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1 5 BLANK PAGE HALAMAN KOSONG [Lihat sebelah
2 6 Section A Bahagian A [ 52 marks ] [ 52 markah ] Answer all questions in this section. Jawab semua soalan dalam bahagian ini 1. On the graph in the answer space, shade the region which satisfies the three inequalities x y 8, y > 3, and 2x y 8. Dalam graf di ruang jawapan, lorekkan rantau yang ditakrifkan oleh ketaksamaan x y 8, y > 3, dan 2x y 8. y 8 3 x y x y 8 x [ 3 marks ] [ 3 markah ]
3 7 2 2( m 6) 2. Solve the quadratic equation 5. m 2 2( m 6) Selesaikan persamaan kuadratik 5. m [ 4 marks ] Answer / Jawapan : [ 4 markah ] 3 Calculate the values of e and of f which satisfy the following simultaneous linear equations : Hitungkan nilai e dan f yang memuaskan persamaan linear serentak berikut : 1 e f 3 2e f 3 11 [ 4 marks ] Answer / Jawapan : [ 4 markah ] [Lihat sebelah
4 8 4. Diagram 1 shows a right prism. The base PQRS is a horizontal rectangle. Right angled triangle QRU is the uniform cross-section of the prism. Rajah 1 menunjukkan sebuah prisma tegak. Tapak segiempat tepat PQRS adalah mengufuk. Segitiga bersudut tegak QRU adalah keratan rentas seragam prisma itu. T U S 8 cm P R 12 cm 9 cm Q Diagram 1 Rajah 1 Identify and calculate the angle between the plane PRU and the plane RSTU. Kenal pasti dan hitung sudut di antara satah PRU dengan satah RSTU. [ 3 marks ] [ 3 markah ] Answer / Jawapan :
5 9 5 In diagram 2, O is the origin. The points P and R lie on the y- axis. Dalam diagram 2, O ialah asalan. Titik P dan titik R terletak pada paksi-y. y P 6 Q ( k, 8 ) -4 O R Diagram 2 Rajah 2 x 1 The gradient of the line PQ is. Find, 3 1 Kecerunan garis lurus PQ ialah. Carikan, 3 (a) the value of k. nilai k. (b) the equation of the straight line QR. persamaan garis lurus QR. (c) the x-intercept of the straight line QR. pintasan-x bagi garis lurus QR. [ 5 marks ] [ 5 markah ] Answer / Jawapan : (a) (b) (c) [Lihat sebelah
6 10 6 Diagram 3 shows a solid, formed by joining a cone to a cuboid. The base diameter of the cone is 6 cm and its height is 4 cm. Rajah 3 menunjukkan suatu pepejal yang terdiri daripada cantuman sebuah kon kepada sebuah kuboid. Diameter tapak kon ialah 6 cm dan tingginya ialah 4 cm. D C 4 cm A E B H 6 cm F 8 cm G Diagram 3 Rajah 3 Calculate the volume, in cm 3, of the solid. Hitung isipadu, dalam cm 3, pepejal itu. [ Use / Guna π = 7 22 ] [ 4 marks ] Answer / Jawapan : [ 4 markah ]
7 11 7 Diagram 4 shows two semicircles, RST and VWU, both with centre O. Rajah 4 menunjukkan dua semibulatan RST dan VWU yang kedua-duanya berpusat O. S R V O U T W Diagram 4 Rajah 4 OS = 14 cm. V and U are midpoints of OR and OT respectively.. OS = 14 cm. V dan U adalah titik tengah bagi OR dan OT masing-masing. 22 [ Use / Guna π = ] 7 Calculate Hitungkan (a) the perimeter, in cm, of the whole diagram, perimeter, dalam cm, seluruh rajah itu, (b) the area, in cm 2, of the shaded region. luas, dalam cm 2, kawasan berlorek. [ 6 marks ] [ 6 markah ] [Lihat sebelah
8 12 Answer / Jawapan : (a) (b)
9 13 8 (a) State whether each of the following statements is true or false. Nyatakan sama ada setiap pernyataan berikut adalah benar atau palsu. (i) - 3 < - 4 (ii) 2 3 > 6 (b) Write down the Conclusion to complete the following argument: Tuliskan Kesimpulan untuk melengkapkan hujah berikut: Premise 1: If x = 6, then 3x = 18. Premis 1: Jika x = 6, maka 3x = 18. Premise 2: 3x 18. Premis 2: 3x 18. Conclusion / kesimpulan: (c) Write down two implications based on the following sentence: t 3 = 64 if and only if t = 4 Tulis dua implikasi berdasarkan pernyataan berikut: t 3 = 64 t 3 = jika 64 dan if and hanya only jika if t = t = 4 4 [5 marks] [5 markah] [Lihat sebelah
10 14 Answer / Jawapan: (a) (i) (ii) (b) Conclusion / Kesimpulan : (c) Implication 1 / Implikasi 1 : Implication 2 / Implikasi 2 :
