Add Mth 1 Johor@ 2008

SULIT 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

I

Untuk Kegunaan Pemeriksa Markah Markah Soalan Penuh Diperolehi 2 1

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

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

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[Lihat sebelah SULIT

1

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For examiner 'S use only

SULIT Answer all questions

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

1

Rajah 1 menunjukkun hubungan antara set P dan set Q,

Set Q

Set P

Diagram 1 Rajah 1 State Nyatakan the codomain of the relation,

(a)

kodomain hubungan itu, ( b ) the type of the relation.

[2 marks]

jenis hubungan itu.

[ 2 markah]

1

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

LE1 -

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

1

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

2!

x-2

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

(a)

#

2.

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

[ 3 mctrks ]

[ 3 markah ]

2

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

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

aminer rse only

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 ]

3

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6

1 Form the quadratic equation which has the roots -5 and - . 4

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. Give your answer in the form

[2 marks]

[ 2 markah]

4

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 : ..............................

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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

>x

0

(7 (6, -13)

1 3

Diagram 3

Rajah 3 Find

C.'arikan (a)

the value of k,

nilai hagi k,

(b) the equation of the axis symmetry, persamaan paksi simetri,

(c)

El

the coordinates of the maximum point. [ 3 marks ]

icoordinat titiic maksimum.

[ 3 markah ]

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

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

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For examiner's use

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8

Given that 32"(9"-') = 1, find the value of x. Diberi 32"(9"-' ) = 1, carikan nilai x. [ 3 marks ] [ 3 markah]

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

8

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

Diberi log, x = r dun log, y = t , ungkapkan log,

(;7i) -

dalam sebutan r dun t. [ 4 marks ]

[ 4 markah ]

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

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exorniner use o n b

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 : ...................................

10

22 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 ]

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

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For xaminer 's use onb

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Given the arithmetic progression 5, 8, 11, .... find the term that has a value of 131 . Diberi janjang arithmetic 5, 8, 11, .... carikan sebutan ke berapakah nilainya sama dengan 13 1.

[ 2 marks] [ 2 markah ]

m

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

12

3 3 3 Given a geometric progression 3, - - 5 ' 2 5 ' 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. [ 4 marks ] [ 4 markah ]

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

.................................

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Given that the variables x and y are related by the equation y = 102x-2. Diberi pembolehubah x and y dihubungkan oleh persamaan y

For examiner's m e only

= lo2'-*.

X.

0 (O,-q Diagram 4 Rajah 4 Find the value of p and q. Hirungkan nilaip dan q.

[ 3 marks ]

[ 3 markah ]

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

14

X Y- = 1 and passes through Find the equation of the straight line which is parallel to -+ 3 4 tlle midpoint of A(-2,3) and B(6,9) .

X +Y- = 1 dan melalui ritik tengah Cari persamaan garis Iurus yang selari dengan 3 4 A(-2,3) dan B(6,9) [3 marks]

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12

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]

15

LiI

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

16

Diagram 5 shows vectors

and z d r a w n on a cartesion plane.

% and @ pada safah cartesion.

Rqjuh 5 menunjukkan vekror

Y 3.. P

'

-3 -2 -1

I

-1-

;

cx

Diagram 5 Rajah 5 (a)

Express

5 in the form

Ungkapkan 16

(b)

tI

.

dalarn bentuk

.

(f z. z.

Find the unit vector in the direction of Cari vektor unit dalam arah

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

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

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The points A , B and C are collinear. It is given that

OC = [:).Find

?%=

[:I, (:) OB =

E'o r raminer S only

and

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 ]

17

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

18

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

Selesaikanpersamaan 8cos2x + 2sin x - 5 = 0 bagi 0' I 6 I 360'. [ 4 marks

:

[ 4 markah ]

3 Answer/ Jawapan:

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0

14

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Diagram 6 shows a circle with centre 0. Rajah 6 menunjukkan suatu bulatan berpusat 0.

Diagram 6 Rajah 6

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]

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

( 2 -~1)'

Diberi f (.r) = , carikan f ' ( x ) .

[3 marks]

x -1

[ 3 markah]

Answer/ Jawapan:

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........................... SULIT

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

Diberi p = 2x - 5 dun y

=

-2

, carikan nilai

d~

- apabila x = 2. dx

P

[3 marks]

[ 3 markah ]

21

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

Given that ig(x)dx = 5. Find the value of k if

2g(x)

-b

dx = - 18.

I

I 3

3

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

I-

3

3

22

I- 2g(x) - b dx

=

- 18.

I

[4 marks] [ 4 markah ]

22

Answer/ Jawapan : k =

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SULIT 23

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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) ....................................

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Diagram 7 shows a standard normal distribution graph.

For examiner 's use only

Rajah 7 menunjukkan graf taburan normal piawai.

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 o f X 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

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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 Lsemua I~ soalan. 3. Give only one answer for each question. Bugi seliup s o a l ~ ~berikan n 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 . If 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~lntulis 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~rdihenarkan 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~lssoulun ini hendaklah diserahkan di akhir peperiksaan.

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347211 Additional Mathematics Kertas 1 Sept. 2008 2 Jam

JABATAN PELAJARAN NEGERI JOHOR KEMENTERIAN PELAJARAN MALAYSIA PEPEPUKSAAN PERCUBAAN SPM 2008

ADDITIONAL MATHEMATICS I

I

Kertas 1 SKEMA PEMARKAHAN

Skema pemarkahan ini mengandungi 7 halaman bercetak

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MARKING SCHEME PEPERllKSAAN PERCUBAAN SPM 2008 MATEMATIK TAMBAHAN ,KERTAS 1

Num 7 Solution and mark scheme

I

Sub marks

Full marks

( 4 { 2,4,6,8, 10 I (b) many to many

(b) x = 0

-5

3

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

3

+=++

B2 : factorize and try to solve

6

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

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B2

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Solution and mark scheme

- - ---

-

Sub

marks

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Full marks

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