peperiksaan percubaan sijil pelajaran malaysia 2008 · sulit 6 3472/1 sulit 5 diagram 2 shows the...

SULIT

[ Lihat sebelah3472/1 SULIT

PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA

PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 2008

MATEMATIK TAMBAHANKertas 1Dua Jam

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

Kertas soalan ini mengandungi 17 halaman bercetak

Nama : ………………..………………..

Tingkatan: ………………………..……

3472/1Matematik TambahanKertas 1Sept 20082 jam

1. This question paper consists of 25 questionsKertas soalan ini mengandungi 25 soalan.

2. Answer all questions.Jawab semua soalan.

3. Give only one answer for each questionBagi setiap soalan berikan SATU jawapan sahaja.

4. Write the answers clearly in the space provide in the question paper.Jawapan hendaklah ditulis pada ruang yang disediakan dalam kertas soalan.

5. Show your working. It may help you to get marks.Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini bolehmembantu anda untuk mendapatkan markah.

6. If you wish to change your answer, cross out the work thatyou have done. Then write down the new answer.Sekiranya anda hendak menukar jawapan, batalkan kerja mengira yang telahdibuat. Kemudian tulis jawapan yang baru.

7 The diagram in the questions provided are not drawn to scale unlessstated.

Rajah yang mengiringi soalan ini tidak dilukiskan mengikut skala kecuali dinyatakan.

8. The marks allocated for each question and sub-part of a question areshown in brackets.Markah yang diperuntukkan bagi setiap soalan atau ceraian soalan ditunjukkandalam kurungan.

9. A list of formulae is provided on page 2 to 3Satu senarai rumus disediakan di halaman 23 hingga 3

10. You may use a non-programmable scientific calculator.Buku sifir matematik empat angka boleh digunakan.

11 This question paper must be handed in at the end of the examination.Kertas soalan ini hendaklah diserahkan pada akhirpeperiksaan .

KodPemeriksa

SoalanMarkahPenuh

MarkahDiperoleh

1 22 23 34 45 36 37 48 39 2

10 311 312 313 314 315 316 417 418 419 220 321 422 323 424 425 4

Jumlah80

http://tutormansor.wordpress.com/

SULIT

3472/2 SULIT

2

The following formulae may be helpful in answering the questions. The symbols given are the onescommonly used.Rumus-rumus berikut boleh digunakan untuk membantu anda menjawab soalan. . Simbol-simbol yang diberi adalah yangbiasa digunakan.

ALGEBRA

12 4

2

b b acx

a

2 am an = a m + n

3 am an = a m - n

4 (am) n = a nm

5 loga mn = log am + loga n

6 logan

m= log am - loga n

7 log a mn = n log a m

8 logab =a

b

c

c

log

log

9 Tn = a + (n -1)d

10 Sn = ])1(2[2

dnan

11 Tn = ar n-1

12 Sn =r

ra

r

ra nn

1

)1(

1

)1(, (r 1)

13r

aS

1, r <1

CALCULUS( KALKULUS)

1 y = uv ,dx

duv

dx

dvu

dx

dy

2v

uy ,

2vdx

dvu

dx

duv

dy

dx

,

3dx

du

du

dy

dx

dy

4 Area under a curve ( Luas dibawah lengkung)

= b

a

y dx or

= b

a

x dy

5 Volume generated ( Isipadu Janaan)

= b

a

y 2 dx or

= b

a

x 2 dy

5 A point dividing a segment of a lineTitik yang membahagi suatu tembereng garis

( x,y) = ,21

nm

mxnx

nm

myny 21

6 Area of triangle ( Luas Segitiga )

= )()(2

1312312133221 1

yxyxyxyxyxyx

1 Distance (Jarak) = 221

221 )()( yyxx

2 Midpoint ( Titik Tengah )

(x , y) =

221 xx

,

221 yy

3 22 yxr

42 2

ˆxi yj

rx y

GEOMETRY


SULIT 3

[ Lihat sebelah3472/1 SULIT

STATISTICS

1 Arc length, s = r( Panjang lengkok) s = j

2 Area of sector , L = 21

2r

( Luas sektor L = 2

2

1j )

