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# Kertas model pep sebenar (pmr)

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1. 50/1 Mathematics Paper 1 July 2009 1¼ hours Set 1 JABATAN PELAJARAN PERAK PENILAIAN MENENGAH RENDAH 2009 ANSWER TO SCORE 2009 PMR FORECAST PAPER MATHEMATICS Paper 1 1 hour 15 minutes DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO 1. This question paper consists of 40 questions. 2. Answer all questions 3. Answer each question by blackening the correct space on the answer sheet 4. Blacken only one space for each question. 5. If you wish to change your answer, erase the blackened mark that you have made. Then blacken the space for your new answer. 6. The diagrams in the questions provided are not drawn to scale unless stated. 7. You may use a non-programmable scientific calculator. 8 A list of formulae is provided. This question paper consists 20 printed pages. 55
2. The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. RELATIONS 1. m n m n a a a + × = 2. m n m n a a a − ÷ = 3. ( )m n mn a a= 4. Distance = 2 2 2 1 2 1( ) ( )x x y y− + − 5. Midpoint ( , )x y =    + 2 21 xx ,   + 2 21 yy 6. Average speed = distance travelled time taken 7. sum of data Mean = number of data 8. Pythagoras Theorem 2 2 2 c a b= + SHAPE AND SPACE 1. Area of rectangle = length × width 2. Area of triangle = 1 base height 2 × × 3. Area of parallelogram = base height× 4. Area of trapezium = 1 sum of parallel sides height 2 × × 56
3. 5. Circumference of circle = 2d rπ π= 6. Area of circle = 2 rπ 7. Curved surface area of cylinder = 2 rhπ 8. Surface area of sphere = 2 4 rπ 9. Volume of right prism = cross sectional area × length 10. Volume of cuboid = length × width × height 11. Volume of cylinder = 2 r hπ 12. Volume of cone = 21 3 r hπ 13. Volume of sphere = 34 3 rπ 14. Volume of right pyramid = 1 3 × base area × height 15. Sum of interior angles of a polygon = ( 2) 180n − × o 16. arc length angle subtended at centre circumference of circle 360 = o 17. area of sector angle subtended at centre area of circle 360 = o 18. Scale factor, k = PA PA ′ 19. Area of image = 2 area of objectk × 57
4. Answer all questions. 1. The number 345 678 is written as 350 000 when it is rounded off to the A nearest ten B nearest hundred C nearest thousand D nearest ten thousand 2. Which of the following fractions has value greater than 4 3 ? A 8 7 B 3 2 C 2 1 D 7 5 3. Express 33 100000 168 as a decimal A 33.168 B 33.0168 C 33.00168 D 33.000168 4. Table 4 shows the temperature for four towns on a particular day. Town Temperature (°C) E -2 F 3 G 9 H -8 Table 4 Which town was the coldest on that day? A E B F C G D H 5. Diagram 5 shows a sequence of prime numbers. 17, 19, m, n, 31 58
5. Diagram 5 Find the value of m + n. A 44 B 48 C 52 D 56 6. Diagram 6 shows some factors of 54. Diagram 6 Identify three other factors of 54. A 2, 3, 18 B 2, 18, 29 C 3, 4, 8 D 3, 4, 18 7. Tharma’s Poultry Farm produces 9 000 eggs a day. If 1% of the eggs are broken, calculate the number of broken eggs produced in a week. A 900 B 630 C 180 D 90 8. Swaran Construction Company built a road from Kampung Menora to Kampung Gelam, a distance of 5.54 km. It then built a road connecting Kampung Gelam to Kampung Aman, a distance of 6.78 km. Calculate the total length of the road constructed by the company A 10 km 320 m B 11 km 320 m C 12 km 320 m D 13 km 320 m 9. In Diagram 9, ABC is a straight line. 59 DD Diagram 9 1 9 54 6 27
6. Calculate the value of x. A 55 B 60 C 70 D 75 10 . In Diagram 10 , PQRST is a pentagon and STU is a straight line Diagram 10 Find the value of p + q + r + s. A 220 B 400 C 500 D 540 11 . Diagram 11 shows a polygon. 60 T p° Q S R 40° U P q° r ° s° F D C E 122° 75° 3x° B A 2x° 3x° 115°
7. Diagram 11 Find the value of x. A 41 B 51 C 55 D 61 12 . Diagram 12 shows two regular polygons. Diagram 12 Find the value of m. A 120 B 132 C 144 D 228 13 . In Diagram 13, PQR is a right-angled triangle, RVU is an equilateral triangle and QRVW is a square. 61 V m° W X Q T R U S 12 cm 5 cm Q W V U R P
