SPM AddMath1 (Kedah)

8/14/2019 SPM AddMath1 (Kedah)

1/16

3472/1Additional Mathematics Narne: .Paper 1Sept 2008 Form: .2 Hours

PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUASEKOLAH MENENGAH

NEGERI KEDAH DARUL AMANPEPERIKSAAN PERCUBAAN SPM 2008

For Examiner's use onlyADDITIONAL MATHEMATICSPaper 1 MarksQuestion Total Markswohours Obtained] 3

SEHINGGA DIBERITAHUJANGAN BUKA KERTAS SOALAN INI 2 43 3

1 This question paper consists of 25 questions. 4 32. Answer allquestions. 5 3

6 33. Give only ODeanswer foreach question. 7 34. Write your answers clearly in the spaces provided in 8 3the question paper. 9 3

10 4. Show your working. /tmay help youtoget marks.11 46. Ifyouwish tochange your answer, cross out the work ]2 3that you have done. Then write down the new 13 4answer. 14 3

7. The diagrams in the questions provided are not 15 2drawn toscale unless stated ]6 38. The marks allocated for each question and sub-part 17 4ofa question are shown inbrlK!kets. 4

1918

39. A list offormulae isprovided onpages 3 to 4. 20 310. A booklet offour-figure mathematil:al tables is 2] 4provided. 22 2

23I You may use a non-programmable scientificcalculator. 24 325 412 This question paper must behanded inat the endof

the examination. TOTAL 80Kertas soalan ini mengandungi 17 halaman bercetak

3472/1 [Lihat sebelahSULIT

2k


2/16

1

SULIT 3 3472/1Thefollowing formulae may be helpful in answering the questions. The symbols given are the onescommonly used.

ALGEBRA8 log..b= loge bloge a

2 d " x d' = am' n 9 Tn::::a+(n-I)dn10 s,= "2[2a+ (n - l )d]

no11 Tn=ara(r"- l ) a( l - r " ) (5Iog.mn::: : log am + logan 12 Sn = = , r * 1)m . r-l l-r6 log. - :::: log am - log ann 13 S = Irl


3/16

SULIT 4 3472/1STATISTIC

1 x = LXN 789

1= Lw\l\LW 1

"P. = n!r (n-r) !

n\ ."C = .r (n - r)!r!

10 P(Au B) = P(A)+P(B) - P(A f '\ B)11 P (X = r) = nc,p'qn-" p + q = 1

5

6

[!NFm = L+ 2 I.. CI=Q\xl00Qo .

121314

Mean s =npu = ~ n p q

x -pz=-o

TRIGONOMETRY

1 Arc length, s = r8 9 sin (A B) =sinA cosB cosA sinH2345

1Area of sector ,A = - r 282sin 2A+ cos 2A =1sec2A =1 + tan2Acosec2 A = 1 + cor A

10 cos (A B) = cosA cosB =1= sinA sinH11 tan (A B) = tan A tan B1=1= tanAtanB12 a b c- -= - -=- sinA sinB sinC

67

sin 2A =2 sinA cosAcos 2A = cos2A sin2 A

=2cos2A- l= 1 - 2 sin2A

13

14

a2 = b2+ C2 -2bccosA

= .!.absinCrea of triangle 28 tan2A = 2 tan Al-tan 2 A

3472/1 ( Lihat sebelahSULIT

- - - -

2k


4/16

SULIT 5Answer all questions.

1. x L. px-31-1q2

Refer to arrow diagram above for the functionJ: x px - 3.Dengan merujuk kepada gambarajahanakpanah di atas bagifungsi J :x px - 3.

Find the value ofCari nilai bagi(a) p,(b) q.

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

(b) ..

2. Given g : x 3x - 2 and gf: x 3x2+4.Diberi g : x ~ 3 x - 2 dan g f : X ~ 3 X 2 +4.

FindCari(a) g-I(2),(b) J(x).

[4 marks][4 markah]

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

3472/1 [ LibatsebelabSULIT

Forexamineruse only

1[[ij

2[Gjo

2k


5/16

For SULIT 6 3472/1examiner'suse only

3. Given that the inverse function of I :x 3x+m is /-1 :x x - 7 ,n.Diberi fungsi songsangbagi /: x 3x+m ialah /-1 :x x - 7 ,nfind the value ofcari nilaibagi(a) m,(b) n,(c) /-1/(5).

[3 marks][3 markah}

AnswerlJawapan: (a) m= .3 (b) n= .[La (c) ..1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

4 One of the roots of the equation x2 +4x =2k+1 is three times the other root. Find2the value of k .[3 marks]

Salahsatupunca bagipersamaan x2 +4x =2k +1 adalahtiga kaligandapunca2yang satu lagi. Cari nilai k: [3 markah)

4[La Answer/Jawapan :0 34= [ Lihat sebelahSULIT

2k


6/16


7/16

3472/1

7

SULIT 8Forexaminer'suse only 7. Solve the equation 3x +3 3x + 234. [3 marks]

Selesaikan persamaan 3x+3 = 3x + 234. [3 markah]

AnswerlJawapan : ..-,:-----::__ : - - - - : - - - - - : - - - : : - ~ - - - : - - - - : - - ~ - : - - - - - - - - : - - - - ~ ~ - - - -8. During a given period, the number of people in each ca r passing a certain location ona road was recorded and the results are shown in the following table. Write down theinequality which must be satisfied by x if

. (a) the mode of the number ofpeople in a car is 2,(b) the median of the number ofpeople in a car is 2. [3 marks]

Pada satu masa tertentu, bilangan orang di dalam kereta yang melalui sesuatulokasi di sebatangjalan tertentu itu dicatat dan keputusan yang diperolehi sepertijadual 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 ofPeople in a car 1 2 3 4Number of cars 50 x 59 64

[3 markah]

o Answer/Jawapan : (a) ..(b) ..[ Libat sebelahSULIT3472/1

2k


8/16

SULIT 9

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 anarithmetic progression, find(a) the value ofy.(b) the common difference of the arithmetic progression;

[4 marks]Diberi log, (y +6), log, (y +2) dan log, yadalah riga sebutan pertama bagi suatujanjang arimetik; cari(a) nilai y.(b) beza sepunyajanjang arimetik. [4 markah]

AnsweriJawapan : .(a) ,(b) .

