1449/ (PP) Matematik Kertas Peraturan Pemarkahan Ogos 011 MAJLIS PENGETUA SEKOLAH MENENGAH NEGERI KEDAH DARUL AMAN PROGRAM PENINGKATAN PRESTASI SPM 011 MATEMATIK Kertas PERATURAN PEMARKAHAN UNTUK KEGUNAAN PEMERIKSA SAHAJA Peraturan pemarkahan ini mengandungi 18 halaman bercetak [Lihat halaman sebelah

Section A [ 5 marks] y 1 1 x = 5 10 y = x + 10 8 6 R 4 O 4 6 x Straight dotted line y = x correctly drawn. Region correctly shaded P Note: 1 Accept solid line y = x for Award to shaded region bounded by two correct lines, including part of R. (Check one vertex from any two correct lines

(a) AMB or BMA (b) Sin 5 AMB = 1.6 or 7 ' x 10x 8 = 0 or equivalent ( )( ) x + x 4 = 0 or equivalent OR ( 10) ± ( 10) 4()( 8) x = () () x = or 0 67 x = 4 4 Note : 1. Accept without = 0.. Accept three terms on the same side, in any order. x x with. Accept + ( 4) x =, 4 for Kk. 4. Accept correct answer from the correct term without factorisation for Kk. [Lihat halaman sebelah

4 4 4x 6y = 4 or 10 5 0 x y = or 6 x + y = or 5 5 5 1 x + y = or equivalent 4 Note : Attempt to equate one of the coefficients the unknowns, award 11y = or OR x = or equivalent x = y 6 or 1 5 x = y or 4 1 x y = or 4x y = or 5 equivalent () Note : Attempt to make one of the unknowns as the subject award. 11y = or equivalent () OR x 1 5 6 y = (1)(5) ( )(4) 4 1 (K) Note : Attempt to write without equation, award () x = y = Note : x = y as final answer, award 4

5 5 (a) 10 6 5 = 00 (b) 1 4 7 r 1 4 7 r + 10 6 5 = 4 56 7 4 Note : 1. Accept π for K mark.. Accept correct value from incomplete substitution for K mark. 6 (a) (b) (c) Some /Sebilangan PQRS is a trapezium / PQRS adalah trapezium / n +, n = 1,,,... (d) If m = 7 then m = // Jika m = 7 maka m = If m = then m = maka m = 7 // Jika m = 7 6 [Lihat halaman sebelah

6 7(a) 0 = x + 15 or equivalent 15 x = or Note: 1 7 or 7 5 1. Accept correct answer without working for. (b) m PQ = y 6 = x 1 * m PQ or 6 = * m QR (1) + c or equivalent y = x + 8 or equivalent 5 8 (a) (b)(i) (, Q), (4, R) (, R), (4, R) 9 (ii) (, Q), (4, Q), (7, P), (7, Q), (7, R) 5 9 5

7 9 (a) 180 14 or 60 7 45 14 60 7 180 14 + 60 7 8 45 14 + 7 +14 + 7 60 7 (b) 180 14 or 60 7 45 14 60 7 180 14 60 7 1 NOTE 45 14 or 60 7 15 14 60 7 6 1. Accept π for K mark.. Accept correct value from incomplete substitution for K mark.. Correct answer from incomplete working, award Kk. 10(a)(i) (ii) 0 9.0 a.m. / pagi or 090 (b)(i) (ii) 8 76 76 1 = (c)(i) (ii) 1 5 0 5 60 6 [Lihat halaman sebelah

8 11(a) (b) k =14 p = -4 x 4 = 4 1 y 1 x 1 1 4 inverse 4 = or y (1) ( )(4) 4 1 matrix 1 1 x = or 0.5 y = 1 6 Note: inverse 1. Do not accept * = matrix 4 1 inverse 1 0 or * = matrix 0 1. 1 x = y 1 as final answer, award. Do not accept any solutions solved not using matrix method