8. Diagram 13 Calculate the perimeter, in cm, of the whole diagram. A 48 B 65 C 66 D 102 14 . Diagram 14 shows two right-angled triangles, XYZ and VWZ. Diagram 14 Find the area in cm², of the shaded region. A 105 B 75 C 35 D 30 15 . Diagram 15 shows the plan of an orchard. 62 4 m 4 m 6 m 10 m 15 m 4 m 4 m 6 m 10 m 15 m X Y V Z 15 cm 4 cm 10 cm 6 cm W X Y V Z 15 cm 4 cm 10 cm 6 cm W
9. Diagram 15 Find the area, in m2 , of the whole diagram. A 70 B 90 C 100 D 130 16 . Which of the following geometric solid is a cone? A B C D 63
10. 17 . In Diagram 17, the volume of the cylinder is equal to the volume of the cone.. Diagram 17 Calculate the height of the cylinder A 21 cm B 16 cm C 14 cm D 7 cm 18 . Diagram 18 shows a solid pyramid with a square base PQRS and height of 4 cm. The area of the base is 36 cm2 . Diagram 18 Find the total surface area, in cm2 , of the solid. A 144 B 96 C 51 D 48 19. Diagram 19 shows a prism with a right angled triangle as its uniform cross section. 64 4 cm4 cm4 cm 21 cm h 4 cm4 cm4 cm 21 cm h P Q R S T P Q R S T
11. Diagram 19 Calculate the total surface area of the prism. A 120 cm² B 156 cm² C 160 cm² D 180 cm² 20. Diagram 20 shows a rectangle PQRS and some construction lines made by a student. The student is constructing the locus of X such that, A PSX = RSX B XP = XS C XS = SP D XS is equidistant from line PQ and line SR 21. In Diagram 21, O is the centre of the circle. 65 P Q R 5 cm 3 cm 12 cm P Q R 5 cm 3 cm 12 cm P S R QP S R Q O 130⁰ x⁰ O 130⁰ x⁰ Diagram 20
12. Diagram 21 Find the value of x. A 115 B 110 C 80 D 50 22 . In Diagram 22, PTR is a diameter of the circle and STQ is a straight line. Diagram 22 Find the value of x. A 55 B 40 C 35 D 30 23 . Diagram 23 shows a circle with centre O. PT, QU, RV and SW are diameters of the circles. 66 P S R Q T x° 50° 70° P S R Q T x° 50° 70°
13. Diagram 23 Which of the following minor arcs is the longest? A TU B UV C WP D RS 24 . In Diagram 24, O is the centre of the bigger circle with a radius of 7 cm. The smaller circle passes through O and touches the bigger circle. Diagram 24 Using π = 7 22 , calculate the area in cm², of the shaded part. A 38.5 B 77.0 C 115.5 D 154.0 25 . In Diagram 25, PQRST is a trapezium, QST and QRS are right-angled triangles. 67 30° 50° O W S U Q P V R T 30° 50° O W S U Q P V R T ●O ●O P Q RT 16 cm 20 cm
14. Diagram 25 Find the length, in cm, of QR. A 12 B 13 C 14 D 15 26 . In Diagram 26, ACD is the image of ABE under an enlargement with centre A. Diagram 26 Given CD = 6 cm, calculate the length, in cm, of BE. A 3 B 4 C 6 D 9 27 . Given 93 =+ yx and 632 =− yx , calculate the value of .x A 2 B 3 C 4 D 5 28. Solve the following inequality. 4 3 y + 3 < 4 3 A y < 3 B y < -3 C y > 3 68 S 5 cm 6 cm 3 cm A E D C B 6 cm
15. D y > -3 29. In Diagram 29, B is the midpoint of the straight line AC. Diagram 29 Find the value of p. A 9 B 6 C 3 D 2 30. Diagram 30 shows five points on a Cartesian plane. 69 y A (-1, 2) B (4, 5) C (p, 8) x 0 ● ● ● y A (-1, 2) B (4, 5) C (p, 8) x 0 ● ● ● R(-9, -2) P(8, 6) T(11, 5) Q(-3, 10) S(-6, -8) x y O - - xx ● ● ● ● ● R(-9, -2) P(8, 6) T(11, 5) Q(-3, 10) S(-6, -8) x y O - - xx ● ● ● ● ●
16. Diagram 30 Which of the following has the same distance as OP? A OQ B OR C OS D OT 31 . Diagram 31 shows a rectangle PQRS. PTU is an arc with centre Q and UVW is an arc with centre R. Diagram 31 Find the perimeter in cm, of the shaded region. ( Use π = 7 22 ) A 54 B 61 C 70 D 82 32 . Table 32 shows the registration fees for an examination Basic fee RM150 Fee per written paper RM35 Fee per oral assessment RM40 Fee per practical assessment RM38 Table 32 Mimi registers for 8 written papers, 3 oral assessments and 3 parctical assessments whereas Roger registers for 7 written papers, 2 oral assessments and 3 practical assessments The difference in the total registration fee paid by Mimi and Roger is A RM75 B RM95 70
