1

PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA

DENGAN KERJASAMA

JABATAN PELAJARAN MELAKA

PEPERIKSAAN PERCUBAAN

SIJIL PELAJARAN MALAYSIA 2010

MATEMATIK TAMBAHAN

Kertas 1

Dua Jam

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

Kertas soalan ini mengandungi 18 halaman bercetak

Nama : ………………..………………..

Tingkatan: ………………………..…… 3472/1

Matematik Tambahan

Kertas 1

Sept 2010

2 jam

1. This question paper consists of 25 questions Kertas soalan ini mengandungi 25 soalan.

2. Answer all questions. Jawab semua soalan.

3. Give only one answer for each question Bagi 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 boleh

membantu anda untuk mendapatkan markah.

6. If you wish to change your answer, cross out the work that

you have done. Then write down the new answer. Sekiranya anda hendak menukar jawapan, batalkan kerja mengira yang telah

dibuat. Kemudian tulis jawapan yang baru.

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

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

8. The marks allocated for each question and sub-part of a question are

shown in brackets. Markah yang diperuntukkan bagi setiap soalan atau ceraian soalan ditunjukkan

dalam kurungan.

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

Kod

Pemeriksa

Soalan Markah

Penuh

Markah

Diperoleh

1 2

2 4

3 3

4 3

5 3

6 3

7 3

8 3

9 3

10 3

11 3

12 3

13 4

14 4

15 3

16 4

17 4

18 3

19 3

20 3

21 3

22 4

23 3

24 3

25 3 Jumlah

80

2

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

commonly used. Rumus-rumus berikut boleh digunakan untuk membantu anda menjawab soalan. . Simbol-simbol yang diberi adalah yang

biasa digunakan. ALGEBRA

1

2 4

2

b b acx

a

2 a

m a

n = a

m + n

3 am a

n = a

m - n

4 (am)

n = a

nm

5 loga mn = log am + loga n

6 loga n

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)

13 r

aS

1 , r <1

CALCULUS( KALKULUS)

1 y = uv , dx

duv

dx

dvu

dx

dy

2 v

uy ,

2v

dx

dvu

dx

duv

dy

dx

,

3 dx

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

1 Distance (Jarak) = 2

21

2

21 )()( yyxx

2 Midpoint ( Titik Tengah )

2),( 21 xx

yx ,

2

21 yy

3 22 yxr

4 22

ˆyx

yxr

ji

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

,),( 21

nm

mxnxyx

nm

myny 21

6 Area of triangle ( Luas Segitiga ) =

)()(2

1312312133221 1

yxyxyxyxyxyx

GEOMETRY

3

1 x = N

x

2 x =

f

fx

3 = N

xx 2)( =

2_2

xN

x

4 =

f

xxf 2)(

= 2

2

xf

fx

5 Cf

FN

Lmm

2

1

6 1000

1 Q

QI

7 1

11

w

IwI

8 )!(

!

rn

nPr

n

9 !)!(

!

rrn

nCr

n

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

11 P (X = r) = rnr

r

n qpC , p + q = 1

12 Mean µ = np

13 npq

14 z =

x

1 Arc length, s = r

( Panjang lengkok) s = j

2 Area of sector , A = 2

2

1r

( Luas sektor L = 2

2

1j )

3 sin 2A + cos

2A = 1

4 sec2A = 1 + tan

2A

5 cosec2 A = 1 + cot

2 A

6 sin 2A = 2 sinA cosA

7 cos 2A = cos2A – sin

2 A

= 2 cos2A - 1

= 1 - 2 sin2A

A

AA

2tan1

tan22tan8

9 sin (A B) = sinA cosB cosA sinB

10 cos (A B) = cosA cosB sinA sinB

11 tan (A B) = BA

BA

tantan1

tantan

12 C

c

B

b

A

a

sinsinsin

13 a2 = b

2 + c

2 - 2bc cosA

14 Area of triangle = Cab sin2

1

( Luas Segitiga )

STATISTICS

TRIGONOMETRY

4

Answer all questions.

