add maths johor spm trial 2008 p1&2

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 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.

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Markah ~ Diperolehi

Johor Trial SPM 2008 http://edu.joshuatly.com/ http://www.joshuatly.com/

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use only

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Answer all questions S

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Diagram 1 shows the relation between set P and set Q. Rajah 1 menunjukkun hubungan antara set P dan set Q,

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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

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[ 3 mctrks ] [ 3 markah ]

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

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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 ]

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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.


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

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

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.

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

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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 ]

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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 ]

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

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For xaminer 's use onb

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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.

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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.


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

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

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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.


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

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Diagram 6

Rajah 6

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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


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

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- 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 = .......................

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SULIT 16 I- 347211

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.


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.


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

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25 Diagram 7 shows a standard normal distribution graph. Rajah 7 menunjukkan graf taburan normal piawai.

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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

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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 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.

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SULlT

Additional Mathematics Kertas 2 Sept. 2008

1 2 - jam 2

JABATAN PELAJARAN NEGERI JOHOR PEPERIKSAAN PERCUBAAN SPM 2008

ADDITIONAL MATHEMATICS Kertas 2

Dua jam tiga puluh minit

JANGAN BUKA KERTAS SOALAN IN1 SEHINGGA DIBERITAHU

1. Kertas soalan ini adalah dalam rhvibahasa.

2. Soalan dalam bahasa Inggeris mendahului soalan yang sepadan dalarn bahasa Meluyu.

3. C'alon dikehendaki membaca maklumat di halaman belakang kertas soalan ini.

4. Calon dikehendaki menceraikan halaman 19 dun ikat sebagai muka hadapan bersama-sama dengan jawapan anda..

Kertas soalan ini ~nengandungi 19 haIaman bercetak dan 2 halaman kosong.

347212 I3ak Cipta JPNJ 2008 SULlT


SULIT

Section A Bahagian A

Answer all questions in this section . Jawab semua soalan.

I Solve thc following simultaneous equations : Scie.suikari persatnuan serentak berikui:

~ , - . r = 2 and y 2 + 2 y + s 2 = 9

Give your answer correct to three decimal places. Berikan julvapun anda betul kepuda 3 iempai perpuluhan.


2 '[he gradicnt function of a curve which passes through the point P(1,2) is 2x3 - 4x. Fungsi kecerunrrn bagi suaiu lengkzrng yang melalui titik P(1 ,2) ialah 2x3 - 4x. Find Cari (a) the equation of the curve,

/~cr.satnaan Iengkzing itu, [3 marks]

[3 markah]

(b) the equation of the normal to the curve at point M. pcrsamuan normal kepuda Iengkung di titik M


3 Given a set of numbers : Diberi scrtzc set nornbor:

3 , 5 , 6 , 8 , 9 , 1 0 , 1 l , 1 2 .

(a) Find the mean and standard deviation of the set of numbers. [4 marks] Carikan min dun sisihan pialvai bagi set nombor tersebut. [4 markah]

(b) Given that each of the number increases by 2 and then divide by 4. Diberi bahaiva setiup notnbor tersebut meningkat sebanyak 2 dan kemudian dibahagi dengan 4.

Find the new standard deviation. C 'trri .ci.sihan pitnvui yang baru.

[3 marks] [3 markah] Johor Trial SPM 2008


SULlT 5

4 Diagram 1 shows part of arrangement of bricks of equal size. Rajah 1 menunjukkan sebahagian daripada susunan baru bara yang sama saiz.

Diagram 1 Rajah 1

The number of bricks in the lowest row is 4096 and the height of each brick is 4 cm. Edham built a wall by arranging bricks such that the number of bricks is half the number of its previous one until the number of bricks in the top most row is 1.

Bilangan baru bara di baris paling bawah adalah 4096 dun tinggi seriap baru bara ialah 4 cm. Edhan? menyusun batu bata untuk membina sebuah tembok dengan keadaan bilangan baru bara adalah separuh daripada bilangan pada baris sebelumnya sehingga bilangan batu bara di haris paling atas adalah 1.

Calculate Hitungkan

(a) the number of bricks in the 71h row, hilangan baru bara pada baris kerujuh,

(b) the height in cm, of the wall. iinggi rembok dalam cm.