17. C RM120 D RM150 33 . The scores obtained by Amani and Bee Leng in a game are in the ratio of 7 : 4 , while the ratio of scores obtained by Bee Leng and Celine is 6 : 5. Find the ratio of scores obtained by Amani, Bee Leng and Celine. A 7 : 12 : 5 B 7 : 12 : 10 C 21 : 12 : 10 D 21 : 12 : 15 34 . Daud drove from Kluang to Ipoh. His journey was expected to take 6 2 1 hours. He started his journey at 7.40 a.m. and arrived Ipoh 20 minutes late. What time did Daud arrive Ipoh? A 2.40 p.m. B 2.30 p.m. C 2.10 p.m. D 1.50 p.m. 35 Diagram 35 is a pie chart showing the number of ice cream sold at a stall on a certain day. Diagram 35 Find the value of x + y. A 68° 71 Chocolate 60 Corn 32 Orange 22 Vanilla 36 Strawberry 10 x y Chocolate 60 Corn 32 Orange 22 Vanilla 36 Strawberry 10 x y
18. B 135° C 153° D 163° 36 . In Diagram 36, the bar chart below shows the number of students in three classes. Diagram 36 Which of the following statement is true? A The total number of students in three classes is 125 B The total number of girls in Class A and Class B is the same. C The number of boys in this school is greater than the number of girls. D The number of girls in class C is greater than the number of girls in class B. 37 . Table 37 shows the number of teachers in five housing estates. Housing estates A B C D E Number of teachers 10 13 p 7 5 Table 37 The mode is B. Find the possible value of p. A 12 B 14 C 25 D 35 72
19. 38 . Table 38 shows the scores in a game Score 0 1 2 3 4 5 Frequenc y 5 7 2 6 4 6 Table 38 The median score is A 1 B 2 C 3 D 4 39 . Table 39 shows the values of variables x and y for the function of y = 3x2 – 2x x -2 -1 0 1 2 y m 5 0 1 8 Table 39 Find the value of m. A 16 B 8 C -8 D -16 40 . Which of the following graphs represents y = x + 6 A 73 (6,0 ) (0,6 ) x y 0 (6,0 ) (0,6 ) x y 0 (6,0 ) (0,-6) x y 0 (6,0 ) (0,-6) x y 0
20. B C D END OF QUESTION PAPER 50/1 Mathematics Paper 1 July 2009 1¼ hours Set 2 74 (6,0 ) (0,-1 ) x y 0 (6,0 ) (0,-1 ) x y 0 (-6,0 ) (0,6 ) x y 0 (-6,0 ) (0,6 ) x y 0
22. 3. ( )m n mn a a= 4. Distance = 2 2 2 1 2 1( ) ( )x x y y− + − 5. Midpoint ( , )x y =    + 2 21 xx ,   + 2 21 yy 6. Average speed = distance travelled time taken 7. sum of data Mean = number of data 8. Pythagoras Theorem 2 2 2 c a b= + SHAPE AND SPACE 1. Area of rectangle = length × width 2. Area of triangle = 1 base height 2 × × 3. Area of parallelogram = base height× 4. Area of trapezium = 1 sum of parallel sides height 2 × × 5. Circumference of circle = 2d rπ π= 6. Area of circle = 2 rπ 7. Curved surface area of cylinder = 2 rhπ 8. Surface area of sphere = 2 4 rπ 9. Volume of right prism = cross sectional area × length 76
23. 10. Volume of cuboid = length × width × height 11. Volume of cylinder = 2 r hπ 12. Volume of cone = 21 3 r hπ 13. Volume of sphere = 34 3 rπ 14. Volume of right pyramid = 1 3 × base area × height 15. Sum of interior angles of a polygon = ( 2) 180n − × o 16. arc length angle subtended at centre circumference of circle 360 = o 17. area of sector angle subtended at centre area of circle 360 = o 18. Scale factor, k = PA PA ′ 19. Area of image = 2 area of objectk × 77
24. Answer all questions. 1. Which of the following numbers when rounded off to the nearest hundred thousand becomes 8 700 000 ? A 8 754 321 B 8 654 321 C 8 643 210 D 8 554 321 2. Table 2 shows the types of item that Sarah bought from a sundry shop. Types of item Price per kg Quantity Item A RM30 4.5 kg Item B RM19 2 kg 500 g Item C RM18 500 g Table 2 Sarah has RM250.00 How much money is left after she has paid for all the items? A RM61.75 B RM5.85 C RM105.50 D RM58.50 3. Ali had 300 durians. He managed to sell 6 5 of the durians . Later he gave 20 of the remaining durians to his friends. Calculate the percentage of the durians that he has left. A 50 B 16.67 C 10 D 6.67 4. Diagram 4 is part of a number line. Diagram 4 78 P -12 0 Q
