soalan add maths kertas 1 pp zon a kuching 2007

8/14/2019 SOALAN ADD MATHS KERTAS 1 PP ZON A KUCHING 2007

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SULIT 3472/1

Matematik

Tambahan

Kertas 1

SEPTEMBER

20072 jam

SEKOLAH-SEKOLAH KUCHING ZON A

PEPERIKSAAN PERCUBAAN SPM

Kertas soalan ini mengandungi 14 halaman bercetak

3472/1 2007 Hak Cipta Sekolah-Sekolah Kuching Zon A SULIT

MATEMATIK TAMBAHAN

Kertas 1

Dua jam

JANGAN BUKA KERTAS SOALAN INI SEHINGGA

DIBERITAHU

1. Kertas soalan ini mengandungi 25 soalan.

2. Jawab semua soalan.

3. Bagi setiap soalan berikan SATU jawapan sahaja.

4. Jawapan hendaklah ditulis pada ruang yang disediakandalam kertas soalan.

5. Tunjukkan langkah-langkah penting dalam kerjamengira anda. Ini boleh membantu anda untuk

mendapatkan markah.

6. Sekiranya anda hendak menukar jawapan. Batalkankerja mengira yang telah dibuat. Kemudian tulislah

jawapan yang baru.

7. Rajah yang mengiringi soalan ini tidak dilukiskan

mengikut skala kecuali dinyatakan.

8. Markah yang diperuntukkan bagi setiap soalan atau

ceraian soalan ditunjukkan dalam kurungan.

9. Satu senarai rumus disediakan di halaman 2hingga 3.

10. Buku sifir matematik empat angka disediakan.

11. Penggunaan kalkulator saintifik yang tidak

boleh diprogramkan adalah dibenarkan.

12. Kertas soalan ini hendaklah diserahkan pada akhirpeperiksaan .

Kod

Pemeriksa

Soalan Markah

Penuh

Markah

Diperoleh1 2

2 3

3 44 2

5 3

6 3

7 3

8 3

9 4

10 4

11 3

12 4

13 3

14 3

15 4

16 3

17 3

18 4

19 3

20 3

21 3

22 3

23 3

24 3

25 4

Jumlah 80

Nama:... Kelas : ..

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SULIT 3472/1

Rumus-rumus berikut boleh digunakan untuk membantu anda menjawab soalan. Simbol-simbol yangdiberi adalah yang biasa digunakan.

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

ALGEBRA1 x =

a

acbb

2

42

2 am an = a m + n

3 am an = a m n

4 (am) n = a nm

5 log amn = log am + log an6 log a

n

m= log am log an

7 log amn = n log am

8 log a b =a

b

c

c

log

log

9 Tn = a + (n 1)d

10 Sn = ])1(2[2

dnan

+

11 Tn = arn 1

12 Sn = r

ra

r

rann

=

1

)1(

1

)1(

, (r 1)

13r

aS

=

1, r < 1

CALCULUS

1 y = uv ,dx

duv

dx

dvu

dx

dy+=

2vuy = ,

2v

dx

dv

udx

du

v

dx

dy = ,

3dx

du

du

dy

dx

dy=

4 Area under a curve

= b

a

y dx or

= b

a

x dy

5 Volume generated

= b

a

y 2 dx or b

a

x2 dy


5 A point dividing a segment of a line

(x,y) = ,21

++

nm

mxnx

++

nm

myny 21

6. Area of triangle =

1 2 2 3 3 1 2 1 3 2 1 3

1( ) ( )

2x y x y x y x y x y x y+ + + +

1 Distance = 221

2

21 )()( yyxx +

2 Midpoint

(x ,y) = +

2

21 xx,

+

2

21 yy

3 2 2x y r

42 2

x y

x y

i jr

GEOMETRY

2


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SULIT 3472/1

STATISTICS


1 Arc length,s = r

2 Area of sector , A =21

2r

3 sin 2A + cos 2A = 1

4 sec2A = 1 + tan2A

5 cosec2A = 1 + cot2A

6 sin 2A = 2 sinA cosA

7 cos 2A = cos2A sin2A

= 2 cos2A 1= 1 2 sin2A

8 tan 2A =A

A2

tan1

tan2

TRIGONOMETRY

9 sin (A B) = sinA cosB cosA sinB

10 cos (A B) = cosA cosBsinA sinB

11 tan (A B) =BA

BA

tantan1

tantan

12C

c

B

b

A

a

sinsinsin==

13 a2 = b2 + c2 2bc cosA

14 Area of triangle = Cabsin2

1

1 x =N

x

2 x =

f

fx

3 =2( )x x

N

=2

2x xN

4 =

2( )f x x

f

=

22fx x

f

5 M = Cf

FN

Lm

+ 2

1

61

0

100Q

IQ

=

71 1

1

w II

w

=

8)!(

!rn

nPrn

=

9!)!(

!

rrn

nCr

n

=

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

11 P(X= r) = rnrrn qpC , p + q = 1

12 Mean, = np

13 npq=

14 z =

x

3

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SULIT 3472/1

Answerallthe questions

1 Diagram 1 below shows a graph of the relation between two variablesx andy.

State

(a) the object of 4.