Jawab semua soalan

1 The relation between two variables is given by {(–3, 3),( –2, –1),( –1, –3),(0, –6)}. State Hubungan antara dua pemboleh ubah diberi dengan {(–3, 3),( –2, –1),( –1, –3),(0, –6)}. Nyatakan

(a) the object of –1,

objek bagi -1

(b) the type of relation.

jenis hubungan

Answer / Jawapan: (a) _________________

(b) _________________

2 The functions g and h are defined as 𝑔 𝑥 = 2𝑥 + 5 and. ℎ 𝑥 =1

6𝑥 + 3 Find

Fungsi – fungsi g and h ditakrifkan sebagai 𝑔 𝑥 = 2𝑥 + 5 and ℎ 𝑥 =1

6𝑥 + 3. Cari

(a) the value of, g-1

( - 1) nilai bagi, g

-1 ( - 1)

(b) hg (x).

Answer / Jawapan: (a) ________________

(b) ________________

For

examiner’s

use only

[2 marks]

[ 2markah]

[4 marks] [ 4markah]

2

1

4

2

5

3 Given function g: x→ x - 4 and function hg(x) = 2x - 5. Find the function of h

Diberi fungsi g: x→ x - 4 dan hg(x) = 2x - 5. Cari fungsi bagi h

[ 3 marks ] [ 3 markah ]

Answer/ Jawapan: _______________________

4 Solve the following quadratic equation, Selesaikan persamaan kuadratik berikut,

𝟐𝑥2−𝟖

𝟓= 𝑥

Give your answer correct to 4 significant figures. Berikan jawapan anda betul kepada 4 angka bererti.

[ 3 marks ] [ 3 markah ]

Answer/Jawapan: (a) _______________________

For

examiner’s

use only

3

3

3

4

6

5 The quadratic equation 𝑥 𝑥 + 1 + 𝑘𝑥 = −9 has no real roots.

Find the range of values of k. Persamaan kuadratik 𝑥 𝑥 + 1 + 𝑘𝑥 = −9 tidak mempunyai punca nyata

Cari julat bagi k

[ 3 marks ] [ 3 markah ]

Answer/Jawapan: ______________________

6 Diagram 6 shows the graph of function 𝑦 = (𝑥 + 𝑞)2 − 4 where q is a constant Rajah 6 menunjukkan graf fungsi dengan keadaan q ialah pemalar

Find Cari

(a) the value of q nilai bagi q

(b) equation of the axis of symmetry persamaan bagi paksi simetri

(c) the coordinate of minimum point koorninat bagi titik minimum

[3 marks] [3markah]

Answer/Jawapan:(a) p =___________________

(b) q =___________________

(c) _____________________

For

examiner’s

use only

3

2

5

3

2

6

Diagram 6 Rajah 6

•

5

0

y

x

7

7 Solve the equation 2 4 𝑥+4 = 8 𝑥+1 Selesaikan persamaan 2 4 x+4 = 8 x+1

[ 3 marks ] [ 3 markah]

Answer /Jawapan: x = _____________________

8 Given that log3 P - 2 = log 9 R. Express R in terms of P Diberi bahawa log3 P - 2 = log 9 R. Ungkapkan R dalam sebutan P.

[ 3 marks ] [ 3 markah ]

Answer /Jawapan : = ______________________

9 Express 2𝑛+2 − 2𝑛 + 9 2𝑛−1 in the simplest form. Ungkapkan 2𝑛+2 − 2𝑛 + 9 2𝑛−1 dalam bentuk yang termudah.

[3 marks]

[3 markah]

Answer/ Jawapan : ______________________

3

7

3

9

8

3

For

examiner’s

use only

8

10 The first three term of an arithmetic progression are q – 5, q + 5, and 2q + 1. Find Tiga sebutan pertama bagi suatu janjang aritmetik adalah q – 5, q + 5, dan 2q + 1. Cari

(a) the value of q nilai bagi q

(b) the sum of the first 6 terms hasiltambah 6 sebutan pertama

[3 marks] [ 3 markah ]

Answer/Jawapan: (a)___________________

(b)___________________

11 The sum of the first n term of a geometric progression 1, 2, 4, 8, … is 1 023. Find Hasil tambah n sebutan pertama janjang geometri 1, 2, 4, 8, … adalah 1 023. Cari

(a) the common ratio of the progression nisbah sepunya bagi janjang itu

(b) the value of n nilai n

[ 3 marks ] [ 3 markah ]

Answer/Jawapan: (a) _____________________

(b) _______________________

12 Given the first and the fourth term of a geometric progression are 6 and 2

9 respectively.

