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65 PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA SEKOLAH MENENGAH NEGERI KEDAH DARUL AMAN PEPERIKSAAN PERCUBAAN SPM /1 MATHEMATICS ANSWER FOR PAPER 1 1 B 11 C 21 C 31 D 2 A 12 D 22 A 32 B 3 D 13 A 23 A 33 B 4 B 14 B 24 B 34 D 5 C 15 C 25 B 35 C 6 B 16 B 26 D 36 B 7 C 17 D 27 A 37 D 8 C 18 C 28 D 38 C 9 A 19 A 29 A 39 D 10 B 20 A 30 C 40 A ANALISIS A 10 B 11 C 10 D 9 ( K1+ K 2) NOTA: MARKAH PELAJAR =

66 SULIT 1449/2(PP) 1449/2 (PP) Matematik Kertas 2 Peraturan Pemarkahan 19 September 2010 PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA SEKOLAH MENENGAH NEGERI KEDAH DARUL AMAN. PEPERIKSAAN PERCUBAAN SPM 2010 MATHEMATICS Kertas 2 PERATURAN PEMARKAHAN UNTUK KEGUNAAN PEMERIKSA SAHAJA Peraturan pemarkahan ini mengandungi 19 halaman bercetak 1449/2(PP) [Lihat halaman sebelah SULIT

67 SULIT 2 Section A [ 52 marks] 1449/2(PP) Question Solution and Mark Scheme Marks 1(a) Q P R K1 (b) Q P R K2 3 Note : Q P R P R correctly shaded, award K1 1449/2(PP) SULIT

68 SULIT /2(PP) Question Solution and Mark Scheme Marks 2 2 4x 3x 7 = 0 ( )( ) x + 1 4x 7 = 0 or equivalent K1 K1 OR 2 ( 3) ± ( 3) 4(4)( 7) x = (K1) 2(4) x = x = or 1 or N1 N1 4 Note : 1. Accept without = Accept three terms on the same side, in any order. 3. Accept correct answer from the correct term without factorisation for Kk p q = or 3 p + 2 q = 18 or equivalent Note: Attempt to equate the coefficient of one of the unknowns award K1 4q = 12 or 4 p = 32 or equivalent OR p = q or 2(9 q) p = or 3 p 14 q = or equivalent (K1) 2 3 q = 9 p or equivalent (K1) 2 Note: Attempt to make one of the unknowns as the subject, award K1 1449/2(PP) [Lihat halaman sebelah SULIT

69 SULIT /2(PP) Question Solution and Mark Scheme Marks OR 1 2 p 1 14 = 3 q ( 1) ( 2) 2 2 or equivalent (K2) p = 8 q = 3 N1 N1 4 Note : Accept 1. p 8 = q 3 as final answer, award N or equivalent seen, award (K1) 1 9 1( 1) ( 2) 2 2 4(a) PTQ or QTP P1 (b) tanθ = or equivalent K or 50 11' or 50 12' N1 3 5(a)(i) (ii) False // Palsu True // Benar P1 P1 (b) If 2 x > 0, then x 0 or x 0 > < // P1 Jika 2 x > 0, maka x > 0 atau x < /2(PP) SULIT

70 SULIT /2(PP) Question Solution and Mark Scheme Marks If x > 0 or x < 0, then 2 x > // 0 P1 Jika x > 0 atau x < 0, maka 2 x > 0 (c) 5 and 9 are odd numbers // 5 dan 9 adalah nombor ganjil K1 5 6(a) 0 = 2x 5 or equivalent K1 5 x = or or N1 (b) m QR = 2 P1 y 6 = x 4 * m QR or 6 = * m QR (4) + c or equivalent K1 y = 2x + 14 or equivalent N1 5 7(a) p = 14 P1 q = 4 P1 2 (b) 2 3 x 13 = 4 1 y 5 P1 x = y (2)(1) ( 3)(4) or K1 * x inverse 13 = y matrix 2 x = 2 N1 y = 3 N /2(PP) [Lihat halaman sebelah SULIT