Section B 9 [ 48 marks] 1(a) 8 4 Note : K only meant for table value. (b) Graph Axes drawn in correct direction, uniform scales in x 4 and 4 y 4. All points and *1 point ( rd quadrant) and 4 Points and * 1 point (1 st quadrant) correctly plotted or curve passes through these points for x 4 and 4 y 4. (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 x 4 and 4 y 4. (depends on P and K) 5 Note : 1. 7 or 8 points correctly plotted, award.. Ignore curve out of range. (c)(i) (ii) 8 5 y 9 5 0 90 x 0 70 Note: 1. Allow P mark if value of x and y are shown on the graph.. Value of x and y obtained by calculation, award P0. (d) Straight line y = x + correctly drawn K Value of x : 1 70 x 1 90 1 Note : 1. Identify equation x + = or y = x + award x. Allow N marks if values of x shown on the graph.. Values x obtained by calculation, award N0. (dep K) 1 [Lihat halaman sebelah

10 Graph for Question 1 Graf untuk Soalan 1 y 5 0 y = 1 x 15 10 y = 9 5 y = x + x = 0 8 1 5 5 x = 1 0 1 4 x x = 1 8 x 1 y = x 10 y = 15 15 0 5

11 1 (a) (i) (1, 1) (ii) (1, ) Note : ( 4, 1) or point (1, ) or point ( 4, 1) marked, award P (b) (i) (a) U = Rotation 90 clockwise / 70 anticlockwise, about point (5, 1) or equivalent P Note : 1. Rotation 90 clockwise / 70 anticlockwise Rotation about point (5, 1), award P OR. Rotation, award (b) V = Enlargement with scale factor at centre L(7, 1) or equivalent P Note : 1. Enlargement with scale factor or Enlargement at centre L(7, 1), award P. Enlargement, award (ii) * 5 5 5 5 K Note : * 5 5, award 76.5 9 1 [Lihat halaman sebelah

1 14(a) (i) Weight Berat Midpoint Titik Tengah Frequency Frekuensi 0 9 4 5 I 40 49 44 5 6 II 50 59 54 5 7 III 60 69 64 5 10 IV 70 79 74 5 8 V 80 89 84 5 4 VI 90 99 94 5 VII Frequency : (I to VII) Class interval : (II to VII) Midpoint : (I to VII) Note : Allow one mistake in frequency for (ii) 4 5 + 44 5 6 + 54 5 7 + 64 5 10 + 74 5 8 + 84 5 4 + 9 + 6 + 7 + 10 + 8 + 4 + 580 40 = 64 5 P K 4 (b) Axes drawn in the correct direction with uniform scale for * 4 5 x 94 5 and 0 y 10 Horizontal axes labeled with values of midpoint / upper boundry / Class interval *7 points correctly plotted Note : *5 or *6 points correctly plotted, award K Frequency polygon passes all 9 correct points. 4 (c) 15 1 1

Frequency 1 10 9 8 7 6 5 4 1 0 4.5 4.5 44.5 54.5 64.5 74.5 84.5 94.5 K 104.5 Weight [Lihat halaman sebelah

14 15 Note : (1) Accept drawing only (not sketch). () Accept diagrams with wrong labels and ignore wrong labels. () Accept correct rotation of diagrams. (4) Lateral inversions are not accepted. (5) If more than 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. 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 4cm, deduct 1 mark from the N mark obtained. (ii) If > 0 4cm, 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.

15 15(a) H G B C Correct shape with trapezium BCHG All solid lines HC > GH > BC > GB dep Measurement correct to ± 0 cm (one way) and all angles B, C = 90 ± 1 dep [Lihat halaman sebelah

16 15(b)(i) Q P E H K F G Correct shape with rectangle EFGH and PQEK All solid lines PQ > KQ > GH > FG > HK > KP dep Measurement correct to ± 0 cm (one way) and all angles at the vertices of rectangles = 90 ± 1 N dep 4

17 15(b)(ii) E H F M G L K A B J Correct shape with rectangle ABHE and FGHE, square ABGF and BJKL All solid lines Note : Ignore straight line ML Dashed line ML dep AJ = AE > AF = AB > HG = BJ = JK dep Measurement correct to ± 0 cm (one way) and all angles at the vertices of rectangles = 90 ± 1 N dep 5 1 [Lihat halaman sebelah

18 16(a) (40 o S, 70 o E) P Note : 1. 70 o E or 70 o T award P. 70 o or E or 70 o or T award (b)(i) (5 + 40) 60 4500 (ii) (80 + 70) 60 cos 40 K 6894.40 or 6894 Note: 80 +70 or cos 40 correctly used, award (c) 180 60 cos 5 K Note : Usage of cos 5, award 180 60 cos 5 600 14.74 4 1 END OF MARK SCHEME