11 15 9 A group of pupils consists of 8 girls and 6 boys. Each day, two pupils are chosen at random to clean the classroom. Satu kumpulan murid terdiri daripada 8 orang murid perempuan dan 6 orang murid lelaki. Setiap hari, dua orang murid dipilih secara rawak untuk membersihkan bilik darjah. (a) Calculate the probability that both pupils chosen to clean the classroom on the fisrt day are girls. Hitungkan kebarangkalian bahawa kedua-dua orang murid yang dipilih untuk membersihkan bilik darjah pada hari pertama ialah murid perempuan. (b) Two girls have cleaned the class on the first day. They are then exempted from cleaning the class on the second day. Calculate the probability that both pupils choosen to clean the class on the second day are of the same gender. Dua orang murid perempuan telah membersihkan bilik darjah pada hari pertama. Kedua-dua orang murid itu dikecualikan daripada membersihkan bilik darjah pada hari kedua. Hitungkan kebarangkalian bahawa kedua-dua murid yang dipilih untuk membersihkan bilik darjah pada hari kedua adalah sama jantina. [ 5 marks ] [ 5 markah ] Answer/ Jawapan : (a) (b) [Lihat sebelah
12 16 10 Diagram 5 shows the speed-time graph of a vehicle for a period of 15 seconds. Rajah 5 menunjukkan graf laju-masa bagi sebuah kenderaan dalam tempoh 15 saat. Speed /Laju(m s -1 ) v Diagram 5 Rajah 5 Calculate Hitungkan (a) the distance, in m, travelled in the first 12 seconds. jarak yang dilalui dalam 12 saat yang pertama. Time (s) Masa (s) (b) the alue of v, in m s -1, if the rate of change of speed in the last 3 seconds is 5 ms -2. nilai v, jika kadar perubahan laju dalam tempoh 3 saat yang akhir ialah 5 ms -2. [ 6 marks ] [ 6 markah ] Answer / Jawapan : (a) (b)
13 It is given that matrix P = and matrix Q = k 1 6 h 1 0 such that PQ = Diberi bahawa matriks P = dan matriks Q = k 1 6 h 1 0 dengan keadaan PQ = (a) Find the value of k and of h. Carikan nilai k dan nilai h. (b) Using matrices, calculate the value of m and of n that satisfy the following simultaneous linear equations: Menggunakan kaedah matriks, hitung nilai m dan nilai n yang memuaskan persamaan serentak berikut : m 4n 5 m 6n 15 [ 7 marks ] Answer / Jawapan : [ 7 markah ] (a) (b) [Lihat sebelah
14 18 Section B Bahagian B [48 marks] [48 markah] Answer any four questions from this section. Jawab mana-mana empat soalan daripada bahagian ini. 12 (a) Complete Table 1 in the answer space for the equation 16 y by writing x down the values of y when x = 1 and x = 2. [2 marks] 16 Lengkapkan Jadual 1 di ruang jawapan bagi persamaan y dengan x menulis nilai-nilai y apabila x 1 dan x = 2. [2 markah] (b) For this part of the question, use the graph paper provided on page 20. You may use a flexible curve. Untuk ceraian soalan ini, gunakan kertas graf yang disediakan pada halaman 20. Anda boleh menggunakan pembaris fleksibel. By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 10 units on the 16 y-axis, draw the graph of y for 3 x 3. [4 marks] x Dengan menggunakan skala 2 cm kepada 1 unit pada paksi-x dan 2 cm kepada unit pada paksi-y, lukiskan graf y bagi 3 x 3. [4 markah] x (c) From your graph, find Daripada graf anda, cari (i) the value of y when x 2 4, nilai y apabila x 2 4, (ii) the value of x when y = -12. nilai x apabila y = [2 marks]
15 19 [2 markah] (d) Draw a suitable straight line on your graph to find all the values of x which satisfy 2 the equation 2x 3x 16 for 3 x 3. State these values of x. [4 marks] Lukis satu garis lurus yang sesuai pada graf anda untuk mencari nilai-nilai x yang 2 memuaskan persamaan 2x 3x 16 bagi 3 x 3. Nyatakan nilai-nlai x itu. [4 markah] Answer / Jawapan: (a) x y (b) Refer graph on page 20. Rujuk graf di halaman 20. Table 1 Jadual 1 (c) (i) y =.. (ii) x =. (d) x =, [Lihat sebelah
16 20 Graph for Question 12 Graf untuk Soalan 12
17 21 13 You are not allowed to use graph paper to answer this question. Anda tidak dibenarkan menggunakan kertas graf untuk menjawab soalan ini. (a) Diagram 6 (i) shows a solid consisting of a cuboid and a half-cylinder which joined at the plane JKGH. The base ABCD is on a horizontal plane and JH = 4 cm. Rajah 6 (i) menunjukkan sebuah pepejal terdiri dari sebuah kuboid dan separuh silinder yang bercantum pada satah JKGH.Tapak ABCD terletak pada satah mengufuk dan JH = 4 cm. L M K J 3 cm H D A G F A E 6 cm B Diagram 6 (i) Rajah 6 (i) 4 cm C Draw full scale, the plan of the solid. Lukis dengan skala penuh, pelan pepejal itu. Answer / Jawapan : ( a ) [3 marks] [3 markah] [Lihat sebelah
