Mathematics 50 PEPERIKSAAN PERCUBAAN SMK DATO SYED ESA, BATU PAHAT UJIAN BERTULIS SEPTEMBER 2014
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1 Mathematics 50 SMK DATO SYED ESA, BATU PAHAT PEPERIKSAAN PERCUBAAN UJIAN BERTULIS SEPTEMBER 014 jam ARAHAN : 1. Buka kertas soalan ini apabila diberitahu.. Tulis nama dan angka giliran anda pada ruang yang disediakan. 3. Jawapan anda hendaklah ditulis pada ruang jawapan yang disediakan dalam kertas soalan ini. 4. Kertas soalan ini hendaklah diserahkan kepada pengawas Peperiksaan pada akhir peperiksaan. Nama Pemeriksa : Untuk Kegunaan Pemeriksa Soalan Markah Penuh Markah Diperoleh Jumlah 100 NAMA :... ANGKA GILIRAN : 1
2 Rumus-rumus berikut boleh membantu anda untuk menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan. The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. 1 a a a a a a 3 ( a m ) a mn m n m n m n m n 4 Jarak / Distance = ( x x ) ( y y ) 1 1 HUBUNGAN RELATIONS 5 Titik Tengah / Midpoint x ( x, y ) = 1 x y, 1 y Jarak Perjalanan 6 Purata Laju = Masa yang diambil Average speed = distance travelled time taken 7 Min = Jumla Data Bilangan Data sum of data Mean = number of data 8 Teorem Pitagoras / Pythagoras Theorem c a b 1 Luas segi empat tepat = panjang lebar Area of rectangle = length width Luas Segitiga = 1 tapak tinggi Area of triangle = 1 base height 3 Luas parallelogram = Tapak x Tinggi Area of parallelogram = base BENTUK DAN RUANG SHAPE AND SPACE height 4 Luas trapezium = 1 jumla sisi selari tinggi Area of trapezium = 1 sum of parallel sides height
3 5 Lilitan bulatan = πd = πj Circumference of circle = d r 6 Luas bulatan = πj Area of circle = r 7 Permukaan melengkung silinder = πjt Curved surface area of cylinder = rh 8 Luas permukaan sfera = 4πj Surface area of sphere = 4 r 9 Jumlah sudut pedalaman bagi polygon sekata = ( n ) 180 Sum of interior angles of a polygon = ( n ) Panjang lengkok panjang lilitan bulatan Lengt arc circumference circle = Sudut mencangkum dipusat bulatan = Angled Subtended at centre Luas sektor Luas Bulatan Area of sector Area of circle Sudut di pusat bulatan = Angle at centre = Faktor Skala / Scale factor, k = PA PA 19 Luas imej = k luas objek Area of image = k area of object 3
4 Jawab semua soalan. Answer all questions. Soalan/Question 1 1 (a) Rajah 1(a) menunjukkan satu garis nombor. Diagram 1(a) shows a number line. Rajah 1(a) Diagram 1(a) Cari nilai bagi Find the value of (i) R, (ii) S, (iii) S R. Jawapan/Answer 3 R 4 S 5 (i) R :... (ii) S :... (iii) S R :... (b)(i) Hitung nilai dan beri jawapan dalam bentuk perpuluhan. Calculate the value of and give the answer in decimal form. [ markah/marks] (ii) Safiah memotong 3 utas benang berukuran 48.5 cm setiap satu daripada segulung benang. Dia memotong seutas lagi benang berukuran 5.4 cm lebih panjang daripada setiap utas benang tadi. Baki benang ialah 5.75 cm. Berapakah panjang asal, dalam cm, bagi segulung benang itu? Safiah cuts 3 pieces of strings with the length of 48.5 cm each from a roll of string. She cuts another piece which is 5.4cm longer than each string piece. The remainder string is 5.75 cm. What is the original length, in cm of the roll of strings? [ markah/marks] 4