[3 marh] [3 markah]

[3 marh] [3 markah]

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SULIT

5 [n Diagram 2, the straight line joining PQ meets the x-axis at R. The point S lies on PR such thatPS:SQ=3:2. Dalatn Rujah 2, garis llrrus PQ menyilangpaksi-x di titik R. Titik S terletak di atas garis PR dengun keadilun PS : SQ = 3 : 2.

Diagram 2 Rajah 2

A straight line passes through S meets the x-axis at Tand L RST = 90'.

Satu garis lurus melalui tirik S menyilang pabi-x di titik T dun L RST = 90'.

Find Cari

(a) the coordinates ofS, koordinaf bagi titik S

(b) the equation of ST. persunlaan garis lurus ST



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6 (a) Prove that tan 0 + cot 0 = sec 0 cosec 0. [2 marks]

Bzrktikan identiti tan 0 + cot 0 = sec 0 cosec 0. [2 markah]

(b) Sketch the graph of y = I sin x 1 + 1 for 0 s x 1 271. Hence, using the same axes, draw a 2x

suitable straight line and state the number of solutions to the equation 1 sinx I= - -1 x

for 01xs2i' l . [6 marks]

Lakarkan graf bagi y = I sin x 1 + 1 untuk 0 5 x 5 2 x . Seterusnya, dengan menggunakan paki yang sama, lukiskan garis lurus yang sesuai dan nyatakan bilangan penyelesian

2x bagipersamaan I sin x 1 = - - 1 untuk 0 x s 2 x . [6 markah] i'l

[ Lihat sebelah SULIT -


Section B Bahagian B [40 marks]

[40 markah]

Answer four questions from this section. Jawab empat soalan dar&ada bahagian ini.

7 Use graph paper to answer this question. G'zrr~akun kcrtus graf untlrk tnenjawab soalan ini.

Table 1 shows the values of two variables, x and y, obtained from an experiment.

Variables x and y are related by the equation y = a b X L , where a and b are constants.

Jadlitrl I menunjukkan nilai-nilai duapembolehubah x dun y , yang diperoleh daripada satu 2

eksperimcn. Pembolchubah x drrn y dihubungkun olch persamaan y = ah' , di mana a dun b ariuluh petnalar.

Table 1 Jadual 1

(a) Plot loglo y against x h y using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 0.2 units on they -axis. Hence, draw the line of bcst fit. [ 5 tnarks]

Plotkan log,, y melawan x2 dengan mcngpnakan skula 2 cm kepada 1 unit padapaksi-x dan 2 cm kepada 0.2 unit pada paksi-y. Seterusnya, lukiskun garis lurus penyuaian terhaik. [5 markuh]

(b) Use your graph from 7(a) to find the value of (;unukrrn grrif undu di 7(u) untuk mencari nilai 6) u (ii) h [5 marks]

[ 5 markuh]



SULIT 9

8 Diagram 3 shows a parallelogram OPQR. Rqjah 3 menunjukkan sebuah segiempat selari OPQR.

Diagram 3 Rajah 3

Given that = 6 j + rn j , ?% = 4j + 3 j and Diberi bahawa = 6i + rn j , OR = 4i + 3 j dan

(a) Find Cari

(i) the positive value o f m ,

Nilui pusitifbagi m.

2 - d (b) Given E= - RQ and ?% = LG. Find H. 3 3 7,

Diberi = - RQ dan = !OR. Cari E. 3 3

(c) Given that T is a point such that = 5 j + 9 j - Diberi bahawa T ioloh satu tilik dengan kcadaan KT = 51 + 9 j .

( i ) Find E, Cari >?.

(ii) Show that the points 0, P and Tare collinear. fitqukkan buha~va titik-titik 0, P dun Tadalah segaris

[3 markr 1 [4 tnarktrh]

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0 I)i,~g:.a~n 1 al~ous a semicircle ABC , centre 0 with radius 5 cm. EBD is a sector of a circle , centre E with radius I0 cm. lic~jrrii 4 t)ii.nrii~jlikkirrr .sehuuh .semihulaian ABC, herpusai 0 dengun jejari 5 cm 1:ljl) icrltrli .sch/rtih .sek~or hagi hulatan, herpusat E dengan jejari I0 cm.

Diagram 4 Rajah 4

( ~ i v e n that 110 is perpendicular to AE. 1)iheri BO hcr.vc~cnjnng dengun AE.

