PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA SEKOLAH MENENGAH NEGERI KEDAH DARUL AMAN PEPERIKSAAN PERCUBAAN SPM 2010 1449/1 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 = 100 140 http://edu.joshuatly.com/
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) http://edu.joshuatly.com/ [Lihat halaman sebelah SULIT
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) http://edu.joshuatly.com/ SULIT
SULIT 3 1449/2(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 = 1 7 3 x = or 1 or 1 75 4 4 N1 N1 4 Note : 1. Accept without = 0. 2. Accept three terms on the same side, in any order. 3. Accept correct answer from the correct term without factorisation for Kk2. 3 3 3 21 2 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 = 14 + 2q 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) http://edu.joshuatly.com/ [Lihat halaman sebelah SULIT
SULIT 4 1449/2(PP) Question Solution and Mark Scheme Marks OR 1 2 p 1 14 = 3 q 3 1 9 1( 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 N1 2. 1 2 1 14 3 3 or equivalent seen, award (K1) 1 9 1( 1) ( 2) 2 2 4(a) PTQ or QTP P1 (b) tanθ = 12 6 + 8 2 2 or equivalent K1 50 19 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 < 0 1449/2(PP) http://edu.joshuatly.com/ SULIT
SULIT 5 1449/2(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 2 1 2 or 2 5 2 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 1 1 3 13 = y (2)(1) ( 3)(4) 4 2 2 or K1 * x inverse 13 = y matrix 2 x = 2 N1 y = 3 N1 4 6 1449/2(PP) http://edu.joshuatly.com/ [Lihat halaman sebelah SULIT
SULIT 6 1449/2(PP) Question Solution and Mark Scheme Marks Note: * 2 3 1 0 1. Do not accept inverse = or. matrix 4 1 0 1 x 2 2. = as final answer, award N1. y 3 3. Do not accept any solutions solved not using matrix method. 1 22 3 5 6 3 7 8 2 K1 22 5 2 4 7 K1 1 22 2 22 2 3 5 6 + 5 4 3 7 7 K1 2739 7 or 2 391 or 391 3 7 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)} K1 4 20 or 1 5 N1 1449/2(PP) http://edu.joshuatly.com/ SULIT
SULIT 7 1449/2(PP) Question Solution and Mark Scheme Marks (ii) {(S,C), (S,R), (C,S), (C,R), (O,E), (R,S), (R,C), (E,O)} K1 8 20 or 2 5 N1 4 Note : 6 Accept answer without working from correct listing, tree diagram or grid. 10(a) 90 22 2 14 or 360 7 120 22 2 7 360 7 K1 90 22 120 22 2 14 + 2 7 + 14 + 7 + 7 or equivalent 360 7 360 7 K1 194 3 or 2 64 or 64 67 3 N1 (b) 90 22 14 2 or 360 7 120 22 7 2 360 7 K1 90 22 14 2 360 7 120 22 7 2 or equivalent 360 7 K1 308 3 or 2 102 3 or 102 7 N1 6 Note : 1. Accept π for K mark. 2. Correct answer from incomplete working, award KK2. 1449/2(PP) http://edu.joshuatly.com/ [Lihat halaman sebelah SULIT
SULIT 8 1449/2(PP) Question Solution and Mark Scheme Marks 11(a) 459 15.3 30 = P1 (b) 11 28 10 or 17 10 K1 7 1 or 1 7 10 N1 Note : Without working, award K1N1 (c) 1 1 ( 11+ 28) 10 + ( 11 12) + ( 11+ v) 8 = 459 2 2 K2 or equivalent method Note: 1 1. ( 11 28) 10 2 + or ( 11 12 ) or 1 ( v ) 2 or equivalent, award K1 2. Accept 195 or 132 for K1 11+ 8 22 N1 6 1449/2(PP) http://edu.joshuatly.com/ SULIT
SULIT 9 1449/2(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 11 0 3 20 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 2 55 3 05 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) 4 12 1449/2(PP) http://edu.joshuatly.com/ [Lihat halaman sebelah SULIT
SULIT 10 1449/2(PP) y y = x x 2 2 3 7 30 25 20 y = 2x + 9 15 10 5 4 3 2 1 O 1 2 3 4 x 5 10 1449/2(PP) http://edu.joshuatly.com/ SULIT
SULIT 11 1449/2(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 3 2 2. P1 : Enlargement. (ii) * 2 3 88 2 K1 * 2 3 88 88 2 K1 110 N1 8 12 1449/2(PP) http://edu.joshuatly.com/ [Lihat halaman sebelah SULIT
SULIT 12 1449/2(PP) Question Solution and Mark Scheme Marks 14(a) Marks Markah Frequency Kekerapan Cumulative Frequency Kekerapan Longgokan Upper Boundary Sempadan Atas 20 29 0 0 29.5 I 30 39 2 2 39.5 II 40 49 3 5 49.5 III 50 59 8 13 59.5 IV 60 69 10 23 69.5 V 70 79 11 34 79.5 VI 80 89 4 38 89.5 VII 90-99 2 40 99.5 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) * * * * * * * ( 34 5 2) + ( 44 5 3) + ( 54 5 8) + ( 64 5 10) + ( 74 5 11) + ( 84 5 4) + ( 94 5 2) 2+ 3+ 8+ 10+ 11+ 4+ 2 * * * * * * * Note : 1. Allow * midpoint for K1 2. Allow two mistakes for the multiplication of midpoint and * frequency, for K1 K2 65 75 Note : Correct answer from incomplete working, award Kk2 e.g. 2630 = 65 75 (without table) 40 N1 3 1449/2(PP) http://edu.joshuatly.com/ SULIT
SULIT 13 1449/2(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 12 1449/2(PP) http://edu.joshuatly.com/ [Lihat halaman sebelah SULIT
SULIT 14 1449/2(PP) Frequency 45 40 35 30 25 20 15 10 5 0 29.5 39.5 49.5 59.5 69.5 79.5 89.5 99.5 Marks 1449/2(PP) http://edu.joshuatly.com/ SULIT
SULIT 15 1449/2(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) http://edu.joshuatly.com/ [Lihat halaman sebelah SULIT
SULIT 16 1449/2(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 K1K1 3 1449/2(PP) http://edu.joshuatly.com/ SULIT
SULIT 17 1449/2(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 K1K1 4 1449/2(PP) http://edu.joshuatly.com/ [Lihat halaman sebelah SULIT
SULIT 18 1449/2(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 K1K1K1 5 12 1449/2(PP) http://edu.joshuatly.com/ SULIT
SULIT 19 1449/2(PP) Question Solution and Mark Scheme Marks 16 (a) (75 S, 100 E) // (75 S, 100 T) P3 3 Note: 1. 100 E or 100 T, award P2 2. 100 or E or T, award P1 (b) 6420 60 or 107 K1 6420 75 60 32S K1 N1 3 (c) ( 80 + 20) 60 cos 75 or 100 60 cos 75 Note: ( 80 + 20) or 100 or using cos 75 correctly, award K1 K2 1552 91 N1 3 (d) 180 60 550 or equivalent K2 Note: ( 180 60) * 550, award K1 19 64 hours or 19 hours 38 minutes N1 3 12 END OF MARK SCHEME 1449/2(PP) http://edu.joshuatly.com/ [Lihat halaman sebelah SULIT