3472/1 [ Libat sebelabSULIT

Forexaminer'suse only

10emo

2k


9/16

SULIT 10 3472/1For

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

we only

(a) the first term.(b) the common differenceof the progression.

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

[4 markah]

AnswerlJawapan: a) .11b) .

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]

W12 AnswerIJawapan: .[ Libat sebelab3472/1 SULIT

2k


10/16

SULIT 11

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

[4 marks]Garis lurus x + py=q melalui titik O. 2) dan berserenjang dengan garis2x- y+7=O. Cart nilai bagi p dan q.

[4markIJh]

Answer/Jawapan: p = .q = ..

14. Given that the points A(3, 6), P(5, I) and B(8, 1) are collinear, find(i) AP: PB(ii) the value of t .

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

(i) AP: PB(ii) nilai I .[3 markah]

Answer/Jawapan : (i} .(ii} .

3472/1 [ Libat sebelahSULIT

Forexaminer'suseonly

13

em

14[fao

2k


11/16

- -

- -

SULIT 12 3472/1Forexaminer'suseon/y 15 Given that a =3; +j , b = -U +j. Ifma + nb =8; +j . Find the value ofm and ofn,[2 marks]

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

15 Answer/Jawapan : m = .n= .Ga1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16 Diagram below shows a triangle ABC. It is given that 2CO =30B, E is the

midpoint ofAB, 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 dany.

c

A L . - - - - . . . . . . . c . = - - - - - - - ~ B E

[3 marks][3 markah]

16

em Answer/Jawapan : .o 472/1 [ Lihat sebelahSULIT

2k


12/16

SULIT 13 Forexaminer's

use only

17. Solve the equation 3 tan 2 X +Stan x = 4sec 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: .. [Dj- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1

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

FindCari(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]

18Answer/Jawapan: {a) .

{b) . [Dj3472/1 [ Lihat sebelahSULIT o

Bo "'--""---------

Scm

D ~

2k


13/16


19em

20emo

SULIT 14 3472/119. 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 berbentuksfera bertambahdengan kadar501Z' em)S-1 , cari kadarperubahanjejari bagi belon tersebut apabilajejarinya ialahScm.[V = ~ l Z ' r ' ) . 3 [ 3markah]

Answer/Jawapan: ..

20. Given that I 4 . k 2 dx =! ,find the value of k . [3 marks]2 (3x-5) 7D 'b I 4 k dx 6 . "1' k. [3 markah] eri 2 2 = - , can nt at(3x-5) 7

Answer: .

3472/1 [Libat sebelab SULIT

2k


14/16

SULIT 1521. Given that J: g(x)dt=10.

(a) If J: kg(x)dt=45.findthevalueofk.(b) If 1,4 [g(x) + p]dt =80. findthevalueofp.

Diberi J: g(x)d%=10.2(a) JiJca Lkg(x)dt=45. cartnilai k .

(b) JiJca J: [g(x)+p]dt=80.carinilaip.

Answer/Jawapan: (a) k =(b)p=

22. Given y = where u =2- 3x2 Find dy in tenns of x .u dtDiberi y = ~ dan u = 2- 3x2 Cari dy dalam sebuum x.u dt

Answer/Jawapan:

3472/1

[4 maries]

[4 marJcah]

.

.

[3 marb]

[3 marJcah]

( Libat sebelahSULIT

Forexaminer 'suseonly

21W

22emo472/1

2k


15/16

23


em

24[[ij0

SULIT 16 3472/1

23. In a multiple choice test consisting of 10 questions, each question has five answers tochoose from. One mark will be given for each correct answer and no marks will bededucted for wrong answers. If a candidate chooses an answer randomly for eachquestion, what is the expected score of the candidate?[2 marks]

Da/am satu ujian pelbagai pilihan yang mengandungi 10 soalan, setiap soalandiberikan 5 pilihan jawapan. Satu markah akan diberikan untuk setiap jawapan yangbetul. Tiada markah dipotong untukjawapan yang salah. Jika seorang cajonmenjawab secara rawak; apakah skor jangkaan bagi cajon itu ? [2 markah]

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 7pe/ajar lelaki dan 5 pe/ajar perempuan. Cari bilangan jawatankuasa berlainan yangbo/eh dibentuk jika .(a) tiada syarat dikenakan(b) sekurang-kurangnya seorang pe/ajar perempuan mesti dipilih. [3 markah}

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

3472/1 [ Lihat sebelahSULIT

2k


16/16

SULIT 17 3472/125. A random variable X is normally distributed with mean 45 and standard deviation 6.Find the value ofSatupembolehubah rawakX bertaburan normaldengan min45dan sisihanpiawai 6.Cari nilai bag;

(a) P(X >48)(b) kif P(X > k)=O.6915.(b) kjika P(X > k)=O.6915.

[4marks]{4markah]

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

END OF QUESTION PAPERKERTAS SOALAN TAMAT

3472/1 [ Lihat sebelahSULIT

25[Gjo

2k

Documents

SPM AddMath1 (Kedah)