18 22 (b) A solid right prism is joined to the solid in Diagram 6(i) at the vertical plane GFCV. The combined solid is as shown in Diagram 6(ii). Trapezium PVTS is the uniform cross-section of the prism and PQRS is an inclined plane. The base BCTUWVDA lies on a horizontal plane whereby CT = 2 cm and PG = 3 cm. Sebuah pepejal prisma tegak dicantumkan kepada pepejal dalam Rajah 6(i) pada satah mencancang GFCV. Gabungan pepejal adalah seperti yang ditunjukkan dalam Rajah 6(ii). Trapezium PVTS ialah keratan rentas seragam prisma itu dan PQRS ialah satah condong. Tapak BCTUWVDA terletak pada satah mengufuk di mana CT = 2 cm dan PG = 3 cm. M K L P Q J 3 cm A H D A E V G w F S R 3 cm X 6 cm B 4 cm C T U 2 cm Diagram 6 (ii) Y Rajah 6 (ii) Draw full scale, Lukis dengan skala penuh, (i) the elevation of the combined solid on a vertical plane parallel to AB as viewed from X. [5 marks] dongakan gabungan pepejal itu pada satah mencancang selari dengan AB sebagaimana dilihat dari X. [5 markah ] (ii) the elevation of the combined solid on a vertical plane parallel to BC as viewed from Y. [4 marks] dongakan gabungan pepejal itu pada satah mencancang selari dengan BC
19 23 sebagaimana dilihat dari Y. Answer / Jawapan : [4 markah] (b) (i), (ii) [Lihat sebelah
20 24 14 Diagram 7 shows four points P, Q, R and M on the surface of the earth. P lies on longitude 80º W. QR is the diameter of the parallel of latitude 55ºS. Rajah 7 menunjukkan empat titik P, Q, R, dan M pada permukaan bumi. P terletak pada longitud 80 B. QR ialah diameter selarian latitud 55º S. N M O 55º R 45º Q P S Diagram 7 Rajah 7 (a) (i) State the longitude of Q. Nyatakan longitud bagi Q. (ii) Calculate the shortest distance, in nautical miles, from Q to R measured along the surface of the earth. Hitung jarak terpendek, dalam batu nautika, dari Q ke R diukur sepanjang permukaan bumi. [4 marks] [4 markah] (b) M lies due north of P and the distance PM measured along the surface of the earth is nautical miles. Calculate the latitude of M. [3 marks]
21 25 M terletak ke utara P dan jarak PM diukur sepanjang permukaan bumi ialah batu nautika. Hitungkan latitud bagi M. [3 markah] (c) An aeroplane took off from Q and flew due east to P and then flew due north to M. The average speed for the whole flight was 600 knots. Sebuah kapal terbang berlepas dari Q arah ke timur ke P dan kemudian terbang ke arah utara ke M. Purata laju seluruh penerbangan ialah 600 knots. Calculate Hitungkan (i) the distance, in nautical miles, travelled by the aeroplane from Q to P measured along the common parallel of latitude, jarak, dalam batu nautika, yang dilalui oleh kapal terbang itu dari Q ke P diukur sepanjang selarian latitud sepunya. (ii) the total time, in hours, taken for the whole flight. Jumlah masa, dalam jam, yang diambil bagi seluruh penerbangan itu. [5 marks] [5 markah] Answer / Jawapan : (a) (i) (ii) [Lihat sebelah
22 26 (b) (c) (i) (ii)
23 27 15 (a) Diagram 8 in the answer space shows point A, point J and a straight line KL drawn on a Cartesian plane. Rajah 8 pada ruang jawapan menunjukkan titik A,titik J dan garis lurus KL dilukis pada suatu satah Cartesian. 5 Traformation T is a translation. 2 Transformation P is a reflection in the straight line x 3. Transformation R is a rotation of 5 Penjelmaan T ialah translasi. 2 o 90 clockwise about the centre A. Penjelmaan P ialah pantulan pada garis lurus x 3. Penjelmaan R ialah putaran o 90 ikut arah jam, pada pusat A. (i) On Diagram 8 in the answer space, draw the image of the straight line KL under translation T. Pada Rajah 8 di ruang jawapan, lukiskan imej bagi garis lurus KL di bawah translasi T. (ii) State the coordinates of the image of point J under the following transformation : Nyatakan koordinat imej bagi titik J di bawah penjelmaan berikut : (a) P (b) RT. [4 marks] [4 markah] [Lihat sebelah
24 28 Answer / Jawapan : (a) (i) y L 6 4 J K 2 A 2 O x 4 2 Diagram 8 Rajah 8 (ii) (a). (b).
