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1 SULIT 449/ 449/ Mathematics Nama : Kertas September Kelas : 008 jam PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 008 SEKOLAH-SEKOLAH ZON A KUCHING MATHEMATICS Kertas Dua jam tiga puluh minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU. Tulis nama dan kelas anda pada ruang yang disediakan.. Kertas soalan ini adalah dalam Bahasa Inggeris sepenuhnya. 3. Calon dikehendaki membaca arahan di halaman. Kod Pemeriksa Bahagian Soalan Markah Penuh A B Jumlah Markah Diperoleh Kertas ini mengandungi 7 halaman bercetak dan halaman tidak bercetak. [ Lihat sebelah 449/ SULIT

2 SULIT 449/ INFORMATION FOR CANDIDATES. This question paper consists of two sections: Section A and section B.. Answer all questions in Section A and four questions from Section B. 3. Write your answers clearly in the spaces provided in the question paper. 4. Show your working. It may help you to get marks. 5. If you wish to change your answer, neatly cross out the answer that you have done. Then write down the new answer. 6. The diagrams in the questions provided are not drawn to scale unless stated. 7. The marks allocated for each question and sub-part of a question are shown in brackets. 8. A list of formulae is provided on pages 3 to A booklet of four-figure mathematical tables is provided. 0. You may use a non-programmable scientific calculator.. This question paper must be handed in at the end of the examination. 449/ SULIT

3 SULIT 3 449/ MATHEMATICAL FORMULAE The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. RELATIONS a m a n a m n Pythagoras Theorem c a b a m n m n a a 3 m y x y x m n mn 3 a a 4 d b 4 A ad bc c a n P n 5 A, A S 6 P A P A m = y intercept x intercept 7 Distance x x y y 8 Midpoint, x, y, x y y x 9 Average speed = distance travelled time taken 0 Mean = Mean = sum of data number of data Sum of ( class mark frequency ) Sum of frequencies [ Lihat sebelah 449/ SULIT

4 SULIT 4 449/ SHAPES AND SPACE Area of trapezium = sum of parallel sides height Circumference of circle = d r 3 Area of circle r 4 Curved surface of cylinder r h 5 Surface area of sphere 4 r 6 Volume of right prism = cross sectional area length 7 Volume of cylinder r h 8 Volume of cone r h 3 9 Volume of sphere 4 r 3 0 Volume of right pyramid 3 3 base area height 0 Sum of interior angles of a polygon n 80 arc length circumference of circle = angle subtended at centre 360 o 3 area of sector area of circle = angle subtended at centre 360 o 4 Scale factor, k =, PA PA 5 Area of image k area of object 449/ SULIT

5 SULIT 5 449/ Section A [ 5 marks ] Answer all questions in this section. For The Venn diagrams show set P, Q and R such that the universal set, ξ = P Q R. On the diagrams, shade the region represented by (a) P R (b) Q (Q R ) [3 marks] Answer: (a) P R Q (b) P Q R 449/ [ Lihat sebelah SULIT

6 For SULIT 6 449/ E F S H P G D R 6cm A 8cm Q 0cm C B DIAGRAM Diagram shows a cuboid with ABCD as the base on the horizontal plane. P, Q, R and S are the midpoints of the respective sides. Identify and calculate the angle between the line PC and the plane CDEH. [4 marks] Answer: 449/ SULIT

7 SULIT 7 449/ For 3 Solve the equation p( p 5) 3 p. Answer : [ 4 marks] 4 Solve the following simultaneous linear equations : Answer : 3x + y = 8 x 3y = [ 4 marks ] 449/ [ Lihat sebelah SULIT

8 For SULIT 8 449/ 5 In Diagram, PQRS is a parallelogram. The equation of the straight line SR is 5y 3x 5. y R (0, ) S Q P(-5, -) O x Find (a) (b) Answer: (a) DIAGRAM the equation of the straight line PQ. the y-intercept of the straight line QR. [6 marks] (b) 449/ SULIT

9 SULIT 9 449/ 6 For 7 cm DIAGRAM 3 Diagram 3 shows a solid formed by joining a right pyramid and a cube. The volume of the solid is 44 cm 3. Calculate the height, in cm, of the pyramid. [ 4 marks ] Answer : 449/ [Lihat sebelah SULIT

