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SULIT 347/ 347/ Matematik Tambaha Kertas Ogos 00 ½ jam PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA SEKOLAH MENENGAH MALAYSIA CAWANGAN NEGERI SEMBILAN DARUL KHUSUS PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN

1 SULIT 347/ 347/ Matematik Tambaha Kertas Ogos 00 ½ jam PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA SEKOLAH MENENGAH MALAYSIA CAWANGAN NEGERI SEMBILAN DARUL KHUSUS PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 00 MATEMATIK TAMBAHAN Kertas Dua jam tiga puluh miit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU. Kertas soala ii adalah dalam dwibahasa.. Soala dalam Bahasa Iggeris medahului soala yag sepada dalam Bahasa Melayu. 3. Calo dikehedaki membaca araha di halama. 4. Calo dikehedaki meceraika halama 0 da ikat sebagai muka hadapa bersama-sama dega kertas jawapa. 347/ 00 Hak Cipta PKPSM SULIT Kertas soala ii megadugi 0 halama bercetak. [ Lihat sebelah

2 SULIT 347/ INFORMATION FOR CANDIDATES MAKLUMAT UNTUK CALON. This questio paper cosists of three sectios: Sectio A, Sectio B ad Sectio C. Kertas soala ii megadugi tiga bahagia: Bahagia A, Bahagia B da Bahagia C.. Aswer all questios i Sectio A, four questios from Sectio B ad two questios from Sectio C. Jawab semua soala dalam Bahagia A, empat soala daripada Bahagia B da dua soala daripada Bahagia C. 3. Show your workig. It may help you to get marks. Tujukka lagkah lagkah petig dalam kerja megira ada. Ii boleh membatu ada utuk medapatka markah. 4. The diagrams i the questios provided are ot draw to scale uless stated. Rajah yag megirigi soala tidak dilukis megikut skala kecuali diyataka. 5. The marks allocated for each questio ad sub-part of a questio are show i brackets. Markah yag diperutukka bagi setiap soala da ceraia soala ditujukka dalam kuruga. 6. A list of formulae is provided o pages 3 to 4. Satu searai rumus disediaka di halama 3 higga Graph papers are provided. Kertas graf disediaka. 8. You may use a o programmable scietific calculator. Ada dibearka megguaka kalkulator saitifik yag tidak boleh diprogram. 347/ 00 Hak Cipta PKPSM SULIT

3 SULIT 3 347/ The followig formulae may be helpful i aswerig the questios. The symbols give are the oes commoly used. ALGEBRA ± x = b b 4ac a 8 log a b = log log c c b a m m a a = a + m m 3 a a = a a m 4 ( ) = a m 5 loga m = loga m + loga 6 m loga loga m loga = 7 log m = log m a a 9 T = a + ( ) d = ar 0 S = [ a + ( ) d ] 3 T S S a( r ) a( r ) = = r r a =, r < r, (r ) y = uv, 3 u y =, v dy dx = dy du dy dv du = u + v dx dx dx du dv v u dy dx dx, = dx v du dx CALCULUS 4 Area uder a curve = b a y dx b = x dy a 5 Volume geerated b = π y dx a = b π x dy a or or GEOMETRY Distace = ( x x ) + ( y y Midpoit x + (x, y) = x 3 r = x + y xi + yj 4 r = x + y ) y + y, 5 A poit dividig a segmet of a lie x + mx y + my ( x, y) =, m + m + 6 Area of triagle = ( x y + x y + x y ) ( x y + x y + x y 3 3 [ Lihat sebelah 347/ 00 Hak Cipta PKPSM SULIT 3 3 )

