spm pahang math p2 2010 ans

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SULIT 1449/2 1449/2 Matematik Kertas2 Peraturan Pemarkahan September 2010 PEPERIKSAAN BERSAMA SEKOLAH-SEKOLAH NEGERI PAHANG 2010 PEPERIKSAAN PERCUBAAN SPM 2010 MATEMATIK Kertas 2 PERATURAN PEMARKAHAN Peraturan pemarkahan ini mengandungi 12 halaman. [Lihat sebelah 1449/2 SULIT Jumlah Markah = 1 2100%140Kertas Kertas + 2 Section A [ 52 marks ] No Marking Scheme Marks 1 a. b. P1 P2 3 3 No Marking Scheme Marks 2 (a) 12 10 631 240 (b) 840 12 10 12 10 631= + GC GC = 5 K1 N1 K1 N1 4 3 Identify Z EAD or ZDAE or angle marked on the diagram correctly tan Z EAD = 123 or equivalent 14.04o or 14o 2' P1 K2 N1 4 4 (a) False (b) Implication 1: If m > n then m 3 > n 3 Implication 2 : if m 3 > n 3 then m > n (c) Conclusion : 4n + n3 , where n = 1,2,3,4, .. P1 P1 P1 P1P1 5 5 2x + 3y = 6 or x 41y = 4 or equivalent 7y = 28 y = 4 x = 3 K1 K1 N1 N1 4 4 No Marking Scheme Marks 6 (a) y = 4 (b) Gradient of JK = 21or the gradient being used c + = ) 5 (213 or 21) 5 () 3 (= xy 2121 = x y or equivalent yintercept = 21 P1 P1 K1 N1 P1 5 7 0 10 32= + x x 0 ) 2 )( 5 3 ( = + x x 2 = x 35= x or 67 . 1 = x K1 K1 N1 N1 4 8 p =3 , k = 10 1 3 62 4 3mn | || | | |= | | |\ .\ . \ . 4 3 612 1 3 4 6mn| | | || |= | | | +\ . \ .\ . 3232mn| | || | = | |\ . | |\ . m = 32 , n = 32 Notes: 1. 3232mn| | || | = | |\ . | |\ . : N1 2. Solution without using matrices method cannot be accepted. P1P1 P1 K1 N1,N1 6 5 No Marking Scheme Marks 9 (a) 12722236040 or 13722236090 12 5 13 1372223609012722236040+ + + + 81 . 58211758 = (b) 12 1272236040 or 13 1372236090 13 137223609012 1272236040 + 07 . 183141183 = K1 K1 N1 K1 K1 N1 6 10 a) (S,A) (S,T) (S,U) (A,S) (A,T) (A,U) (T,S) (T,A) (T,U) (U,S) (U,A) (U,T) b) (i) (T,S) (T,A) (T,U) 41123or (ii) (S,A) (S,U) (A,S) (A,T) (T,A) (T,U) (U,S) (U,T) 32128or P1 K1 N1 K1 N1 5 11 (a) 45 (b) (i) 8.45 a.m (ii) 70 km (c) |.|

\|607590 72 P1 P1 P2 K1 N1 6 6 Section B [48 marks] No Marking Scheme Marks 12(a) (b) (c) (d) 8 -16 Graph Axes are drawn in the correct direction, uniform scale for 4 s x s 4 and 24 s y s 24 7 points and 2 points* plotted accurately Smooth and continuous curve without straight line(s) and passes through all the 9 correct points for 4 s x s 4 Notes : (1) 7 or 8 points plotted correctly, award K1 (2) Other scale being used, subtract 1 mark from the KN marks obtained. -8.0 < y < -9.0 1.8 < x < 1.9 Note : Do not accept the values of x and y obtained by calculation Identify the equation y = -2x+1 or equivalent The straight line y = -2x+1 drawn correctly The values of x : 3.6 < x < 3.7 -3.3 < x < -3.1 Notes : (1) Award N mark(s) if the value(s) of x shown on the graph (2) Do not accept the value(s) of x obtained by calculation K1 K1 K1 K2 N1 P1 P1 K1 K1 N1 N1 12 7 No Marking Scheme Marks 13 (a) (b) i) (1 , 8) Notes : 1. (2, 6) : P1 