Negeri Sembilan SPM 2013

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1 SULIT 347/1 347/1 MATEMATIK TAMBAHAN KERTAS 1 OGOS 013 Jam NAMA : KELAS : PEPERIKSAAN PRASPM SEKOLAH-SEKOLAH MENENGAH 013 MATEMATIK TAMBAHAN Kertas 1 Dua Jam JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU Negeri Sembilan SPM 013 [Lihat sebelah]

2 SULIT 347/1 INFORMATION FOR CANDIDATES MAKLUMAT UNTUK CALON all semua one satu Negeri Sembilan SPM 013 [Lihat sebelah]

3 SULIT 3 347/1 ALGEBRA CALCULUS / KALKULUS Negeri Sembilan SPM 013

4 SULIT 4 347/1 STATISTICS / STATISTIK GEOMETRY / GEOMETRI Negeri Sembilan SPM 013

5 SULIT 5 347/1 TRIGONOMETRY / TRIGONOMETRI θ j θ [Lihat sebelah] Negeri Sembilan SPM 013

6 SULIT 6 347/1 Negeri Sembilan SPM 013 [Lihat sebelah]

7 SULIT 7 347/1 all semua 1 1 Negeri Sembilan SPM 013 [Lihat sebelah]

8 SULIT 8 347/1 3 3 Negeri Sembilan SPM 013 [Lihat sebelah]

9 SULIT 9 347/ Negeri Sembilan SPM 013 [Lihat sebelah] 5

10 SULIT /1 6 6 Negeri Sembilan SPM 013 [Lihat sebelah]

11 SULIT / Negeri Sembilan SPM 013 [Lihat sebelah] 8

12 9 SULIT 1 347/ Negeri Sembilan SPM 013 [Lihat sebelah]

13 SULIT / [Lihat sebelah] Negeri Sembilan SPM 013

14 13 SULIT /1 13 Negeri Sembilan SPM 013 [Lihat sebelah]

15 SULIT / sin x = k, 90 sin x = k, 90 Negeri Sembilan SPM 013 [Lihat sebelah] 14 15

16 SULIT /1 16OA =4i 3jOB = i+j OA = 4i 3jOB = i + j AB AB 16 Negeri Sembilan SPM 013 [Lihat sebelah]

17 SULIT /1 17 Negeri Sembilan SPM 013 [Lihat sebelah] 17

18 SULIT / Negeri Sembilan SPM 013 [Lihat sebelah]

19 SULIT / Negeri Sembilan SPM 013 [Lihat sebelah] 19 0

20 SULIT 0 347/1 1 f(x)dx =3 f(x)dx =3 1 f(x)dx (x f(x))dx Negeri Sembilan SPM 013 [Lihat sebelah]

21 SULIT 1 347/1 P Q R S T Negeri Sembilan SPM 013 [Lihat sebelah]

22 SULIT 347/1 3 3 Negeri Sembilan SPM 013 [Lihat sebelah]

23 SULIT 3 347/1 4 4 Negeri Sembilan SPM 013 [Lihat sebelah]

24 SULIT 4 347/1 5 5 END OF QUESTION PAPER KERTAS SOALAN TAMAT Negeri Sembilan SPM 013

25 Negeri Sembilan SPM 013

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27 Negeri Sembilan SPM 013

28 Negeri Sembilan SPM 013

29 Negeri Sembilan SPM 013

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35 Negeri Sembilan SPM 013

36 Price (RM) for the year Ingredient Price index based on the year Weightage Negeri Sembilan SPM 013

37 Negeri Sembilan SPM 013

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40 Section A, Section B Section allsection AfourSection Btwo Section C Negeri Sembilan SPM 013

41 KEBARANGKALIAN HUJUNG ATAS Q BAGI TABURAN NORMAL Negeri Sembilan SPM 013

42 Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan. Negeri Sembilan SPM 013