25. What is the value of P and Q? A P = -18 , Q = 18 B P = -14 , Q = 12 C P = -12 , Q = 9 D P = -6 , Q = 18 5. The original price of a T-shirt is RM24.00. The selling price of the T-shirt is 12 11 of its original price. Swee Lan uses 2 1 of her savings to buy the T-shirt. What was her savings before she bought the T-shirt? A RM22.00 B RM28.80 C RM44.00 D RM39.60 6. Which of the following is the common multiple of 3 and 5? A 8 B 9 C 25 D 45 7. Ali has 5 rolls of rope. Each roll is 2 1 3 m long. He used 1.69 m of the rope from each roll. Find the length of the remaining rope. A 9.15 m B 9.05 m C 9.00 m D 8.05 m 8. A bus started its journey from Kuala Lumpur and arrived at Johor Bahru at 4.45 a.m. on the next day. If the journey took 4 1 5 hours, the bus left Kuala Lumpur at A 1000 hours B 2200 hours 79
26. C 2230 hours D 2330 hours 9. In Diagram 9, ABC is a triangle Find the value of x. A 15 B 18 C 20 D 25 10 . In Diagram 10, pentagon P’Q’R’S’T is the image of pentagon PQRST under an enlargement 80 S’ T’ P’ R’ Q’ P Q T R S A x° x°35° 62° 147° B CA x° x°35° 62° 147° B C Diagram 9
27. Diagram 10 Find the scale factor of this enlargement. A 1 B 2 C 3 D 4 11 . Diagram 11 shows a regular hexagon. Diagram 11 Find the value of y A 30 B 35 C 40 D 45 12 . In Diagram 12, PQRT are five vertices of a regular polygon. 81 y° 3x° x° P Q R U S T
28. Diagram 12 Find the number of sides of the polygon? A 6 B 8 C 10 D 12 13 . The cost of a metre of fencing is RM13.60. The Vision Home for the Poor wants to fence a rectangular compound 25 m by 75 m. How much is the cost of fencing the rectangular compound? A RM2 520 B RM2 620 C RM2 720 D RM2 820 14 . In Diagram 14, ACD is a right-angled triangle. The area of triangle ABD is 168 cm². Find its height, h in cm. A 11 B 14 C 20 D 24 15 . In Diagram 15, DEGH is a parallelogram and FGH ia a straight line. 82 h cm C 15cm 14cmA B D Diagram 14
29. Diagram 15 Given DE = 12 cm and HF = 15 cm. If the area of triangle EFG is 6 cm², find the area of the whole diagram. A 40 B 54 C 60 D 96 16 . Diagram 16 shows the net of a geometric solid. Diagram 16 Name the geometric solid. A Right prism B cuboid C pyramid 83 F GH D E
30. D cone 17 . Diagram 17 shows two containers in the shape of a cuboid and right prism. The cuboid is fully filled with water. All the water in the cuboid is then poured into the right prism. The base area of the right prism is 66 cm2 . Calculate the height, in cm of the water level in the right prism. A 13 B 21 C 88 D 66 18 . Aminah is 4 3 4 years old. Bala is 12 1 9 years older than Aminah. Chee Meng’s age is 2 1 2 times the sum of the ages of Aminah and Bala. What is Chee Meng’s age? A 8 7 11 B 6 5 13 C 3 1 16 D 24 11 46 84 6 cm 21 cm 11 cm Diagram 17
31. 19 . In Diagram 19, JOL is a diameter of the circle JKLM with centre O. MLN is a straight line. Diagram 19 Find the value of x. A 20 B 25 C 30 D 70 20 . In Diagram 20, DEFG is a cyclic quadrilateral. Diagram 11 Find the value x. A 50° B 60° 85 ● J K L M O N x° 70° 130° ● J K L M O N x° 70° 130° D E F G H x 30° 100° D E F G H x 30° 100°
32. C 80° D 100° 21 . In Diagram 21, PQR and STU are two circles with a common centre, O. PSOUR is a straight line. Diagram 21 Given that PS = SO = 4 cm, calculate the area, in cm², of the shaded region. A 8π B 16π C 32π D 64π 22 . In Diagram 22, O is the centre of the circle and POR is a diameter of the circle. PQR is a right-angled triangle. Diagram 22 Find the area, in cm², of the coloured region. A 25π - 24 B 25π - 30 86 ● O P R Q 10 cm 8 cm ● O P R Q 10 cm 8 cm R S T U P Q O R S T U P Q O
33. C 25π - 48 D 100π - 48 23 . In Diagram 23, PQRS is a cyclic quadrilateral. NPQ is a straight line and O is the centre of the circle. Diagram 23 Find the value of x. A 50° B 60° C 70° D 120° 24 . Diagram 24 shows a triangular pattern on a wall. Diagram 24 A tin of paint is required to paint an area of 5 m². How many tins of paint if needed to paint the surface of the triangle? A 12 B 24 C 25 D 32 87 15 m 17 m 15 m 17 m
34. 25 . Which of the following diagram shows line XY non-parallel to line PQ ? A. B. C. D. 88 X Y P Q 70O 70O 70O 70O X Y P Q 70O 70O X Y P Q 110O 110O X Y P Q