10 For SULIT 0 449/ 7 Diagram 4 shows a semicircle PSTQ and sector ROU with a common O. POQR is a straight line. Given OQ is 7 cm, OR = OQ and ROU = POS = 45 o. Using (a) (b) Answer : (a), calculate, 7 the perimeter, in cm, of the whole diagram, the area, in cm, of the shaded region. [ 7 marks ] (b) 449/ SULIT

11 SULIT 449/ 8 (a) Determine if the following sentence is a statement or non statement. For 3 x 5 > 8 x (b) Write two implications from the following sentence: 6 x 7 = 7 if and only if x = 4 Implication :.. Implication :... (c ) Write a conclusion based on the following premises. Premise : If 3 a 3 b 3 then a b Premise : a b Conclusion : [ 4 marks ] Answer : (a).. (b) Implication : Implication :.. (c ) Conclusion : / [ Lihat sebelah SULIT

12 For SULIT 449/ 9 Table shows the number of blue, yellow, and red balls in two bags X And Y. Bag Ball X Y Blue 5 Yellow 4 3 Red 4 7 TABLE Noor Hayati chooses a ball at random. Calculate the probability that Noor Hayati chooses a) a blue ball, b) a yellow ball or a red ball, c) a blue ball from bag X and a red ball from bag Y. [5 marks] Answer: (a) (b) (c) 449/ SULIT

13 SULIT 3 449/ 0 Diagram 5 shows the distance-time graph of a lorry. For DIAGRAM 5 The lorry travels to town Y from town X. After resting for 5 minutes at town Y, it travels to town Z. (a) Find the distance, in km, from town Y to town Z. (b) Calculate the speed of the lorry, in kmh -, from town X to town Y. (c) Calculate the value of t, if the speed of the lorry from town Y to town Z is 75 kmh -. [ 5 marks] Answer : (a) (b) (c) 449/ [ Lihat sebelah SULIT

14 For SULIT 4 449/ 4 (a) The inverse of the matrix is. Find the value 3 k m 4 of k and m. (b) Using matrices, calculate the value of x and of y that satisfy the following matrix equation: 4x y = 6 3x + y = 0 [6 marks] Answer : (a) (b) 449/ SULIT

15 SULIT 5 449/ Section B [ 48 marks ] Answer any four questions from the section. For (a) Complete the table below for the equation y. x [ marks ] x y (b) For this part of the question, use the graph paper provided. You may use a flexible curve ruler. By using a scale of cm to units on the x -axis and cm to 4 units on the y -axis, draw the graph of y for 6 x 6. x [4 marks] (c) From your graph, find (i) the value of y when x = 3. (ii) the value of x when y = 5. [ marks] (d) Draw a suitable straight line on your graph to find all the values of x which 3 satisfy the equation x for 6 x 6. State the values of x. x [4 marks] 449/ [ Lihat sebelah SULIT

16 For SULIT 6 449/ Answer: (a) x 4 y (b) Refer to the graph paper. (c) (i) y =.. (ii) x =.. (d) x =.,.. 449/ SULIT

17 SULIT 7 449/ Graph for Question For 449/ [ Lihat sebelah SULIT

18 For SULIT 8 449/ 3 3 (a) Transformation T represents a translation and transformation S 3 represents a reflection in the line y =. State the coordinates of the image of point (, 4) under the following transformations : (i) S (ii) TT (iii) ST [ 5 marks ] b) Diagram 6 shows quadrilaterals OABH, OHCD and OEFG drawn on square grids. DIAGRAM 6 i) Given that transformation V is a reflection in the line OHG and transformation W is a reflection in the line ODE. If OABH experiences the transformation of WV, describe in full, a single transformation which is equivalent to transformation WV. ii) Given that OEFG is the image of ODCH under a transformation M. (a) Describe in full, transformation M. (b) Find the area of the shaded region if the area of ODCH is.8 cm. [ 7 marks] 449/ SULIT

