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# Maths Ppsmi 2006 F4 P2

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### Maths Ppsmi 2006 F4 P2

1. 1. Panel Pakar Runding GC MMMT Form Four 1449/2 Mathematics Name : ………………………………… Paper 2 October Form : ………………………………… 2006 1 2 hours 2 JABATAN PELAJARAN NEGERI NEGERI SEMBILAN DARUL KHUSUS PPSMI ASSESSMENT 2006 For examiner’s use only MATHEMATICS Total Marks Section Question Paper 2 Marks Obtained 1 3 Two hours and thirty minutes 2 4 DO NOT OPEN THIS QUESTION PAPER 3 4 UNTIL YOU ARE TOLD TO DO SO 4 6 1 This question paper consists of two sections, 5 4 Section A and Section B. Answer all questions in Section A and four questions in Section B. A 6 5 7 5 2 Write your answers clearly in the spaces provided in the question paper. 8 4 3 Write in blue / black pen. You may use a pencil for 9 5 diagrams or graphs. 10 6 4 The marks allocated are given in brackets at the 11 6 end of each question or part question. 12 12 5 Diagrams in the question paper are not drawn to 13 12 scale unless stated. B 14 12 6 Show all your working. Omission of essential working will result in loss of marks. 15 12 16 12 7 You are allowed to use non-programmable calculators. Total 9 This question paper must be handed in at the end of the examination. This question paper has 26 printed pages [Turn Over https://panelmathsaddmathswordpress.com/
2. 2. 2 Panel Pakar Runding GC MMMT The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. RELATIONS 1 am × an = am+n 2 am ÷ an = am−n 3 (am) n = amn 1 ⎛ d − b⎞ 4 A −1 = ⎜ ⎟ ad − bc ⎜ − c a ⎟ ⎝ ⎠ n (A) 5 P(A) = n (S) 6 P(A’) = 1 − P(A) 7 Distance = ( x1 − x 2 ) 2 + ( y1 − y 2 ) 2 8 Midpoint ⎛ x + x 2 y1 + y 2 ⎞ (x, y ) = ⎜ 1 , ⎟ ⎝ 2 2 ⎠ dis tan ce travelled 9 Average speed = time taken sum of data 10 Mean = number of data sum of (class mark × frequency) 11 Mean = sum of frequencies 12 Phythagoras Theorem c2 = a2 + b2 y 2 − y1 13 m= x 2 − x1 y − int ercept 14 m= − x − int ercept PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
3. 3. 3 Panel Pakar Runding GC MMMT SHAPE AND SPACE 1 1 Area of trapezium = × sum of parallel sides × height 2 2 Circumference of circle = πd = 2πr 3 Area of circle = πr2 4 Curved surface area of cylinder = 2πrh 5 Surface area of sphere = 4πr2 6 Volume of right prism = cross sectional area × length 7 Volume of cylinder = πr2h 1 2 8 Volume of cone = πr h 3 4 9 Volume of sphere = πr3 3 1 10 Volume of right pyramid = × base area × height 3 11 Sum of interior angles of a polygon = ( n − 2) × 180° arc length angle subtended at centre 12 = circumference of circle 360 o area of sec tor angle subtended at centre 13 = area of circle 360 o PA ' 14 Scale factor, k = PA 15 Area of image = k2 × area of object PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
4. 4. 4 Panel Pakar Runding GC MMMT 1449/2 For Section A Examiner’s Use [52 marks] Answer all questions in this section. 1. The Venn diagrams in the answer space shows sets P, Q and R. On the diagram provided in the answer spaces, shade (a) the set P’ ∩ Q’ (b) the set (Q ∩ R)’ ∩ P [3 marks] Answer: (a) ξ P Q R (b) ξ P R Q 1449/2 PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
5. 5. 5 Panel Pakar Runding GC MMMT 1449/2 2. Diagram 1 shows a solid formed when a cylinder is taken out from the pyramid. For The base of the pyramid is a square. Examiner’s Use 15 cm DIAGRAM 1 The height of the cylinder is 9 cm and the diameter is 7 cm. The height of the pyramid is 21 cm. 22 By using π = , calculate the volume, in cm3, of the solid. 7 [4 marks] Answer: 1449/2 [ Turn Over PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
6. 6. 6 Panel Pakar Runding GC MMMT 1449/2 For 3. Calculate the values of m and n that satisfy the following simultaneous linear Examiner’s equations: Use 2m + n = 3 4m − 3n = 11 [4 marks] Answer: 1449/2 PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
7. 7. 7 Panel Pakar Runding GC MMMT 1449/2 4. Diagram 2 shows two sectors OPJQ and OSR with the same centre O. For Examiner’s Use S J P 60° Q O R DIAGRAM 2 OR = 21cm and OQ = 14cm. 22 Using π = , calculate 7 (a) the perimeter, in cm, of the whole diagram, (b) the area, in cm2 , of the shaded region. [6 marks] Answer: 1449/2 [ Turn Over PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
