SULIT 3472/2. Section A Bahagian A. [5 marks]
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1 SULIT 347/ Section A Bahagian A [40 marks] [40 markah] Answer all questions. Jawab semua soalan. 1 Solve the following simultaneous equations: Selesaikan persamaan serentak ang berikut: 4, Give our answers correct to three decimal places. Berikan jawapan anda betul kepada tiga tempat perpuluhan. [5 marks] [5 markah] It is given that f : 1 and Diberi bahawa f : 1 dan (a) Show that 1 1 Tunjukkan bahawa Hence, find Seterusna, cari g : 4 1, g : 4 1, f ( ) (1 ). [ marks] 1 1 f ( ) (1 ). [ markah] (i) gf 1 ( ), [ marks] [ markah] (ii) h ( ) h ( ) such that 1 gh( ) f ( ). [ marks] dengan keadaan bahawa 1 gh( ) f ( ). [ markah] 347/ (C) 016 Hak Cipta SM Zon B Kuching Sarawak [ Lihat halaman sebelah SULIT
2 3 In a factor, a machine produces a batch of straight plastic rods with the shape of right clinder. All plastic rods in the batch have the same volume but different radii and lengths. On a particular da, the machine produced the batch of plastic rods in such a wa that the radius of the net plastic rod to be produced was twice the radius of the plastic rod that had been made before. It was known that the volume of the first plastic rod made in the batch on that da was 3 56π cm Dalam sebuah kilang, sebuah mesin menghasilkan sekumpulan rod plastik lurus ang berbentuk silinder tegak. Semua rod plastik dalam kumpulan tersebut mempunai isipadu ang sama tetapi berjejari dan panjang ang berbeza. Pada hari tertentu, mesin tersebut menghasilkan kumpulan rod plastik itu dengan keadaan bahawa jejari bagi rod plastik ang dihasilkan seterusna adalah dua kali ganda jejari bagi rod plastik ang dihasilkan sebelumna. Diketahui bahawa isipadu bagi rod plastik ang pertama dihasilkan dalam kumpulan tersebut ialah. 3 56π cm (a) Given that the fourth plastic rod made in the batch had the length of 1 cm, calculate the radius, in cm, of the first plastic rod made in the batch. [ marks] Diberi bahawa rod plastik ang keempat dihasilkan dalam kumpulan itu mempunai panjang 1 cm, hitungkan jejari, dalam cm, bagi rod plastik ang pertama dihasilkan dalam kumpulan itu. [ markah] All plastic rods in the batch were connected b their ends to form a long plastic rod. B assuming that the plastic rods were infinitel produced in the batch, calculate the length, in cm, of the combined plastic rod. [4 marks] Semua rod plastik dalam kumpulan itu disambungkan untuk menjadi sebatang rod plastik ang panjang. Dengan menganggap bahawa rod-rod plastik itu dihasilkan secara tak terhingga dalam kumpulan tersebut, hitungkan panjang, dalam cm, bagi rod plastik ang disambungkan itu.. 4 The gradient function of a curve which passes through A1, 1 is Fungsi kecerunan suatu lengkung ang melalui A1, 1 ialah Find Cari (a) the equation of the curve, [3 marks] persamaan lengkung itu, the coordinates of the turning points of the curve and determine whether each of the turning points is a maimum or a minimum. [5 marks] Koordinat titik-titik pusingan lengkung dan tentukan sama ada titik-titik pusingan itu adalah maksimum atau minimum. [5 markah] 347/ (C) 016 Hak Cipta SM Zon B Kuching Sarawak SULIT
3 SULIT 347/ 5 (a) Prove that Buktikan bahawa sin( A B) tan Atan B. [ marks] cos Acos B (i) Sketch the graph of sin for (ii) Lakar graf sin( A B) tan Atan B. [ markah] kos Akos B sin untuk 0 3π. [3 marks] 0 3π. Hence, using the same aes, sketch a suitable straight line to find the number of solutions to the equation sin 1 for 0 3π. State the π number of solutions. [3 marks] Seterusna, dengan menggunakan paksi ang sama, lakar satu garis lurus ang sesuai untuk mencari bilangan penelesaian bagi persamaan sin 1 untuk 0 3π. Natakan bilangan penelesaian itu. π 6 Diagram 6 shows the cross section of a floating clindrical container. The cross section of the container is a circle with centre O and radius 60 cm. The segment