43 Negeri Sembilan SPM 013

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45 Negeri Sembilan SPM 013

46 No. Suggested solution and marking scheme Sub Marks Total Marks 1. (a) 3. (b) 4 (c) many to many relation ( hubungan banyak kepada banyak ), m m, mm. ( a) 6 ( b) k 3 B1: k(6) + 3 = 7 or 6k = fg 1x 13 B: 6 ( x 3 ) B1: g x 3 3 p B: SOR 3 and B1: SOR 3 or 5. x, x 8 POR ( 3 ) POR ( 3 ) p (Both) or equivalent. p B: x - or 8-8 x B1: ( x )( x 8) 0 or ( x )( x 8) 0 6 (a) k = 8 (b) a = (c) x = x or x = 1.5 B: 3 4 x B1: Seen x or 3x or 3 or OR using logarithms method: equivalent. x = 1.5 (accept ) 4 3 or equivalent. B: (x+) x (0.4771) = or x =.86 B1: log10 3 x+ + log10 7 x = log ( (accept any base) Negeri Sembilan SPM

47 8. x 1 B: x 8 9 x or x + 8 = 9x or equivalent B1: x 8 x 8 log 3 or log 3 log 3 3 x x or 17 terms or n = 17 B1: 13 + (n 1)(5) = 67 or by listing method: (Must list all the terms and correct ) 13, 8, 3,, 7, 1, 17,, 7, 3, 37, 4, 47, 5, 57, 6, a, r or equivalent (Both correct ) 7 7 B : ar 3 4 and ar 6 (Both ) B1 : ar 4 or ar h = 41, k = B: S = or S = B1: r = 0.01 or or or S = or S = h =100, k = 7 (both ) B3: h =100 or k = 7 1 k 1 B: log 10 h or k (10) 3 or B1: log10 y log10 x log10 h accept Y X ( a ) x y 1 or equivalent 5 ( 6 ) (b) 10x + 1y + 11 = B: x 10x 5 y x y 1y 36 or equivalent B1: x 10x 5 y or x y 1y o, o or 41 49, B3 : sin x = 3, sin x = 4 ( both) 4 4 B : (3 sin x )(sin x + 4) = 0 B1 : 3( 1 sin x ) 10sin Negeri x+ 5 Sembilan = 0 SPM 013

48 15. (a) k (b) 1 k 0 0 B1: cos180 cos x sin180 sin x or cos x 16. (a) 5 5 i 4 j,accept 4 3 B1: 4 i 3 j i j or equivalent (b) 41 or (a) AC 6 a 4 b (b) 9 BD a b B: 1 3 6a ( 6 a 4 b ) or 4b ( 6 a 4 b ) 4 4 B1: 1 3 ( 6 a 4 b ) or ( 6 a 4 b ) (a) or 1 accept (b) B1 : or ( 6 x 1 ) dy B: 3 u 6 dx 4 dy or 1 (3)(6x 1) (6) dx 4 B1: 3 u 4 dy du or 6 du dx p 3 B: 6p(-1) 1 (-1) = 8 or equivalent B1 : dy dx dy 6 px 1x or 8 dx 3 3 Negeri Sembilan SPM 013

49 1. (a) (b) 1 3 x B : B1 : xdx f ( x) dx 1 4. (a) 4030 (b) 430 B1 : 3! or 6! or equivalent (a) B1 : (b) 35 B1 : k u 3 B : k = 4 3u 3 3 B1 : 10 ( 5 3 u ) 5 (a) B1 : (b) k = 0.39 B1 : 0.39 Negeri Sembilan SPM 013

50 SULIT 347/1 347/1 MATEMATIK TAMBAHAN KERTAS 1 OGOS 013 Jam PEPERIKSAAN PRASPM SEKOLAH-SEKOLAH MENENGAH 013 MATEMATIK TAMBAHAN / ADDITIONAL MATHEMATICS KERTAS 1 / PAPER 1 SKEMA PERMARKAHAN / MARKING SCHEME Negeri Sembilan SPM 013

51 PEPERIKSAAN PERCUBAAN / ADDITIONAL MATHEMATICS Kertas Ogos 1 jam. Duajamtigapuluhminit SKEMA PERMARKAHAN MATEMATIK TAMBAHAN KERTAS PEPERIKSAAN PRASPM TINGKATAN 5, 013 No Solution and mark scheme Sub Marks 1 y = x 4 Or y 4 P1 x = Full Marks (x 4) = 4(x+5) y = y 4 5 x 5 x 1 0 y y 8 0 Solve the equation x = ( 5) ( 5) ( 1 ) 4(1)( 1) x = 5.193, y= 6.386, Solve the equation ( ) ( ) 4(1)( 8) y = ( 1 ) y = 6.385, x=5.193, x = (a) (i) x 7x 1 0 ( x 3)( x 4) 0 x = 3, x = 4, since <, = 3, = 4. (ii) x 7x 1 0 ( x 3)( x 4) x 4 Negeri Sembilan SPM 013

