1. SULIT1449/2 1449/2 MathematicsNAMA : Kertas 2 TINGKATAN : Mei 2010 1 2 jam 2 UNIT PEPERIKSAAN & PENILAIANSMK TUNKU BESAR BURHANUDDIN71550 SERI MENANTI, N. SEMBILANPEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN 5 2010 PemeriksaMATHEMATICSMarkah Markah Bahagian Soalan Penuh DiperolehKertas 2A1 4 Dua jam tiga puluh minit2 43 3 JANGAN BUKA KERTAS SOALAN INI 4 3 SEHINGGA DIBERITAHU 5 5 1. Kertas soalan ini mengandungi dua bahagian : 6 6Bahagian A dan Bahagian B. Jawab semua 7 5soalan daripada Bahagian A dan empat soalandalam Bahagian B.8 5 9 6 2. Jawapan hendaklah ditulis dengan jelas dalamruang yang disediakan dalam kertas soalan.10 6Tunjukkan langkah-langkah penting. Ini bolehmembantu anda untuk mendapatkan markah. 11 512 12 3. Rajah yang mengiringi soalan tidak dilukismengikut skala kecuali dinyatakan.13 12B 14 12 4. Satu senarai rumus disediakan di halaman 2 &3 15 125. Anda dibenarkan menggunakan kalkulatorsaintifik yang tidak boleh diprogram. Jumlah Kertas soalan ini mengandungi 14 halaman bercetak 1449/2@2010[Lihat sebelah Di Sediakan Oleh Di Semak Oleh SULIT______________________(Sunita binti Mukhtar )Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan.Panatia Matematik SMKTBB

2. Untuk SULITKegunaanPemeriksaPERKAITAN1. am an = am+n .2. am an = amn3. (a )m n= a mn 1 d b 4. A1 = ad bc c a n( A) 5. P ( A) = n( S )6. P ( A' ) = 1 P ( A)7. Jarak = ( x1 x2 ) 2 + ( y1 y2 ) 28. Titik Tengah( x, y ) = x1 + x2 , y1 + y2 22 jarak yang dilalui 9. Purata laju =masa yang diambil hasil tambah nilai data 10.Min = bilangan data hasil tambah( nilai titik tengah ke ker apan ) 11.Min =hasil tambah ke ker apan12.Teorem Pithagorasc 2 = a 2 + b2 y2 y1 13.m=x2 x1p int asan y 14.m= p int asan xBENTUK DAN RUANG 2[Lihat sebelah 1449/2 SULIT 3. SULIT Untuk Kegunaan1 Pemeriksa1.Luas trapezium = hasil tambah dua sisi selari tinggi 2 2.Lilitan bulatan = d = 2j 3.Luas bulatan = j2 4.Luas permukaan melengkung silinder = 2jt 5.Luas permukaan sfera = 4j2 6.Isipadu prisma tegak = luas keratan rentas panjang 7.Isipadu silinder= j2t1 28.Isipadu kon =j t 3 4 39.Isipadu sfera = j3 110. Isipadu piramid tegak = luas tapak tinggi 3 11. Hasil tambah sudut pedalaman poligon = ( n 2 ) 180 0 panjang lengkok sudut pusat12.= lili tan bula tan 360 0luas sektorsudut pusat13. =luas bula tan360 0PA '14. Faktor skala, k = PA 15. Luas imej = k 2 luas objek 1449/2 3SULIT 4. Untuk SULITKegunaanPemeriksaSection A[52 marks] Answer all questions in this section1 Using factorisation, solve the following quadratic equation : h2 = 9( h 1) 2[4 marks]Answer:2 Calculate the value of v dan w taht satisfy the following simultaneous linear equations : v + 2 w = 1 and 4v 3w = 18[4 marks] Answer : 3 Venn Diagram in diagram 1(a) and 1(b) shows set , P, Q dan R . In diagram provided in theanswer spances. shade (a) P (Q R ) (b) P (Q R )Jawapan :(a) (b)PPQ Q R RDiagram 1(a)Diagram 1(b)[3 marks]4 [Lihat sebelah 1449/2SULIT 5. SULIT Untuk Kegunaan 4The diagram shows a solid formed by joining a cone with hemisfere Pemeriksa The height of the con is 7cm, Diameter of the cone and the hemisfere is 6 cm Diagram 2 22 Using =, Calculate the volume, in cm3 , of the solid 7Answer :5. yKM( -3, 7) L NxIn Diagram 2, O is the origin. Straight line KL is parallel to straight line MN. The equation ofstraight line KL is 2x + y = 4The points L and N lie on the y- axis Find 1449/25SULIT 6. Untuk SULIT Kegunaan Pemeriksa(a) The equation of straight line MN (b) The x intercept of the straight line MN[5 marks] Jawapan : (a) (b) (c) 6 34 10(a) M is a 2 X 2 matrix where M = , find the matrix of M 25 01(b)Write the following simultaneous linear equations as matrix equation : 3 p + 4q = 52 p + 5q = 8 Hence, using matrix method, calculate the value of p and q[6 marks]Answer : (a) (b) . 