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

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1 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 SOALAN INI SEHINGGA DIBERITAHU. Kertas soala ii adalah dalam dwibahasa.. Soala dalam bahasa Iggeris medahului soala ag sepada dalam bahasa Melau.. Calo dikehedaki membaca maklumat di halama belakag kertas soala ii.. Calo dikehedaki meceraika halama 9 da ikat sebagai muka hadapa bersama-sama dega kertas jawapa. Kertas soala ii megadugi 0 halama bercetak. [Lihat halama sebelah

2 THE UPPER TAIL PROBABILITY Q(z) FOR THE NORMAL DISTRIBUTION N(0, ) KEBARANGKALIAN HUJUNG ATAS Q(z) BAGI TABURAN NORMAL N(0, ) z Mius / Tolak Eample / Cotoh: f (z) f ( z) ep z Q(z) If X ~ N(0, ), the Jika X ~ N(0, ), maka k z Q ( z) f ( z) dz O k P(X > k) = Q(k) P(X >.) = Q(.) = 0.09 / Hak cipta KM/0 PPDU 0

3 The followig formulae ma be helpful i aswerig the questios. The smbols give are the oes commol used. Rumus-rumus berikut boleh membatu ada mejawab soala. Simbol-simbol ag diberi adalah ag biasa diguaka. ALGEBRA = b b ac a log a b = log log c c b a a m a = a m + 9 T = a + ( ) d a m a = a m - 0 S = a ( ) d (a m ) = a m T = ar log a m = log a m + log a S =, r a r r a r r m log a = loga m log a a S, r r < log a m = log a m = uv, d d CALCULUS KALKULUS dv du u v Area uder a curve d d du dv v u b u d =, d d = v d v Luas di bawah legkug a d or (atau) d d b d du = du d d a Volume of revolutio Isi padu kisara b = a b = a d d or (atau) [Lihat halama sebelah / Hak cipta KM/0 PPDU 0

4 / Hak cipta KM/0 PPDU 0 STATISTICS STATISTIK N i i i W W I I f f!! r P r = N = N 9!!! r r C r = f f = f f 0 P(A ) ( ) ( ) ( ) B A P B P A P B P(X = r) = C r p r q r, p + q = m = L + C f F N m Mea / Mi, μ = p pq I = 0 Q Q 00 Z = X GEOMETRY GEOMETRI Distace /Jarak r = Midpoit /Titik tegah r j i (, ) =, A poit dividig a segmet of a lie Titik ag membahagi suatu tembereg garis (, ) = m m m m, Area of triagle /Luas segi tiga

5 TRIGONOMETRY TRIGONOMETRI Arc legth, s = rθ Pajag legkok, s = jθ si (A B) = si A cos B cos A si B si (A B) = si A kos B kos A si B Area of sector, A = r Luas sektor, L = j 9 cos (A B) = cos A cos B si A si B kos (A B) = kos A kos B si A si B si A + cos A = si A + kos A = 0 ta (A B) = ta A ta B ta A ta B sec A = + ta A sek A = + ta A ta A = ta A ta A cosec A = + cot A a b c kosek A = + kot A si A si B si C si A = si A cos A si A = si A kos A a = b + c bc cos A. a = b + c bc kos A. cos A = cos A si A = cos A = si A kos A = kos A si A = kos A = si A Area of triagle / Luas segi tiga = ab si C / Hak cipta KM/0 PPDU 0

6 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. Sectio A Bahagia A [0 marks] [0 markah] Aswer all questios. Jawab semua soala. ( ) cm ( + ) cm P Q R Diagram Rajah I diagram, a straight lie PQR is divided such that PQ = ( ) cm ad QR = ( + ) cm. Give that the legth of PR = 9 cm ad the product of the legths PQ ad QR is 0 cm. Fid the values of ad Dalam rajah, garis lurus PQR dibahagika dega keadaa PQ = ( ) cm da QR = ( + ) cm. diberika bahawa pajag PR = 9 cm da hasil darab pajag PQ da QR ialah 0 cm. Cari ilai-ilai da [ marks ] [ markah ] (a) Sketch the graph of = + si for 0 π. O the same aes, draw a suitable straight lie to solve the equatio π si = 0. Lakar graf bagi = + si utuk 0 π. Pada paksi ag sama, lukis satu garis lurus ag sesuai utuk meelesaika persamaa π si = 0. [ marks ] [ markah ] (b) Hece, fid the umber of solutios for the equatio π si = 0. Seterusa, cari bilaga peelesaia bagi persamaa π si = 0. [ marks ] [ markah ] / Hak cipta KM/0 PPDU 0

