sulit peperiksaan percubaan spm 2008 ... 347211 additional mathematics kertas 1 sept. 2008 2 jam...

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347211 Additional Mathematics Kertas 1 Sept. 2008 2 Jam

JABATAN PELAJARAN NEGERI JOHOR PEPERIKSAAN PERCUBAAN SPM 2008

ADDITIONAL MATHEMATICS Kertas 1 Dua jam

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1 Tu1i.r nama dun kelas anda pada

ruangan yang disediakan.

2 Kertas soalan ini adalah dalam

dw ihahasa

3 Soalan dalam bahasa 1nggeri.r mendahului soalan yang .repadan dalam haha.sa Melayu.

I Untuk Kegunaan Pemeriksa 1

4. Calon dibenarkan rnenjawab keseluruhan atau sebahagian soalan sama ada dalam bahasa Inggeris atau bahasa Melayu.

Soalan

1

5. Calon dihhendaki membaca maklumat di halarnan belakang kertus soalan ini.

347211 2008 Hak Cpra JPllll

Markah Penuh

2

[Lihat sebelah SULIT

Markah ~ Diperolehi

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For examiner '

use only

1

LE

2

Answer all questions S

1 1

1

Diagram 1 shows the relation between set P and set Q.

Rajah 1 menunjukkun hubungan antara set P dan set Q,

SULIT

1

-

2

I

Set P Set Q

Diagram 1 Rajah 1

State

Nyatakan

(a) the codomain of the relation,

kodomain hubungan itu,

(b) the type of the relation.

jenis hubungan itu.

[2 marks]

[ 2 markah]

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

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

! 7

Given the inverse of function k is k-' : x -+ - , x t 2 . x - 2

7 Diben, firngsi songsangan bagi k adalah k-' : x -+ - , x # 2 .

x - 2

(a) Calculate the value of k(3).

Hitungkan nilai bagi k(3).

(b ) State the value of x where function k is not defined.

Nyatakan nilai bagi x di mana fungsi k tidak tertakriJ

347211 2008 Hnk Cipra JPNJ

[ 3 mctrks ]

[ 3 markah ]

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

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SULIT 5 347211

3 Diagram 2 shows the function f that maps set A to set B and the function g

that maps set B to set C.

Rojnh 2 rnenunjukkan fungsi f memetakan set A kepada set B dun fungsi g rnemetaknn

set B kepada set C.

Diagram 2 Rajah 2

Given f ( x ) = rnx + 1 and d ( x ) = 2 x + n. Find the values of m and n.

Diberi f ( x ) = mx + 1 dun g f ( x ) = 2 x + n. Carikan nilai bagi rn dun n. [ 3 rnarb ]

[ 3 rnarkah ]

347211 2008 Hok Cipro JPNJ SULIT

For aminer rse only

3

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For examiner

use only

4

ULIT - 6

1 Form the quadratic equation which has the roots -5 and - .

4

Give your answer in the form d + bx + c = 0, where a, b and c are constants. 1

Bentukkan persamaan kuadratik yang mempunyai punca- punca -5 and - . Berikan 4

jawapan anda dalam bentuk ax2 + bx + c = 0, di mana a, b dun c adalah pemalar.

[2 marks]

[ 2 markah]

Answer / Jawapan: .................................

i Find the range of x for which (x + 3)(x - 4) < - 6.

Cari julat x bagi (x + 3)(x - 4) <- 6.

[ 3 marks ]

[ 3 markah ]

Answer/ Jawapan : ..............................

347211 2008 Hak Cipra JPNJ SULIT http://tutormansor.wordpress.com/

Find

C.'arikan

(a) the value of k,

nilai hagi k,

(b) the equation of the axis symmetry,

persamaan paksi simetri,

(c) the coordinates of the maximum point.

icoordinat titiic maksimum.

