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SULIT 1 34723472MatematikTambahanSEPT 20072 jam

SEKOLAH MENENGAH KEBANGSAAN SEKSYEN 18

SHAH ALAM

PEPERIKSAAN AKHIR TAHUN 2007

TINGKATAN 4

MATEMATIK TAMBAHAN

KERTAS 1

Dua jam

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Kertas soalan ini mengandungi 25 soalan.

2. Jawab semuasoalan.

3. Bagi setiap soalan berikan SATU jawapan / penyelesaian sahaja

4. Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantuanda untuk mendapatkan markah

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

6. Markah yang diperuntukan bagi setiap soalan atau ceraian soalan ditunjukkandalam kurungan

7. Satu senarai rumus disediakan di halaman 2 hingga 3

8. Penggunaan kalkulator saintifik yangtidak boleh diprogramkan adalah dibenarkan

Disediakan oleh Disemak oleh Disahkan oleh

_______________ ___________________ __________________

(Ms Liew Hui Kin) (Pn Norizan Kasim) (Pn Rosnah Abd Rahman)

Kertas soalan ini mengandungi 14 halaman bercetak

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SULIT 3472

Following formulae may be helpful in answering the questions. The symbols given are theones commonly used.

ALGEBRA

1 x =a

acbb2

4

2

2 am an = a m + n

3 am an = a m - n

4 (am) n = a nm

5 logamn = log am + logan

6 loga

n

m= log am - logan

7 log amn = n log am

8 logab =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

ra nn

=

1

)1(

1

)1(, (r 1)

13r

aS = 1 , r

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SULIT 3472

STATISTIC

1 Arc length,s = r

2 Area of a sector , A = 2

2

1r

3 sin 2A + cos 2A = 1

4 sek2A = 1 + tan2A

5 cosek2 A = 1 + kot2 A

6 sin2A = 2 sinAcosA

7 cos 2A = cos2A sin2 A

= 2 cos2A-1

= 1- 2 sin2A

8 tan2A =A

A2tan1

tan2

TRIGONOMETRY

9 sin (A B) = sinAcosB cosAsinB

10 cos (A B) = cosAcosB sinAsinB

11 tan (A B) =BA

BA

tantan1

tantan

12C

c

B

b

A

a

sinsinsin==

13 a2 = b2 +c2 - 2bccosA

14 Area of triangle = Cabsin2

1

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

FN

Lm

+ 2

1

6 1000

1 =P

PI

71

11

w

IwI

=

8)!(

!rn

nPrn

=

9!)!(

!

rrn

nCr

n

=

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

11 p (X=r) =rnr

r

n qpC , p + q = 1

12 Min(mean) = np

13 npq=

14 z =

x

3

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P Q

1

2

4

5

a

3

7

9

Answer all questions .

1 Diagram 1 represents a functionf that maps elements in setPto elements in set Q. Each

objects in setPis multiplied by two then minus by 1.

State the

(a) value of a

(b) functionf in the form of function notation[2 marks]

Answer: (a) ....

(b)

____________________________________________________________________________________

2 Given ,3

23)(

1 =x

xh find the value of

(a) h(4)

(b) m such that 32)3(1 = mmh

[4 marks]

Answer: (a)

(b)

4

Untuk

Kegunaan

Pemeriksa

Diagram 1

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SULIT 5

3 The roots for quadratic equation 033102 =+ kxx are in the ratio 2 : 3.

Find the,

(a) roots,

(b) value ofk.

[4 marks]

Answer: (a)

(b)....

______________________________________________________________________________

4 Given 2)1()( += pxxpxxf . Find the range of values ofp iff(x) is always positive.

[3 marks]

Answer:

______________________________________________________________________________

5 A function g and its inverse are defined as g: x3

+x

bax, x 3 and g-1: x

2

23

x

x, x

respectively.

Finda) Values of a and b

b) Value of x such that g(x) = 3

[4 marks]

Answer: (a)

(b)

3472/1 SULI

Untuk

Kegunaan

Pemeriksa

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UntukKegunaan

Pemeriksa

6 Solve 2422 2343 = ++ xx .[4 marks]

Answer:

____________________________________________________________________________________

7 Given ym =27log and xn =3log . Express 349log nm in terms ofx andy.[4 marks]

Answer:

____________________________________________________________________________________

8 Find the roots of the following quadratic equation

a) x (2x - 3) = 5

[2 marks]

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SULIT 7

Answer: (a)

9 Diagram 2 shows a straight line 63 += xy that is perpendicular to a straight line that connects

pointA (2, 3) andB(s, t).

Express tin terms of s. [4 marks]

Answer: __________________________________________________________________________________

10 Given = -3 and = 4. Form a quadratic equation that has 2 + 5 and 3 7 as the roots.

[3 marks]

Answer:

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y

B(s, t)

A(2 , 3)x

Diagram 2

Untuk

Kegunaan

Pemeriksa

y=3x+6

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(b)..

16 Express each of the following in terms of log axandlog a y.

a) 2

5

logyxa

b) 37log yx

aa

[4 marks]

Answer: (a)

(b)..____________________________________________________________________________________

17 N is a point that lies on the straight line that connects Q (-1,-3) and R (4, 1) such thatQN = 4NR. Find the coordinate of point N.

[2 mark

Untuk

Kegunaan

Pemeriksa

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SULIT 11

Answer:

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18 Calculates the mean, standard deviation and variance for 14, 16, 20 ,23 ,30.[4 marks]

Answer:

____________________________________________________________________________________

19 Find the median for 4, 7, 3, 7, 2, 5, 3 and 7.

[2 marks]

Answer:

Untuk

Kegunaan

Pemeriksa

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SULIT 13

20 The mean and standard deviation for the set of number x1, x2, x3,.., xn are 6 and 2 respectively.

Find the mean and standard deviation set for 5x1 + 2, 5x2 + 2, 5x3 + 2, , 5xn + 2

[4 marks]

Answer: (a)

(b) ..

____________________________________________________________________________________21

Diagram 4

Diagram 4 shows a sector with radius of 6 cm. The arc AB is 4 cm. Find

a) Angle AOB

b) Area of the shaded region [3 marks]

[3 march]

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Untuk

Kegunaan

Pemeriksa

6 cm 4 cm

A

B

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Answer: (a)

(b) .

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Answer:

24 Given y = 15x ( 3 - x ), calculate thea) value of x when y is maximum

b) maximum value of y

[3 marks]

Answer:(a).

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

______________________________________________________________________

25 Given y = x2 + 3x, find the small changes in y when x increases from 2 to 2.01.

[3 marks]

Answer: ..

Untukegunaan

meriksa

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SULIT 17

KERTAS SOALAN TAMAT

3472/1 SULIT