

35

0.

3

.3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483 4 7 11 1

4

1

9

2

2

2

6

3

0

34

0.

4

.3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121 4 7 11 1

4

1

8

2

2

2

5

2

9

32

0.

5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776 3 7

1

0

1

4

1

7

2

0

2

4

2

7 310.

6

.2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451 3 7 1

0

1

3

1

6

2

0

2

3

2

6

29

0.

7

.2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148 3 6 9 1

2

1

5

1

8

2

1

2

4

27

0.8

.2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867 3 5 8 11 14

16

19

22

25

0.9

.1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611 3 5 8 10

13

15

18

20

23

1.

0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379 2 5 7 9

1

2

1

4

1

6

1

9 211.

1

.1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 2 4 6 8 1

0

1

2

1

4

1

6

18

1.

2

.1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985 2 4 6 7 9 11 1

3

1

5

17

1.

3

.0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823 2 3 5 6 8 1

0

11 1

3

14

1.

4

.0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0694 .0681 1 3 4 6 7 8 1

0

11 13

1.5 .0666 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559 1 2 4 5 6 7 8

10 11

1.

6

.0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 1 2 3 4 5 6 7 8 9

1.

7

.0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367 1 2 3 4 4 5 6 7 8

1.

8

.0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294 1 1 2 3 4 4 5 6 6

1.

9

.0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233 1 1 2 2 3 4 4 5 5

2.

0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183 0 1 1 2 2 3 3 4 42.

1

.0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143 0 1 1 2 2 2 3 3 4

2.

2

.0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 0 1 1 1 2 2 2 3 3

2.3

.0107 .0104 .0102 0 1 1 1 1 2 2 2 2

.02990 .02964 .02939 .02914 3 5 8 1

0

1

3

1

5

1

8

2

0

23

.02889 .02866 .02842 2 5 7 9 1

2

1

4

1

6

1

8

21

2.

4

.02820 .02798 .02776 .02755 .02734 2 4 6 8 11 1

3

1

5

1

7

19

.02714 .02695 .02676 .02657 .02639 2 4 6 7 9 11 1

3

1

5

17

2.

5 .02621 .02604 .02587 .02570 .02554 .02539 .02523 .02508 .02494 .02480 2 3 5 6 8 9 11

1

2 142.

6

.02466

.02

453 .02

440 .02

427 .02

415 .02

402 .02

391 .02

379 .02

168 .02

357

1 2 3 5 6 7 8 9 10

2.7

.02347.02336 .02326 .02317 .02307 .02298 .02189 .02280 .02272 .02164

1 2 3 4 5 6 7 8 9

2.8

.02256.02248 .02240 .02233 .02226 .02219 .02212 .02205 .02199 .02193

1 1 2 3 4 4 5 6 6


5/19

2.9

.03968 .02181 .02175 .02169 .02164 .02159 .02154 .02149 .02144 .02139 0 1 1 2 2 3 3 4 4

3.

0 .02135 .02130 .02126 .02122 .02118 .02114 .02111 .02107 .02104 .02100 0 1 1 2 2 2 3 3 43.

1

.03968 .03935 .03904 3 6 9 1

3

1

6

1

9

2

2

2

5

28

.03874 .03845 .03816 .03739 3 6 8 11 1

4

1

7

2

0

2

2

25

.03762 .03736 .03711 2 5 7 1

0

1

2

1

5

1

7

2

0

22

3.

2

.03687 .03664 .03641 .03619 .03598 2 4 7 9 11 1

3

1

5

1

8

20

.03577 .03557 .03538 .03519 .03501 2 4 6 8 9 11 1

3

1

5

17

3.3

.03483 .03466 .03450 .03434 .03419 2 3 5 6 8 10

11 13

14

.03404 .03390 .03376 .03362 .03349 1 3 4 5 7 8 9 10

12

3.

4

.03337 .03325 .03313 .03302 .03291 .03180 .03270 .03260 .03251 .03242 1 2 3 4 5 6 7 8 9

3.