7 f g A B C m Diagram Rajah Based o diagram, give f: + Berdasarka rajah, diberi f: + ad g : +. da g : +. Fid / Cari ( a ) the values of m ad [ marks ] ilai m da [ markah ] ( b ) gf( ) [ marks ] [ markah ] (a) Give log = m ad log = p. Epress log i terms of m ad or p. [ marks] Diberi log = m da log =. Ugkapka log p dalam sebuta m da atau p. [ markah] (b) Solve the equatio + = +0. [ marks] Selesaika persamaa + = +0 [ markah] / Hak cipta KM/0 PPDU 0

8 Diagram shows the positio of houses A, B, C, P, Q ad R. Rajah meujukka keduduka buah rumah A, B, C, P, Q ad R. R A C Q B P Diagram Rajah R is situated 00 meter from P ad Q is situated 00 meter from P. C is situated 0 meter from P i the directio PR ad B is situated 0 meter from P i the directio PQ. A is betwee R ad B such that BA : AR = :. Takig a to represet 0 meter i the directio PR ad b to represet 0 meter i the directio ~ ~ PQ, R berada 00 meter dari P da Q berada 00 meter dari P. C berada 0 meter dari P dalam arah PR da B berada 0 meter dari P dalam arah PQ. A berada di atara R da B dega keadaa BA : AR = :. Megambil a utuk mewakili 0 meter dalam arah PR da b utuk mewakili 0 meter dalam ~ ~ arah PQ. Fid, i terms of ~ a ad b : ~ Cari, dalam sebuta a da b : ~ ~ ( a ) RB ( b ) CA ( c ) AQ [ marks ] [ markah ] / Hak cipta KM/0 PPDU 0

9 9 Diagram shows the curve =. PQ is the taget to the curve at poit P(, ). Rajah meujukka legkug =. PQ adalah tage kepada legkug itu pada titik P(, ). = P(, ) O Q Diagram Rajah Calculate Kiraka (a) the coordiates of Q, [ marks] koordiat Q, [ markah] (b) the area of the shaded regio. [ marks] luas ratau berlorek. [ markah] / Hak cipta KM/0 PPDU 0

10 0 Sectio B Bahagia B [0 marks] [0 markah] Aswer a four questios from this sectio. Jawab maa-maa empat soala daripada bahagia ii. The itake of studets to certai uiversit is determied b a special test. The scores of this test follow a ormal distributio with a stadard deviatio of 00. Diagram shows the graph of the distributio of the scores Pegambila pelajar ke sebuah uiversit ditetuka oleh suatu ujia khas. Skor ujia ii adalah megikut tabura ormal dega sisiha piawai 00. Rajah meujukka graf bagi skor itu. f() O 00 X ( score / skor ) Diagram Rajah ( a ) ( i ) State the mea of this ormal distributio [ mark ] Nataka mi bagi tabura ormal ii ( ii ) Fid the percetage that the studets score more tha 00 poits Cari peratus pelajar ag skor lebih daripada 00 mata [ marks ] [ markah ] ( b ) It is foud that 0.% studets who sat for the test qualif to eter the uiversit. Saiful obtaied a score of 0 poits. Determie whether Saiful qualifies to eter the uiversit. Give our reaso mathematicall. [ marks ] Didapati bahawa 0.% pelajar ag meduduki ujia itu laak utuk memasuki uiversiti itu. Saiful memperoleh skor 0 mata. Tetuka sama ada Saiful laak memasuki uiversiti tersebut. Berika alasa ada secara matematik. [ markah ] / Hak cipta KM/0 PPDU 0

