09 trial melaka_p1

SULIT

[ Lihat sebelah3472/1 SULIT

PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA

PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 2009

MATEMATIK TAMBAHANKertas 1Dua Jam

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

Kertas soalan ini mengandungi 17 halaman bercetak

Nama : ………………..………………..

Tingkatan: ………………………..……

3472/1Matematik TambahanKertas 1Sept 20092 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 provided 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 32 33 44 45 36 37 38 39 3

10 311 312 313 314 315 216 417 318 319 320 321 322 323 424 425 4

Jumlah80

http://mathsmozac.blogspot.com

www.cikgurohaiza.com

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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



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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



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Answer all questions.Jawab semua soalan

1 Diagram 1 shows the relation between two sets of number .Rajah 1 menunjukkan satu hubungan diantara dua set nombor.

Diagram 1 / Rajah 1State,Nyatakan,

(a) the images of 1,imej-imej bagi 1

(b) the object of 9objek bagi 9

(c) the type of relation.jenis hubungan itu.

[ 3 marks ][ 3 markah ]

Answer/Jawapan: (a) ……………………..

(b) ……………………...

(c) ..................................

2 Given the function f : x → 3x + 2 and g : x → x2 +1 , find the values of x if fg(x) = 17Di beri f : x → 3x + 2 dan g : x → x2 +1 . Cari nilai –nilai x jika fg(x) = 17


Answer/Jawapan: …………………....…..

3

2

3

1

Forexaminer’s

use only

1 2 3

9

12

15

6

3

0



SULIT 5

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3 Given function f : x→ 7 – 2x and function g : x x 2 - 5.Diberi fungsi f : x→ 7 – 2x dan fungsi g : x x 2 - 5.Find:Cari

(a) f -1(x)

(b) the value of f g(2).nilai f g(2).


Answer/ Jawapan: (a) ...…………………….....

(b)......................................

4 If one of the roots of the quadratics equation 2x2 – px = 12 is 3Jika salah satu daripada punca-punca persamaan kuadratik 2x2 – px = 12 ialah 3findcari(a) the value of p

nilai p(b) the other root

punca yang satu lagi


Answer/Jawapan: (a) p = ……………………………

(b) ……………………………….

Forexaminer’s

use only

4

3

4

4



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5

Diagram 5 shows the graph of the function y = f(x), where cbxaxf 2)( . Find the

values of a, b and c.

Rajah 5 menunjukkan graf bagi fungsi y = f(x), di mana cbxaxf 2)( . Cari nilai a,

b and c.[ 3 marks ]

[ 3 markah ]

Answer/Jawapan: a =………………………….

b = ……………………………..

c =…………………………..

6 Given that the quadratic equation 2)1()( txxtxxf . Find the range of value of t if

f(x) is always positive.Diberi fungsi kuadratik 2)1()( txxtxxf . Cari julat nilai t jika f(x) sentiasa

positif[3 marks]

2

8

4x

Diagram 5Rajah 5

Forexaminer’s

use only

3

6

3

5

y



SULIT 7


Answer/ Jawapan: ........……........................7 Solve the equation 5 n + 1 - 5 n + 5 n – 1 = 105.

Selesaikan persamaan 5 n + 1 - 5 n + 5 n – 1 = 105[ 3 marks ]

[ 3 markah]

Answer /Jawapan: n = ………………………...

8 Given that 3 + log2 k = log 2 (h + 5). Express k in terms of hDiberi bahawa 3 + log2 k = log 2 (h + 5). Ungkapkan k dalam sebutan h


:

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

Forexaminer’s

use only

3

8

3

7



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3472/1 SULIT

9 Given that ma 3log and ,6log na express36

27log

3aa in the terms of m and n.

Diberi bahawa ma 3log dan ,6log na Ungkapkan36

27log

3aa dalam sebutan m dan n.

[3 marks][ 3 markah ]

Answer/Jawapan: ……..……...……….....