5 .03

233 .03

224 .03

216 .03

208 .03

200 .03

193 .03

185 .03

178 .03

172 .03

165 1 1 2 3 4 4 5 6 73.

6

.03159 .03153 .03147 .03142 .03136 .03131 .03126 .03121 .03117 .03112 0 1 1 2 2 3 3 4 5

3.

7

.03108 .03104 .03100 .0496 .0492 .0488 .0485 .0482 .0478 .0475

3.

8

.0472 .0469 .0467 .0464 .0462 .0459 .0457 .0454 .0452 .0450

3.

9

.0448 .0446 .0444 .0442 .0441 .0439 .0437 .0436 .0434 .0433

For negative z use the relation: Q(z) = 1 Q(z) = P(z)

Example: if u N(0, 1), find (a) Prob (u > 2), (b) Prob (0 < u < 2), (c) Prob (|u| > 2), (d) Prob (|u| < 2). The desired probabilities are (a) Q(2) =0.0228, (b) Q(0) Q(2) = 0.5000 0.0228 = 0.4772, (c) 2Q(2) = 0.0456, (d) 1 2Q(2) = 0.9544.

If v N(, 2), Prob (v > x) is given by Q(z) with z = (x )/

5


6/19

5

ForExaminers

Use

SULIT 3472/1

Answer all questions

(80 marks)

1. The above arrow diagram shows the relation between set A and set B.

(a) Represent the above relation using ordered pairs.

(b) State the type of the above relation.[2 marks]

Answer (a)

(b)2. Diagram below shows the function :

m xh x

x,x 0, where m is a constant.

Find the value ofm. [3 marks]

Answer: m =..


SULIT 3472/1 For

1

2

3


7/19

ExaminersUse

3. Given function xaxf 3: and 12

:2 3

b

f x x , where a and b are

constants. Find the value ofa and ofb. [3 marks]

Answer: a = , b = ..

4. Given that 3 and kare the roots of quadratic equationx2 +x =p, find the values

ofkand ofp. [4 marks]

Answer: k= ,p = ..

3472/1

2008 Hak Cipta Jawatankuasa Kurikulum Zon C, Pelajaran Gabungan Kuching [SMKTAR]

[lihat sebelah

SULIT

ForExaminers

SULIT 3472/1

3

3

4

4

7


8/19

Use

5. Find the range of values ofx such that 4x < 3 +x2. [3 marks]

[3 marks]

Answer: ..

6. Diagram above shows the graph of a quadratic functiony =f(x). The straightliney = 4 is a tangent to the curvey =f(x).(a) Write the equation of the axis of symmetry of the curve.

(b) Expressf(x) in the form of (x + b) 2 + c, where b and c are constants.

[3 marks]

Answer: (a)

(b)


SULIT 3472/1 For

5

3

3

8


9/19

ExaminersUse

7. Solve the equation 6log ( 2 1)6 11. t [4 marks]

Answer: t= ..

8. Show that for all positive integern, 4(3n+2) 7(3n) + 3n 1 is divisible by 8.[3 marks]

3472/1 2008 Hak Cipta Jawatankuasa Kurikulum Zon C, Pelajaran Gabungan Kuching [SMKTAR]

SULIT

For

ExaminersSULIT 3472/1

4

8

3

9


10/19

Use

9. Find the sum of all terms of the following geometric progressions

1, 2, 4, , 512 [2 marks]

Answer:

10. Given that 2.424242...h

k is a recurring decimal, find the value ofh and ofk.

[3 marks]

Answer: h = , k=


SULIT 3472/1 ForExaminers

Use

9

2

10

3

10


11/19

11. The nth term of an arithmetic progression is given by 2 3nT n . Find(a) the common difference,

(b) the sum of all the terms from the 3rd term to the 10th term.

