Spm Addmath1 (kedah)

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3472/1 Additional Mathematics Paper 1

Sept 2008 2 Hours

Narne:

.

Form:

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PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

SEKOLAH MENENGAH

NEGERI KEDAH DARUL AMAN

PEPERIKSAAN PERCUBAAN SPM 2008

ADDITIONAL MATHEMATICS

Paper 1

Two hours

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1

This question paper consists of 25 questions.

2. Answer allquestions. 3. Give only ODe answerforeach question.

4. Write your answers clearly in the spaces provided in the question paper. 5. Show your working. /t may help youtoget marks.

6.

Ifyouwish tochange your answer, cross out the work that you have done. answer.

Then write down the new

7. The diagrams in the questions provided are not drawn toscale unless stated 8. The marks allocated for each question and sub-part ofa question are shown inbrlK!kets. 9. A list offormulae is provided onpages 3 to 4.

10. A booklet offour-figure mathematil:al tables is provided. II You may use a non-programmable scientific

calculator.

12 This question paper must be handed in at the endof the examination.

For Examiner's use only Marks Question Total Marks Obtained ] 3

2

4

3

3

4

3

5

3

6

3

7

3

8

3

9

3

10

4

11

4

]2 3

13

4

14

3

15

2

]6 3

17

4

4

18

19

3

20

3

2] 4

22

2

2

23

24

3

25

4

TOTAL

80

Kertas soalan ini mengandungi 17 halaman bercetak 3472/1

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Thefollowing formulae may be helpful in answering the questions. The symbols given are the ones commonly used. ALGEBRA 8

1

loge a

2d" x d'

=

am' n

5Iog.mn::::log am + logan

m

6

log..b = loge b

Tn::::a+(n-I)d

10

n s, = "2[2a + (n -l)d]

11

Tn=ar

12 Sn =

.

:::: log am - log a n

log. -

9

nol

a(r"-l) r-l

13 S =~ '" l - r '

n

7 log a m" = n log. m

=

a(l-r") l-r

(

, r * 1)

Irl
CALCULUS 4 Area under a curve

dy dv du 1 y=uv, -=u-+vdx dx dx

b

Jy dx or du dv v--u­ u dx dx 'dx : : Jx dy y=-, - = a

b

2

v2

dy

V

a

5 Volume generated

dy dx

b

dy du du dx

3 - = - x ­

=

J1Q!2

dx or

a

a

GEOMETRY

5

A point dividing a segment of a line (x,y) =

2 Midpoint (x , y)

3

=

(XI; x

Irl=~x2 + l

(nx + mx l

2,

m+n

m

nyJ + y 2 ) m+n

2

6 Area of triangle

,Y2 + X 2Y3 + .X3YI ) - (X 2YI + X3Y2 + x.Y3)1 =.!.I(X 2 I

4

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STATISTIC

x=

1

LX

7

N

1= Lw\l\ LW1

8

"P. = r

9

"C r

!N -F] I.. C [

5

m = L+ 2

=

n\

.

.

(n ­ r)!r!

10

P(Au B) = P(A)+P(B) - P(A f'\ B)

11

P (X = r)

12

Mean s =np

13

u=~npq x-p z=-­ o

14

6

n! (n-r)!

= nc,p'qn-"

p+q = 1

I=Q\xl00

Qo

. TRIGONOMETRY

1 Arc length, s = r 8

9 sin (A ± B) = sinA cosB ± cosA sinH

1 2 Area of sector ,A = -r 28 2 3 sin 2A + cos 2A = 1

10 cos (A ± B) = cosA cosB

4 sec2A

11 tan (A ± B) = tan A ± tan B 1=1= tanAtanB

= 1 + tan2A

5 cosec 2 A = 1 + cor A

6 sin 2A = 2 sinA cosA 2

2

7 cos 2A = cos A ­ sin A =2cos2A-l = 1 - 2 sin2A 8 tan2A =

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=1= sinA sinH

12

a b c --=--=-­ sinA sinB sinC

2 2 13 a2 = b + C -2bccosA 14

Area of triangle

= .!.absinC 2

2 tan A l-tan 2 A

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For examiner use only

Answer all questions. 1.

x

L.

px-3

-1

1

2

q

Refer to arrow diagram above for the functionJ: x~ px - 3.

Dengan merujuk kepada gambarajah anak panah di atas bagifungsi J : x ~ px - 3.

Find the value of Cari nilai bagi (a) p,

(b) q.

[3 marks] [3 markah] Answer/Jawapan : (a) 1 (b)

..

[[ij

2. Given g : x ~ 3x - 2 and gf: x ~ 3x 2 + 4.

Diberi g:x~3x-2 dan gf:X~3X2 +4. Find Cari (a) g-I(2), (b) J(x).

[4 marks] [4 markah]

2

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Answer/Jawapan : (a)

.

(b)

..

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3.

6

Given that the inverse function of I

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: x ~ 3x + m is /-1 :x ~ x -

7,

n.