2. Accept answers without bracket. ii) (7 , 5) Notes : 1. (8, 3) : P1 2. Accept answers without bracket. i) (a) V : Enlargement with scale factor 21 centered at point (1, 2). (b) W : Reflection in the line 3 = x Notes: 1. Enlargement, scale factor 21 or Enlargemant at point (1, 2).: P2 2. Enlargement only : P1 3. Reflection only : P1 ii) 22 20.4 or equivalent 22 20.4 20.4 61.2 P2 P2 P3 P2 K1 K1 N1 12 8 No Marking Scheme Marks 14(a) (b) (c) Marks Upper Boundary Frequency Cumulative Frequency 6 - 10 10.5 0 0 11 - 15 15.5 1 1 16 - 20 20.5 3 4 21 - 25 25.5 6 10 26 - 30 30.5 10 20 31 - 35 35.5 11 31 36 - 40 40.5 7 38 41 - 45 45.5 2 40 Column I (all class interval correct) Column II (all upper boundary correct) Column III (all frequency correct) Column IV(all cumulative frequency correct) Note : Allow two mistakes in column III for P1 Ogive Axes are drawn in the correct direction, uniform scale for 10.5 s x s 45.5 and 0 s y s 40 The horizontal axis labeled with upper boundary or use the values of upper boundary for plotting Plot 7 points* Smooth and continuous curve without straight line(s) and passes through all the 8 correct points for 20.5 s x s 55.5. Notes : (1) 5 or 6 points* plotted correctly, award K1 (2) Mark(s) for plotting can be given to a curve which passes through 7 points* and point (10.5, 0) (3) Other scale being used, subtract 1 mark from the KN marks obtained. First Quartile = 25.5 or Third Quartile = 35 0.5 Interquartile range = 35 25.5 = 9.5 0.5 P1 P1 P1 P1 K1 K1 K2 N1 K1 K1 N1 12 9 No Marking Scheme Marks 15 (a) Correct shape with rectangles VUKJ and GKMB. All solid lines. Note: Ignore straight line JR J and R joined with dashed line to form rectangle JRBG GJ = VU = KM > UK The measurement is accurate to 0.2 cm. (one way ) and the angles at all verticals of the rectangle are 90 1 K1 K1 K1 N1 U K R M B G J V 10No Marking Scheme Marks (b) (i) Correct shape with rectangles ADEF and IULF. All solid lines. Semicircle VSU drawn FL> UL > DE=AD The measurement is accurate to 0.2 cm. (one way ) and the angles at all verticals of the rectangle are 90 1 K1 K1 K1 N1 11No Marking Scheme Marks (ii) Correct shape with rectangles USTN, NKLM and EFLH. All solid lines. Note: Ignore straight line HC H and C joined with dashed line to form rectangle HLMC ST = TM > LM > LF > FE = HK =US The measurement is accurate to 0.2 cm. (one way ) and the angles at all verticals of the rectangle are 90 1 K1 K1 K1 N1 12 U S C N ML F E T K H 12No Marking Scheme Marks 16. (a) (i) (ii) (b) (c) (d) 750N C(750N, 300E) 750N or 300E : P1 30 x 60 1800 n.m. 20x60xcos 750 : Award K1 for using cos 630 310.58 n.m. (75x2)x60 9000 310.58 + 9000 9310.58 1058 . 9310 931.058 P1 P2 K1 N1 K1K1 N1 K1 K1 K1 N1 12 13Graph for number 12 Graph for number 14 14Graph for number 14 0 5 10 15 20 25 30 35 40 15.5 20.5 25.5 30.5 35.5 40.5 45.5 10.5