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1 1449/2 Mathematics Kertas 2 Mei jam 2 NAMA : TINGKATAN : UNIT PEPERIKSAAN & PENILAIAN SMK TUNKU BESAR BURHANUDDIN SERI MENANTI, N. SEMBILAN PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN /2 MATHEMATICS Kertas 2 Dua jam tiga puluh minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 1. Kertas soalan ini mengandungi dua bahagian : Bahagian A dan Bahagian B. Jawab semua soalan daripada Bahagian A dan empat soalan dalam Bahagian B. 2. Jawapan hendaklah ditulis dengan jelas dalam ruang yang disediakan dalam kertas soalan. Tunjukkan langkah-langkah penting. Ini boleh membantu anda untuk mendapatkan markah.. Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan. 4. Satu senarai rumus disediakan di halaman 2 & 5. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram. Bahagian A B Soalan Markah Penuh Jumlah Markah Diperoleh 1449/2@2010 Kertas soalan ini mengandungi 14 halaman bercetak Di Sediakan Oleh Di Semak Oleh (Sunita binti Mukhtar ) Panatia Matematik SMKTBB

2 Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan. PERKAITAN 1. a m n m+ n a = a. 2. a m a n = a m n m mn. ( ) n a = a 1 1 d b 4. A = ad bc c a 5. P ( A) = n( A) n( S) 6. P( A') = 1 P( A) 7. Jarak = ( x x ) + ( y y ) Titik Tengah x + x2 y1 + x y =, (, ) 1 y 9. Purata laju = jarak yang dilalui masa yang diambil 10. Min = 11. Min = hasil tambah nilai data bilangan data hasil tambah( nilai titik tengah keker apan ) hasil tambah keker apan 12. Teorem Pithagoras c = a + b 1. m = y x 2 2 y1 x m = pint asan pint asan y x /2

3 1 1. Luas trapezium = 2 BENTUK DAN RUANG hasil tambah dua sisi selari tinggi 2. Lilitan bulatan = πd = 2πj. Luas bulatan = πj 2 4. Luas permukaan melengkung silinder = 2πjt 5. Luas permukaan sfera = 4πj 2 6. Isipadu prisma tegak = luas keratan rentas panjang 7. Isipadu silinder = πj 2 t 8. Isipadu kon = 1 πj 2 t 9. Isipadu sfera = 4 πj Isipadu piramid tegak = luas tapak tinggi 11. Hasil tambah sudut pedalaman poligon = ( n 2 ) panjang lengkok sudut pusat 12. = 0 lilitan bulatan 60 luas sektor sudut pusat 1. = 0 luas bula tan 60 PA ' 14. Faktor skala, k = PA 15. Luas imej = k 2 luas objek 1449/2

4 Section A [52 marks] Answer all questions in this section 1 Using factorisation, solve the following quadratic equation : Answer: h 2 = 9( h 1) 2 [4 marks] 2 Calculate the value of v dan w taht satisfy the following simultaneous linear equations : v+ 2w= 1 and 4v w= 18 [4 marks] Venn Diagram in diagram 1 and 1 shows set ξ, P, Q dan R. In diagram provided in the answer spances. shade P ( Q R) P ( Q R) Jawapan : ξ ξ P P Q R R Q Diagram 1 Diagram 1 [ marks] /2

5 4 The diagram shows a solid formed by joining a cone with hemisfere The height of the con is 7cm, Diameter of the cone and the hemisfere is 6 cm Diagram 2 22 Using π =, Calculate the volume, in cm, of the solid 7 5. y M( -, 7) K L N x In Diagram 2, O is the origin. Straight line KL is parallel to straight line MN. The equation of straight line KL is 2x + y = 4 The points L and N lie on the y- axis 1449/2 5

6 Find The equation of straight line MN The x intercept of the straight line MN [5 marks] Jawapan : (c) M is a 2 X 2 matrix where M =, find the matrix of M Write the following simultaneous linear equations as matrix equation : p+ 4q= 5 2p+ 5q= 8 Hence, using matrix method, calculate the value of p and q [6 marks] /2