3 sin 2A + cos 2A = 1

4 sec2A = 1 + tan2A

5 cosec2 A = 1 + cot2 A

6 sin 2A = 2 sinA cosA

7 cos 2A = cos2A – sin2 A= 2 cos2A - 1= 1 - 2 sin2A

8 tan 2A =A

A2tan1

tan2

TRIGONOMETRY

9 sin (A B) = sinA cosB cosA sinB

10 cos (A B) = cosA cosB sinA sinB

11 tan (A B) =BtanAtan

BtanAtan

1

12C

c

B

b

A

a

sinsinsin

13 a2 = b2 + c2 - 2bc cosA

14 Area of triangle = Cabsin2

1

( Luas Segitiga )

1 x =N

x

2 x =

f

fx

3 =N

xx 2)(=

2_2

xN

x

4 =

f

xxf 2)(=

22

xf

fx

5 m = Cf

FNL

m

2

1

6 1

0

100Q

IQ

71

11

w

IwI

8)!(

!

rn

nPr

n

9!)!(

!

rrn

nCr

n

10 P(AB) = P(A)+P(B)- P(AB)

11 P (X = r) = rnrr

n qpC , p + q = 1

12 Mean µ = np

13 npq

14 z =

x


SULIT 4

3472/1 SULIT

Answer all questions.Jawab semua soalan

1. In diagram 1 set B shows the images of the elements of set A.Dalam rajah 1, set B menunjukkan imej-imej bagi unsur-unsur dalam set A.

a) State the type of relation between set A and set B.Nyatakan jenis hubungan antara set A dan set B.

b) Write a relation between set A and set B by using the function notation.Tuliskan hubungan antara set A dan set B menggunakan tatatanda fungsi.

[ 2 marks ][ 2 markah ]

Answer/Jawapan: (a) ……………………..

(b) ……………………...

2. Given the function 34: xxf , find

Diberi fungsi 34: xxf , cari

a) the image of 2Imej bagi 2

b) the object of - 5Objek bagi - 5


Answer/Jawapan: (a) …………………....…..

(b) …….....…….................

Set A

Set B6

5

- 5

- 6

36

25

Diagram 1Rajah 1

2

2

2

1

Forexaminer’s

use only


SULIT 5

[Lihat sebelah3472/1 SULIT

3. Given that .16and23 xx:hxx:g Find .)(1 xhg

Diberi .16dan23 xx:hxx:g Cari .)(1 xhg


Answer/ Jawapan: ...…………………….........

4. The roots of the quadratic equation 02 2 qxx are the same as the roots of the

quadratic equation .023 2 xpx Find the value of p and of q.

Punca-punca bagi persamaan kuadratik 02 2 qxx adalah sama dengan punca-

punca bagi persamaan kuadratik .023 2 xpx Cari nilai p dan nilai q.


Answer/Jawapan: p = ……………………………

q = ……………………………

Forexaminer’s

use only

3

3

4

4


SULIT 6

3472/1 SULIT

5

Diagram 2 shows the graph of the function y = f(x), where cbxaxf 2)( . Find the

values of a, b and c.

Rajah 2 menunjukkan graf bagi fungsi y = f(x), di mana cbxaxf 2)( . Cari nilai

a, b and c.[ 3 marks ]

[ 3 markah ]

Answer/Jawapan: a =………………………….

c = ………………………………

b =…………………………..

6 Find the range of values of x for which x( x – 8 )> x – 20Cari julat bagi nilai x apabila x( x – 8 )> x – 20


Answer/ Jawapan: x = ……........................

2

0

-1

3

y

x

Diagram 2Rajah 2

Forexaminer’s

use only

3

6

3

5


SULIT 7


7 Given that 1log 210 yx and 1log 2

10 yx , find the values of x and y.

Diberi 1log 210 yx dan 1log 2

10 yx , cari nilai x dan y.


Answer /Jawapan: x = ………………………...

y =.......................................

8 Solve the equation .79 3log

x

Selesaikan persamaan .79 3log

x


:

Answer /Jawapan : = .................................

Forexaminer’s

use only

3

8

4

7


SULIT 8

3472/1 SULIT

9. The first and second terms of a geometric progression are 9 and 3 respectively. Find thesum to infinity of the geometric progression.Sebutan pertama dan sebutan kedua bagi suatu janjang geometri masing-masing ialah 9dan 3 Cari hasil tambah hingga ketakterhinggaan bagi janjang geometri tersebut.