(a) i B E 0 in radian, L' 1~1

10 (a) Diagram 5 shows part of the curve y = 9 - x2 . The straight line intersects the y-axis at (0, k ) and intersects the x-axis at (6,O). Kujuh 5 menlrnjlrkkan sehahagian daripada lengkung y = 9 - x 2 . Garis lurus hcr5ilung rior~gan paksi-y di (ilik (0, k) dun bersilang denganpaksi-x di (ilik (6, 0).

Rajah 5

Given that the area of the shaded region is 12 unit2 Find the value of k . Dibcri luas ka~rasan hcrlorck ialah 12 unit ('uri nilui k,

[ 5 marks]

[ 5 markah]

(b) Diagram 6 shows part of the curve x = y 2 . The curve intersects the straight line x = 4 at point A.

Rnjalr 6 rnenunjukkan sebahagian daripada lengklrng x = y '. Lengkung bersilang tiengan gnris lurus x = 4 di (irik A.

Diagram 6 ~ a j a h 6

Calculate the volume generated, in terms of .rr , when the shaded region is revolved through 360" about the y-axis. [ 5 marks] Hitungkan isipndu yang dijanakan , dalam sebutan x apabila kawasan berlorek dikisnrkon rnelallri 36U0pada pnksi-y. [ 5 rnarkah]



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2 11 (a) In an archery competition, the probability that Amir strikes the target is -. 3

[ f he tries six attempts, calculate the probability that,

Dalam satu pertandingan memanah, kebarangkulian Amir ferkena sasaran ialah 5 . 3

Jika dia rnelukukan enam kali cubaan, cari kebarangkalian bahawa

(i) he miss the target twice, rliu tiduk terkena sasaran dua kali,

(ii) hc hits the target at least twice. dra terhnu sasaran sektrrang-kurangnya dua kali.

[5 mark] [5 markah]

(b) ?'he mass of students of a school are normally distributed with a mean of 45 kg and the variance is 25 kg2. Jisim bagi sekumpulan murid dalam sebuah sekolah adalah mengikut taburan normal

dengan min 45 kg don varians 25 kg2.

( i ) Find the percentage of students with weigh more than 50 kg, Carikan pera/uspelajar yang mempunyai jisim melebihi 50 kg.

( i i ) Given that 35.2% of the students have a mass less than m kg, find the value of m . Diberi bahawa 35.2% daripadapelajar itu mempunyai jisim tidak melebihi m kg, cur; nilai rn.


SULIT


Section C Bahagian C

[20 marks] [20 nlarkah]

Answer two questions from this section. Ja~vah dua soalan duripuda bahagian in;.

12 The displacement of a particle Q that moves in a straight line from a fixed point 0, is given by s = t3 -6t2 + 91 .

Su.sutwrr h~rgi surllzr zuruh Llyung hergeruk di sepanjang suatzr garis lurus clan rnclalui .crrirr titik letup 0, diberi oleh s = 1' - 6r2 + 91 .

Find

( b r i

( u ) the initial velocity of particle Q, halqjzi ultlul zarah Q,

[ 2 marks] [2 markuh]

( h ) the values of t when the particle Q change its direction of the motion, [ 2 marks] nilai-nilai f apabila zuruh Q herrukar arah gerakari, [2 markah]

(c) the acceleratio~l of particle Q after 4 seconds. pccrrtan zaruh Q selepas 4 saar.

(4 [he maximum velocity of particle Q. [3 marks] huluju mu~itnum zarah Q. [3 nrurkuh]



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14 Ilse graph paper to answer this question. Gur~ukan ker-tas gruf untuk menjuwub soalam ini.

A cake shop produces two types of cake, A and B . Each type of cake is made by using two ingredients, flour and butter. Sehzruh kedui kek menghasilkun duo jenis kek, A dun B. Setiap jenis kek diperbuat dari dua ,jenis huhan. tc7pung dun ntcntega.

Table 3 shows the masses of the ingredients to make the two types of cakes. Joduul mcnunjukkun,jisim kand14ngan untuk membuat kedua-dua jenis kek.

1 Cake Mass in (g) f i k Jisim dalam ( )

Flour Butter E Table 3

Jadual3

Tepung

A i 100

The cake shop produces x cakes A and y cakes B. The making of cakes per day is based on the following constraints:

Keriai tersebut rnenghasilkan x biji kek '4 dun y biji kek B. Penghasilan bilangan biji kek dolam sehnri adalah berdasarkan kekangan berikut:

Menlega 100

I : The minirnum mass of flour used is 8 kg. h!inimum jisim tepung yang digunakan ialah 8 kg.