4 STATISTICS x = x N fx x = f 3 σ = 4 σ = ( x x ) = x x N N f ( x x ) f N F 5 M = L + c P 6 I = 00 P 0 f m = fx f x I iwi I = w P r C r i! = ( r)!! = ( r)! r! 0 P( A B) = P( A) + P( B) P( A B) P( X = r) = C Mea, µ = p 3 σ = pq 4 z = x µ σ r p r q r, p + q = TRIGONOMETRY Arc legth, s = rθ Area of sector, 3 A = si A + cos A = 4 sec A = + ta A 5 cos ec A = + cot A 6 si A = si Acos A 7 r θ cos A = cos A si A = cos A = si A 9 si( A ± B) = si Acos B ± cos Asi B 0 cos( A ± B) = cos Acos B msi Asi B ta A ± ta B ta( A ± B) = m ta Ata B a si A = b si B 3 = c si C a = b + c bc cos A 4 Area of triagle = ab si C ta A ta A = ta A 8

5 5. Solve the simultaeous equatios Selesaika persamaa seretak berikut: x y 5 = 0 x 3x y y 4 0 Sectio A Bahagia A [40 marks] [40 markah] Aswer all questios. Jawab semua soala. + + = [5 marks] [5 markah]. Diagram shows the curve of a quadratic fuctio y = 4x qx + 5. The curve has a miimum poit at A(p,0) ad itersects the y-axis at poit B. Rajah meujukka legkug bagi suatu fugsi kuadratik y = 4x qx + 5. Legkug itu mempuyai titik miimum pada A(p,0) da bersilag pada paksi-y di titik B. y B f ( x) = 4x qx A (p, 0) x x Diagram Rajah (a) State the coordiates of B. [ mark] Nyataka koordiat titik B. [ markah] (b) By usig the method of completig the square, fid the value of p ad of q. [6 marks] Dega megguaka kaedah melegkapka kuasadua, carika ilai p da q. [6 markah]

6 3. Two factories, A ad B, start to produce gloves at the same time. Dua buah kilag, A da B, mula megeluarka sarug taga pada masa yag sama. (a) Factory A produces h pairs of gloves i the first moth ad its productio icreases costatly by k pairs of gloves every subsequet moth. It produces 300 pairs of gloves i the 5 th moth ad the total productio for first seve moths is 750. Fid the value of h ad of k. [5 marks] Kilag A megeluarka h pasag sarug taga dalam bula yag pertama da meigkat sebayak k pasag sarug taga pada setiap bula. Kilag ii megeluarka 300 pasag sarug taga dalam bula ke lima da sejumlah 750 pasag sarug taga telah dikeluarka bagi tujuh bula pertama. Carika ilai h da k. [5 markah] (b) Factory B produces 00 pairs of gloves i the first moth ad its productio icreases costatly by 5 pairs of gloves every subsequet moth. Fid the moth whe both of the factories produce the same total umber of gloves. [ marks] Kilag B megeluarka 00 pasag sarug taga dalam bula pertama da meigkat sebayak 5 pasag sarug taga setiap bula. Pada bula ke berapakah kedua- dua kilag megeluarka jumlah sarug taga yag sama. [ markah] 4 (a) Prove that Buktika ta x sec x + = cos x sec x [ marks] [ markah] b) (i) Sketch the graph of y = cosx for 0 x π. Lakarka graf bagi y = cosx utuk 0 x π. (ii) Hece, usig the same axes, draw a suitable straight lie to fid the umber of solutios for the equatio cos x = x for 0 x π. State the umber of solutios. π [6 marks] Seterusya, pada paksi yag sama, lukiska satu garis lurus yag sesuai utuk mecari bilaga peyelesaia bagi persamaa cos x = x π utuk 0 x π. Nyataka bilaga peyelesaiaya. [6 markah] 347/ 00 Hak Cipta PKPSM SULIT

7 SULIT 7 347/ 5. Table shows the frequecy distributio of the scores of a group of 40 pupils i a quiz. Jadual meujukka tabura kekerapa bagi skor utuk 40 orag pelajar dalam suatu kuiz. Score Skor Number of pupils Bilaga pelajar h 4 k Table Jadual (a) It is give that the media score of the distributio is 4, fid the value of h ad of k. Diberi skor media bagi tabura itu ialah 4, carika ilai h da ilai k. (b) State the modal class of the distributio. Nyataka kelas mod bagi tabura itu. [5 marks] [5 markah] [ Lihat sebelah 347/ 00 Hak Cipta PKPSM SULIT