Answer/Jawapan: ……..……...……….....

10. Find the number of terms of the arithmetic progression 9, 12 , 15, … , 30.Cari bilangan sebutan bagi janjang arithmatik 9, 12 , 15, … , 30.


Answer /Jawapan: ……………...………....

11 Given the geometric progression 27, 9, 3, … . Find the sum of all the terms from the fifthterm to the eighth term.Diberi janjang geometri 27, 9, 3, … . Cari hasil tambah bagi semua sebutan darisebutan kelima hingga sebutan kelapan.


Answer/Jawapan: ……………………………

3

10

2

9

3

11

Forexaminer’s

use only


SULIT 9


12 Diagram 3 shows a straight line graph ofx

yagainst x. Given that 26 xxy ,

calculate the value of k and of h .

Rajah 3 menunjukkan garis lurus bagi grafx

ymelawan x. Diberi 26 xxy , kira

nilai k dan nilai h .[ 3 marks ]

[ 3 markah ]

Answer/Jawapan: k=………………………

h=……………………………..

x

y

x

( h , 3 )

( 2, k ) Diagram 3Rajah 3

3

12

Forexaminer’s

use only


SULIT 10

3472/1 SULIT

13 Given B(4,6) divides the line segment joining the points A(3 ,5) and C internally in theratio AB : AC = 1 : 3. Find the coordinates of C.

Diberi titik B(4,6) membahagikan dalam garis lurus yang menyambungkan A(3,5) dan Cmengikut nisbah AB : AC = 1 : 3. Cari koordinat C.

[3 marks][3 markah]

Answer/Jawapan: ………………………..

.

14

Diagram 4 shows a straight line AB of equation .175

yxThe point A lies on the x-

axis and the point B lies on the y-axis. Find the equation of the straight lineperpendicular to AB and passing through the point A.

Rajah 4 menunjukkan garis lurus AB dengan persamaan .175

yxTitik A terletak

pada paksi x dan B pada paksi y. Cari persamaan garis lurus yang berserenjangdengan AB dan melalui titik A.

[3 marks][3 marks]

Answer/Jawapan: …………………………..

Forexaminer’s

use only

3

13

3

141

y

175

yx

A

B

x

Diagram 4Rajah 4


SULIT 11


15 Given that

12

6

5

3v2uu and

Findi) v [1 mark]ii) the unit vector in the direction of v [2 marks]

Diberi

12

6dan

5

3v2uu ,

Carii) v [1 markah]ii) vektor unit dalam arah v [2 markah]

Answer/Jawapan: ........................................... 3

15

Forexaminer’s

use only


SULIT 12

3472/1 SULIT

16 Diagram 5 shows a parallelogram ABCD and BED is a straight line.

Given that EDBEandBCAB 36,10 qp . Express in terms of p and q,

a) BD

b) ECRajah 5 menunjukkan segiempat selari ABCD dan BED adalah satu garis lurus. Diberi

EDBEandBCAB 36,10 qp , ungkapkan dalam sebutan p dan q,

a) BD

b) EC[4 marks]

[4 markah]

Answer /Jawapan: a).....…………..……..…...

b).........................................

4

16

A B

CD

EDiagram 5Rajah 5

Forexaminer’s

use only


SULIT 13


17. Solve the equation sin322cos for 0˚ ≤ ≤ 360˚.

Selesaikan persamaan sin322 kos untuk 0˚ ≤ ≤ 360˚.

[4 marks][4 markah]

Answer/Jawapan: …...…………..…......

18

Diagram 6 shows two sectors OPQ and ORS with a common centre O.Given that OQ = 4 cm, QS = 2 cm and POQ = 65˚, find the area of the shaded

region PQSR in terms of π.Rajah 6 menunjukkan dua sektor OPQ dan ORS, mempunyai pusat sepunya di O.Diberi OQ = 4 cm, QS = 2 cm dan POQ = 65˚, cari luas kawasan berlorek PQRS

dalam sebutan π.[4 marks]

[4 markah]

Answer/Jawapan: …………………………..4

18

4

17

Forexaminer’s

use only

O

Q

S

P

R

65˚ Diagram 6Rajah 6


SULIT 14

3472/1 SULIT

19 Evaluate2

4

16lim( )

4x

x

x

.