I I : The maximum mass of butter used is 9 kg.

Mnk~imum jisim rnentega yang digunakan ialah 9 kg.

111 : The number of cake A produced is not more than the number of cake B.

Dilungun biji kek A adalah tidak melebihi bilangan biji kek B.

( ( I ) Write three inequalities, other than x 2 0 and y 2 0 , which satisfy all the above constraints. [3 marks] fii1i.s tiga ketuksamaan, selain x 2 0 dun y 2 0 , yang memenuhi sentua kcktrngun tli ata.s. [3 markah]



SULIT

( h ) Using a scale of 2 cm to 10 cakes on both axes, construct and shade the region R which satisfies all of the above constraints. [ 3 mark] Dengan menggunakan skala 2 cm kepada 10 kekpada kedua-duapaksi, bina dun lorek ranfau R yang memenuhi semua kekangan di atas.

[3 markah]

(c ) Use your graph in 14(b), to find Glrnakan graf anda di 14(b), untuk mencari

(i) the minimum number of cakes B, if 15 of cakes A are produced per day, hilangan minimum kek B, jika 15 biji kek A dihasilkan dalam sehari,

( i i ) the maximum profit per day ifthe profit of each cake A and B is RM12 and RM9 respectively. [4 marks] Jumlah keuntungan maksimum dalam sehari jika keuntungan bagi sebiji kek A dun kek B adalah musing-masing RM12 dun RM9.

[4 markah]



SULIT 17 347212

15 Diagram 7 shows quadrilateral PQRST. Given QRS is a straight line, LPRQ is an obtuse angle and the area of triangle PST is 25 cm2. Rajah 7 menunjukkan sisiempat PQRST. Diberi bahawa QRS ialah garis lurus, LPRQ ialah sudut cakah dun luas bagi segitiga PST ialah 25 cm2.

~ i a ~ r a m 7 Rajah 7

Calculate

Hitungkan

(a) the length, in cm, of PS, panjang, dalam cm, bagi PS,

(b) LSPT .

(c) the area of APQS. Luas APQS




END OF QUESTION PAPER



1-3 l ,~hli. 2 xho~z i llic prices and tht: heightage for the lbur ingredients, A , B, C and I ) in 2007 ~ n d 1008. L I ~ in nlahing a particular chocolate.

.Jiriirra/ 2 nic~nliiij~ikkor~ h a r p dmpernherut hag; Jjenis bahun, A, 5, C dun Dpudu tuhun 2007 ,lii~i 3008. \ ang d~,yrrnak(~n lrntuk rriembttut .sejenis coklar.

( ' 1 ) C',ilci~lnle thc index numbers of each ingredients, A , 5, C and L) in 2008 with '3(07 '15 the b ~ s e yeas. 11iillil~yk~111 irleick.~ hui.gil bog; sctiup hal~url/i, B, C t b n Dpudu ~ullun 2008 dcngan itrc~/g~~iuc/kii/i 2007 .sehu,yrri tuliun cisus. 1 I ~ n c e , cnlculdte ~ h c cornposite index for the cost of rnaking the chocolate in 2008 with 2007 as thc basc year.

[ 5 morks] . S c ' ~ ~ ~ / . i t \ r i \ ( I . Iiifzin~kuti riomhor hideks gt~bairan bugi kov rnembzrat coklat pada 2008 / I ~ ' I , ~ I \ ~ I \ kun ttriircn 1007.

[ 5 markuh]

( h I I I' the cl~uculall: is sold at RM 150 per pack in 2007, calculate the selling 1'1 icc per pack in 1008. ( 2 rnarks]

(c.) I I IC ~ ~ I C C 111j ice~ of a commodity in 2007 and 2008 based on 2006 are I25 and 120 rcspect~vely. If the price of the commodity in 2007 is Rkl.1150, crrlsulate its price in 2008. [3 tnarks] I~itii~li.~ 11~11.gtr hogi surlc kor?lorlitipada 2007 dur~ 2008 bcrususkan tuhun 2000 ~~i~t.\.irl,y-rnrr.siti~q utiuluh 125 iiun 120. ,lib 11urgu hagi konloditi tersebur pada ?0117 ict/u/l Rk1 1 00, Ilif~irigk~iri /i~~qyc~n?'o padu 2008.