Diberi ungkapan pertama dan keempat suatu janjang geometri adalah 6 dan 2

3 masing-masing

Find the sum to infinity of the progression. Cari jumlah hingga tak terhingga janjang itu.

[3 marks] [ 3 markah]

Answer: __________________________

For

examiner’s

use only

3

11

10

3

3

12

9

13 Diagram 13 shows the graph of the straight line that is related by the equation

y = pxq where p and q are constants.

Rajah 13 menunjukkan graf garis lurus yang dihubungkan oleh persamaan y = pxq di mana p dan q

adalah pemalar.

Find, Cari

(a) the values of p and q, nilai-nilai p dan q

(b) the value of y when x = 5. nilai y apabila x = 5

[4 marks]

[4 markah]

Answer/Jawapan: (a) p =__________q =__________

(b) ____________________

For

examiner’s

use only

4

13

log x

(0,-2)

(4,0)

log y

Diagram13

Rajah 13

10

14 A point P (8, s ) divides the line joining G (4, 1) and H ( r , 7 ) such that

3GP = 2PH. Find the value of Titik P (8,s) membahagi garis yang menghubungkan G (4,1) dan H(r,7) dalam keadaan

3GP=2PH. Carikan nilai

(a) r

(b) s

[4 marks] [4 markah]

Answer : (a)__________________________

(b)__________________________

For

examiner’s

use only

4

14

1

11

15 Diagram 15 shows a parallelogram PQRS with QTS as a straight line. Rajah 15 menunjukkan segiempat selari PQRS dengan QTS merupakan garis lurus

Given that 𝑃𝑄 = 5𝒙, 𝑄𝑅 = 3𝒚 and 4ST = TQ. Express in terms of x and y.

Diberi 𝑃𝑄 = 5𝒙, 𝑄𝑅 = 3𝒚 , dan 4ST = TQ . Ungkapkan dalam sebutan x dan y.

(a) 𝑄𝑆

(b) 𝑇𝑅 [3 marks]

[3 markah ]

Answer / Jawapan: (a)_________________________

(b)_________________________

For

examiner’s

use only

3

15

P

Q

R

S

T

Diagram 15 Rajah 15

12

16 Diagram 16 shows triangle OPQ. Rajah 16 menunjukkan segi tiga OPQ

Given that 𝑂𝑃 = −5𝑖 − 4𝑗 and 𝑂𝑄 = 6𝑖 − 2𝑗 . Find

Diberi bahawa 𝑂𝑃 = −5𝑖 − 4�̰� dan 𝑂𝑄 = 6𝑖 − 2�̰�. Cari

a) 𝑃𝑄

b) unit vector in the direction of 𝑃𝑄 .

vektor unit dalam arah 𝑃𝑄

[4 marks] [4 markah]

Answer /Jawapan: ( a)___________________

( b)___________________

For

examiner’s

use only

4

16

y

x O

P

Q

Diagram 16 Rajah 16

13

17 Solve the equation cos 2𝜃 =− 5 cos 𝜃+4

2 for 0

o ≤ θ ≤ 360

o .

Selesaikan persamaan kos 2𝜃 =− 5 kos 𝜃+4

2 bagi 0

o ≤ θ ≤ 360

o

[ 4 marks ] [ 4 markah ]

Answer/ Jawapan: ………………………..

18 Diagram 18 shows a circle with centre O Rajah 18 menunjukkan sebuah bulatan berpusat O.

Given the radius of the circle is 8 cm and the angle of minor sector is 0.2736 rad. Using

= 3.142, find the perimeter of major sector PQR.

Diberi jejari bulatan ialah 8 cm dan sudut sektor minor ialah 0.2736 rad. Dengan

menggunakan = 3.142 , carikan perimeter major POQ .