71 SULIT /2(PP) Question Solution and Mark Scheme Marks Note: * Do not accept inverse = or. matrix x 2 2. = as final answer, award N1. y 3 3. Do not accept any solutions solved not using matrix method K K K or or N1 4 Note : 1. Accept π for K mark. 2. Correct answer from incomplete working, award Kk2. 9(a) {(S,C), (S,O), (S,R), (S,E), (C,S), (C,O), (C,R), (C,E), (O,S), (O,C), (O,R), (O,E), (R,S), (R,C), (R,O), (R,E), (E,S), (E,C), (E,O), (E,R)} P2 2 Note : 1. Accept correct tree diagram or grid for P2 2. Accept 10 correct listings for P1 (b)(i) {(C,S), (C,O), (C,R), (C,E)} K or 1 5 N1 1449/2(PP) SULIT

72 SULIT /2(PP) Question Solution and Mark Scheme Marks (ii) {(S,C), (S,R), (C,S), (C,R), (O,E), (R,S), (R,C), (E,O)} K or 2 5 N1 4 Note : 6 Accept answer without working from correct listing, tree diagram or grid. 10(a) or K or equivalent K or 2 64 or N1 (b) or K or equivalent K or or N1 6 Note : 1. Accept π for K mark. 2. Correct answer from incomplete working, award KK /2(PP) [Lihat halaman sebelah SULIT

73 SULIT /2(PP) Question Solution and Mark Scheme Marks 11(a) = P1 (b) or K1 7 1 or N1 Note : Without working, award K1N1 (c) 1 1 ( ) 10 + ( 11 12) + ( 11+ v) 8 = K2 or equivalent method Note: 1 1. ( 11 28) or ( ) or 1 ( v ) 2 or equivalent, award K1 2. Accept 195 or 132 for K N /2(PP) SULIT

74 SULIT /2(PP) Question Solution and Mark Scheme Marks 12(a) 7 K1 2 K1 2 Note : K only meant for table value. (b) Graph Axes drawn in correct direction, uniform scales in 3 5 x 4 and 8 y 28. P1 All 7 points and *2 points correctly plotted or curve passes through these points for 3 5 x 4 and 8 y 28. K2 (does not depend on P) A smooth and continuous curve without any straight line and passes through all 9 correct points using the given scale for 3 5 x 4. Note : 1. 7 or 8 points correctly plotted, award K1. N1 (depends on P and K) 4 2. Ignore curve out of range. (c)(i) (ii) 10 0 y x 3 10 Note: 1. Allow P mark if value of x and y are shown on the graph. 2. Value of x and y obtained by calculation, award P0. P1 P1 2 (d) Identify equation y = 2x + 9 or equivalent. Straight line y = 2x + 9 correctly drawn. K1 K1 Values of x : 2 65 x x 3 15 Note : 1. Allow N marks if values of x shown on the graph. 2. Values x obtained by calculation, award N0. N1 (dep 2 nd K1) N1 (dep 2 nd K1) /2(PP) [Lihat halaman sebelah SULIT

75 SULIT /2(PP) y y = x x y = 2x O x /2(PP) SULIT

76 SULIT /2(PP) Question Solution and Mark Scheme Marks 13(a)(i) (6, 1) P2 Note: (6, 1) marked or (1, 4) seen or (1, 4) marked, award P1 (ii) (8, 5) P2 4 Note: (8, 5) marked or (3, 8) seen or (3, 8) marked, award P1 (b)(i)(a) W: Reflection in the line x = 1 Note : 1. P1 : Reflection // Pantulan. P2 (b) V: Enlargement at centre K or (6, 10) with scale factor 3 2 Note : 1. P2 : Enlargement at centre K or (2, 1) or P3 Enlargement scale factor P1 : Enlargement. (ii) * K1 * K1 110 N /2(PP) [Lihat halaman sebelah SULIT

77 SULIT /2(PP) Question Solution and Mark Scheme Marks 14(a) Marks Markah Frequency Kekerapan Cumulative Frequency Kekerapan Longgokan Upper Boundary Sempadan Atas I II III IV V VI VII VIII Frequency : (I to VIII) Cumulative frequency : (I to VIII) Upper Boundary : (I to VIII) Note : Allow one mistake in frequency for P1 P2 P1 P1 4 (b) * * * * * * * ( ) + ( ) + ( ) + ( ) + ( ) + ( ) + ( ) * * * * * * * Note : 1. Allow * midpoint for K1 2. Allow two mistakes for the multiplication of midpoint and * frequency, for K1 K Note : Correct answer from incomplete working, award Kk2 e.g = (without table) 40 N /2(PP) SULIT