8. 8. 8 Panel Pakar Runding GC MMMT 1449/2 For 5. Solve the equation x(2x – 5) + 3 = 0 Examiner’s [4 marks] Use Answer: 1449/2 PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
9. 9. 9 Panel Pakar Runding GC MMMT 1449/2 6. (a) Is the sentence below a statement or non-statement? For Examiner’s Use “ 3 + 5 = 1 + 9 ”. (b) Write down two implications based on the following sentence. “ 4k < 20 if and only if k < 5” (c) Complete the premise in the following argument : Premise I : If n + 1 is an even number then n is an odd number. Premise II : n is not an odd number. Conclusion : [4 marks] Answer: (a) (b) Implication 1: Implication 2: (c) Conclusion: 1449/2 [ Turn Over PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
10. 10. 10 Panel Pakar Runding GC MMMT 1449/2 For 7. In Diagram 3, the graph shows the straight lines JK, JL and RS. Examiner’s Use y S(13,20) K J L x O R DIAGRAM 3 J is on the y-axis and R is on the x-axis. JL is parallel to the x-axis and JK is parallel to RS. The equation of JK is 2y = 6x + 8. (a) State the equation of the straight line JL. (b) Find the equation of the straight line RS. (c) State the x-intercept of the straight line RS. [6 marks] Answer: (a) (b) (c) 1449/2 PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
11. 11. 11 Panel Pakar Runding GC MMMT 1449/2 8. Diagram 4 shows a cube with DCGH as the horizontal base. For Examiner’s A B Use E F 6 cm D C 3 cm H 4 cm G DIAGRAM 4 [4 marks] Calculate the angle between the line AG and the plane DCGH. Answer: 1449/2 [ Turn Over PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
12. 12. 12 Panel Pakar Runding GC MMMT 1449/2 For 9. (a) While on vacation in Cherating, Samuri decides to buy 6 postcards for Examiner’s Jamil, 3 postcards for Mala and 2 postcards for Teck Sin. All the Use postcards are kept in a bag. If a postcard is taken at random from the bag, find the probability that the postcard is for Jamil. (b) In a class, 12 pupils are from Perak. If a pupil is chosen at random from the class, the probability of choosing a 1 pupil from Perak is . 3 Find the number of pupils in the class. [5 marks] Answer: (a) (b) 1449/2 PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
13. 13. 13 Panel Pakar Runding GC MMMT 1449/2 10. In Diagram 5 , O is the origin. For Examiners’s y Use P(9,15) Q(3,10) x R O DIAGRAM 5 OP is parallel to RQ. Find (a) the gradient of RQ, (b) the equation of the straight line RQ, (c) the x-intercept of RQ. [6 marks] Answer: (a) (b) (c) 1449/2 [ Turn Over PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
14. 14. 14 Panel Pakar Runding GC MMMT 1449/2 For 11. (a) Complete the following mathematical statements in the using the Examiner’s Use symbols < or > to form (i) a true statement 2×3 2+3 (ii) a false statement (2 +3)2 22 + 32 (b) Complete the premise in the following argument: Premise 1 : All pentagons have five sides. Premise 2 : ________________________ Conclusion : PQRST has five sides. (c) 0 = 3(0)2 3 = 3(1)2 12 = 3(2)2 27 = 3(3)2 Based on the information above, make a general conclusion by induction regarding the number sequence 0 , 3 , 12 , 27 , . . . [6 marks] Answer: (a) (i) 2×3 2+3 (ii) (2 +3)2 22 + 32 (b) Premise 2 : (c) 1449/2 PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
15. 15. 15 Panel Pakar Runding GC MMMT 1449/2 Section B For [48 marks] Examiner’s Use Answer four questions in this section. 12. (a) In Diagram 6, OABC is a parallelogram. O is the origin. y B A(1,4) C(5,2) O x DIAGRAM 6 Find (i) the gradient of OA (ii) the equation of the straight line BC (iii) the y-intercept of the line AB. [5 marks] (b) Diagram 7 shows a pyramid JKLMN. N 5 cm K J L M DIAGRAM 7 The base JKLM is a square. MN = 13 cm. (i) Calculate the angle between the line NL and the base JKLM. (ii) Calculate the angle between the plane NLM and the base JKLM. [7 marks] 1449/2 [ Turn Over PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