[ 3marks] [ 3 markah ]

Answer/Jawapan: ___________________

For

examiner’s

use only

3

4

18

P

Q

O

Diagram 18 Rajah 18

4

17

14

19 Find the values of x for y = 2

2

27x

x when

2

20

d y

dx

Carikan nilai-nilai x bagi y = 2

2

27x

x apabila

2

20

d y

dx .

[ 3 marks]

[ 3 markah ]

Answer/Jawapan: _______________________

20 A curve y = px² + 3

𝑥 has an equation of normal x + 5y = 6 at x = 1 .

Find the value of p

Suatu lengkung y = px² + 3

𝑥 mempunyai persamaan normal x + 5y = 6 pada x = 1 . Cari nilai

bagi p.

[ 3 marks] [ 3 markah]

Answer/Jawapan:_______________________

For

examiner’

s use only

3

19

3

20

15

21 Given that 𝑔 𝑥 𝑑𝑥 = 55

1, find the value of t if 𝑡𝑥 − 2𝑔 𝑥 𝑑𝑥 = −3𝑡

5

1

Diberi bahawa 𝑔 𝑥 𝑑𝑥 = 55

1, cari nilai bagi t jika 𝑡𝑥 − 2𝑔 𝑥 𝑑𝑥 = −3𝑡

5

1

[3 marks] [ 3 markah ]

Answer/Jawapan : ________________________

22 The mean of the set of data 5, 2p - 1, 8, 5 and ( p2 – 2) is 10.

Min bagi set data 5, 2p - 1, 8, 5 and ( p2 – 2) adalah 10.

(a) Find the possible values of p. Cari nilai yang mungkin bagi p.

(b) Hence, find the mode and the median of the set of the data based on the positive

value of p. Seterusnya, cari nilai mod dan median bagi data tersebut berdasarkan nilai positif p

[4 marks] [ 4 markah ]

.

Answer / Jawapan: a) p= _____________________

b) mode =__________________

median =_________________

For

examiner’s

use only

3

21

4

3

22

16

23 The probability that Ihsan being chosen as a school prefect is 5

3 while the probability of

Akram being chosen is 9

4.

Kebarangkalian Ihsan dipilih sebagai pengawas sekolah ialah 5

3 manakala kebarangkalian

Akram dipilih ialah 9

4.

Find the probability that Cari kebarangkalian bahawa

(a) neither of them is chosen as a school prefect, kedua-duanya tidak dipilih sebagai pengawas sekolah,

(b) only one of them is chosen as a school prefect. hanya seorang daripada mereka dipilih sebagai pengawas sekolah.

[3 marks] [3 markah]

Answer/ Jawapan : (a) __________________

(b) _________________

For

examiner’s

use only

3

3

23

17

24 6 students are chosen to take part in a leadership course. These 6 students are chosen

from 4 monitors, 3 assistant monitors and 5 prefects. 6 orang pelajar dipilih untuk mengikuti kursus kepimpinan. 6 orang pelajar itu dipilih daripada 4

ketua darjah, 3 penolong ketua darjah dan 5 pengawas.

Calculate the number of different ways the team can be formed if Hitung bilangan cara yang berlainan pasukan itu boleh dibentuk jika

(a) there is no restriction, tiada syarat dikenakan,

(b) the team contains only 1 monitor and exactly 4 prefects. pasukan itu mengandungi hanya 1 ketua darjah dan tepat 4 pengawas.

[3 marks] [ 3 markah]

Answer/ Jawapan : (a) _________________

(b) _________________

25 X is a random variable of a normal distribution with mean of 4.2 and a variance of 1.21.Find X adalah pembolehubah rawak bagi suatu taburan normal dengan min 4.2 dan varians 1.21. Cari

(a) the z-score if X=6.1 nilai skor - z apabila X = 6.1

(b) P 6.52.4 x

[3 marks] [3 markah]

Answer/ Jawapan:(a)___________________

(b)___________________

END OF THE QUESTION PAPER

KERTAS SOALAN TAMAT

For

examiner’s

use only

3

3

25

3

3

24

18