11 A car maufacturer produced 000 uits of cars i the ear 00. Ever ear, the maufacturer icreased its productio b % of the previous ear's productio. Kilag kereta meghasilka 000 uit kereta pada tahu 00. Setiap tahu, kilag tersebut meigkatka pegeluaraa sebaak % pada tahu sebeluma. Determie Tetuka ( a ) the umber of cars produced for the ear 0 bilaga kereta ag dihasilka pada tahu 0 [ marks] [ markah] ( b ) the ear whe the umber of cars produced is two times of the ear 00 pada tahu apakah bilaga kereta ag dihasilka adalah dua kali gada dari tahu 00 [ marks] [ markah] ( c ) the total umber of cars produced from the ears 00 to 0 jumlah kereta ag dihasilka dari tahu 00 higga 0 [ marks] [ markah] / Hak cipta KM/0 PPDU 0

12 9 Use graph paper to aswer this questio Guaka kertas graf utuk mejawab soala ii. Table 9 shows the values of two variables, ad, obtaied from a eperimet. p q The variables ad are related b the equatio, where p ad q are costats. Jadual 9 meujukka ilai-ilai bagi dua pemboleh ubah, da, ag boleh diperoleh daripada satu eksperime. Pemboleh ubah da dihubugka oleh p q persamaa dega keadaa p da q adalah pemalar Table 9 Jadual 9 ( a ) Based o Table 9, costruct a table for the values of Berdasarka Jadual 9, bia satu jadual bagi ilai-ilai ad ad [ marks ] [ markah ] ( b ) Plot agaist, b usig a scale of cm to 0. uits o the -ais ad cm to 0. uits o the -ais. Hece, draw the lie of best fit. Plotka melawa, dega megguaka skala cm kepada 0. uit pada paks i- da cm kepada 0. uit pada paksi -. Seterusa, lukiska garis lurus peuaia terbaik. (c ) Use our graph i (b) to fid the values of Guaka graf ada di (b) utuk mecari ilai ( i ) p ( ii ) q [ marks ] [ markah ] [ marks ] [ markah ] / Hak cipta KM/0 PPDU 0

13 0 Diagram 0 shows a straight lie OA that is perpedicular to the straight lie BC. Give equatio OA is = ad equatio BC is + k = Rajah 0 meujukka garis lurus OA ag berserejag dega garis lurus BC. Diberi persamaa OA ialah = da persamaa BC ialah + k = A = D(, ) B + k = O C Diagram 0 Rajah 0 ( a ) Fid the value of k. [ marks ] Cari ilai k. [ markah ] ( b ) Determie whether the straight lie CD is parallel to OA. [ marks ] Tetuka samada garis lurus CD adalah selari dega OA. [ markah ] ( c ) Fid the equatio of the straight lie that is parallel to lie OA ad passes through poit B. [ marks ] Cari persamaa garis lurus ag selari dega garis OA da melalui titik B. [ markah] ( d ) A poit P moves such that its distace from D is alwas uits. Fid the equatio of locus P. [ marks ] Satu titik P bergerak dega keadaa jaraka dari titik D setiasa uit. Cari persamaa lokus titik bergerak P. [ markah ] / Hak cipta KM/0 PPDU 0

Diagram shows two semi circles PQR ad STU with cetre O. It is give that OR = cm, legth of arc ST =. cm ad legth of arc PQ = cm. Rajah meujukka dua semibulata, PQR da STU berpusat di O.

14 Diagram shows two semi circles PQR ad STU with cetre O. It is give that OR = cm, legth of arc ST =. cm ad legth of arc PQ = cm. Rajah meujukka dua semibulata, PQR da STU berpusat di O. Diberi bahawa OR = cm, pajag legkok ST =. cm da pajag legkok PQ = cm. Diagram Rajah [ Use / gua π =. ] Calculate Hitugka ( a ) the agle θ i radia [ marks ] ilai θ dalam radia [ markah ] ( b ) the perimeter of the shaded regio [ marks ] perimeter kawasa berlorek [ markah ] ( c ) the area of the shaded regio [ marks ] luas kawasa berlorek [ markah ] / Hak cipta KM/0 PPDU 0