10 The sum of the first n terms of an arithmetic progression is given by Sn = 3n2 – 5nFind the common difference of the progressionHasil tambah n sebutan pertama suatu janjang aritmetik diberi oleh Sn = 3n2 – 5n .Cari beza sepunya bagi janjang itu.


Answer /Jawapan: ……………...………....

11 The first three terms of a geometric progression are x + 10, x – 2 and x – 10. Find the sum toinfinity of the progression.Tiga sebutan pertama suatu Janjang Geometri ialah x + 10, x – 2 and x – 10. Cari jumlahsebutan ke takterhinggaan janjang itu.


Answer/Jawapan: ……………………………

3

10

3

11

Forexaminer’s

use only

3

9



SULIT 9


12 x and y are related by the equation y = px2 + qx , where p and q are constants.

A straight line is obtained by plottingx

yagainst x, as shown in Diagram 12.

x dan y dihubungkan oleh persamaan y = px2 + qx , dimana p dana q ialah pemalar

Satu garisurus diperolehi dengan memplotkanx

ymelawan x, sebagaimana ditunjukan

dalam Rajah 12

x

y

ODiagram 12Rajah 12

Calculate the value of p and of q.Kira nilai p dan nilai q .

[ 3 marks][ 3 markah]

Answer/Jawapan: p =………………………

q=……………………………..

3

12

Forexaminer’s

use only

(6, 1)

(2,9 )

x



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13 EFG is a straight line such that EF : FG = 1 : 2. Given point E(-1, 3) and point F(2, 5).Find the coordinates of G.EFG ialah garis lurus di mana EF : FG = 1 : 2. Diberi titik E(-1, 3) dan titik F(2, 5). Carikoordinat titik G. [3 marks]

[3 markah]

Answer/Jawapan: ………………………..

.

14 Diagram 14 shows a straight line 63 xy which is perpendicular to a straight line

that passes through A(2, 3) and point B.Rajah 14 menunjukkan garis lurus 63 xy yang berserenjang dengan garis lurus

yang melalui A(2, 3) dan titik B.

Determine the y-intercept for the straight line AB. [3 marks]Tentukan pintasan - y bagi garis lurus AB [ 3markah]

Answer/Jawapan: …………………………..

Forexaminer’s

use only

3

13

3

141

y=3x+6

y

B

A(2 , 3)

x

Diagram 14



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15 Diagram 15 shows PRQ is a straight line.Rajah 15 menunjukkan PRQ satu garis lurus.

Given PR : RQ = 2 : 1,~

OP p

and~

OQ q

, express OR

in terms of~p and

~q .

Diberi PR : RQ = 2 : 1,~

OP p

dan~

OQ q

, ungkapkan OR

dalam sebutan~p dan

~q .


Answer/Jawapan: ...........................................2

15

Forexaminer’s

use only

P R Q

O



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16 It is given that WXYZ is a parallelogram,~~

3 jiXY

andYZ =

~~22 ji .

Diberi bahawa WXYZ merupakan sebuah segiempat selari,,~~

3 jiXY

danYZ =

~~22 ji .

FindCari

( a)

WY

( b) the unit vector in the direction of

WY

vektor unit dalam arah

WY[ 4 marks ]

[4 markah ]

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

( b).........................................

4

16

Forexaminer’s

use only



SULIT 13


17 Solve the equation sin (2x – 100) = 0.6258 for 00 0x 360 . ˚.

Selesaikan persamaan sin (2x – 100) = 0.6258 untuk 00 0x 360 .

[3 marks][3 markah]

Answer/Jawapan: …...…………..…......

18 Diagram 18 shows a semicircle OWXY with centre O and a radius of 3cm. If the lengthof the arc XY is 9cm, find the perimeter of the shaded region in terms of .Rajah 18 menunjukkan sebuah semibulatan OWXY dengan pusat O dan jejari 3 cm.Jika panjang lengkung XY ialah 9 cm, carikan perimeter bagi rantau terlorek dalamsebutan .