[4 marks]

Answer: (a)

(b)

12. The diagram shows a part of the straight line graph of1

yagainst

1

x. Expressy

in terms ofx. [4 marks]

Answer:


ForExaminers

Use

SULIT 3472/1

11

4

12

4

11


12/19

13. Given that the coordinates of pointsPand Q are (2, 1) and (3, 5) respectively,

find the equation of the locus of pointR which moves such thatPR :RQ = 3 : 2.

[3 marks]

Answer:

14. Diagram below shows two vectors, OAuuu

and BOuuu

.

Express,

(a) OAuuu

in the form

y

x

(b) BOuuu

in the form xi yj% %

. [2 marks]

Answer: (a)

(b)



Use

15.

13

3

14

2

12


13/19

Use the above information to find the values ofh and kwhen 5 4r p q % % %

.

[3 marks]

Answer: h = , k=

16. In diagram below, PQRS is a parallelogram and STQ is a straight line.

If 5 PQ xuuu

%, 4 PS yuuu

%

, and ST= 3TQ, express in terms ofx% and y

%,

(a) SQuuu

(b) TRuu

[4 marks]

Answer: (a)

(b)


For

ExaminersUse

SULIT 3472/1

15

3

16

4

13


14/19

17. Solve the equation 3sin 2 5cos 0x x for 0 360x . [4 marks]

Answer: ..

18. Diagram below shows a sectorOAB with centre O and radius 6 cm. Given that

the perimeter of the sector is 24 cm, find the angle of the sector in degree and

minutes. [3 marks]

Answer: ..



Use

19. Given that4( ) 5( 3) f x x , find the value of '(2)f . [2 marks]

17

4

18

3

14


15/19

Answer: ..

20. Given that 1 2x p and 21 3y p , find the rate of change ofy whenx is

increased at the rate of 4 units s -1 at the instantp = 6. [4 marks]

Answer: ..


For

Examiners

Use

SULIT 3472/1

19

2

20

4

15


16/19

21. Given that =3

,4)34(k

dxx where k> 0, find the value ofk. [3 marks]

Answer: k=

22. The table shows the distribution of the score a competition.

Score 2 3 4 5 6 7

Frequency 2 x 12 8 7 3 Find the

range of values ofx, given that the median is 4. [3 marks]

Answer:



Use

23. Seven prefects are to be selected from a group of 8 boys and 15 girls.

21

3

22

3

16


17/19

(a) Find the number of selection that can be carried out if 3 boys and 4 girls

are to be selected.

(b) Find the number of ways these seven prefects can be arranged in a row

for a group photograph if the three boys sit next to each other in the

middle of the row. [4 marks]

Answer: (a)

(b)

24. A box contains 4 blue balls, 3 red balls and 5 white balls. Two balls are picked

at random from the box. Find the probability that both balls are of the same

colour. [3 marks]

Answer:


ForExaminers

Use

SULIT 3472/1

23

4

24

3

17


18/19

25. The marks, X, of a group of students in an examination are normally distributed

with a mean of 65 and a standard deviation of 15.

(a) Find the z-score, if the mark of a student is 62 marks.

(b) Find the probability of a student chosen at random obtained higher than

70 marks. [4 marks]

Answer: (a)

(b)


SULIT

25

4

18


19/19

INFORMATION FOR CANDIDATES

1. This question paper consists of 25 questions.

2. Answer all questions

3. Give only one answer for each question.

4. Write your answer clearly in the spaces provided in the question paper.

5. Show your working. It may help you to get marks.

6. If you wish to change your answer, cross out the work you have done. Then write down the

new answer.

7. The diagrams in the questions provided are not drawn to scale unless stated.

8. The marks allocated for each question are shown in brackets.

9. A list of formulae is provided on page 2 and 3.

10. The four-figure table for probability of upper tail Q(z) for normal distribution N(0, 1) is

provided on page 4.

11. You may use a non-programmable scientific calculator.

12. This question paper must be handed in at the end of the examination.


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mt 2008 zon c kuching k1

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