Nilaikan2

x 4

x 16had( )

x 4

[ 2 marks]

[ 2 markah ]

Answer/Jawapan: ………………………….

20 Given that 23 5 7y x x , if x increases by 0.02 at the instant when 3x , find the

approximate change in y .

Diberi 2y 3x 5x 7 . Jika x bertambah sebanyak 0.02 apabila nilai x = 3, cari

perubahan hampir yang sepadan bagi y.[ 3 marks]

[ 3 markah]

Answer/Jawapan: ………………………….….

Forexaminer’s

use only

3

20

2

19


SULIT 15


21 Given that8

1

f (x)dx 8 . Find the value of

a)8

1

1f (x)dx

4

b) The constant c, if4 8

1 4

f (x)dx [f (x) cx]dx 24

Diberi8

1

f ( x )dx 8 . Cari nilai bagi

a)8

1

1f ( x )dx

4

b) pemalar c jika4 8

1 4

f ( x )dx [ f ( x ) cx ]dx 24


Answer/Jawapan (a) ………………………………..

(b)………………………………..

Forexaminer’s

use only

4

21


SULIT 16

3472/1 SULIT

22

Time (hour)

Masa (jam)5 – 14 15 – 24 25 – 34 35 – 44 45 – 54

Number of

pupils

Bilangan murid

5 7 19 17 7

Table 1

Jadual 1

Table 1 shows the time distribution, in hour, taken by a group of pupils to complete

their projects.

Find the median, in hour, of the distribution. [3 marks]

Jadual 1 menunjukkan taburan masa, dalam jam, yang digunakan oleh sekumpulan

pelajar untuk melengkapkan projek mereka.

Carikan median, dalam jam, bagi taburan itu. [3 markah]

Answer/Jawapan: …...…………..……........

23

Diagram 7Rajah 7

Diagram 7 shows two straight lines. One of the lines has 4 points and the other line has5 points. Find the number of triangles that can be formed by joining any 3 points.Rajah 7 menunjukkan dua garis lurus. Satu daripada garis itu mempunyai 4 titik dangaris yang satu lagi mempunyai 5 titik. Cari bilangan segitiga yang dapat dibentukdengan menyambungkan mana-mana tiga titik.

[ 4 marks ][ 4 markah]

Forexaminer’s

use only

4

23

3

22


SULIT 17


Answer/ Jawapan: …...…………..……..

24.Team Number of students

male femaleA 24 16B 12 18

Table 2Table 2 shows the number of male and female students in team A and team B in a Scienceand Mathematics Club. A fair dice is tossed. If a number which is a multiple of three isobtained, a student from team A will be chosen to represent the club in an inter-clubcompetition. Otherwise, a student from team B will be chosen. Calculate the probabilitythata) a female student from team A is chosenb) a male student from team B is chosen

Pasukan Bilangan pelajarLelaki perempuan

A 24 16B 12 18

Jadual 2Jadual 2 menunjukkan bilangan pelajar lelaki dan perempuani pasukan A dan pasukan Bdalam Kelab Sains dan Matematik. Sebuah dadu adil dilambung, jika nombor gandaan 3diperolehi, maka seorang pelajar daripada pasukan A akan dipilih untuk mewakili kelabdalam suatu pertandingan antara kelab. Sebaliknya seorang pelajar dari pasukan B akandipilih. Kirakan kebarangkalian untuk :a) seorang pelajar perempuan dari pasukan A dipilihb) seorang pelajar lelaki dari pasukan B dipilih.


Answer/Jawapan : a)…………………..

b)………………………4

24

Forexaminer’s

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SULIT 18

3472/1 SULIT

25 It is found that the height of the students in a school are normally distributed with a meanof 165 cm and a standard deviation of 15 cm. If 6% of the students in that school hasheight more than h cm, find the value of h.Ketinggian pelajar di sebuah sekolah didapati bertabur secara normal dengan nilai min165 cm dan sisihan piawai 15 cm. Jika terdapat 6% daripada pelajar sekolah inimempunyai ketinggian melebihi h cm, carikan nilai h.