PQR is the section of the container which is above the surface of the water. Q is the highest point and is 0 cm above the water surface. Rajah 6 menunjukkan keratan rentas sebuah bekas berbentuk silinder ang terapung di dalam air. Keratan rentas bekas itu ialah sebuah bulatan berpusat O dan berjejari 60 cm. Tembereng PQR ialah bahagian bekas ang berada lebih tinggi daripada paras air. Titik tertinggi Q adalah 0 cm lebih tinggi daripada permukaan air. P Q R O 60 cm B using π 3.14, find Dengan menggunakan π 3.14, cari (a) Diagram 6 Rajah 6 POR, in radians, [3 marks] POR, dalam radian, the area, in luas, dalam cm, of the cross section below the water surface. [4 marks] cm, bahagian keratan rentas ang di bawah paras air. 347/ (C) 016 Hak Cipta SM Zon B Kuching Sarawak [ Lihat halaman sebelah SULIT
4 4 Section B Bahagian B [40 marks] [40 markah] Answer four questions from this section. Jawab empat soalan daripada bahagian ini. 7 Solution b scale drawing is not accepted. Penelesaian secara lukisan berskala tidak diterima. Diagram 7 shows a triangle QOR, where O is the origin. The point T lies on the side of the triangle. QR Rajah 7 menunjukkan sebuah segi tiga QOR, dengan keadaan O ialah asalan. Titik T terletak pada sisi QR segi tiga itu. R 5,4 T O (a) Diagram 7 Rajah 7 Given that T divides QR in the ratio :1, show that T has the coordinates 4,. [ marks] Diberi bahawa T membahagikan QR dalam nisbah :1, tunjukkan bahawa koodinat T ialah 4,. [ markah] Q, Calculate the area, in Hitung luas, dalam unit, of triangle QOR. unit, segi tiga QOR. [ marks] [ markah] (c) Find the equation of the straight line that passes through point T perpendicular to straight line QR. and [4 marks] Cari persamaan garis lurus ang melalui titik T dan berserenjang dengan garis lurus QR. (d) A point P moves such that its distance from T is alwas 3 units. Find the equation of locus of P. [ marks] Titik P bergerak dengan keadaan jarakna dari T sentiasa 3 unit. Cari persamaan lokus P. [ markah] 347/ (C) 016 Hak Cipta SM Zon B Kuching Sarawak SULIT
5 SULIT 347/ 8 Diagram 8 shows the straight line and a graph of quadratic function ( 4). B is the maimum point. Rajah 8 menunjukkan suatu garis lurus dan graf bagi satu fungsi kuadratik ( 4). B ialah titik maksimum bagi lengkung itu. B ( 4) O A Diagram 8 Rajah 8 (a) State the coordinates of the point A Natakan koordinat bagi titik A and point B. [ marks] dan titik B. [ markah] Find the area of the region bounded b the curve ( 4) and the straight line. [4 marks] Cari luas rantau ang dibatasi oleh lengkung ( 4) dan garis lurus. (c) Find the volume of the solid generated, in terms of π, when the shaded region is revolved through 360 abaut the -ais. [4 marks] Cari isipadu bagi pepejal ang terjana, dalam sebutan π, apabila rantau berlorek diputarkan melalui 360 sekitar paksi-. 347/ (C) 016 Hak Cipta SM Zon B Kuching Sarawak [ Lihat halaman sebelah SULIT
6 6 9 Table 9 shows a frequenc distribution of marks obtained b a group of students in a monthl test. Jadual 9 menunjukkan taburan kekerapan markah ang diperolehi sekumpulan pelajar dalam satu ujian bulanan. Marks Markah Number of students Bilangan pelajar Based on Table 9, calculate Berdasarkan Jadual 9, hitung Table 9 Jadual 9 (a) the range, [1 mark] julat [1 markah] (i) the variance of marks. [4 marks] (c) varians markah, (ii) if each students are added 3 marks, find the new variance. [1 mark] jika setiap pelajar ditambah 3 Use graph paper to answer this part of the question. Gunakan kertas graf untuk menjawab ceraian soalan ini. markah, cari varians ang baharu.[1 markah] Using a scale of cm to 10 marks on the horizontal ais and cm to students on the vertical ais, draw a histogram to represent the frequenc distribution of the marks in Table 9. Hence, find the mode mark. [4 marks] Dengan menggunakan skala cm kepada 10 markah pada paksi mengufuk dan cm kepada orang murid pada paksi mencancang, lukis sebuah histogram bagi mewakili taburan kekerapan markah dalam Jadual 9. Seterusna, cari markah mod. 347/ (C) 016 Hak Cipta SM Zon B Kuching Sarawak SULIT