5 (c) Kartik menyimpan sejumlah wang di dalam bank dengan faedah mudah 4% setahun. Dia mendapat RM 000 setahun sebagai faedah. Selepas 8 tahun, dia bercadang untuk membeli sebuah kereta yang berharga RM menggunakan simpanannya itu. Adakah wang simpanannya mencukupi untuk membeli kereta itu? Beri alasan anda. Kartik saved some money in a bank for a simple interest of 4% per annum. She got RM 000 per year as interest. After 8 years, she decided to buy a car costs RM using her saving. Is her money enough to buy the car? Give your reason. Soalan/Question (a) Senaraikan tiga gandaan sepunya yang pertama bagi 6 dan 8. List the first three common multiples of 6 and 8. (b) Lengkapkan langkah-langkah pengiraan yang berikut ke dalam petak dengan jawapan yang betul. Ungkapkan jawapan sebagai pecahan dalam sebutan terendah. Complete the following steps by filling in the correct answers. Express the answer as a fraction in its lowest term. [4 markah/marks] = = = = 5
6 (c) Berat sebuah bakul kosong ialah kg. Apabila 7 biji betik yang bersaiz sama diisi ke dalam bakul itu, beratnya ialah 1.5 kg. Hitung purata jisim, dalam g, bagi setiap biji betik itu. The mass of an empty basket is kg. When 7 papayas of equal size are placed in the basket, the mass is 1.5 kg. Calculate the average mass, in g, of each papaya. Soalan/Question 3 3 (a) Berdasarkan rajah 3(a), nyatakan sama ada pernyataan yang berikut adalah Benar atau Palsu. Based on diagram 3(a), state whether the following statements are Correct or False. P Q V M U T W N S Rajah 3(a) Diagram 3(a) (i) Garis VW dan MN adalah selari The lines of VW and MN are parallel. (ii) Garis TU berserenjang dengan garis PS. The line TU is perpendicular to the line PS. (iii) PQW dan VQP adalah sudut pelengkap antara satu sama lain. PQW and VQP are the angles that complementary to each other. (b) Tanpa menggunakan kalkulator, nilaikan : Without using a calculator, evaluate :
7 (c) Rajah 3(c) menunjukkan bilangan guli yang berbeza di dalam sebuah kotak. Bilangan guli biru dan kuning tidak ditunjukkan. Diagram 3(c) shows the number of different marbles in a box. The number of blue and yellow marbles are not shown. Merah / Red : 30 Biru / Blue : x Kuning / Yellow : y Rajah 3(c) Diagram 3(c) Nisbah guli merah, biru dan kuning di dalam kotak itu ialah 5 : 7 : 3. Cari nilai x - y. The ratio of red, blue and yellow marbles in the box is 5 : 7 : 3. Find the value of x-y. [4 markah/marks] Soalan/Question 4 4 (a) Namakan setiap pepejal berikut dan nyatakan bilangan permukaannya. Name each of the following solids and state the number of faces. Pepejal Solid Nama Pepejal Solid Name Bilangan Permukaan Number of Faces 7
8 (b) Rajah 4(b) menunjukkan sebuah segiempat tepat dan dua buah semi bulatan yang menyentuh satu sama lain. Diagram 4(b) shows a rectangle and two semicircles touching each other. 7 cm 5 cm Rajah 4(b) Diagram 4(b) Hitung luas, dalam cm, rantau berlorek itu. Calculate the area, in cm, of the shaded region. [ Guna / use π = 3.14] (c) Rajah 4(c) menunjukkan sebuah prisma. Diagram 4(c) shows a prism. 8 cm 3 cm 4 cm 6 cm Rajah 4(c) Diagram 4(c) Hitung jumlah luas permukaan, dalam cm, prisma itu. Calculate the total surface area, in cm, of the prism. [4 markah/marks] Soalan/Question 5 8