35. 26 . It is given that 1732 −=− yx and 4−=x . Calculate the value of y. A 3 B 4 C 5 D 6 27 . Diagram 27 represent two simultaneous linear inequalities on a number line. Diagram 27 Which of the following inequalities is the solution for both of the inequalities on the number line ? A –3 ≤ x ≤ 2 B –3 < x < 2 C –3 ≤ x < 2 D –3 < x ≤ 2 28. In Diagram 28, CE are points on a Cartesian plane. Diagram 28 D is the midpoint of CE. The coordinates of D are A (1, 3) B (2, 3) 89 –4 –3 –2 –1 0 1 2 C (-7, 8) E (5, -2) x y 0 ● ● C (-7, 8) E (5, -2) x y 0 ● ●
36. C (-1, 3) D (-2, 3) 29. Diagram 29 shows points J, K, L and M marked on a grid of equal squares with sides of 1 unit. Diagram 29 Which points are equidistant from point O? A M and J B M and K C K and L D K and J 30. In Diagram 30, C is the centre of the circle and ABC is a right-angled triangle. Calculate the perimeter of the whole diagram. A 60.29 cm B 72.59 cm C 75.29 cm D 75.59 cm 31 . Sally, Shirley and Susan invested a sum of money in a bookstore in the ratio 7 : 5 : 6. The total amount invested by Sally and Susan was RM624. find the total amount invested by 90 A B D 12 cm 150º C9 cm A B D 12 cm 150º C9 cm Diagram 30 ● ● ● ● ● J K LM O ● ● ● ● ● J K LM O
37. Sally and Shirley. A RM864 B RM576 C RM288 D RM48 32 . Table 32 shows the price of mangoesteens sold at four stalls, W, X, Y and Z W X 3 mangoesteens for RM 15 5 mangoesteen for RM 20 2 mangoesteens for RM 8 5 mangoesteens for RM 15 Y Z 3 mangoesteens for RM 21 6 mangoesteens for RM 42 5 mangoesteens for RM 25 8 mangoesteens for RM 48 Table 32 Which stall sells mangoesteens at a price that is proportional to the number of mangoesteens? A W B X C Y D Z 33 . Table 33 shows the number of computers sold by a company from January to April Month January February March April Number of computer sold 1450 1800 1650 1600 Table 33 Based on the data in table above, which of the following statements is not true ? A The difference between the highest and the lowest number of computers sold in a month is 350 B The mean number of computers sold for a month over this four month period is 1625 C The total number of computer sold after February is 3250 D The number of computers sold in April is equivalent to 30% of the total number of computer sold over the four month period 34 . Diagram 34 is a bar chart which shows the number of books sold by a bookshop in six months 91
38. Diagram 34 If the number of books sold in March is 20 000, find the number of books sold in February A 8 000 B 10 000 C 12 000 D 16 000 35 . Diagram 21 is a pie chart showing the types of fruits in a trolley. Diagram 21 There are 252 rambutans. How many mangosteens are in the trolley? A 98 B 70 C 42 D 28 36 . The line graph in Diagram 36 shows the income of a hawker in 4 months. 92 January Month February March April May Numberofbooks June January Month February March April May Numberofbooks June Rambutan 160˚ Mangosteen Guava Durian 5y 2y 60˚ Rambutan 160˚ Mangosteen Guava Durian 5y 2y 60˚
39. Diagram 36 Calculate the total income in 4 months. A RM 6505 B RM 6500 C RM 6250 D RM 6600 37 . Table 37 shows the numbers of book read by Zulkifli in 5 months. Month Jan Feb Mac Apr May Number of books 5 3 2 6 4 Table 37 Calculate the mean number of books read by Zulkifli in 5 months. A 3 B 4 C 5 D 6 93 Income of a hawker in 4 months 1400 1800 1350 1700 0 500 1000 1500 2000 Jan Feb Mac Apr Month Income(RM)
40. 38 . Diagram 38 shows a graph of a function on a Cartesian plane. Diagram 38 The equation that represents the function is A y = x - 2 B y = - x C y = x + 2 D y = - x + 2 39 . Table 39 shows the values of variables x and y for the function of y = -2x2 + 1 x -2 -1 0 1 2 y -7 s 1 -1 t Table 39 Calculate the value of s + t A -1 B -6 C -7 D -8 94 2 -2 0 2-4
41. 40 . In Diagram 40 ABCDEFGH is a regular octagon with sides 3 cm. Diagram 40 X is the locus of a point which moves such that it is always equidistant from point B and D. Y is the locus of a point which moves such that its distance from point H is always 3 cm. Which of the following points is the intersection of locus X and locus Y A C B G C A D E END OF QUESTION PAPER 95 B C A D E FG H