8 6. Diagram shows OSR ad PSQ are two straight lies. Rajah meujukka OSR da PSQ adalah dua garis lurus. Diagram Rajah uuur Give that OP = 5p, OQ = 0q, PS : SQ = : 3, % % PR = moq ad OS = OR. Diberi OP = 5p %, OQ = 0q %, PS : SQ = : 3, PR = moq da OS = OR. (a) Express OR i terms of Ugkapka OR dalam sebuta (i) m, p % ad q, [ marks] % m, p % da q, [ markah] % (ii), p % ad q. [ marks] %, p % da q. [ markah] % (b) Hece, fid the value of m ad of. [4 marks] Seterusya, carika ilai bagi m da. [4 markah] Sectio B Bahagia B 347/ 00 Hak Cipta PKPSM SULIT

9 SULIT 9 347/ [40 marks] [40 markah] Aswer ay four questios from this sectio. Jawab maa-maa empat soala daripada bahagia ii. 7 (a) Give that a curve has a gradiet fuctio hx + x such that h is a costat. If y = 5 4x is the equatio of taget to the curve at poit (, k ), fid the value of h ad of k. [3 marks] Diberi suatu legkug dega fugsi kecerua hx + x dega keadaa h ialah pemalar. Jika y = 5 4x ialah persamaa tage bagi legkug itu pada titik (, k ), cari ilai h da ilai k. [3 markah] (b) Diagram 3 shows a curve poit (, 4). y = ( x 3) ad the straight lie y x = + itersect at Rajah 3 meujukka legkug bersilag pada titik (, 4). y y = ( x 3) da garis lurus y x = + yag y = x + O (, 4) y = ( x 3) x Diagram 3 Rajah 3 Calculate Hitug (i) the area of the shaded regio, [4 marks] luas kawasa berlorek, [4 markah] (ii) the volume of revolutio, i terms of π, whe the regio bouded by the curve, the x-axis, the y-axis ad the straight lie x = is revolved through 360 about the x-axis. [3 marks] isipadu jaaa, dalam sebuta π, apabila ratau yag dibatasi oleh legkug, paksi-x, paksi-y da garis lurus x = dikisarka melalui 360 pada paksi-x. [3 markah] 8 Use graph paper to aswer this questio. [ Lihat sebelah 347/ 00 Hak Cipta PKPSM SULIT

10 Guaka kertas graf utuk mejawab soala ii. Table shows the values of two variables, x ad y, obtaied from a experimet. Variables x x ad y are related by the equatio y = ab, where a ad b are costats. Jadual meujukka ilai-ilai bagi dua pembolehubah, x da y, yag diperoleh x daripada satu eksperime. Pembolehubah x da y dihubugka oleh persamaa y = ab, dega keadaa a da b ialah pemalar. x y Table Jadual (a) Plot log0 y agaist x, usig a scale of cm to uit o the x - axis ad cm to 0. uit o the log0 y - axis. Hece, draw the lie of best fit. [5 marks] Plot log0 y melawa x, dega megguaka skala cm kepada uit pada paksi- x da cm kepada 0. uit pada paksi- log0 y. Seterusya, lukiska garis lurus peyuaia terbaik. [5 markah] (b) Use your graph from 8(a) to fid the value of Guaka graf di 8(a) utuk mecari ilai (i) a (ii) b [5marks] [5 markah] 347/ 00 Hak Cipta PKPSM SULIT