[3 murkah]



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


1449/2 Matematics Kertas 2 Sept. 2008

.JABATAN PELAJARAN NEGERI JOHOR

PEPERIKSAAN PERCUBAAN SPM TAIFL. 2008

SKEMA PEMARKAHAN

P v] MATEMATICS Kertas 2

Duajam tiga puluh minit

144912 0 Hak Cipta .lPNJ 2008 SULIT


SKEMA PERMARKAHAN MATEMATIK TAMBAIUN KERTAS 2 PEPERIKSAAN PERCURAAN SPM TAHUN 2008

Number

I

Full Marks Solution and mark scheme

x = y - 2 y 2 + 2 y + ( y - 2 y = 9 2y2 - 2 y - 5 = 0

-(2) + J-40(-5) Y =

2(2)

5

6

5

Sub Marks P 1

K1

KI

N1 N1

K I

K l

N1

P 1 P 1

N1

NI

P 1

N1

K1

N1

x =0.158,-3.158

(b)

3(a)

(b)

= J(2x3 - dx)dr 1

=-x4 -2x2 +C 2 1 4 2 7 v=-x -2x +-

- 2 2

m, = 2(113 -4(1) = -2 1

M , = - 2

2 y = x + 3

- 64 x = - - = $ 8 ,

G x 2 = 580

o = /? -- = 2.9155

- 2.9 1 55 on, - ---- 4

= 0.7289 Johor Trial SPM 2008


Number of solutions = 3

6(a)

N1

N1 for Sin shape

tan2 8 + 1 tan B

sec2 B tan B

sec B cos ec8

N1 for 1 periodic and max = 2

N1 for modulus

N1 for

K1 for straight line


Number

7

8(a>(i>

(ii)

(b)

(c>(i>

( i i )

Solution and mark scheme

logy = log a + x2 log h log a = 0.19(+0.0 1)

a = 1.55

log b = 0.889 - 0.493 - = 0.0792

9 - 4

Graph: K I for uniform scale on both axes N 1 for a1 l correct points N I for best fit line

JG=Io m = 8

L = --(10!+l l j )

3 -

0, P and T are collinear.

Sub Marks

NI NI

P 1

Kl N1

KI NI

KI NI

K1 N1

K1

N1

K1 N1

K1

N1

Full Marks

10

I

10


Perimeter of shaded region =AB+BD+AD = 5j1.572) + 1 O(0.5237) + 3.6602 = 1 6 . 7 5 2 2 ~ ~

Number

9ja)

Area of the shaded region = ABEO + sector AOB - sector BED


sin LBEO = 0.5

Sub Marks K1 N1 :. LBEO = 30 = 0.5237rads

K1 for any correct formula used

N1 for any correct answer

K 1 for all correct operation

Full Marks 1


--

1 1 (a)

- -

Solution and mark scheme Full Marks --

Sub -7 Marks

K1

N1

K1 for

I ncrprqn-r K1 for operation N1

K1 for x-P z=-

LT

N l

K1 for x-P z=--

LT

KI

NI


Number -..-----.pp--


v,,,, = 3(2)' - 12(2) + 9 = -3 m/s

2 1 I,, =--x 100 = 140 15

---

Sub Marks K1

K1 for formula I

Full Marks


---

Number Solution and mark scheme -

sin LQRP - sin 30' --

9.5 5.8 LQRP = 125'1' LPRS = 180'-125'11= 54'59'

1 - (6.322)(1 1.2) sin LSPT = 25 2

SPT = 44'55'

LQPR = 24'59' Area APQS

1 1 = -(9.5)(5.8) sin 24'59'+-(5.9)(7.5)sin 54O59'

2 2 = 11.6359+18.12 = 29.7559cm2

Sub Marks -

K1

NI NI

Kl N I

KI N1

P 1

K1

N1

Full Marks



I :100x+400y28000 II : 1 OOx + 200y I 9000 III : x < y

refer to the graph:

K 1 for uniform scale on both axes K I for any one correct straight line drawn N 1 for correct region R

(i) 16

( i i ) 1 2 x 4 9 ~ = 180 ,(30,30) Maximum profit = 30(RM12) + 30(RM9)

= RM630

Sub Marks

K1 N1

K1

Kl

N1

N1 Nl N1

K1 K1 N1

PI

N1 K1 for k=ax+by N1

Full Marks

10

10

~ Johor Trial SPM 2008


PAPER 1PAPER 2SCHEME PAPER 1SCHEME PAPER 2

add maths johor spm trial 2008 p1&2

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