42. 50/1 Mathematics Paper 2 July 2009 1¾ hours Set 1 JABATAN PELAJARAN PERAK PENILAIAN MENENGAH RENDAH 2009 ANSWER TO SCORE 2009 PMR FORECAST PAPER This question paper consists 18 printed pages. 96 MATHEMATICS Paper 2 1 hour 45 minutes DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO 1. This question paper consists of 20 questions. 2. Answer all questions. Answer all questions 3. Write your answers clearly in the spaces provided in the question paper. 4. Diagrams are not drawn to scale unless stated. 5. The marks allocated are shown in brackets. Question Allocated Marks Marks Obtained 1 2 2 2 3 3 4 3 5 2 6 2 7 3 8 3 9 3 10 3 11 3 12 3 13 4 14 3 15 2 16 5 17 4 18 5 19 2 20 3 Total
43. INFORMATION FOR CANDIDATES 1. This question paper consists of 20 questions. 2. Answer all questions. 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 provided in the questions are not drawn to scale unless stated. 7. The marks allocated for each question are shown in brackets. 8. A list of formulae is provided on pages 3 and 4. 9. A booklet of four-figure mathematical tables is provided. 10. Calculators are not allowed. 11. This question paper must be handed in at the end of the examination. 97
44. The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. RELATIONS 1. m n m n a a a + × = 2. m n m n a a a − ÷ = 3. ( )m n mn a a= 4. Distance = 2 2 2 1 2 1( ) ( )x x y y− + − 5. Midpoint ( , )x y =    + 2 21 xx ,   + 2 21 yy 6. Average speed = distance travelled time taken 7. sum of data Mean = number of data 8. Pythagoras Theorem 2 2 2 c a b= + SHAPE AND SPACE 1. Area of rectangle = length × width 2. Area of triangle = 1 base height 2 × × 3. Area of parallelogram = base height× 4. Area of trapezium = 1 sum of parallel sides height 2 × × 98
45. 5. Circumference of circle = 2d rπ π= 6. Area of circle = 2 rπ 7. Curved surface area of cylinder = 2 rhπ 8. Surface area of sphere = 2 4 rπ 9. Volume of right prism = cross sectional area × length 10. Volume of cuboid = length × width × height 11. Volume of cylinder = 2 r hπ 12. Volume of cone = 21 3 r hπ 13. Volume of sphere = 34 3 rπ 14. Volume of right pyramid = 1 3 × base area × height 15. Sum of interior angles of a polygon = ( 2) 180n − × o 16. arc length angle subtended at centre circumference of circle 360 = o 17. area of sector angle subtended at centre area of circle 360 = o 18. Scale factor, k = PA PA ′ 19. Area of image = 2 area of objectk × 99
46. 1. Calculate the value of – 42 ÷ 6 – 10 = Answer : [ 2 marks] 2. Calculate the value of 4.0 24.06× = Answer : [ 2 marks] 3. a) Find the value of 3 216 1 = b) Calculate the value of ( )[ ]23 1693 +− = Answer : a) b) [ 3 marks] 4. Solve each of the following equations : 100
47. a) 2 ( r – 2 ) = 10 – 5r b) 2 6+s = 4s Answer : a) b) [ 3 marks] 5. Diagram 5 in the answer space shows quadrilateral ABCD. C’D’ is the image of CD under a reflection in the straight line LM. On Diagram 5 in the answer space, complete the image of quadrilateral ABCD. Answer: Diagram 5 [ 2 marks] 6. Diagram 6 shows two quadrilaterals, KLMN and K’L’M’N’, drawn on a grid of equal 101 L M A B C D C’ D’ L M A B C D C’ D’
48. squares with sides of 1 unit. Diagram 6 K’L’M’N’ is the image of KLMN under transformation P. Describe in full transformation P. Answer: [2 marks] 7. Factorise completely each of the following expressions : 102 K L M N K’ L’ M’ N’ K L M N K’ L’ M’ N’
49. a) x8 ² xy4− b) k6 ² 183 −+ k Answer : a) b) [ 2 marks] 8. Simplify each of the following a) ( )342 +x b) ( ) ( )443 −−−− xx Answer : a) b) [ 3 marks ] 9. Express       − − mn n m 2 5 3 as a single fraction in its simplest form. Answer : [ 3 marks] 10. a) Solve the inequality 8 + x < 14 b) List all the integer values of x which satisfy the inequalities 103
50. 2 - 3x < 11 and 8 - 3 1 x ≥ 7 Answer : a) b) [ 3 marks] 11. Given that k m = + 4 52 , express m in terms of k Answer : [ 3 marks] 12. (a) Simplify (p 4− q 2 ) 2 1 ÷ (p 2 q − 1 ) 2 104
51. (b) Find the value of 3 2 3 × 3 2 1 Answer : a) b) [ 3 marks] 13. The frequency table in table 13 shows the number of car owners in a housing park. 105
52. Table 13 Represent all the data by drawing a horizontal dual bar chart in the answer space. Answer : Women Men [4 marks] 106 Types of Cars Number of Women Number of Man Kancil 15 5 Persona 18 22 Waja 20 28