11 SULIT 347/ 9 Diagram 4 shows a circular sector POQ cetre O with radius of 5 cm ad POQ =. radia. RQ is a arc of the circle with cetre P. Rajah 4 meujukka sebuah sektor POQ berpusat O da berjejari 5 cm da POQ =. radia. RQ ialah legkok bulata berpusat di P. Diagram 4 Rajah 4 Calculate Hitug (a) the legth, i cm, of a arc PQ, [ marks] pajag, dalam cm, legkok PQ, [ markah] (b) the legth, i cm, of the radius PR, [ marks] pajag, dalam cm, jejari PR, [ markah] (c) RQP, i radia, [ marks] RQP, dalam radia, [ markah] (d) the area i cm, of the shaded regio. [4 marks] luas dalam cm, kawasa berlorek. [4 markah] [ Lihat sebelah 347/ 00 Hak Cipta PKPSM SULIT

12 0 Solutio by scale drawig is ot accepted. Peyelesaia secara lukisa berskala tidak diterima. Diagram 5 shows a triagle ABC with poit A o the y-axis. The equatio of the straight lie ADC is y x + 4 = 0. Give that straight lie BD is perpedicular to straight lie ADC. Rajah 5 meujukka segitiga ABC dega titik A berada di atas paksi-y. Diberi persamaa garis lurus ADC ialah y x + 4 = 0. Diberi bahawa garis lurus BD berserejag dega garis ADC. y C ( 5, 6 ) D ( B ( 6, 3) O x A Diagram 5 Rajah 5 Fid Cari (a) the coordiates of poit A, [ mark] koordiat titik A, [ markah] (b) equatio of the straight lie BD, [3 marks] persamaa garis lurus BD, [3 markah] (c) the coordiates of poit D, [3 marks] koordiat titik D, [3 markah] (d) the ratio of AD : DC. [3 marks] isbah AD : DC. [3 markah] 347/ 00 Hak Cipta PKPSM SULIT

13 SULIT 3 347/ (a) A hockey club orgaizes a practice sessio for traiees o scorig goals from pealty strokes. Each traiees takes 5 pealty strokes. The probability that a traiee scores a goal from a pealty stroke is p. After the sessio, it is foud that the mea umber of goals scored by a traiee is.75. Sebuah kelab hoki telah megajurka sesi latiha dalam mejarigka gol utuk pemai kelabya. Setiap pemai perlu membuat 5 pukula pealti. Kebaragkalia pemai mejarigka gol adalah p. Setelah sesi tersebut didapati bahawa mi jariga gol ialah.75. (i) Fid the value of p. Cari ilai p. (ii) If a traiee is chose at radom, fid the probability that he scores at least two goals. Jika seorag pemai dipilih secara rawak, cari kebaragkalia bahawa pemai itu mejarigka sekurag kuragya gol. [5 marks] [5markah] (b) The body masses a group of studets i a particular tow have a ormal distributio with a mea of 5 kg ad a variace of 44 kg. Jisim bada bagi suatu kumpula pelajar di sebuah badar adalah megikut satu tabura ormal dega mi 5 kg da varias 44 kg. (i) If a studet is chose at radom from the tow, fid the probability that the mass of the studet is less tha 4 kg. Jika seorag pelajar dipilih secara rawak dari badar itu, cari kebaragkalia bahawa jisim pelajar itu kurag daripada 4 kg. (ii) Give that 80% of the studet have a mass of more tha t kg, fid the value of t. Diberi bahawa 80% daripada pelajar tersebut mempuyai jisim melebihi t kg, cari ilai t. [5 marks] [5 markah] [ Lihat sebelah 347/ 00 Hak Cipta PKPSM SULIT