15 Sectio C Bahagia C [0 marks] [0 markah] Aswer a two questios from this sectio. Jawab maa-maa dua soala daripada bahagia ii. A particle moves alog a straight lie ad passes through a fied poit O with velocit ms -. Its acceleratio, a ms -, is give b a = pt + q, where t is the time, i secods, after leavig O ad p ad q are costats. The particle achieves maimum velocit of 9 ms - whe t = s. Suatu zarah bergerak di sepajag suatu garis lurus melalui satu titik tetap O dega halaju ms -. Pecuta zarah itu, a ms -, diberi oleh a = pt + q, dega keadaa t ialah masa, dalam saat, selepas melalui O da p da q ialah pemalar. Zarah itu mecapai halaju maksimum 9 ms - pada masa t = s. [Assume motio to the right is positive] [Aggap geraka ke arah kaa sebagai positif ] Fid Cari (a) the value of p ad of q. [ marks] ilai p da ilai q. [ markah] (b) (c) the time iterval, i secods, durig which the particle moves towards the left. [ marks] julat masa, dalam saat, apabila zarah itu bergerak ke kiri [ markah] the acceleratio whe the particle is movs to the left with a velocit of ms -. [ marks] pecuta zarah itu ketika halajua ms - ke arah kiri. [ markah] / Hak cipta KM/0 PPDU 0

16 Diagram shows a PQR. Rajah meujukka PQR. Q cm 0 P 0 S R Diagram Rajah Poit S lie o the straight lie PR with PS : SR = :. It is give that PQ = cm, PQS = 0 ad QSP = 0 Titik S terletak pada garis lurus PR dega PS : SR = :. Diberi PQ = cm, PQS = 0 da QSP = 0 (a) Calculate Hitugka (i) legth of SR i cm, pajag SR dalam cm (ii) legth of QR i cm, pajag QR dalam cm [ marks] [ markah] (b) (i) Sketch a Q ' R ' S ' which has a differet shape from QRS such that S ' R ' = SR, Q ' S ' = QS ad Q ' R ' S ' = QRS. Lakarka sebuah Q ' R ' S ' ag mempuai betuk berbeza dari QRS Dega keadaa S ' R ' = SR, Q ' S ' = QS da Q ' R ' S ' = QRS. (ii) Hece, state the size of S ' Q ' R '. Seterusa, ataka saiz S ' Q ' R ' (iii) Fid the area, i cm, of Q ' R ' S '. Cari luas, dalam cm, bagi Q ' R ' S ' [ marks] [ markah] / Hak cipta KM/0 PPDU 0

17 Use graph paper to aswer this questio. Guaka kertas graf utuk mejawab soala ii. Raihai makes chocolate cakes ad baaa cakes for a part. The umber of cakes is based o the followig costraits: Raihai membuat ketul kek coklat da ketul kek pisag utuk satu jamua. Bilaga kek adalah berdasarka kekaga berikut: I II III The total umber of cakes caot eceed 0 pieces. Jumlah bilaga kek tidak boleh melebihi 0 ketul. The umber of chocolate cakes caot eceed times the umber of baaa cakes. Bilaga kek coklat tidak melebihi kali bilaga kek pisag. The umber of baaa cakes caot eceed the umber of chocolate cakes b more tha pieces. Bilaga kek pisag tidak boleh melebihi bilaga kek coklat. ( a ) Write three iequalities, other tha 0 ad 0, which satisf all the above costraits. [ marks ] Tulis tiga ketaksamaa, selai 0 da 0, ag memeuhi semua kekaga di atas. [ markah ] ( b ) Usig a scale of cm to 0 cakes o both aes, costruct ad shade the regio R which satisfies all the above costraits. [ marks ] Dega megguaka skala cm kepada 0 ketul kek pada kedua-dua paksi, bia da lorek ratau R ag memeuhi semua kekaga di atas. ( c ) Usig the graph costructed i (b), fid Dega megguaka graf ag dibia di (b), cari [ markah ] ( i ) the maimum umber of chocolate cakes that ca be made, bilaga maksimum kek coklat ag boleh dibuat, ( ii ) the maimum total cost for the cakes if the cost for a chocolate cake is RM0.0 ad the cost for a baaa cake is RM.00. jumlah kos maksimum pembuata kek jika kos seketul kek coklat ialah RM0.0 da kos seketul kek pisag ialah RM.00. [ marks ] [ markah] / Hak cipta KM/0 PPDU 0