53. 14. The diagram 14 below shows the number of books borrowed from a school library by 14 students. Diagram 14 a ) Using the data, complete the frequency table below. b) State the median . Answer : a) Number Frequency 2 3 4 5 6 b) [3 marks] 107 3 2 4 3 5 6 2 4 2 5 5 3 2 6
54. 15. Diagram 15 shows surfaces of a right prism drawn in the square grid of 1 cm. Diagram 15 When the right prism is constructed, what would be its volume? Answer : [3 marks] 108
55. 16. Diagram 16 below shows a circle with centre O, which is divided into four equal parts. W, X and Y are three moving points in the diagram. a) W is a moving point such that it is always equidistant from point Q and point S. By using the letters in the diagram, state the locus of W. b) On the diagram draw i) The locus of point X such that it is equidistant from line OP and line OQ. ii) The locus of point Y such that YR = RQ. c) Hence, mark with the symbol ⊗the intersection of the locus of X and the locus of Y. Answer : Diagram 16 [5 marks] 109 P Q R S O P Q R S O
56. 17. Use the graph paper provided to answer this question. Table 17 shows the values of two variables, x and y, for a function. x -3 -2.5 -2 -1 0 1 2 3 4 y 0 -10 -15 -14 -9 0 10 21 32.5 Table 17 The x – axis and the y – axis are provided on the graph paper. a) By using a scale of 2cm to 5 units, complete and label the y – axis. b) Based on table 17, plot the points on the graph paper. c) Hence, draw the graph of the function. [4 marks] 110
58. 18. Set squares and protractors are not allowed for this question. Diagram 18 in the answer space shows two straight lines, PQ and QR. Using only a ruler and a pair of compasses, i) construct a rectangle PQRS. ii) construct a perpendicular line RT from the point R to the straight line QS where the point T lies on the straight line QS. Answer : Diagram 18 [5 marks] 19. Diagram 19 in the answer space shows triangle PQR drawn on a grid of the equal squares. Triangle PQR is enlarged by the scale factor 2 from the centre O. Draw the image of triangle PQR in the answer space. Answer : 112 P Q R
59. Q Diagram 19 [2 marks] 20. Diagram 20 shows two right angled triangles, PMN and PQR. MPQ is straight line. 113 P Q R M 6 cm N x˚ 12 cm y˚ P R O
60. Diagram 20 It is given that cos xo = 5 3 and sin yo = 5 4 a) Find the value of tan xo b) Calculate the length of MPQ in cm Answer : a) b) [3 marks] 50/1 Mathematics Paper 2 July 2009 1¾ hours Set 2 JABATAN PELAJARAN PERAK PENILAIAN MENENGAH RENDAH 2009 ANSWER TO SCORE 114
62. 7. The marks allocated for each question are shown in brackets. 8. A list of formulae is provided on pages 3 and 4. 9. A booklet of four-figure mathematical tables is provided. 10. Calculators are not allowed. 11. This question paper must be handed in at the end of the examination. The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. RELATIONS 1. m n m n a a a + × = 2. m n m n a a a − ÷ = 3. ( )m n mn a a= 4. Distance = 2 2 2 1 2 1( ) ( )x x y y− + − 116
63. 5. Midpoint ( , )x y =    + 2 21 xx ,   + 2 21 yy 6. Average speed = distance travelled time taken 7. sum of data Mean = number of data 8. Pythagoras Theorem 2 2 2 c a b= + SHAPE AND SPACE 1. Area of rectangle = length × width 2. Area of triangle = 1 base height 2 × × 3. Area of parallelogram = base height× 4. Area of trapezium = 1 sum of parallel sides height 2 × × 5. Circumference of circle = 2d rπ π= 6. Area of circle = 2 rπ 7. Curved surface area of cylinder = 2 rhπ 8. Surface area of sphere = 2 4 rπ 9. Volume of right prism = cross sectional area × length 10. Volume of cuboid = length × width × height 11. Volume of cylinder = 2 r hπ 12. Volume of cone = 21 3 r hπ 117
64. 13. Volume of sphere = 34 3 rπ 14. Volume of right pyramid = 1 3 × base area × height 15. Sum of interior angles of a polygon = ( 2) 180n − × o 16. arc length angle subtended at centre circumference of circle 360 = o 17. area of sector angle subtended at centre area of circle 360 = o 18. Scale factor, k = PA PA ′ 19. Area of image = 2 area of objectk × 1. Calculate the value of 2 3 ×       − 3 2 5 7 Answer : [2 marks] 118