347211 2008 Hak Cipro JPNJ

expminer 's use only

El

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6 Diagram 3 shows the graph y = - 4 - (x - ic)2, where k is a constant. Rqjah 2 menunjukkan graf y = - 4 - (x - k)2, dengan keadaan k adalah pernalar.

y

0

1 3

> x

(6 , -13) (7 Diagram 3

Rajah 3

[ 3 marks ]

[ 3 markah ]

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

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[ 3 marks ]

[ 3 markah]

............................. Answer/ Jawapan :

Answer/ Jawapan : ...............................

SULIT For - 8 examiner's

use 7 Given that 32" (9"-') = 1, find the value of x.

Diberi 32" (9"-' ) = 1, carikan nilai x.

fa

0

(;7;) in terms of r and t . 8 Given that log, x = r and log, y = t , express log, -

(;7i) dalam sebutan r dun t. Diberi log, x = r dun log, y = t , ungkapkan log, -

[ 4 marks ]

[ 4 markah ]

347211 2008 Hak Cipta JPNJ SULIT http://tutormansor.wordpress.com/

SULIT 9 347211

9 The first three terms of an arithmetic progression are h, 2h - 2 and 2h + 1 .

Find the value of h.

Tiga sebutan pertama suatu janjang arithmetik adalah h. 2h - 2 und 2h + 1.

Carikan nilai bagi h .

[ 2 murky ]

[ 2 markah]

................................... Answer/ Jawapan :

22 10 The sum of the first five terms of a geometric progression is 7- and the common

27

2 ratio is - . Find the first term.

3

22 Hasil tambah lima sebutan pertama suatu janjang geometri ialah 7 - dun nisbah

27

2 sepitnyanya adalah - . Carikan nilai sebutan pertama.

3

[ 3 marks ]

[ 3 markah ]

347211 2008 Ifak Cipta JPNJ

Answer/ Jawapan: ................................... .,,

SULIl

For exorniner

use onb

9


[ 4 marks ]

[ 4 markah ]

For xaminer 's use onb

m

iI, ........................... Answer/ Jawapan : (a)

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

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. 11 Given the arithmetic progression 5, 8, 1 1, .... find the term that has a value of 13 1

Diberi janjang arithmetic 5, 8, 11, .... carikan sebutan ke berapakah nilainya sama

dengan 13 1. [ 2 marks]

[ 2 markah ]

................................. Answer/ Jawapan :

3 3 3 12 Given a geometric progression 3, - - -

5 ' 25 ' 125'""

3 3 3 Diheri suatu janjang geometri 3 , - - -

5 ' 2 5 ' 125'""

Find

Cari

(a) the common ratio

nisbah sepunya

(b) the sum to infinity of the progression.

hasil lambah ke ~akterhinggaan janjang I ersebut.

347211 2008 Hak Cipfa JPNJ SULIT http://tutormansor.wordpress.com/

SULIT 347211 I For

13 Given that the variables x and y are related by the equation y = 1 02x-2.

Diberi pembolehubah x and y dihubungkan oleh persamaan y = lo2'-*.

0 .X

(O,-q

Diagram 4 Rajah 4

Find the value of p and q.

Hirungkan nilaip dan q.

[ 3 marks ]

[ 3 markah ]

examiner's m e only

Answer/ Jawapan: p=. . . . .. . . . .q= .. . . . .. . . .. .

X Y 14 Find the equation of the straight line which is parallel to -+ - = 1 and passes through 3 4

tlle midpoint of A(-2,3) and B(6,9) . I X Y Cari persamaan garis Iurus yang selari dengan - + - = 1 dan melalui ritik tengah 3 4

A(-2,3) dan B(6,9)

[3 marks] I 14

347211 20061 Ifak Cipta JPNJ http://tutormansor.wordpress.com/

For examiner's

uYe only

15

LiI

16

SULIT 12

15 The point A is (4, -3) and the point B is (1, -2) . The point P moves such that

PA : PB = 3 : 2 . Find the equation of the locus of P.

Tirik A ialah (4, -3) dun tirik B ialah (1, -2). Saru titik P bergerak dengan keadaan

supaya PA : PB = 3 : 2. Cari persamaan lokus P.