25 29 (b) Diagram 9 shows three quadrilaterals ABCD, EFGH and PQRS, drawn on a Cartesian plane. Rajah 9 menunjukkan tiga sisiempat ABCD, EFGH dan PQRS yang dilukis pada suatu satah Cartesan. y 6 D F E P 4 2 S H 4 2 O Q A C B R x G 2 EFGH is the image of ABCD under transformation V. PQRS is the image of ABCD under transformation W. EFGH ialah imej bagi ABCD di bawah penjelmaan V. PQRS ialah imej bagi ABCD di bawah penjelmaan W. (i) Describe in full the transformation: Huraikan selengkapnya penjelmaan: (a) V, (b) W. (ii) Given that the area of the quadrilateral ABCD is area of quadrilateral PQRS. Diberi bahawa luas sisiempat ABCD ialah sisiempat PQRS. Diagram 9 Rajah m, calculate the m, hitungkan luas [8 marks] [Lihat sebelah
26 30 Answer / Jawapan : [8 markah] (b) (i) (a) (b) (ii)
27 31 16 The data in Table 2 shows the History marks obtained by 42 pupils in a monthly test. Data dalam Jadual 2 menunjukkan markah yang diperoleh bagi 42 orang murid dalam suatu ujian Sejarah Table 2 Jadual 2 (a) Using data in Table 2 and a class interval of 5 marks, complete Table 3 in the answer space. [4 marks] Menggunakan data dalam Jadual 2 dan dengan saiz selang kelas 5 markah, lengkapkan Jadual 3 pada ruang jawapan. (b) Based on your table in (a), Berdasarkan jadual anda di (a), (i) state the modal class, nyatakan kelas mod, [4 markah] (ii) calculate the mean mark for the History monthly test and give your answer correct to two decimal places. [4 marks] hitungkan min markah ujian bulanan Sejarah dan berikan jawapan anda betul kepada dua tempat perpuluhan. [4 markah] [Lihat sebelah
28 32 (c) For this part of the question, use the graph paper provided on page 34. Untuk ceraian soalan ini, gunakan kertas graf yang disediakan di halaman 34. By using a scale of 2 cm to 5 marks on the horizontal axis and 2 cm to 1 pupil on the vertical axis, draw a histogram for the data. [4 marks] Dengan menggunakan skala 2 cm kepada 5 markah pada paksi mengufuk dan 2 cm kepada 1 orang murid pada paksi mencancang, lukis satu histogram bagi data itu. [4 markah]
29 33 Answer / Jawapan : (a) Marks Midpoint Markah Titik tengah Frequency Kekerapan Table 3 Jadual 3 (b) (i) (ii) (c) Refer graph on page 34. Rujuk graf di halaman 34. [Lihat sebelah
30 34 Graph for Question 16 Graf untuk Soalan 16
31 35 END OF QUESTION PAPER KERTAS SOALAN TAMAT [Lihat sebelah
32 36
33 JABATAN PELAJARAN NEGERI SELANGOR PROGRAM PENINGKATAN PRESTASI SAINS & MATEMATIK SIJIL PELAJARAN MALAYSIA 2008 MATEMATIK KERTAS 2 PERATURAN PEMARKAHAN
34 2 MARKING SCHEME MATHEMATICS PAPER 2 (1449/2)-2008 No Answers Marks Total 1 The line y = 3 shown by dotted line. y 8 3 x y 8 y = 3 K x 2 2x y 8 2m 2 5m - 12 = 0 or equivalent (2m + 3) ( m - 4 ) = 0 3 x = 2 x = 4 N1 N e + f = 9 or equivalent 4 5e = 20 or equivalent e = 4 f = -3 PRS is identified N1 N1 4 Tan PRS = 12 9 or equivalent PRS = ( or equivalent ) N1 3
35 3 5 (a) k = 6 P1 (b) m = 2 y = 2x - 4 (c) 2x 4 0, y = 0 x = 2 or x-intercept is 2 N x 6 x N1 4 7 (a) or N or 7 14 or N1 6