9 5 (a) Nyatakan sama ada persamaan yang berikut adalah persamaan linear dalam satu pembolehubah. Bulatkan jawapan anda. State whether the following equations are linear equations in one unknown. Circle your answer. Jawapan / Answer: (i) 7y = 8 y Ya / Yes Tidak / No (ii) 4k + 10 = 30mm Ya / Yes Tidak / No (iii) 1 x = 0x + 1 Ya / Yes Tidak / No 8 5(b) Rajah 5(b) di ruang jawapan yang dilukis pada segi empat grid yang bersisi 1 unit. W, X dan Y adalah tiga titik yang bergerak dalam rajah itu. Diagram 5(b) in the answer space is drawn on a square grid of sides 1 unit.w, X and Y are three moving points on the diagram. Pada rajah tersebut, lukiskan On the diagram, draw (i) Lokus X dengan keadaan AX = AG, The locus of X such that AX = AG, (ii) Lokus bagi titik Y yang bergerak dengan keadaan titik itu sentiasa berjarak 5 unit dari titik H. The locus of point Y which moves such that its distance is constantly 5 units from the point H. (iii) Seterusnya, tandakan dengan simbol semua kedudukan bagi persilangan lokus X dan lokus Y itu. Hence, mark with the symbol all the intersection of the locus of X and locus of Y. Jawapan / Answer: A N [4 markah/marks] B M C L D K E J F I G H Rajah 5(b) Diagram 5(b) 9
10 5(c) Dalam Rajah 5(c), segitiga R dan segitiga S dilukis pada satah Cartesan. In diagram 5(c), triangles R and S are drawn on a Cartesian plane. y 10 8 R 6 4 S x Rajah 5(c) Diagram 5(c) S ialah imej bagi R di bawah suatu putaran. S is the image of R under rotation. (i) Nyatakan sudut putaran itu. State the angle of rotation (ii) Nyatakan arah putaran State the direction of rotation (iii) Cari koordinat bagi pusat putaran itu. Find the coordinates of the centre of rotation [3 markah/ marks] Jawapan /Answer : (i) (ii) (iii) 10
11 Soalan/Question 6 6(a) Selesaikan tiap-tiap persamaan linear yang berikut. Solve each of the following linear equations. (i) 7u 5 u (ii) 3 (4 w 8) 7 w 6(b) Diberi 18 T Fm. Ungkapkan T dalam sebutan F dan m. 18Fm Given that. Express T in terms of F and m. T 11
12 6(c) Senaraikan semua integer m yang memuaskan ketaksamaan linear 7 m 3 dan m 4. List all the integer values of m which satisfy both the inequalities 7 m 3 and m 4. [4 markah/marks] Soalan/Question 7 7(a)(i) Rajah 7(a)(i) menunjukkan separuh bulatan berpusat di O. Diberi bahawa FG =GH. Diagram 7(a((i) shows a semicircle EFGH with centre O. Given that FG = GH. E O 0 F H y G Rajah 7(a)(i) Diagram 7(a)(i) Cari nilai y. Find the value of y, 1
13 7(a)(ii) Dalam rajah 7(a)(ii), PQRSV ialah pentagon sekata dan STUV ialah segiempat selari. RST ialah garis lurus dan PUV=1 0. In diagram 7(a)(ii), PQRSV is a regular pentagon and STUV is a parallelogram. RST is a straight line and PUV=1 0. Q P V x U R S T Rajah 6(b)(ii) Diagram 6(b)(ii) Cari nilai x. Find the value of x. [4 markah/marks] 7(b) Jadual 7(b) menunjukkan masa yang diambil oleh 4 buah bas J, K, L dan M dalam satu perjalanan. Table 7(b) shows the time taken by four bus J, K, L and M on a journey. Bas Bus Jarak (km) Distance (km) Masa (j) Time (h) J K L 10.5 M Jadual 7(b) Table 7(b) Bas yang manakah dipandu di bawah halaju purata 90 km/j. Buktikan. Which bus that move below an average speed of 90 km/h. Prove it. 13
14 7(c) Rajah 7(c) menunjukkan sebuah piramid segi empat sama. Diagram 7(c), shows a square base right pyramid. 5 units 6 units Rajah 7(c) Diagram 7(c) Lukis bentangan bagi piramid tersebut selengkapnya. Draw the net of the pyramid completely. [3 Markah/marks] Jawapan/Answer: 14
15 Soalan/Question 8 8(a) Faktorkan selengkapnya tiap-tiap ungkapan berikut : Factorise completely each of the following expressions: (i) (ii) 6 3y px qx + p q 8(b) Permudahkan tiap-tiap yang berikut: Simplify each of the following: (a) m 5 (b) k 4 k 3 k 15