14 Sectio C Bahagia C [0 marks] [0 markah] Aswer ay two questios from this sectio. Jawab maa-maa dua soala daripada bahagia ii. A particle moves alog a straight lie ad passes through a fixed poit O. Its velocity, v m s -, is give by v = 5 + 4t 3t, where t is the time, i secods, after passig through O. Suatu zarah bergerak di sepajag suatu garis lurus da melalui satu titik tetap O. Halajuya, v m s -, diberi oleh v = 5 + 4t 3t, dega keadaa t ialah masa, dalam saat, selepas melalui O. [Assume motio to the right is positive.] [Aggapka geraka ke arah kaa sebagai positif.] Fid Cari (a) the iitial velocity of the particle, i m s -, [ mark] halaju awal zarah itu, dalam m s -, [ markah] (b) the time iterval durig which the acceleratio of the particle is positive, julat masa apabila pecuta zarah itu adalah positif, [3 marks] [3 markah] (c) the maximum velocity, i m s -. [3 marks] halaju maksimum, dalam m s -. [3 markah] (d) sketch the velocity-time graph of the motio of the particle for 0 t 5. [3 marks] lakarka graf halaju melawa masa bagi pergeraka zarah itu utuk 0 t 5. [3 markah] 347/ 00 Hak Cipta PKPSM SULIT

15 SULIT 5 347/ 3 Table 3 shows the prices ad price idices for the four igrediets, A, B, C ad D used i makig a type of biscuit. Diagram 6 is a pie chart which represets the usage of four igrediets, A, B, C ad D used i the productio of this biscuit. Jadual 3 meujukka harga da ideks harga bagi empat baha yag diguaka utuk membuat sejeis biskut. Rajah 6 meujukka carta pai yag mewakili kuatiti relatif bagi pegguaa baha A, B, C da D dalam pembuata biskut ii. Igrediets Baha Price (RM) for the year Harga (RM) pada tahu Price idex for the year 008 based o the year 006 Ideks harga pada tahu 008 berasaska tahu 006 A x B 5.00 y 40 C D z Table 3 Jadual 3 Diagram 6 Rajah 6 (a) Fid the value Cari ilai i) x ii) y iii) z [3 marks] [3 markah] (b) i) Calculate the composite idex for the cost of productio of this biscuit i the year 008 based o the year 006. Hitug ideks gubaha bagi kos pembuata biskut tahu 008 berasaska tahu [ Lihat sebelah 347/ 00 Hak Cipta PKPSM SULIT

16 006. ii) Hece, calculate the cost of the productio of this biscuit i the year 006 if the cost of the productio i the year 008 was RM Seterusya, hitug kos pembuata biskut itu pada tahu 006 jika kos pembuataya pada tahu 008 ialah RM [5 marks] [5 markah] (c) The cost of productio of this biscuit is expected to decrease by 0% from the year 008 to the year 00. Fid the expected composite idex for the year 00 based o the year 006. Kos pembuata biskut ii dijagka meuru sebayak 0% dari tahu 008 ke tahu 00. Cari jagkaa ideks gubaha pada tahu 00 berasaska tahu 006. [ marks] [ markah] 347/ 00 Hak Cipta PKPSM SULIT

17 SULIT 7 347/ 4 Pak Samad wats to divide a piece of triagular shaped lad ABC ito three parts as i Diagram 7. AFB, AEDC ad BGC are straight lies. Give that BF = 8 m, AF = 96 m, 5 AE = 6 m, CE = 70 m ad si BAC =. 3 Pak Samad igi membahagika sebidag taahya yag berbetuk segi tiga ABC kepada tiga bahagia seperti dalam Rajah 7. AFB, AEDC da BGC ialah garis lurus. 5 Diberi BF = 8 m, AF = 96 m, AE = 6 m, CE = 70 m da si BAC =. 3 Diagram 7 Rajah 7 (a) Calculate the legth of BC. [3 marks] Hitug pajag BC. [3 markah] (b) Calculate ACB. [ marks] Hitug ACB. [ markah] (c) Fid the area of triagle AEF. [ marks] Cari luas segi tiga AEF. [ markah] (d) Give the area of triagle AEF is equal to the area of triagle CDG, calculate the legth of CD. Diberi luas segi tiga AEF adalah sama dega luas segi tiga CDG, hitug pajag CD. [3 marks] [3 markah] [ Lihat sebelah 347/ 00 Hak Cipta PKPSM SULIT