Diberi fungsi songsangbagi /: x ~ 3x + m ialah /-1 :x ~ x - 7 , n find the value of

cari nilai bagi (a) m, (b) n, (c) /-1/(5). [3 marks]

[3 markah}

AnswerlJawapan: (a) m=

. .

(b) n= (c)

3

..

[La 1------------------------------­ 4

One of the roots of the equation x 2 + 4x = 2k + 2 the value of k .

1

is three times the other root. Find

[3 marks]

Salahsatupunca bagipersamaan x + 4x = 2k + 1 adalahtiga kali gandapunca 2

2

yang satu lagi. Cari nilai k: [3 markah)

4

[La

0

Answer/Jawapan : 34

=

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For

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examiner'! use only

y

5.

--t----~+x

Diagram above show the graph of the function y

=p -

(x - q)2 . The curve intersects the

y-axis at 10 and has the maximum point (2, 10+k). Find the value of (a) q, (b)p, (c) k.

[3 marks 1 Gambar rajah di atas menunjukkan grafbagi fungsi y = p - (x - q)2. Lengkung tersebut bersilang dengan paksi-y pada 10 dan mempunyai tltik maksimum (2, 1O+k). Car; nilai bag; (a) q, (b) p, (e)k

.[3 markah]

6. The curve of the quadratic functionf(x) points. Find the range of values ofp.

Answer /Jawapan: (a)

.

(b)

.

(e)

..

= px 2 -

5x + P cuts the x-axis at two distinct

[3 marks 1 Lengkung bagi fungsi kuadratikf(x) = px' - 5x + p memotong paksi-x pada dua titik yang berbeza. Car; julat bagi nilai p. [3 markah]

6

AnswerlJawapan : '" 3472/1

..

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7.

8

Solve the equation

3x +3

Selesaikan persamaan

3x+3

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3x + 234.

=

[3 marks]

3x + 234.

[3 markah]

7

~ 8.

AnswerlJawapan :

..

I-,:-----::__:----:-----:---::-~---:----:--~-:--------:----~~----

During a given period, the number of people in each car passing a certain location on a road was recorded and the results are shown in the following table. Write down the inequality which must be satisfied by x if

. (a) the mode of the number of people in a car is 2, (b) the median of the number of people in a car is 2.

[3 marks]

Pada satu masa tertentu, bilangan orang di dalam kereta yang melalui sesuatu lokasi di sebatangjalan tertentu itu dicatat dan keputusan yang diperolehi seperti jadual di bawah. Tuliskan ketaksamaan yang mesti dipenuhi oleh x jika (a) mod untuk bi/angan orang di dalam kereta ialah 2, (b) median untuk bi/angan orang di dalam kereta ialah 2. Number of People in a car Number of cars

1

2

50

x

4

3 59

64

[3 markah]

o

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Answer/Jawapan : (a)

..

(b)

..

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9.

Given log, 2 = P and log, 5 = q. Express logs 4.J5 in terms of p and q.

[3 marks] Diberi logs 2 = p dan log85 = q. Ungkapkan log8 4.J5 dalam sebutan p dan q. [3 markah]

AnswerlJawapan:

10.

.

Given that log, (y + 6), log, (y + 2) and log, yare the first three terms of an arithmetic progression, find (a) the value of y. (b) the common difference of the arithmetic progression; [4 marks] Diberi log, (y + 6), log, (y + 2) dan log, yadalah riga sebutan pertama bagi suatu janjang arimetik; cari (a) nilai y. (b) beza sepunyajanjang arimetik.

[4 markah]

em

10

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AnsweriJawapan : .(a)

,

(b)

.

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11. The sum of the first n terms ofan arithmetic progression is given by Sn =2n(n+ 3). Find (a) the first term. (b) the common difference

of the progression.

[4 marks ] Hasil tambah n sebutan yang pertama bagi suatu janjang arimetik diberi oleh S. =2n(n+3). Cari (a) sebutan pertama (b) beza sepunya janjang itu. [4 markah]

11

AnswerlJawapan: a)

.

b)

.

[Gjl-----­ 12. The sum of the first it terms of the geometric progression 64, 32, 16, ... is 126. Find the value of n.

Hasil tambah n sebutan pertama bagi janjang geometri 64. 32, 16..... ialah 126. Cari ni/ai n.

[3 marks] [3 markah]

12

W

o

AnswerIJawapan:

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11

For examiner's useonly

The straight line x + py =q passes through the point (1, 2) and is perpendicular to the line 2x - y + 7 =O. Find the value ofp and of q .

[4 marks] Garis lurus x + py=q melalui titik O. 2) dan berserenjang dengan garis

2x- y+7=O. Cart nilai bagi p dan q.

[4markIJh]

Answer/Jawapan: p =

.

q =

..

13

em

14. Given that the points A(3, 6), P(5, I) and B(8, 1) are collinear, find

(i) (ii)

AP: PB the value of t.

[3 marks] Diberi titik-titik A (3, 6). prj. I) dan B(8, 1) adalah segaris, cari (i) (ii)

AP: PB nilai I. [3 markah]

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Answer/Jawapan : (i}

.

(ii}

.