7 SULIT 347/ 10 (a) In a surve carried out in a particular state it is found that two out of five families own an imported car. If ten families are chosen b random from the state, calculate the probabilit that at least eight families own an imported car. [4 marks] Dalam suatu kajian di sebuah negeri tertentu, didapati dua daripada lima keluarga memiliki sebuah kereta ang diimport. Jika sepuluh keluarga dari negeri itu dipilih secara rawak, hitung kebarangkalian bahawa sekurang-kurangna lapan keluarga memiliki kereta ang diimport. In a school, 400 students sat for a test. The marks obtained follow a normal distribution with a mean of 6 and a standard deviation of 8. Dalam sebuah sekolah, 400 orang murid menduduki suatu ujian. Markah ang diperoleh adalah mengikut taburan normal dengan min 6 dan sisihan piawai 8. (i) Find the number of students who pass the test if the passing mark is 50. Cari bilangan murid ang lulus ujian itu jika markah lulus ialah 50. (ii) If 10% of the students pass the test with grade A, find the minimum mark to obtain grade A. Jika 10% daripada murid itu lulus ujian dengan mendapat gred A, cari markah minimum untuk mendapat gred A. [6 marks] [6 markah] 347/ (C) 016 Hak Cipta SM Zon B Kuching Sarawak [ Lihat halaman sebelah SULIT
8 8 11 Use graph paper to answer this question. Gunakan kertas graf untuk menjawab soalan ini. Table 11 shows the values of two variables, Variables and are related b the equation and, obtained from an eperiment. 1 ab Jadual 11 menunjukkan nilai-nilai bagi dua pembolehubah, daripada satu ujikaji. Pembolehubah dan dengan keadaan a and b ialah pemalar., where a and b are constants. dan dihubungkan oleh persamaan Table 11 Jadual 11, ang diperoleh 1 ab, (a) (c) Based on Table 11, construct a table for the values of log10 Berdasarkan Jadual 11, bina satu jadual bagi nilai-nilai Plot log10 against 1, using a scale of cm to 1 unit log10 against 1. [ marks] melawan [ markah] 1. on the ( 1) -ais and cm to 0.5 unit on the log10 -ais. Hence, draw the line of best fit. [3 marks] Plot log10 melawan paksi- ( 1) dan cm kepada 0.5 unit pada paksi-log10 garis lurus penuaian terbaik. Use the graph in to find the value of Guna graf di untuk mencari nilai (i) a, (ii) b. 1, dengan menggunakan cm kepada 1 unit pada. Seterusna, lukis [5 marks] [5 markah] 347/ (C) 016 Hak Cipta SM Zon B Kuching Sarawak SULIT
9 SULIT 347/ Section C Bahagian C [0 marks] [0 markah] Answer two questions from this section. Jawab dua soalan daripada bahagian ini. 1 A particle moves along a straight line and passes through a fied point O. The velocit,, at time t seconds after leaving the point O is given b v 6 t t. v cm s 1 Satu zarah bergerak di sepanjang suatu garis lurus dan melalui satu titik tetap O. Halaju, bagi zarah itu pada masa t saat selepas meninggalkan titik O adalah diberi oleh v 6 t t. Find Cari v cm s 1 (a) the maimum velocit, in halaju maksimum, dalam cm s 1, of the particle, [4 marks] cm s 1, zarah itu, the initial acceleration, in pecutan awal, dalam cm s, of the particle, cm s, zarah itu, [ marks] [ markah] (c) the distance, in cm, from O jarak, dalam cm, dari O when the particle stops instantaneousl. apabila zarah itu berhenti seketika. [4 marks] 347/ (C) 016 Hak Cipta SM Zon B Kuching Sarawak [ Lihat halaman sebelah SULIT
10 10 13 Diagram 13 shows quadrilateral PQRS.It is given that QR 8.5 cm, RS 7 cm, PS 18 cm, PQR 110 and PSR 75. Rajah 13 menunjukkan sebuah sisi empat PQRS. Diberi bahawa RS 7 cm, PS 18 cm, PQR 110 dan PSR 75. P QR 8.5 cm, Q cm 8.5cm R 7cm 75 S (a) Find Cari (i) the length, in cm, of PR, (ii) panjang, dalam cm, PR, QPR. Diagram 13 Rajah 13 [4 marks] Find the area, in Cari luas, dalam cm, of the quadrilateral PQRS. [4 marks] cm, bagi sisi empat PQRS. (c) Find the shortest distance, in cm, from point Q to the line PR. Cari jarak terdekat, dalam cm, dari titik Q ke garis lurus PR. [ marks] [ markah] 347/ (C) 016 Hak Cipta SM Zon B Kuching Sarawak SULIT