36 4 8 (a) (i) (ii) False True P1 P1 (b) Conclusion : x 6 (c) Implication 1 : If t 3 64, then t = 4. Implication 2 : If t = 4, then t (a) (b) 10 (a) (b) Note: or award or v v N1 K2 N1 5 K2 N1 K2 N1 6
37 5 11 (a) K = (-1) (6) - (4)(1) award P1 h = -1 P2 P1 (b) m 5 6 n 15 m 1 = n or equivalent m 3 n 2 m 3 n 2 m 3 Note : n 2 12 (a) 16 8 as final answer award N1 N1 N1 7 2 (b) Axes drawn in correct direction and uniform scales in 3 x 3 and 40 y points and *2 points correctly plotted or curve passes through these points for 3 x 3. Smooth and continuous curve without any straight line passes through all 8 correct points using the given scales for 3 x 3. Note : 6 or 7 points correctly plotted, award (c) (i) 6 1 y 7 1 (ii) 1 3 x 1. 5 (d) Identify y 2 3x Straight line y 2 3x correctly drawn 2.1 x 1.9, 2 5 x 2 7 P1 K2 N1 P1 P1 N1N
38 6 13 (a) A D H G B C Correct shape with rectangles AHGD and BHGC. All solid lines. AB > BC, AH > HB Measurement correct to ± 0.2 cm and all angles at vertices of rectangles = 90º ± 1º dep N1 dep 3 (b) (i) P, Q J H E,F S, R A V B, C T, U
39 7 Correct shapes with hexagon PSTBEH, rectangle ABEJ and a semicircle with radius 2 cm. H and V joined with dotted line. AT> JE >AV > JA = PH =ST Measurement correct to ± 0.2 cm and A, B, T, E, J and H = 90º ± 1º dep dep N2 dep 5 (ii) P Q M L E R B T, C U Correct shape with rectangles BTSE, TURS, PQRS and MLSE. All solid lines. BU = UQ > BM > BT > CU Measurement correct to ± 0.2 cm and all angles at vertices of rectangles = 90º ± 1º dep N2 dep 4 12
40 8 14 a) (i) 125ºW (ii) (180º 55º 55º) P1P1 N1 4 (b) (105º 55 º)N 50ºN (c) (i) 45º 60 cos 55º Note: 45º 60 or cos 55º used correctly award n.m N1 K2 N (ii) or hours N (a) (i) Image of straight line KL drawn where K (3,1) and L (4,3) P1 12 (ii) (a) (-7, 4) (b) (0, -4) P1 P2 4 (b) (i) (a) Rotation, 90 0 clockwise, at (-3,5) or Rotation, anticlockwise, at (-3,5) P3 Note : Rotation, 90 0 clockwise Rotation, anticlockwise Rotation at (-3,5) Rotation P2 P2 P2 P1
41 9 (b) Enlargement, centre (4,7), scale factor 2 P3 Note : Enlargement, (4,7) Enlargement, scale factor 2 Enlargement P2 P2 P1 (ii) 22.7 x*( 2) N (a) 12 Marks Markah Midpoint Titik tengah Frequency Kekerapan Marks : Midpoint : Frequency : 3 rd row to 7 th row all correct 2 nd row to 7 th row all correct 1 st row to 7 th row all correct P1 P1 P2 4 Note : Allow one mistake in frequency for P1 (b) (i) P1 (ii) (32x5)+(37x7)+(42x8)+(47x10)+(52x6)+(57x4)+ (62x2) K2 N1 4
42 10 (c) Axes drawn in correct direction, uniformed scales used for 29.5 x and 0 y 10 Horizontal axis labelled by using upper boundaryl or midpoint and 7* bars drawn correctly Histogram drawn correctly Note : 1. 5 or 6 bars drawn correctly award 2 Other uniformed scales used award N0. K2 N1 4 12
43 11 Graph for Question 12
44 12 Question 12 graph of 16 y x
45 13 10 Question 16 Histogram Frequency Marks
46 14-4-
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