[ 3 marks ][ 3markah]

Diagram

Answer/Jawapan: …………………………..3

18

3

17

Forexaminer’s

use only

W

X

O

3 cm

9 cm

Y

Diagram 18Rajah 18



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3472/1 SULIT

19 Differentiate 2 6(1 2 )x x with respect to x .

Bezakan 2 6(1 2 )x x terhadap x

[ 3 marks][ 3 markah ]

Answer/Jawapan: ………………………….

20 The radius of a sphere increases at the rate of 0.1 cms-1, when its radius is 5 cm, find therate of increase of its surface area.[ Given the surface area of a sphere is A = 4πr2 ]Jejari sebuah sfera bertambah dengan kadar 0.1 cms-1. Apabila jejarinya bersamaandengan 5 cm, carikan kadar penambahan luas permukaannya[ Diberi luas permukaan sfera A = 4πr2]

[ 3 marks][ 3 markah]

Answer/Jawapan: ………………………….….

Forexaminer’s

use only

3

20

3

19



SULIT 15


21 Given that 3

1

5)( dxxf Find the value of the constant m if 2

1

3

2

15])([)( dxmxxfdxxf

Diberi bahawa 3

1

5)( dxxf Cari nilai pemalar m sekirnya 2

1

3

2

15])([)( dxmxxfdxxf


Answer/Jawapan (a) ………………………………..

(b)………………………………..

Forexaminer’s

use only

3

21



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22 Table 22 shows the scores of a group of students in a quiz, calculate the standarddeviation of the scores.Jadual 22 menunjukkan skor-skor sekumpulan pelajar dalam suatu kuiz, kirakan sisihanpiawai skor tersebut

ScoreSkor

1 2 3 4

Number ofstudentsBilanganPelajar

4 23 10 5

Table 22

Jadual 22 [3 marks]

[3 markah]

Answer/Jawapan: …...…………..…….......

23 A Science and Mathematics club in a girl’s school has 10 Form Five students and 8 Formfour students. One of the Form Five students is the sister of one of the Form Four girlstudents. If a committee of 3 form five members and 2 form four members is to be formed,findSebuah persatuan sains dan matematik mempunyai 10 orang pelajar tingkatan lima dan 8 orang

pelajar tingkatan empat. Salah seorang daripada pelajar tingkatan lima merupakan kakak kepadaseorang daripada pelajar perempuan tingkatan empat. Jika sebuah jawatankuasa terdiri daripada3 orang pelajar tingkatan lima dan 2 orang pelajar tingkatan empat hendak dibentuk, cari

a) the number of ways in which the committee can be formed,bilangan cara di mana jawatan kuasa itu dapat dibentuk,

b) the number of ways in which the committee can be formed if the pair of sisters mustbe in the committee.

bilangan cara di mana jawatan kuasa itu dapat dibentuk sekiranya pasangan adik beradik itu mesti

berada dalam jawatan kuasa itu

[ 4 marks ][ 4 markah]

Answer/ Jawapan: (a) …...…………..……..

(c) ..................................(d)

Forexaminer’s

use only

4

23

3

22



SULIT 17


24 Ali has three 20 sen coins and five 50 sen coins in his wallet. He takes out two coins atrandom from his wallet, one after the other without replacement.Calculate the probability that the total value of the two coins isAli mempunyai tiga keping syiling 20 sen dan lima keping syiling 50 sen dalam poketnya. Diamengeluarkan dua keping syiling secara rawak dari poketnya satu demi satu tanpa gantian.Kirakan kebarangkalian di mana jumlah nilai dua keping syiling itu ialah

(a) RM 1(b) 90 sen(c) 70 sen


Answer/Jawapan a)……………………….

b)……………………………

(e) ………………………

25 X is a random variable of a normal distribution with a mean of 6.3 and a variance of 1.24.X merupakan pembolehubah rawak bagi suatu taburan normal dengan nilai min 6.3 danvarian 1.24find,cari ,a) the Z score if x = 7.5,

skor Z jika x = 7.5

b) )5.73.6( XP

[ 4 marks ]

[ 4 markah ]

Answer/Jawapan: (a) ………………..………….

(b) .............................................

END OF THE QUESTION PAPER

4

25

Forexaminer’s

use only

4

24



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