18 5 Use the graph paper to aswer this questio. Guaka kertas graf utuk mejawab soala ii. I Istitute A, two types of courses are offered. Table 4 shows the umber of studets ad the mothly fee for each course. Istitut A meawarka dua jeis kursus. Jadual 4 meujukka jumlah pelajar da yura bulaa bagi setiap kursus. Course Kursus Number of studets Bilaga pelajar Mothly fee Yura Bulaa Computer Komputer x RM80 Eglish Bahasa Iggeris y RM60 Table 4 Jadual 4 The recruitmet of studets for the courses is subject to the followig costraits: Pegambila pelajar utuk kursus tersebut adalah berdasarka kekaga berikut: I The maximum umber of studets is 400. Bilaga maksimum pelajar ialah 400. II The umber of studets who erol i the computer course is at most three times the umber of studets who erol i the Eglish course. Bilaga pelajar yag medaftar utuk kursus computer selebih-lebihya tiga kali bilaga pelajar yag medaftar utuk kursus Bahasa Iggeris. III The miimum total collectio of mothly fees is RM700. Jumlah miimum kutipa yura bulaa ialah RM700. (a) Write three iequalities, other tha x 0 ad y 0, which satisfy all the above costraits. [3 marks] Tulis tiga ketaksamaa, selai daripada x 0 da y 0, yag memeuhi semua kekaga di atas. [3 markah] (b) Usig a scale of cm to 50 uits o both axes, costruct ad shade the regio R which satisfies all of the above costraits. [3 marks] Megguaka skala cm kepada 50 uit pada kedua-dua paksi, bia da lorek ratau R yag memeuhi semua kekaga di atas. [3 markah] 347/ 00 Hak Cipta PKPSM SULIT

19 SULIT 9 347/ (c) Use the graph costructed i 5(b), to fid Guaka graf yag dibia di 5(b), utuk mecari i) the maximum collectio of mothly fees. kutipa maksimum yura bulaa ii) the miimum umber of studets erolled i the Eglish course if the umber of studets who erolled for computer course is 50. bilaga miimum pelajar yag medaftar utuk kursus Bahasa Iggeris jika blaga pelajar yag medaftar utuk kursus computer ialah 50. [4 marks] [4 markah] END OF QUESTION PAPER KERTAS SOALAN TAMAT [ Lihat sebelah 347/ 00 Hak Cipta PKPSM SULIT

20 Nama:.. Kelas:... Araha Kepada Calo Tulis ama da kelas ada pada ruag yag disediaka. Tadaka ( ) utuk soala yag dijawab. 3 Ceraika helaia ii da ikat sebagai muka hadapa bersama-sama dega buku jawapa. Bahagia A B C Soala Soala Dijawab Markah Peuh Markah Diperolehi (Utuk Keguaa Pemeriksa) 347/ 00 Hak Cipta PKPSM SULIT

21 SULIT 347/ 5 0 Jumlah [ Lihat sebelah 347/ 00 Hak Cipta PKPSM SULIT

22 Numbe r y = x 5 Solutio ad markig scheme Sub Marks Full Mark s x + 3 x + (x 5) (x 5) 4 = 0 ( x )( x ) = 0 x = or x = y = or y = 39 5 (a) (b) (0,5) 4 x 4 q x 8 q 5 6 q = 0 q q x = 0 0 x = p = + q q (a) (b) h + 4k = ( h + 6k ) ( 300 4k ) k = 50 h = 00 = k = ) ( )(50 (00) ( )(5) = 9 ( + ) = [ + ] 7

23 Numbe r 4(a) LHS = sec x sec x + sec x = cos x Solutio ad markig scheme Sub Marks Full Mark s (b) ½ Shape of cos graph Max & mi value of y Period 0 π π - y = x π Draw the straight lie Number of solutios = h + k = 40 0 (3 + h) 4 = h = 4 k = 7 Modal class = (a)(i) (ii) (b) OR = m ( 0 q) 0 mq + 5p + 5p 5 p + 5p + 0q 5 3p + 4q uuur OR = ( 3 p + 4 q ) 3 4 = 5, = 0m 3 =, m = 5 3 ( ) 8