(b) the image of 5.[2 marks]

Answer : (a)

(b)

2 Given that : 3 2f x x a and : 4g x xa . Find

(a) 1f x

(b) 1f g x

[3 marks]

Answer : (a)

(b)


4

1

2

DIAGRAM 1

y

x

0 1 2 3 4 5 6

24

68

10

12


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SULIT 3472/1

3 Given that functions : 3f x xa , 2:g x px q+a , where p, q are constants andcomposite function

2: 3 18 10gf x x x +a .Find the value ofp and ofq .

[4 marks]

Answer : (a)

(b)

4 Find the range of values of p if the quadratic equation 025 2 =+ pxx has real anddistinct roots.

[2 marks]

Answer : ..


5

3

4

2

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SULIT 3472/1

5 Solve the quadratic equation 15)5)(1( =+ xx . Give your answer correct to foursignificant figures.

[3 marks]

Answer :

6 Diagram 2 shows the graph of a quadratic function )(xfy = .

DIAGRAM 2

(a) Find the coordinates of the minimum point.

(b) Express )(xf in the form of 2( )x p q+ + , wherep and q are constants.[3 marks]

Answer :

7 Find the range of values ofx for xxx 32)1)(23( + . [3marks]


6

6

3

5

7

3

4

x

y

0 2

)(xfy = )(xfy =

6. .


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SULIT 3472/1

Answer :

8 Solve the equation42

2

5

1125

+

=x

x

.

[3 marks]

Answer :

9 Given that 5 5log 7 1 2091 and log 2 0 4307= = , evaluate 28log25[4 marks]

Answer :

10 In an arithmetic progression, the fourth term is 8 and the sum of the first ten terms is 50.

Find the first term and the common difference of the progression. .

[4 marks]


7

9

8

3

10

4


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SULIT 3472/1

Answer :

11 The sum of the first n terms of the geometric progression 3, 6, 12 is 129.Find the value ofn.

[3 marks]

Answer :

12 The variables x and y are related in such a way that when y is plotted against

x + 1, a straight line that passes through the points (2, 0) and (1, 3) is obtained, asshown in the diagram 3. Calculate the value ofx wheny = 4.

[4 marks]

Answer


8

12

11

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DIAGRAM 3


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SULIT 3472/1

13 A pointPmoves such that its distance fromB(2, 0) is1

2of its distance from A(0, 1).

Find the equation of the locus ofP. [3 marks]

Answer:

14 Two points have coordinates A(4, 2m) andB(6, 4). IfP(2, 10) divides the straight lineAB in the ratio of 3 : k, find the value ofkand ofm. [3

marks]


9

14

3

13

3


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SULIT 3472/1

Answer :

15 Given the points P, Q and R are collinear. Given that 4 3 PQ b a

% %

and

( 1) 2QR k a b

% %

where kis a constant. Find

(a) the value of k,

(b) the ratio of : PQ QR.

[4 marks]

Answer : (a)

(b)

16 Given that 5 4i jOA

% %

, mi kjOB

% %

, 2i kjAB

% %

, find the value of m and of k.

[3 marks]


10

154

16

3

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SULIT 3472/1

Answer:

17 Given that sinA = tand 0A 90, express each of the following in terms oft.

(a) secA,

(b) cos (90 A).

[3 marks]

Answer :

18 Solve the equation 4 sinx cosx = 3 for 0 x 2 .

[4

marks]


11

17

3

18


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SULIT 3472/1

Answer :

19 Given3 23

( )2 4

x xf x

x

, find the value off(1). [3

marks]

Answer :

20 Given y = (3x + 2) 4 , find2

2

d y

dx. [3 marks]

Answer :

21 The radius of a balloon in the shape of a sphere increases at the rate of 2 cm s1.

Find the rate of change of the volume of the balloon when the radius is 5 cm.

[Volume of sphere, V=34

3r ] [3 marks]


12

19

3

20

21

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SULIT 3472/1

Answer :

22 Given that

24 4

mx dx

. Find the values ofm. [3 marks]

Answer: .

23 A password consists of 4 letters, followed by 3 digits. The letters and digits are chosen

from the letters and digits as shown in the diagram 4,

F U N D S 1 2 3 4 5

If no letter or digit is repeated in the password, find the number of passwords that beginwith a consonant.

[3 marks]


13

23

3

22

3

DIAGRAM 4


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SULIT 3472/1

Answer :

24 Siti has six T-shirts where 2 are blue, 2 are yellow and 2 are red. She also has five skirtswhere 1 is green, 1 is blue and 3 are yellow. Siti selects a T-shirt and a skirt at random.

Calculate the probability that the T-shirt and skirt selected are of the same colour.

[3 marks]

Answer :..

25 In a study carried out in a housing estate, it is found that 3 out of 5 houses have a Proton

car. If a sample of 10 houses is chosen at random, calculate the probability that not more

than 1 house has a Proton car.

[4 marks]

Answer :

END OF THE QUESTION PAPER


14

24

3

25

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soalan add maths kertas 1 pp zon a kuching 2007

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