11 SULIT 347/ 14 A florist wants to make bouquet of rose flowers and bouquet of anggerik flowers. Ever bouquet of anggerik will take 30 minutes to be finished and roses will take 0 minutes. Seorang peniaga ingin membuat jambangan bunga ros dan jambangan bunga anggerik. Setiap jambangan bunga anggerik mengambil masa 30 minit untuk disiapkan dan setiap jambangan bunga ros mengambil masa 0 minit untuk disiapkan. The process of making the bouquets are based the following constraints: Proses membuat jambangan bunga itu mesti berdasarkan kekangan berikut: I The number of bouquet of anggerik must not eceed times the number of bouquet of roses. II III Bilangan jambangan bunga angggerik mestilah tidak melebihi kali bilangan jambangan bunga ros. The number of bouquet of anggerik is at least roses. 347/ (C) 016 Hak Cipta SM Zon B Kuching Sarawak [ Lihat halaman sebelah SULIT 1 4 time the number of bouquet of Bilangan jambangan bunga anggerik mestilah sekurang-kurangna bilangan jambangan bunga ros. The total time allocated to make the bouquet does not eceed 0 hours. Jumlah masa ang diperuntukkan untuk membuat jambangan bunga tidak melebihi 0 jam. 1 4 daripada (a) Write three inequalities, other than 0 and 0, which satisf all the given constraints. [3 marks] Tulis tiga ketaksamaan, selain 0 dan 0, ang memenuhi semua kekangan ang di atas. Using a scale of cm to 10 bouquet of roses on -ais and cm to 5 bouquet of anggerik on -ais, construct and shade the region R which satisfies all the constraints. [3 marks] (c) B using the graph in, find Dengan menggunakan graf di, cari (i) (ii) the minimum number of bouquet of anggerik if the number of bouquet of roses is 30, [1 mark] bilangan minimum jambangan bunga anggerik jika bilangan jambangan bunga ros adalah 30. [1 markah] the maimum total profit the florist can make if the profit of ever bouquet of anggerik and roses are RM 5 and RM 35 respectivel. [3 marks] jumlah hasil jualan maksimum peniaga tersebut jika keuntungan setiap jambangan bunga anggerik dan ros adalah RM 5 dan RM 35 masingmasing. Dengan menggunakan skala cm kepada 10 jambangan ros pada paksi- dan cm kepada 5 jambangan anggerik di paksi-, bina dan lorek rantau R ang memenuhi semua kekangan di atas.
12 15 Table 15 shows the price indices and percentage ependiture of four ingredients, M,, P and Q, used in making a kind of food. N 1 Jadual 15 menunjukkan indeks harga dan peratus perbelanjaan bagi empat jenis ramuan, M, N, P dan Q, ang digunakan untuk membuat sejenis makanan. Ingredients Bahan Price (RM) per kg Harga (RM) per kg Price inde in ear 014 based on the ear 010 Indeks harga pada tahun 014 berasaskan tahun 010 Percentage ependiture (%) Peratus perbelanjaan (%) M N P Q z (a) Find the value of, Cari nilai bagi, Table 15 Jadual 15 and z. [3 marks] dan z. Calculate the composite inde for the cost of making the food in the ear 014 based on the ear 010. [3 marks] Hitungkan indeks gubahan bagi kos pembuatan makanan itu pada tahun 014 berasaskan tahun 010. (c) (i) The cost of making a packet of the food in ear 010 was RM Calculate the corresponding cost in the ear 014. [ marks] Kos untuk membuat sebungkus makanan itu pada tahun 010 ialah RM Hitung kos sepadan pada tahun 014. [ markah] (ii) The cost of all the ingredients increase b 15% from the ear 014 to the ear 016. Find the composite inde for the ear 016 based on the ear 010. [ marks] Kos bagi semua ramuan itu meningkat sebanak 15% dari tahun 014 ke tahun 016. Cari indek gubahan bagi tahun 016 berasaskan tahun 010. [ markah] End of Question Paper Kertas Soalan Tamat 347/ (C) 016 Hak Cipta SM Zon B Kuching Sarawak SULIT
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