Mathematics Mid Year Form 5 Paper 2 2010

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Mathematics Mid Year Form 5 Paper 2 2010

  1. 1. SULIT 1449/2 1449/2 Mathematics NAMA : Kertas 2 TINGKATAN : Mei 2010 1 2 jam 2 UNIT PEPERIKSAAN & PENILAIAN SMK TUNKU BESAR BURHANUDDIN 71550 SERI MENANTI, N. SEMBILAN PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN 5 2010 Pemeriksa MATHEMATICS Markah Markah Bahagian Soalan Penuh Diperoleh Kertas 2 A 1 4 Dua jam tiga puluh minit 2 4 3 3 JANGAN BUKA KERTAS SOALAN INI 4 3 SEHINGGA DIBERITAHU 5 5 1. Kertas soalan ini mengandungi dua bahagian : 6 6 Bahagian A dan Bahagian B. Jawab semua 7 5 soalan daripada Bahagian A dan empat soalan dalam Bahagian B. 8 5 9 6 2. Jawapan hendaklah ditulis dengan jelas dalam ruang yang disediakan dalam kertas soalan. 10 6 Tunjukkan langkah-langkah penting. Ini boleh membantu anda untuk mendapatkan markah. 11 5 12 12 3. Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan. 13 12 B 14 12 4. Satu senarai rumus disediakan di halaman 2 & 3 15 12 5. Anda dibenarkan menggunakan kalkulator saintifik 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. 2. Untuk SULIT Kegunaan Pemeriksa PERKAITAN 1. am × an = am+n . 2. am ÷ an = am−n 3. (a ) m n = a mn 1  d − b 4. A−1 =   ad − bc  − c a    n( A) 5. P ( A) = n( S ) 6. P ( A' ) = 1 − P ( A) 7. Jarak = ( x1 − x2 ) 2 + ( y1 − y2 ) 2 8. Titik Tengah ( x, y ) =  x1 + x2 , y1 + y2     2 2  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 apan 12. Teorem Pithagoras c 2 = a 2 + b2 y2 − y1 13. m= x2 − x1 p int asan − y 14. m=− p int asan − x BENTUK DAN RUANG 2 [Lihat sebelah 1449/2 SULIT
  3. 3. SULIT Untuk Kegunaan 1 Pemeriksa 1. Luas trapezium = × hasil tambah dua sisi selari × tinggi 2 2. Lilitan bulatan = πd = 2πj 3. Luas bulatan = πj2 4. Luas permukaan melengkung silinder = 2πjt 5. Luas permukaan sfera = 4πj2 6. Isipadu prisma tegak = luas keratan rentas × panjang 7. Isipadu silinder = πj2t 1 2 8. Isipadu kon = πj t 3 4 3 9. Isipadu sfera = πj 3 1 10. Isipadu piramid tegak = × luas tapak × tinggi 3 11. Hasil tambah sudut pedalaman poligon = ( n − 2 ) × 180 0 panjang lengkok sudut pusat 12. = lili tan bula tan 360 0 luas sektor sudut pusat 13. = luas bula tan 360 0 PA ' 14. Faktor skala, k = PA 15. Luas imej = k 2 × luas objek 1449/2 3 SULIT
  4. 4. Untuk SULIT Kegunaan Pemeriksa Section A [52 marks] Answer all questions in this section 1 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 ξ, P, Q dan R . In diagram provided in the answer spances. shade (a) P ∩ (Q ∪ R )′ (b) P ′ ∩ (Q ∩ R ) Jawapan : (a) (b) ξ ξ P P Q Q R R Diagram 1(a) Diagram 1(b) [3 marks] 4 [Lihat sebelah 1449/2 SULIT
  5. 5. SULIT Untuk Kegunaan 4 The 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 π = , Calculate the volume, in cm3 , of the solid 7 Answer : 5. y K M( -3, 7) 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 Find 1449/2 5 SULIT
  6. 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 3 4  1 0 (a) M is a 2 X 2 matrix where M   = , find the matrix of M 2 5  0 1 (b) Write the following simultaneous linear equations as matrix equation : 3 p + 4q = 5 2 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 1449/2 SULIT
  7. 7. SULIT Untuk Kegunaan Speed(ms/s) Pemeriksa 22 u 4 6 10 Time(s) 18 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] 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 4 2 t (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. 8. Untuk SULIT Kegunaan Pemeriksa [5 marks] Answer : (a) (b) (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 = 28 22 Using π = , calculate 7 (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. 9. SULIT Untuk Kegunaan a) Pemeriksa b) 10 Diagram 7 shows three numbered cards in box P and four numbered in box Q 5 15 19 3 6 15 17 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 ] Answer : a) b) 1449/2 9 SULIT
  10. 10. Untuk SULIT Kegunaan Pemeriksa 11 (a) ( 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 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 24 Prermise 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 1449/2 SULIT
  11. 11. SULIT Untuk Kegunaan Section 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 x −4 −2.5 −1 -0.5 0.5 1 2 3.2 4 y 1 1.6 8 -8 -4 -1.25 -1 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 (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 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 = 3.4 [2 marks] (a) 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 [3 marks] Answer : (a) x −4 −2.5 −1 -0.5 0.5 1 2 3.2 4 y 1 1.6 8 -8 -4 -1.25 -1 Table 1 (c) ( i ) y = ____________________ ( ii) x = _____________________ (d) x = _______________________, _______________________ 1449/2 11 SULIT
  12. 12. Untuk SULIT Kegunaan Pemeriksa 13 Diagram 7 shows rectangle D, E, F dan G. y 7 D 6 5 G 4 E 3 2 F • K 1 -2 -1 O 1 2 3 4 5 6 7 8 x RAJAH 7 (a) Transformation P is a reflection about line x = 3and transformation R is clockwise rotation of 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 the image 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 1449/2 SULIT
  13. 13. SULIT Untuk Kegunaan (ii) Pemeriksa 14 The Data in diagram 8 shows the donations, in RM, of families to their children’s school welfared fund. 4 24 17 30 22 26 35 19 0 2 28 33 33 39 34 39 28 3 2 35 45 21 38 22 27 35 7 3 34 31 37 40 32 14 28 0 2 32 29 26 32 22 38 44 0 Diagram 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 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 (b) ( i ) Find the third quartile (ii ) hence, explain briefly the meaning of the third quartile Answer : (c) (i) (ii) 1449/2 13 SULIT
  14. 14. Untuk SULIT Kegunaan Pemeriksa 15 (a) Complete Table 1 in the answer space fo the equation y = 6 − x 3 x −3 −2.5 −2 -1 0 1 2 2.5 y 33 21.63 14 6 5 -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 the equation x 3 − 8 x − 6 = 0 for −3 ≤ x ≤ 2.5 . State these values of x [4 marks] Answer : (a) x −3 −2.5 −2 -1 0 1 2 2.5 y 33 21.63 14 6 5 -9.63 Table 1 (c) ( i ) y = ____________________ ( ii) x = _____________________ (d) x = _________________________ ,_________________________ 14 [Lihat sebelah 1449/2 SULIT
  15. 15. SULIT Untuk Kegunaan Pemeriksa 1449/2 15 SULIT

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