18 A electrical item cosists of ol four parts, A, B, C ad D. Table shows the uitprice ad the price idices of the four parts i the ear 0 based o the ear 0 ad the umber of parts used i producig the electrical item. Suatu baraga elektrik megadugi empat bahagia, A, B, C ad D. Jadual meujukka harga uit da harga ideks keempat-empat bahagia itu pada tahu 0 berasaska tahu 0 da bilaga bahagia ag diguaka dalam meghasilka baraga elektrik tersebut. Part Bahagia Price i 0 Harga pada tahu 0 Price i 0 Harga pada tahu 0 Price ide i 0 based o 0 Ideks harga pada tahu 0 berasaska tahu 0 Number of parts Bilaga bahagia A 0 m B p 0 C q D 0 r Table Jadual (a) Fid the value of p, q ad r. Cari ilai-ilai p, q da r. [ marks] [ markah] (b) Fid the value of m, if the composite ide for the ear 0 takig the ear 0 as the base ear is.. [ marks] Cari ilai m, jika ideks gubaha bagi tahu 0 berasaska tahu 0 ialah.. [ markah] (c) Fid the uit price of the electric item i 0 if the uit price of the item i 0 is RM. [ marks] Cari harga uit baraga elektrik itu pada tahu 0 jika harga uit baraga tersebut pada tahu 0 ialah RM. [ markah] END OF QUESTION PAPER KERTAS PEPERIKSAAN TAMAT / Hak cipta KM/0 PPDU 0

19 9 NAMA : TINGKATAN : NO. KAD PENGENALAN - - ANGKA GILIRAN Araha Kepada Calo Tulis ombor kad pegeala da agka gilira ada pada petak ag disediaka. Tadaka ( ) utuk soala ag dijawab. Ceraika helaia ii da ikat sebagai muka hadapa bersama-sama dega helaia jawapa. Kod Pemeriksa Bahagia A B C Soala Soala Dijawab Markah Peuh Markah Diperoleh (Utuk Keguaa Pemeriksa) Jumlah / Hak cipta KM/0 PPDU 0

20 0 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, a four questios from Sectio B ad a two questios from Sectio C. Jawab semua soala dalam Bahagia A, maa-maa empat soala daripada Bahagia B da maa-maa dua soala daripada Bahagia C.. Write our aswers o the papers provided. If the papers are isufficiet, ou ma ask for etra papers from the ivigilator. Jawapa ada hedaklah ditulis di dalam kertas jawapa ag disediaka. Sekiraa kertas jawapa tidak mecukupi, sila dapatka helaia tambaha daripada pegawas peperiksaa.. Show our workig. It ma help ou to get marks. Tujukka lagkah-lagkah petig dalam kerja megira ada. Ii boleh membatu ada utuk medapatka markah.. The diagrams i the questios provided are ot draw to scale uless stated. Rajah ag megirigi soala tidak dilukis megikut skala kecuali diataka.. The marks allocated for each questio ad sub-part of a questio are show i brackets. Markah ag diperutukka bagi setiap soala da ceraia soala ditujukka dalam kuruga.. The Upper Tail Probabilit Q(z) For The Normal Distributio N(0, ) Table is provided o page. Jadual Kebaragkalia Hujug Atas Q(z) Bagi Tabura Normal N(0, ) disediaka di halama.. A list of formulae is provided o pages to. Satu searai rumus disediaka di halama higga. 9. Graph papers are provided. Kertas graf disediaka. 0. You ma use a scietific calculator. Ada dibearka megguaka kalkulator saitifik.. Tie the papers ad the graph papers together ad had i to the ivigilator at the ed of the eamiatio. Ikat kertas jawapa bersama-sama dega kertas graf da serahka kepada pegawas peperiksaa pada akhir peperiksaa. / Hak cipta KM/0 PPDU 0

SULIT /. This questio paper cosists of questios. Kertas soala ii megadugi soala.. Aswer all questios. Jawab semua soala.. Give ol oe aswer for each qu

SULIT /. This questio paper cosists of questios. Kertas soala ii megadugi soala.. Aswer all questios. Jawab semua soala.. Give ol oe aswer for each qu SULIT / NAMA ANGKA GILIRAN PEPERIKSAAN PERCUBAAN SPM TAHUN 9 / ADDITIONAL MATHEMATICS Kertas September 9 jam Dua jam JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU. Kertas soala ii adalah dalam dwibahasa..