78 SULIT /2(PP) Question Solution and Mark Scheme Marks (c) Axes drawn in correct direction and uniform scale for 29 5 x 99 5 and 0 y 40 Note : Do not accept wrong label P1 * 8 points correctly plotted K2 Note : * 6 or * 7 points correctly plotted or curve passes through using at least 6 correct upper boundary, award K1 Smooth and continuous curve without any straight line passes through 8 correct points for using given scales 29 5 x 99 5 N1 4 (d) Any true statement from the ogive K1 1 Note : Do not accept answer without an ogive /2(PP) [Lihat halaman sebelah SULIT

79 SULIT /2(PP) Frequency Marks 1449/2(PP) SULIT

80 SULIT /2(PP) Question Solution and Mark Scheme Marks 15 Note : (1) Accept drawing only (not sketch). (2) Accept diagrams with wrong labels and ignore wrong labels. (3) Accept correct rotation of diagrams. (4) Lateral inversions are not accepted. (5) If more than 3 diagrams are drawn, award mark to the correct ones only. (6) For extra lines (dotted or solid) except construction lines, no mark is awarded. (7) If other scales are used with accuracy of ± 0.2 cm one way, deduct 1 mark from the N mark obtained, for each part attempted. (8) Accept small gaps extensions at the corners. For each part attempted : (i) If 0 4 cm, deduct 1 mark from the N mark obtained. (ii) If > 0 4 cm, no N mark is awarded. (9) If the construction lines cannot be differentiated from the actual lines: (i) Dotted line : If outside the diagram, award the N mark. If inside the diagram, award N0. (ii) Solid line : If outside the diagram, award N0. If inside the diagram, no mark is awarded. (10) For double lines or non-collinear or bold lines, deduct 1 mark from the N mark obtained, for each part attempted. 1449/2(PP) [Lihat halaman sebelah SULIT

81 SULIT /2(PP) Question Solution and Mark Scheme Marks 15(a) F G H A B Correct shape with pentagon ABHGF All solid lines. K1 BA > AF > HG > BH K1 dep K1 Measurement correct to ± 0 2 cm (one way) and all angles at vertices of rectangles = 90 ± 1 N1 dep K1K /2(PP) SULIT

82 SULIT /2(PP) Question Solution and Mark Scheme Marks 15(b)(i) N M P L J F G H Correct shape with rectangles PNML, FPLG, GLJH and FPJH All solid lines K1 FN > FH > HJ = FP > MN = FG > LJ = GH = LM K1 dep K1 Measurement correct to ± 0 2 cm (one way) and all angles at the vertices of rectangles = 90 ± 1 N2 dep K1K /2(PP) [Lihat halaman sebelah SULIT

83 SULIT /2(PP) Question Solution and Mark Scheme Marks 15(b)(ii) N P E F K G Q D A Correct shape with rectangles QNPD and ADEF All solid lines K1 Note : Ignore straight line KG K and G joined with dashed line to form rectangles ADKG and GKEF K1 dep K1 QN = QA > AF > EF = AD > KE = GF > NP = QD > EP = AG = DK K1 dep K1K1 Measurement correct to ± 0 2 cm (one way) and all angles at the vertices of rectangles = 90 ± 1 N2 dep K1K1K /2(PP) SULIT

84 SULIT /2(PP) Question Solution and Mark Scheme Marks 16 (a) (75 S, 100 E) // (75 S, 100 T) P3 3 Note: E or 100 T, award P or E or T, award P1 (b) or 107 K S K1 N1 3 (c) ( ) 60 cos 75 or cos 75 Note: ( ) or 100 or using cos 75 correctly, award K1 K N1 3 (d) or equivalent K2 Note: ( ) * 550, award K hours or 19 hours 38 minutes N END OF MARK SCHEME 1449/2(PP) [Lihat halaman sebelah SULIT

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