65. 2. Calculate the value of 2.6 × 3.5 ÷       − 5 3 2 and express the answer as a decimal. Answer : [3 marks] 3. Diagram 3, in the answer space shows two triangles, PQR and P’Q’R’, drawn on a grid of equal squares. P’Q’R’ is the image of PQR under an enlargement. On Diagram 3 in the answer space, mark T as the centre of enlargement. Answer: 119
66. Diagram 3 [2 marks] 4. Diagram 4 in the answer space shows quadrilaterals PQRS and straight line WX drawn on a grid of equal squares. Starting from the line WX, draw quadrilateral WXYZ which is congruent to quadrilateral PQRS. 120 - 6 - 4 - 2 0 2 4 6 8 8 6 4 2 -2 x y P Q R Q’ R’ P’ - 6 - 4 - 2 0 2 4 6 8 8 6 4 2 -2 x y P Q R Q’ R’ P’
67. Answer: Diagram 4 [2 marks] 5. Diagram 5 in the answer space shows triangle KLM drawn on a grid of equal squares. On the diagram in the answer space, draw the image of the triangle KLM under a rotation of 90˚ clockwise about the point P. Answer: Diagram 5 [2 marks] 6. Given that, 5 3 = − k p express p in terms of k Answer : 121 P Q R S W X P Q R S W X P L M K ● L M K ●
68. [2 marks] 7. Solve each of the following equations : a) - 4 – 6x = 14 b) m m 4 103 − = 2 Answer : a) b) [4 marks] 8. Simplify : 736 +− bab ( )abb 4522 −+− Answer : [2 marks] 122
69. 9. Diagram 9 shows polygon ABCDEF drawn on a grid of equal squares. . Diagram 9 On the grid in the answer space, redraw the polygon using the scale of 1 : 2. 123 E BA C F D Answer :
70. [3 marks] 10. The diagram 10 in the answer space shows a rectangle, PQRS which is drawn on a grid of squares with sides 1 unit. O is the midpoint of PQ. X, Y and Z are three moving points in the diagram. (a) On the diagram draw (i) The locus of X such that it is constantly 3 units from line PQ. (ii) (iii) The locus of Y such that it is always 5 units from line RQ. The locus of Z such that point Z from O is always 5 units. (b) Hence, mark with the symbol ⊗the intersection of the locus of Y and the locus of Z. Answer : Diagram 10 [4 marks] 11. Expand each of the following expressions : (a) 2− ( )3+x + 5( )2+x (b) ( )mn − ( )mn 3− Answer : a) 124 O S P R Q
71. b) [3 marks] 12. Express 2 32 +a 3 4− − a as a single fraction in its simplest form. Answer : [3 marks] 13. In Diagram 13, triangles JKN and JLM are similar. Diagram 13 State (a) The angle in triangle JLM which corresponds to ∠JKN. (b) Find the length, in cm, of LM. Answer : a) 125 3 cm 2 cm 6 cm J N ML K
72. b) [3 marks] 14. List all the integer values of k which satisfy both the inequalities 2k + 2 ≥ - 4 and 4 - k > 0 Answer : [3 marks] 15. Diagram 15 is an incomplete line graph which shows the monthly sales of chickens in a market. 126
73. Diagram 15 (a) In which month the number of chickens sold are the highest ? (b) If the number of chickens sold in January is half of that in Mac, how many chickens are sold in January? Answer : a) b) [3 marks] 16. Use the graph paper provided to answer this question. Table 16 shows the values of two variables, x and y of a function. x -2 -1 0 1 2 3 4 y 4 0 -2 -2 0 4 10 Table 16 127 Month
74. The x-axis and the y-axis are provided on the graph paper. (a) By using the scale of 2 cm to 2 units, complete and label the y-axis. (b) Based on table 1, plot the points on the graph paper. (c) Hence, draw the graph of the function. Answer : 128
75. [5 marks] 17. Use of set squares and protractors are not allowed for this question. Diagram 17 shows a quadrilateral ABCD. 129 x -2 -1 0 1 2 3 y x -2 -1 0 1 2 3 y
76. Diagram 17 Using only a ruler and a pair of compasses, construct diagram 17, beginning from the line AB provided in the answer space. Answer : [5 marks] 18. Simplify (3hm 2 ) 4 × (m 2 ) 1− ÷ h 7 m 3− . Answer : [3 marks] 19. Find the value of 3 2 1 × 54 2 1 × 2 2 3 . 130 C BA D 60˚ 6 cm3 cm A B
77. Answer : [3 marks] 20. Diagram 20 shows a right - angled triangle PQR. Diagram 20 It is given that tan x○ = 3 4 . calculate the length, in cm, of PR. Answer : [3 marks] 131 P Q R x○ 9 cm