20 For SULIT 0 449/ 4 The data in Diagram 7 shows the masses, in kg, of 40 students in Form 5 A (a) (b) DIAGRAM 7 Based on the data in Diagram 7 and by using a class interval of 5 kg, complete Table 3. [ 3 marks ] State the modal class and calculate the mean mass of the students. [ 4 marks ] (c) Answer : For this part of question, use the graph paper provided. By using the scale of cm to 5 kg on the x axis and cm to student on the y axis, draw a frequency polygon based on Table 3 constructed in (a). [ 5 marks ] Mass ( kg ) Frequency Midpoint TABLE 3 (b) (c) Refer to the graph drawn. 449/ SULIT

21 SULIT 9 449/ Answer : For a) i).. ii) iii). b) i). ii) a).. b) 449/ [ Lihat sebelah SULIT

22 For SULIT 449/ BLANK PAGE 449/ SULIT

23 SULIT 449/ Graph for Question 4 For 449/ [ Lihat sebelah SULIT

24 For SULIT 3 449/ 5 You are not allowed to use graph paper to answer this question. (a) Diagram 8(i) shows a solid prism with a rectangular base ABCD on a horizontal table. The surface ABTQP is the uniform cross- section of the prism. Rectangle PQRS is horizontal plane and rectangle QTUR is an inclined plane. PA and TB are vertical edges. S cm R U P Q 4cm 6cm T D C 8cm x A 4cm B DIAGRAM 8(i) Draw to full scale, the elevation of the solid on a vertical plane parallel to BC as viewed from x. [ 3 marks ] Answer : a) 449/ SULIT

25 SULIT 4 449/ (b) A solid pyramid with triangular base BTQ is removed from the solid in Diagram 8(i). The remaining solid is as shown in Diagram 8(ii) For S cm R P Q U 4cm 6cm D C 8cm A 4cm B Y DIAGRAM 8(ii) Draw to full scale, (i) the plan of the remaining solid, [ 4 marks ] (ii) the elevation of the remaining solid on a vertical plane parallel to AB as viewed from Y. [ 5 marks ] 449/ [Lihatsebelah SULIT

26 For SULIT 5 449/ Answer: (b)(i) (ii) 449/ SULIT

27 SULIT 6 449/ 6. A(30 o N, 65 o W), B(30 o N, 55 o E), C and D are four points on the surface For of the earth. AC is a diameter of the earth and D is located at the distance of nautical miles due north of C. (a) State the position of C. [ marks ] (b) Find the latitude of D. [ marks] (c) Calculate the distance of B from A along a parallel of latitude. [4 marks] (d) A plane took off from A and flew due north via the North Pole to D at a speed of 700 knots. Find the total times taken for the whole flight. [4 marks] Answer: (a) 449/ [Lihatsebelah SULIT

28 For SULIT 7 449/ b) c) (d) END OF QUESTION PAPER 449/ SULIT

30 SULIT 449/ SECTION A Zone A SPM Mock Exam 008 Marking Scheme Paper No. Solution Marks (a) P Q R N (b) P R Q N 3 p( p 5) 3 p p( p + 5 ) = 3( p + ) p² + 5p = 6p + 3 p² + 5p 6p 3 = 0 p² p 3 = 0 ( p 3 )( p + ) = 0 p 3 = 0 or p + = 0 p = 3 p = p = 3 N N 4

31 SULIT 449/ 3 3x + y = () x 3y = () () x 6x + 4y = (3) () x 3 6x 9y = (4) (3) (4) 4y ( 9y) = 6 3 3y = 3 y = 3 3 = Substitute y = into (), 3x + () = 8 3x + = 8 3x = 8 3x = 6 x = 6 3 = Thus, x =, y =. N, N 4 Remark : Accept any sufficient methods. 4 Angle between PC and plane CDEF is PCS N Tan PCS = 0 73, PCS = 49º 9' N 4

32 SULIT 449/ 5 (a) 5y 3x = 5 5y = 5 + 3x y = x Line SR is parallel with line PQ. Therefore, m SR = m PQ = 5 3 y = 3 x c 5 Substitute P 5, 3 = ( 5) c 5 into the equation = 3 + c c = Therefore, the equation of the straight line 3 PQ is y = x. 5 5, b) S = (0, 5), P = N m QR = m PS 5 = 5 0 = 6 5 = 5 6 Therefore, 6 y x c, substitute R(0,) into 5 the equation 6 (0) c 5 c c = Therefore, the y-intercept of the straight line QR is. N 6