16. 16. 16 Panel Pakar Runding GC MMMT 1449/2 For Answer: Examiner’s Use 12. (a) (i) (ii) (iii) (b) (i) (ii) 1449/2 PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
17. 17. 17 Panel Pakar Runding GC MMMT 1449/2 13. (a) Diagram 8 shows some number cards. For Examiner’s Use 2 3 5 6 8 9 11 12 DIAGRAM 8 All the cards are put inside a box. A card is drawn at random from the box. (i) List its sample space. (ii) List the elements of the event of getting even number (iii) Find the probability of getting an odd number (iv) A boy adds 2 even numbered cards to the box. A card is then drawn at random from the box. Find the probability of getting an even number. [6 marks] (b) In Diagram 9, JK and PQ are arcs of two different circles with centre O. K Q T J P 150° O R DIAGRAM 9 ORTQ is a square. OJ = 28 cm and P is a centre of OJ. 22 Using π = , calculate 7 (i) the perimeter, in cm, of the whole diagram. (ii) the area, in cm2, of the shaded region. [6 marks] 1449/2 [ Turn Over PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
18. 18. 18 Panel Pakar Runding GC MMMT 1449/2 For Answer: Examiner’s Use 13. (a) (i) (ii) (iii) (iv) (b) (i) (ii) 1449/2 PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
19. 19. 19 Panel Pakar Runding GC MMMT 1449/2 For Examiner’s 14. (a) Solve the equation 3n − 4 = 11n. 2 Use [4 marks] 1 2 (b) Solve the equation 20 + x = x +8. 2 [4 marks] (c) Diagram 10 shows a solid formed by joining a half cone and a half cylinder. 10 cm DIAGRAM 10 The diameters of the cylinder and the base of the cone are both 14 cm. The height of the cone is 5 cm. 22 Using π = , calculate the volume, in cm3 , of the solid. 7 [4 marks] 1449/2 [ Turn Over PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
20. 20. 20 Panel Pakar Runding GC MMMT 1449/2 For 14. (a) Examiner’s Use (b) (c) 1449/2 PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
21. 21. 21 Panel Pakar Runding GC MMMT 1449/2 15. Diagram 11 shows the ages, in years, of 30 participants in a game on a family day. For Examiner’s Use 3 11 13 14 18 12 23 24 7 13 22 13 19 27 6 16 24 29 13 25 8 11 20 17 14 17 18 16 9 16 DIAGRAM 11 a) Based on the data in the diagram above, complete the following table in the answer space. Age Frequency Midpoint Upper boundary 1 - 5 6 - 10 11 - 15 16 - 20 21 - 25 26 - 30 [4 marks] b) Based on the table in (a), calculate the estimated mean age of the participants. [3 marks] c) By using a scale of 2 cm to 5 years on x-axis and 2 cm to 1 participant on the y-axis, draw a histogram for the data. [4 marks] d) From the histogram, find the percentage of participants who are more than 15 years old. [1 mark] 1449/2 [ Turn Over PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
22. 22. 22 Panel Pakar Runding GC MMMT 1449/2 For Examiner’s Answer: Use 15. (a) Age Frequency Midpoint Upper (Years) Boundary 1−5 6 − 10 11 − 15 16 − 20 21 − 25 26 − 30 (b) (c) Refer to page 23 (d) 1449/2 PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
23. 23. 23 Panel Pakar Runding GC MMMT PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
24. 24. 24 Panel Pakar Runding GC MMMT 1449/2 For Examiner’s 16. Table 1 shows the distribution of the ages of 200 participants in a big walk event. Use Age ( years) Frequency 15 - 19 10 20 - 24 20 25 - 29 50 30 - 34 60 35 - 34 36 40 - 44 18 45 - 49 6 TABLE 1 (a) Using the data in Table 1, complete the table provided in the answer space. [4 marks] (b) Calculate the estimated mean age of the participants. [3 marks] (c) By using a scale of 2 cm to 5 years on the x-axis and 2 cm to 20 participants on the y-axis , draw an ogive for the data. [5 marks] 1449/2 PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
25. 25. 25 Panel Pakar Runding GC MMMT 1449/2 Answer: For Examiner’s Use (a) Age (years) Frequency Cumulative Upper Frequency Boundary 15 − 19 10 20 − 24 20 25 − 29 50 30 − 34 60 35 − 39 36 40 − 44 18 45 − 49 6 (b) (c) Refer to page 26 1449/2 [ Turn Over PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/
26. 26. 26 Panel Pakar Runding GC MMMT PPSMI/Maths/F4/P2 https://panelmathsaddmathswordpress.com/