16 8(c) Rajah 8(c) menunjukkan sebuah sisi empat PQRS. Diagram 8(c) shows a quadrilateral PQRS. S P 6 cm 10 0 Q R Rajah 8(c) Diagram 8(c) (i) (ii) Dengan menggunakan pembaris dan jangka lukis sahaja, bina Rajah 8(c) mengikut ukuran yang diberi, bermula dengan garis QR yang disediakan di ruang jawapan. By using only a ruler and a pair of compasses, construct Diagram 8(c) using the given measurements, beginning from line QR provided in the answer space. Berdasarkan rajah yang dibina dalam (c)(i), ukur panjang, dalam cm, bagi PS. Based on the diagram constructed in (c)(i), measure the length, in cm, of PS. [4 markah/marks] (i) Q R (ii) PS =
17 Soalan/Question 9 9(a) Jadual 9(a) di bawah menunjukkan kekerapan skor bagi sekumpulan pelajar dalam satu kuiz. Table 9(a) below shows the frequency of the scores of a group of students in a quiz. Skor / Score Kekerapan / Frequency 5 m 6 4 Jika terdapat 0 orang pelajar, If there are 0 students, Jadual 9(a) Table 9(a) (i) Cari nilai m. find the value of m. (ii) Hitungkan nilai min skor. Calculate the mean score. 9(b) Rafiqi memandu pada kelajuan tetap 90 kmh -1 dan dia telah memecut dengan kelajuan 105 kmh -1 selama 0 minit. Kirakan kadar pecutannya dalam kmh -. Rafiqi was driving at a constant speed of 90kmh -1 and he accelerated to 105kmh -1 in 0 minutes. Find the acceleration of the car in kmh
18 9(c) Rajah 9(c) di bawah menunjukkan umur bagi keluarga Ali dan Bakar. Diberi min umur bagi keluarga Bakar ialah 31 tahun dan umur Ali adalah 9 tahun lebih muda daripada Bakar. Diagram 9(c) below shows the age of the family of Ali and Bakar. Given the mean age of the family Bakar is 31 years old and Ali age is 9 years younger than Bakar. Keluarga Ali Ali s Family Keluarga Bakar Bakar s Family Bapa/Father 35 tahun 35 years old Ibu/Mother 34 tahun 34 years old Ali Bakar Bapa/Father 45 tahun 45 years old Ibu/Mother 4 tahun 4 years old Kakak/Sister 19 tahun 19 years old Hitungkan min umur bagi keluarga Ali. Calculate the mean age of the family of Ali. Rajah 9(c) Diagram 9(c) [4 markah/marks] Soalan/Question 10 10(a) Dalam Rajah 10(a), PQRS ialah suatu garis lurus. In Diagram 10(a), PQRS is a straight line. y P(-,-3) x Rajah 10(a) Diagram 10(a) Q ialah titik tengah bagi PS dan R ialah titik tengah bagi QS. Cari koordinat R. Q is the midpoint of PS and R is the midpoint of QS. Find the coordinates of R. 18
19 10(b) Rajah 10(b) di bawah menunjukkan dua segitiga bersudut tegak, PQS dan QRS. Diberi sin a = 3 5 dan kos b = Diagram 10(b) below shows two right-angled triangles, PQS and QRS. It is given that sin a = 3 5 and cos b = (i) Carikan nilai tan a. Find the value of tan a. Rajah 10(b) Diagram 10(b) (ii) Kirakan panjang sisi PS, dalam cm. Calculate the length, in cm, of PS. 10(c) Dengan menggunakan kertas graf yang disediakan, jawab soalan berikut; Use the graph paper provided to answer this question. x y Jadual 10(c) Table 10(c) Jadual 10(c) menunjukkan jadual nilai bagi sesuatu fungsi. Dengan menggunakan skala cm kepada 1 unit bagi paksi-x dan cm kepada unit bagi paksi-y, lukiskan graf bagi fungsi tersebut. Table 10(c) represents the table of value for a certain function. Using a scale of cm to 1 unit on the x-axis and cm to units on the y-axis, draw the graph. [4 markah/marks] SOALAN TAMAT. 19
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