33 SULIT 449/ 6 Volume of the cube = 7 3 = 343 cm 3 Volume of the pyramid = x 7 x 7 x h = 98 3 x 49 x h = 98 3 h = h = 6 = 98 cm The height of the pyramid is 6 cm a) Length of arc PST = cm Length of arc UR = 4 cm Length of TU = 7 cm N 4 Length of POQR = cm Perimeter of whole diagram = = 55.5 cm. b) Area of shaded region = 90 Area of shaded sector SOT = 7 7 = 38.5 cm Area of sector ROU = 44 = 77 cm Area of sector TOQ = 7 7 = 9.5 cm N Therefore, area of shaded region = SOT + ROU TOQ = = 96.5 cm N 7

34 SULIT 449/ 8 a ) Statement. b) Implication : If 6x 7 = 7, then x = 4 Implication : If x =4, then 6x 7 = 7. N N N c. Conclusion : a b N a) 5 N b) , N c) , N 5 0 a) 5 0 = 5 km N b) speed = = 0 0 km 0 0min 0km 0 h 60 = 60 km / h c) = 60 kmh - N 75km h 75km 60 min 0 t t 5 t 7 min (5 0) km ( t 5) min 0km ( t 5) min N 5

35 SULIT 449/ (a) m k, (b) y x y x y x y x y x y x y x, ** Note if y x only, then N Don t accept if using simultaneous linear equation. N, N N,N 6

36 SULIT 449/ SECTION B (a) x y T (b) Refer to the graph drawn by the student. Axes labeled with the correct scale. 8 points plotted correctly. Note: If 7 points plotted correctly give P A smooth graph is drawn. S P G

37 SULIT 449/ (c) (i) y = 4 (ii) x =.4 N N (d) Linear equation, y = 4x 4 Graph drawn correctly. x =.35 x.5.5 x.35 L G N N 3 a) i) (, ) ii ) (, 3 ) = ( 4, ) iii) (, 3 ) = (, ) b) i) Rotation of 90 o clockwise about point O. ii) a) M is an enlargement at centre O with a scale factor of 3. N N N N,N,N N,N,N b) Image = k x object = 3 x.8 = 06. cm Area of the shaded region = = 94.4 cm N

38 SULIT 449/ 4 a). Mass (Kg) Frequency Midpoint Class interval Frequency Midpoint fx : all correct : all correct : all correct : all correct P P P P b) Modal class = P Midpoint, x Frequency, f fx Total Mean mass = 57 kg 40, N

39 SULIT 449/ c) Refer to the graph drawn by the student. Axes labeled with the correct scale. 7 points plotted correctly. Noted : If 6 points plotted correctly give P Joint all points. N P P

40 SULIT 449/ 5 Shape looks correct with two rectangles QTBCUR, all solid lines. QT = RU = cm, UC = TB = 4 cm. Note : If TU drawn in dashed line --- minus mark. Correct measurement to 0.cm ( one way) o 0 Right angles of the rectangle = 90. N Dep. N Dep. 3

41 SULIT 449/ Shapes looks correct with two rectangles PQRS and RQBU respectively. All joint with a solid lines. SR = PQ = cm, SP = RQ = 8 cm Correct measurements to 0.cm ( one way ) Right angles of the rectangle = N Dep. NDep. NDep. 4

42 SULIT 449/ Shape looks correct with trapezium ABUP and a triangle QBU. All joints with a solid lines. Q and B joined with solid line to form triangle QUB. N Dep. PQ = cm, PA = 6 cm AB = 4 cm, UC = 4 cm Correct measurement to 0.cm ( one way ) Right angles of the rectangle = NDep. NDep. k N Dep.k 5

43 SULIT 449/ 6 a) Longitude of C = (80 o 65 o ) E = 5 o E Latitude of C = 30 o S Therefore, C is ( 30 o S, 5 o E ). N b) 4500 DOC 75 o 60 Latitude of D = ( 75 o 30 o ) N = 45 o N. N c) ( ) 60 cos 30 o = nautical miles.,, N

44 SULIT 449/ d) Distance from A to D = ( ) x 60 = 6300 nautical miles. = 700 knots = 700 n.m = hour 6300 Therefore, 9 hours. 700,, N.

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