[3 marks]

[3 markah]

................................. Answer/ Jawapan :

16 Diagram 5 shows vectors and z d r a w n on a cartesion plane.

Rqjuh 5 menunjukkan vekror % and @ pada safah cartesion.

Y

3..

P

c x -3 -2 -1 '

- 1 - I ;

Diagram 5 Rajah 5

(a) Express 5 in the form . t I Ungkapkan dalarn bentuk .

(b) Find the unit vector in the direction (f of z. Cari vektor unit dalam arah z.

............................. Answer/ Jawupan : (a)

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

347211 2008 Hak Cipm JPNJ SULI? http://tutormansor.wordpress.com/

SULIT - 13 347211

17 The points A, B and C are collinear. It is given that ?% = [:I, OB = (:) and

OC = [:).Find the value of k .

Titik- titik A, B dun C adalah segaris. Diberi = (')% = ('1 dun z = (:I. C'arikan nilai k.

[ 4 marks ]

[ 4 markah ]

......................... Answer/ Jawapan:

18 Solve the equation 8 cos2 x + 2sin x - 5 = 0 for 0' I 6 5 360'.

Selesaikanpersamaan 8cos2 x + 2sin x - 5 = 0 bagi 0' I 6 I 360'.

[ 4 marks : [ 4 markah ]

............................. Answer/ Jawapan:

347211 2008 Hak Cipro JPNJ

E'o r raminer S

only

17

1

3 0


Diagram 6

Rajah 6

SULIT 14

Given that the length of the minor arc AB is 12.57 cm, find the length, in cm, of the

radius. (use ~r = 3.142 )

Diberi panjang lengkok minor AB ialah 12.57 cm, caripanjang, dalam cm, jejari

bulatan itu.

[ 3 marks ]

[ 3 markah]

For examiner's

use only

................................. Answer/ Jawapan :

19 Diagram 6 shows a circle with centre 0.

Rajah 6 menunjukkan suatu bulatan berpusat 0.

( 2 ~ - 1)' Diberi f (.r) = - , carikan f ' ( x ) .

x - 1

2008 Hak Cipra JPNJ

[3 marks]

[ 3 markah]

Answer/ Jawapan: ...........................

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SULIT 15 347211

347211 2008 Hak Cipta JPNJ

- 2 d~ 21 Given that p = 2x - 5 and y = 7 , find the value of - when x = 2.

dx P

- 2 d~ Diberi p = 2x - 5 dun y = , carikan nilai - apabila x = 2.

P dx

[3 marks]

[ 3 markah ]

Answer1 Jawapan : .........................

3 3

22 Given that ig(x)dx = 5. Find the value of k if I- 2g(x) - b dx = - 18. I I

3 3

Diberi ig(x)dx = 5 . Carikan nilai k j i b I- 2g(x) - b dx = - 18. I I

[4 marks]

[ 4 markah ]

Answer/ Jawapan : k = .......................

SULIT

).'or exorniner :s

use only

2 1

22

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For examiner '3

use only

SULIT 16 I-

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23 Given six digits 1, 3 ,4 , 5, 6 and 8. A digit number is to be formed using

four of these digits. Find

Diberi enam digif 1, 3, 4, 5, 6 dun 8. Suafu nombor empaf digit

hendak dibenfuk dengan mengpinakan empaf daripada digit tersebut.Curi

(a) the number of different four -digit numbers that can be formed,

bilungun nombor empar digit yang berlainan yang dapat dibentuk

(b) the number of different four-digit odd numbers which are greater than 6000.

bilungun nornbor empat digir yang ganjil dun berlainan yung melebihi 6000.

[ 4 marks ]

[ 4 markah ]

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

24 Given two bags P and Q, each contains blue and red marbles. Bag P contains 3 blue

marbles and 4 red marbles. Bag Q contains 3 blue marbles and 5 red marbles. A bag is

chosen at random and a marble is picked from it. Find the probability that

Diberi dua beg, musing- musing mengandungi guli berwcrrna biru dun merah. Beg P mengandzingi 3 biji guli biru dun 4 biji guli merah. Bag Q mengandungi 3 biji guli biru dun 5 biji gull merah. Sebuah beg dipilih secara rawak dun sebiji guli akan dikeluurkan dari beg tersebut. Carikan kebarangkalian bahawa

(a) a red marble from bag Q is chosen.

sebiji guli merah dari beg Q dipilih.