24 Numbe r 7(a) hx + x = 4 ( ) ( ) h + = 4 h = 3, k = 9 Solutio ad markig scheme Sub Marks Full Mark s (b) (c) ( + ) ( + ) Area= x 6x 9 dx x dx x 8x = + 7x or equivalet = = 3 uit 3 Volume = π ( 3) x 0 ( x 3) 4 dx 5 Volume = π 5 0 Volume = 4 π or 48 π (a) (b) x log 0 y Usig the correct, uiform scale ad axes All poits plotted correctly Lie of best fit ( ) log y = log b x + log a use m = log 0 b b =. 493± 0. 0 use c = log 0 a a =. 30 ±

25 Numbe r 9(a) ( ) s = 5. = 6cm Solutio ad markig scheme Sub Marks Full Mark s (b) (c) (d) 0 x si = or equivalet 5 x =.83cm PQ =.83cm = 5.646cm rad.7rad RQP = π rad Area sector PQR = ( ) (.7 ) = cm Area sector POQ = ( 5 ) (. ) = 5 cm or 0 Area triagle= (5)(5)si =.65 cm Area of shaded regio = ( 5.65 ) cm Area of shaded regio = 3.53 cm 0 0(a) (b) (c) (d) A ( 0, 4) m = y 3 = ( x 6) y = x + 6 Solve y x + 4 = 0 ad y = x + 6 x = 4, y = 4 D ( 4,4) 5m 4 m + = m 4 = m : = 4 : 4

26 0 Numbe r (a)(i) (a)(ii) (b)(i) (b)(ii).75 p = 5 p = 0.55 Solutio ad markig scheme Sub Marks Full Mark s ( ) = ( = 0) ( = ) P X P X P X C = P Z < P Z < ( ) C = ( 0.55) ( 0.45) ( 0.55) ( 0.45) = 0.05 t 5 P Z > = 0.8 t 5 = 0.84 t = 4.9kg 0 (a) (b) (c) (d) 5 = a = 4 6 v t t 4 6t > 0 0 < t < 3 t = 3 v = = 6 3 t Betuk Melalui titik (0, 5), (3, 0) 5

27 da (5, -40) 0 Numbe r 3(a) i) x = 5 ii) y = 7 iii) z = 3.0 Solutio ad markig scheme Sub Marks Full Mark s (b) (i) (ii) (c) 4 (a) (b) (c) (d) or 360 5(60) + 40(0) + 50(0) + 5(70) 360 = = 00 Q 0 Q 0 = = 3.88 a) cos BAC = 3 BC = (4)(96) cos BAC BC = = 5 si ACB 3 0 ACB = ( 96) ( 6) GC cos DCG = CD 0 5(a) (b) ( CD ) ( GC ) si DCG = 480 ( CD ) ( CD cos DCG ) si DCG 480 = CD = x + y 400 x 3y 80x + 60y 700 or 4x + 3y 360 (Refer to graph) 0 6

28 log0. (c)(i) y(ii) titik (300, 00) 80(300) + 60(00) RM Questio No X.0 X X X X 0.3 X 0. 7

29 0. y No x (b) Draw correctly at least oe straight lie Draw correctly all straight lies Correct shaded regio 400 x + y = R x = 3y 00 (300, 00) x +3 50y = x

SMK DATUK HAJI ABDUL KADIR KEPALA BATAS PULAU PINANG PERCUBAAN SPM 2017 MATEMATIK TAMBAHAN KERTAS 2. Dua jam tiga puluh minit

NAMA : TINGKATAN : / MATEMATIK TAMBAHAN Kertas September 0 jam SMK DATUK HAJI ABDUL KADIR KEPALA BATAS PULAU PINANG PERCUBAAN SPM 0 MATEMATIK TAMBAHAN KERTAS Dua jam tiga puluh miit JANGAN BUKA KERTAS