[ 4 marks ]

[ 4 markah ]

Answer/Jawapan: h =………………..……

END OF THE QUESTION PAPER

4

25

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SULIT

3472/1

Additional

Mathematics

Paper 1

Sept

2008

PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA

PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 2008

ADDITIONAL MATHEMATICS

Paper 1

MARKING SCHEME

This marking scheme consists of printed pages


PAPER1

QUESTIONNUMBERS

WORKING MARKSFULL

MARKS

1a) Many to one

b) 2: xxf 11 2

2

f(x) = 4 x – 3

a) 5

b) x =2

1

1

1 2

3

2

3x

26

13)(1

x

xhg

6

1)(1 x

xh

3

2

1 3

4

2

3p ,

3

4q

(all correct)

Comparing SOR, POR

SOR =3

pand POR =

3

2

SOR =2

1and POR =

2

q

4

1,1

1

1 4

5

b = 3 c = - 1

( 0, 2 ) : f( x ) = a ( x – 3 ) 2 – 1

2 = a ( 0 – 3 ) 2 – 1

a =3

1

1

1

1 3

6

x<4 or x>5

or (x – 4) (x – 5) > 0

x2 – 9x + 20 > 0

3

2

1 3

7

1010

1 yandx

1010

1 yorx

4

3

4 5


QUESTIONNUMBERS

WORKING MARKSFULL

MARKS

(1) = ( 2 ) :yy 10

1102

or alternative answer

210

11

102

y

xy

x [ either one ]

2

1 4

87log9log

7log)3log)(log(2

76460.2

3log

3

333

3

x

x

xorx 3

21 3

9

3

11

9

2

27

S

S 2

1 2

10

n = 8

30 = 9 + ( n – 1 ) ( 3 )

a = 9 d = 3 [ either one ]

3

2

1 3

11 48

4

4

4

3

11

3

11

3

1

81

40

SSorS

S

new a =3

1or a = 27 and r =

3

2

1 3

12

( 2, k ): k = - 2 + 6

k = 4

( h, 3 ) 3 = - h + 6

h = 3

6 xx

y

1

1

1


QUESTIONNUMBERS

WORKING MARKSFULL

MARKS

13

C(6, 8)

63

104

3

6

86

kh

kh

3

)(1)5(2,

3

)(1)3(2)6,4(

kh

3

1,1

1 3

14

7

5

5

7

)5(7

50

02575

21

morm

xy

yx 3

2

1 3

15

i)

2

12v

2

12

148

1ˆ) vii

2

12

148

1ˆ

148ˆ

v

v

1

2

3

16

a) 6q – 10p

DCEDEC

pq

BDED

ppqEC

pqECb

)106(4

1

4

1

102

5

2

3

2

15

2

3)

)153(2

1pq

1

3 4

17

sin =2

1or sin = 1 (all correct)

30˚, 150˚ or 90˚

(2 sin –1)(sin –1) = 0

2 sin2 –3 sin +1 = 0

1– 2 sin2 = 2 – 3 sin

4

3

2

1 4


QUESTIONNUMBERS

WORKING MARKSFULL

MARKS

18

180

65

180

654

2

1

180

656

2

1

180

654

2

1

180

656

2

1

18

113

22

22

2

oneeitheror

unit

4

3

2

1 4

198

x + 4

2

1 3

20

0.26

y = (6x – 5) x 0.02

dy6 x 5

dx

3

2

1 3

21

a) 2

b) C =2

3

8 +

82

4

cx24

2

8

1 f(x) dx +

8

4cx dx = 24

1

3

2

1

4

22

32.66

median = 1019

12)55(5.24 2

1

3

1,1 3

23

= 70= 40 + 30

c x c4 51 2 or c x c4 5

2 1

431 4

24

a)2

15

2

1


QUESTIONNUMBERS

WORKING MARKSFULL

MARKS

x16 2

40 6

b)4

15

x12 4

30 6

2

1

4

25

h = 188.325 cm

h 165

15

= 1.555

P ( z >h 165

15

) = 0.06

P(x > h ) = 0.06

4

3

21 4


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