(b) the marble is blue.

[ 3 marks ]

[ 3 markah ]

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

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

347211 2008 Hak Cipra JPNJ SULIT http://tutormansor.wordpress.com/

SULIT

25 Diagram 7 shows a standard normal distribution graph.

Rajah 7 menunjukkan graf taburan normal piawai.

347211

For examiner 's

use only

Given the probability represented by the area of the shaded region is 0.7019.

Diheri keharangkalian yang diwakili oleh luas kawasan berlorek ialah 0.7019.

(a) Find the value of k.

Carikan nilai k.

(b) Xis a random variable of a normal distribution with a mean of 45 and a

variance of 25. Find the value ofX when the Z-score is k.

X ialah pemboleh ubah rawak suatu taburan normal dengan min 45 dun

varians 25. Cari nilai X jika skor-Z ialah k.

END OF QUESTION PAPER

347211 2008 Hak Cipfa JPNJ SULIT


SlJLIT

INFORMATION FOR CANDIDATES MAKL UMA T UNTUK CALON

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

2. Answer all questions. J U W L I ~ semua soalan.

3. Give only one answer for each question. Bugi seliup s o a l ~ ~ n berikan satu jawapan sahaja..

4. Write your answers clearly in the spaces provided in the question paper. Jawupan hendaklah ditulis dengan jelas dalam ruang yang disediakan dalam kertas soalcrn.

5 . Show your working. It may help you to get marks. Tzinjukkcrn langkah-langkah penting dalam kerja mengira andu. Ini boleh membantu undu unruk mendapatkan markah.

6 . I f you wish to change your answer, cross out the work that you have done. Then write down the new answer. Sekircrnya anda hendak menukar jawapan, batalkan kerja mengira ylrng teluh dibuat. Kemudi~ln tulis jawupan yang baru.

7 . The diagrams in the questions provided are not drawn to scale unless stated. Rojah yang rnengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.

8. Thc marks allocated for each question are shown in brackets. Alurkah yang diperuntukkan hagi set@ soalan ditunjukkan dalarn kurungan.

9. A list of formulae is provided on pages 2 to 3. Sutu senarai rlrmus disediakan di halaman 2 hingga 3.

10. You may use a non - programmable scientific calculator. .4nJ~r dihenarkan rnenggunakan kalkulator saintlfik yang tidak holeh diprogram.

1 1 . Hand in this question paper to the invigilator at the end of the examination. k'err~ls soulun ini hendaklah diserahkan di akhir peperiksaan.

347211 2008 IIuk Cipra JPNJ SlJLIT


347211 Additional Mathematics Kertas 1 Sept. 2008 2 Jam

JABATAN PELAJARAN NEGERI JOHOR KEMENTERIAN PELAJARAN MALAYSIA

PEPEPUKSAAN PERCUBAAN SPM

2008

ADDITIONAL MATHEMATICS

I

Kertas 1 I

SKEMA PEMARKAHAN

Skema pemarkahan ini mengandungi 7 halaman bercetak

347211 Hak Cipta JPNJ 2008


MARKING SCHEME PEPERllKSAAN PERCUBAAN SPM 2008 MATEMATIK TAMBAHAN , KERTAS 1

Solution and mark scheme Number 7

(b) x = 0

I

Sub marks

( 4 { 2,4,6,8, 10 I

(b) many to many

Full marks

--

5

6

- 2 < ~ < 3

(x-3)(x+2) < O

+=++ B2 : factorize and try to solve

(a) k = 3 (b) x = 3 (c) ( 3, - 4

3

B2 3


-- - - ---

Solution and mark scheme -

Sub marks

Full marks


sulit peperiksaan percubaan spm 2008 ... 347211 additional mathematics kertas 1 sept. 2008 2 jam...

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