7. Diagram 4 shows the speed-time graph of a particle for a period of 18 seconds 6[Lihat sebelah 1449/2SULIT 7. SULIT Untuk Kegunaan Speed(ms/s) Pemeriksa22 u4 6 10 Time(s) 18 Diagram 4a) State the the length time, in seconds, the particle moves with uniform speedb) Calculate the rate of change, in ms-2, in the first 6 secondsc) Calculate the value of u, if the average speed of the particle in the last 12 seconds [5marks] Answer : a) b) c)8 Diagram 5 shows the distance time of the journey of a car from Pulau Pinang to Johor Bahru over a period of t hours. Distance (km) 800 300 Time (hour) 0 42t(a) State the length of time, that car is stationary (b) State the distance in km, from Johor Bahru when the car is stationary (c) Calculate the car average speed, in km h-1, during the 6 first hours (d) If the average speed of the car for the whole journey is 80km/h Calculate the value of t 1449/2 7 SULIT 8. Untuk SULITKegunaanPemeriksa [5 marks]Answer : (a) (b)(cd)9. Diagram 6Diagram 6,shows OKJH with the centre O and a circle FGH with centre M.F is the midpoint of OH and OK = 2822Using =, calculate7 (a) The perimeter in cm of the whole diagram(b) The area cm of the shaded region [6 marks]Answer 8 [Lihat sebelah 1449/2 SULIT 9. SULIT Untuk Kegunaan a) Pemeriksa b) 10 Diagram 7 shows three numbered cards in box P and four numbered in box Q 5 1519 3 6 1517Box P Box QA card is picked at random from each of the boxes By Listing the possible outcomes, find the probability thata) a card with a number which is a multiple of 2 or a multiple of 5 are pickedb) a card with a number which is a multiple of 2 and a multiple of 5 are picked[ 5 marks ]Answer : a) b) 1449/29 SULIT 10. Untuk SULITKegunaanPemeriksa11 (a) ( I ) Complete the following mathematical sentence in the answer space by105 ( ii ) Complete the following statement the quantifier all or some to make it a true statement . --------------------------- multiples of 3 are divisible by 2[2 marks ](b) Complete the conclusion in the following argument Premise 1 : If x is a factor of 12, then x is a factor of 24Prermise 2 : x is not a factor of 24 Conclution : _____________________________________[1 marks] (c) Write down two implications based on the following sentence :3m > 15 if and only if m > 5[2 marks] Answer : (a) ( I )_____________________________________________________________________( ii ) ____________________________________________________________________(b)Conclusion:____________________________________________________________________(c)Implication 1 : ______________________________________________________________Implication 2 :______________________________________________________________10[Lihat sebelah 1449/2SULIT 11. SULIT Untuk KegunaanSection B Pemeriksa[48 marks]Answer four questions from this section.4 12 (a) Complete Table 1 in the answer space fo the equation y = x x4 2.5 1 -0.5 0.51 23.24 y1 