7 7. Diagram 4 shows the speed-time graph of a particle for a period of 18 seconds Speed(ms/s) 22 u Time(s) Diagram 4 a) State the the length time, in seconds, the particle moves with uniform speed b) Calculate the rate of change, in ms -2, in the first 6 seconds c) Calculate the value of u, if the average speed of the particle in the last 12 seconds [5marks] 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) (c) (d) Time (hour) t State the length of time, that car is stationary State the distance in km, from Johor Bahru when the car is stationary Calculate the car average speed, in km h -1, during the 6 first hours If the average speed of the car for the whole journey is 80km/h Calculate the value of t 1449/2 7

8 [5 marks] (c d) 9. Diagram 6 Diagram 6,shows OKJH with the centre O and a circle FGH with centre M. F is the midpoint of OH and OK = Using π =, calculate 7 The perimeter in cm of the whole diagram The area cm of the shaded region [6 marks] /2

9 Answer a) b) 10 Diagram 7 shows three numbered cards in box P and four numbered in box Q Box P Box Q A card is picked at random from each of the boxes By Listing the possible outcomes, find the probability that a) a card with a number which is a multiple of 2 or a multiple of 5 are picked b) a card with a number which is a multiple of 2 and a multiple of 5 are picked [ 5 marks ] a) b) 1449/2 9

10 11 ( I ) Complete the following mathematical sentence in the answer space by 10 5 ( ii ) Complete the following statement the quantifier all or some to make it a true statement multiples of are divisible by 2 Complete the conclusion in the following argument Premise 1 : If x is a factor of 12, then x is a factor of 24 Prermise 2 : x is not a factor of 24 Conclution : [2 marks ] [1 marks] (c) Write down two implications based on the following sentence : m > 15 if and only if m > 5 [2 marks] ( I ) ( ii ) Conclusion: (c)implication 1 : Implication 2 : /2

11 Section B [48 marks] Answer four questions from this section. 12 Complete Table 1 in the answer space fo the equation 4 y = x x y Table 1 [2 marks] For this part of the question, use the graph paper provided on page 1. You may use a flexible curve rule By using a scale of 2 cm to 1 unit on the x-axis and 2 cm kepada 2 unit on the-yaxis, draw the 4 graph 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 =.4 [2 marks] Draw a suitable straight line on your graph to find all the value of x which satisfy the 4 equation y = for 4 x 4 x State these values of x [ marks] x y Table 1 (c) ( i ) y = ( ii) x = (d) x =, 1449/2 11

12 1 Diagram 7 shows rectangle D, E, F dan G. y D E F K G -2-1 O x Transformation P is a reflection about line x = and transformation R is clockwise rotation of 90 0 about the point (4, 4). State the coordinate of image of point K under (i) Transformation P (ii) Transformation PR [ marks] Rectangle D is the image of rectangle of F under transformation V and rectangle E is the image of rectangle D under transformation W. Describe in full (i) (ii) Transformation V A single transformation which equavalent to transformation WV. (c) Rectangle G is the image of rectangle F under an enlargement (i) RAJAH 7 State the centre coordinate of the centre of the enlargement (ii) Given the area of rectangle F is 7 unit 2, calculate the area of rectangle of G. [5 marks] Answer: (i) [4 marks] (ii) (i) (ii) (c) (i) (ii) /2

13 14 The Data in diagram 8 shows the donations, in RM, of families to their children s school welfared fund Using data in diagram 8 and a class interval of RM 5, complete the table 2 in the answer space [4 marks] Donations (RM) frequency Cumulative frequency Diagram 8 Table 2 For this part of the questions, use the graph paper provided By 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 ( i ) Find the third quartile (ii ) hence, explain briefly the meaning of the third quartile ( c ) (i) (ii) 15 Complete Table 1 in the answer space fo the equation y = 6 x 1449/2 1

14 x y Table 1 [2 marks] For this part of the question, use the graph paper provided on page 1. 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 bagi nilai x dalam julat 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] Draw a suitable straight line on your graph to find all the value of x which satisfy the equation x 8x 6= 0 for x 2.5. State these values of x [4 marks] x y (c) Table 1 ( i ) y = ( ii) x = (d) x =, /2

15 1449/2 15

SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN LIMA 2007

1449/2 Matematik Kertas 2 Mei 2007 1 2 jam 2 NAMA : TINGKATAN : 1449/2 SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN LIMA 2007 MATEMATIK