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15

Given that a

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= 3; +j, b = -U +j. Ifma + nb = 8; +j. Find the value ofm and of n, [2 marks]

Diberi a

= 3; + j, b = -2; + j. Jika ma + nb = 8; + j. Cari nilai m dan n. [2markah]

15

Answer/Jawapan : m =

.

Ga 1-----------------------------­ n=

16

.

Diagram below shows a triangle ABC. It is given that 2CO = 30B, E is the

-

-

midpoint of AB, AC = 3x and AB =4y . Express ED, in terms ofx andy. Rajah di bawah menunjukkan sebuah segttiga ABC. Diberi bahawa 2CD = 3DB,

-

-

E ialah titik tengah AB. AC = 3x dan AB =4y. Ungkapkan ED dalam sebutan x dan y.

c

AL.----.......c.=-------~B

E

[3 marks] [3 markah]

16

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Answer/Jawapan : 3472/1

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For examiner's use only

13

Solve the equation 3 tan 2 X + S tan x = 4 sec 2 x for 0° s: x s: 360° .

[4 marks] Selesaikan persamaan 3 tan 2 x+Stanx=4sec 2 x bagi 0° s:xS:3600.

[4 markah]

17 '

Answer/Jawapan:

..

------------------------------1 18.

[Dj

Diagram below shows two sectors, OAB and OCD with centre O. Rajah di bawah menunjukkan dua sektor, OAB dan OCD dengan pusat O.

D~A

o "'--""--------Scm

C

B

Find Cari (a) L AOB , in radian. (a) LAOB, dalam radian. (b) the area of the shaded region ABCD. (b) luas bagi rantau berlorekABCD. [4 marks] [4 markah]

18

Answer/Jawapan: {a) {b)

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19.

Given that the volume of a spherical balloon is increasing at the rate of 501Z' em's -I , find the rate of change of the radius of the balloon when its radius is 5 em.

4

,

[V = 3"1Z' r ].

[3 marks]

Diberi bahawa tsipadu bag; suatu belon berbentuk sfera bertambah dengan kadar 501Z' em) S-1 , cari kadar perubahanjejari bagi belon tersebut apabilajejarinya ialah

Scm. [V = ~lZ'r'). 3

[ 3markah]

19

em

Answer/Jawapan:

20.

Given that

D I'beri

I

24

I

4 . k 2 2 (3x-5)

dx

=! , find the value of k .

..

[3 marks]

7

k 2 dx = -, 6.can"1' nt at k. (3x-5) 7

[3 markah]

20

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SULIT 21.

15 Given that (a)

If

J:

(b)

If

1,4

Diberi

J:

J:

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g(x)dt=10.

kg(x)dt=45.findthevalueofk. [g(x) + p]dt =80. findthevalueofp.

[4 maries] g(x)d%=10.

Lkg(x)dt=45. cartnilai k . 2

(a)

JiJca

(b)

JiJca

J:

[g(x)+p]dt=80.carinilaip. [4 marJcah]

22.

Given y

Answer/Jawapan: (a) k =

.

(b)p=

.

=~ •where u = 2 - 3x 2 • Find dy u dt

21

W

in tenns of x . [3 marb]

Diberi y = ~. dan u = 2 - 3x 2 • Cari dy dalam sebuum x.

u

dt·

[3 marJcah]

22

em

Answer/Jawapan: 3472/1

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For

examiner's use only 23.

In a multiple choice test consisting of 10 questions, each question has five answers to choose from. One mark will be given for each correct answer and no marks will be deducted for wrong answers. If a candidate chooses an answer randomly for each question, what is the expected score of the candidate? [2 marks] Da/am satu ujian pelbagai pilihan yang mengandungi 10 soalan, setiap soalan diberikan 5 pilihan jawapan. Satu markah akan diberikan untuk setiap jawapan yang betul. Tiada markah dipotong untukjawapan yang salah. Jika seorang cajon menjawab secara rawak; apakah skor jangkaan bagi cajon itu ? [2 markah]

23

em

AnswerlJawapan:

..

24. A student committee consisting of six members is to be formed from 7 boys and 5 girls. Find the possible number of committees that can be formed if (a) there are no restrictions. (b) at least one girl must be chosen.

[3 marks] Satu jawatankuasa pe/ajar yang terdiri daripada enam ahli akan dibentuk daripada 7 pe/ajar lelaki dan 5 pe/ajar perempuan. Cari bilangan jawatankuasa berlainan yang bo/eh dibentuk jika . (a) tiada syarat dikenakan (b) sekurang-kurangnya seorang pe/ajar perempuan mesti dipilih. [3 markah}

24

[[ij

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Answer/Jawapan: (a)

.

(b)

.

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25. A random variable X is normally distributed with mean 45 and standard deviation 6. Find the value of Satupembolehubah rawakX bertaburan normaldengan min 45 dan sisihanpiawai 6.

Cari nilai bag; (a) P(X >48) (b) kif P(X > k)=O.6915. (b) kjika P(X > k)=O.6915.

[4 marks] {4markah]

25

Answer/Jawapan: (a)

.

(b)

.

END OF QUESTION PAPER KERTAS SOALAN TAMAT

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