1.6 8 -8-4 -1.25-1Table 1 [2 marks] For this part of the question, use the graph paper provided on page 31. You may use a flexible curve rule(b) By using a scale of 2 cm to 1 unit on the x-axis and 2 cm kepada 2 unit on the-yaxis, draw the4graph y = for 4 x 4 .x[5 marks]( c ) From your graph, find( i) the value of y when x = 1.8(ii) the value of x when y = 3.4[2 marks](a)Draw a suitable straight line on your graph to find all the value of x which satisfy the4 equation y = for 4 x 4xState these values of x [3 marks]Answer : (a)x4 2.5 1 -0.5 0.51 23.24 y1 1.6 8 -8-4 -1.25-1 Table 1(c)( i ) y = ____________________ ( ii) x = _____________________(d)x = _______________________, _______________________ 1449/211 SULIT 12. Untuk SULIT Kegunaan Pemeriksa 13Diagram 7 shows rectangle D, E, F dan G.y 7D 65 G 4E 32FK 1 -2 -1 O12345 6 7 8 x RAJAH 7 (a) Transformation P is a reflection about line x = 3and transformation R is clockwise rotationof 900 about the point (4, 4). State the coordinate of image of point K under(i)Transformation P(ii) Transformation PR [3 marks](b) Rectangle D is the image of rectangle of F under transformation V and rectangle E is theimage of rectangle D under transformation W.Describe in full(i)Transformation V(ii) A single transformation which equavalent to transformation WV. [5 marks](c) Rectangle G is the image of rectangle F under an enlargement(i)State the centre coordinate of the centre of the enlargement(ii) Given the area of rectangle F is 7 unit2, calculate the area of rectangle of G.[4 marks]Answer:(a)(i)(ii) (b)(i) (ii) (c)(i) 12[Lihat sebelah 1449/2SULIT 13. SULIT Untuk Kegunaan (ii) Pemeriksa 14 The Data in diagram 8 shows the donations, in RM, of families to their childrens school welfaredfund.424 17 3022 2635 19 0 228 33 3339 3439 28 3 235 45 2138 2227 35 7 334 31 3740 3214 28 0 232 29 2632 2238 44 0Diagram 8 (a) Using data in diagram 8 and a class interval of RM 5 , complete the table 2 in the answer space[4 marks]Answer : Donations (RM) frequency Cumulative frequency 11 - 15 16 20 Table 2 (b) For this part of the questions, use the graph paper providedBy using a scale of 2 cm to RM 5 on the x- axis and 2 cm to 5 families on the y-axis, draw an ogive based on the data[6 marks] (c) From your ogive in (b)( i ) Find the third quartile(ii ) hence, explain briefly the meaning of the third quartile Answer :(c) (i) (ii)1449/213SULIT 14. Untuk SULIT Kegunaan Pemeriksa 15 (a) Complete Table 1 in the answer space fo the equation y = 6 x 3x3 2.5 2-1 0122.5y3321.631465-9.63 Table 1[2 marks] For this part of the question, use the graph paper provided on page 31. You may use a flexible curve rule(c) By using a scale of 2 cm to 1 unit on the x-axis and 2 cm kepada 5 unit on the-yaxis, draw the graph y = 6 x 3 bagi nilai x dalam julat 3 x 2.5 .[4 marks]( c ) From your graph, find( i) the value of y when x = 1.5(ii) the value of x when y = 10[2 marks](b) Draw a suitable straight line on your graph to find all the value of x which satisfy theequation x 3 8 x 6 = 0 for 3 x 2.5 .State these values of x [4 marks]Answer : (a) x3 2.5 2-1 0122.5y3321.631465-9.63 Table 1(c) ( i ) y = ____________________( ii) x = _____________________(d) x = _________________________ ,_________________________14 [Lihat sebelah 1449/2 SULIT 15. SULIT Untuk Kegunaan Pemeriksa 1449/2 15 SULIT