52 No Solution and mark scheme Sub Marks Full Marks (b) 1 = 3 1 = 1 = (4) + 1 = 9. x x ( 9 ) x ( 9 ) 0 11x (a) T1 = 1 (160)(80) = 6400 T= 1600 T3=400 P1 r = 1 or P1 6 Tn> ( 0.5 ) n-1 > 30 log 6400 ( 0.5 ) n-1 > log 30 log log( 0.5 ) n-1 > log 30 log( 0.5 ) n-1 > log 30 log 6400 log 30 log 6400 n 1 < log 0.5 n < n = 4 listing method or 6400,1600,400,100, 5..all correct n = 4 Negeri Sembilan SPM 013

53 No Solution and mark scheme Sub Marks Full Marks (b) S = (a) LHS sin x sin xkosx tan x (b) y = - x x 8 Shape as in the above diagram Amplitude is 4 Number of cycle is 1 Modulus Equation of straight line y = x Straight line is drawn Number of solution 4 P1 P1 P1 Negeri Sembilan SPM 013

54 No Solution and mark scheme Sub Marks Full Marks 5 a) or b) i) ii) P1 8 Comparing,, 3 k 4 6 (a) (b) (i) 90 x // x x 0 Negeri Sembilan SPM 013 P1

55 No Solution and mark scheme Sub Marks Full Marks (ii) x = 4 // (a) (b) Plot x log 10 y log y against x (Correct axes and uniform scales) points are correctly plotted. Note: 5 or 4 points correctly plotted Award 1 mark N Line of best fit (c) (i) log10 y (log10 t ) x log10 s Use c log10 log 10 s 0.6 s s = P1 (ii) Use m log10 t log 10 t t Negeri Sembilan SPM 013

56 No Solution and mark scheme Sub Marks 8 dy a) x 4, dx Full Marks y 9 = 4 (x 4) y = 4x 7 b) Area Area x under curve 4 1 dx 0 3 x = 6 x 4 0 = // // Area = = or 18 or c) Volume y dy 15 (a) kos = = y y 9 1 = = 96 SOT = 60 SOT = rad (b) Lengkok ST = (1.047)(15) = ST=TR PT=TQ PT = = Negeri Sembilan SPM 013

57 No Solution and mark scheme Sub Marks Full Marks Perimeter kawasan berlorek =ST + TR + RQ + TQ +SP + PT = = (c) Luassektor OST = 1 (15) (1.047) Luas SOT = luas OTR = Luassegitiga OPQ = (5.981) 15 = Luasakawasanberlorek = luas OPQ (luas OST) = ( ) = (a) or = 8 unit (b) = (-1, 3) (c) P1 10 or Negeri Sembilan SPM 013

58 No Solution and mark scheme Sub Marks (d) Use PA = 5 P1 (x - 3) (y 5) = 5 Full Marks x y 6x 10y (a) (i0 p = 10 1 // 0.1, q = 10 9 // 0.9 P ( X 3 ) C3 = (ii) P ( X ) 1 [ P ( X 0) P ( X 1) P ( X )] C C C or = P1 10 (b) (i) z 0. 5 P or P z // (ii) Seen m m =.8075 P1 Negeri Sembilan SPM 013

59 No Solution and mark scheme Sub Marks Full Marks 1 (a) a = 9 4 t = 0 9 t= V mak V mak 10 or or (b) 9t s t 3 3 c t =, s 1 // 3 1 ort = 3, s // d s 3 s 5 9 // 9.83 m 6 38 // //.5 9t t (c) s t = 0 7 t // 6.75 s 4 (d) v 9 t t t // 4.5 s Negeri Sembilan SPM 013

60 No Solution and mark scheme Sub Marks Full Marks 13 (a) Q Guna I = Q 0 p= 1.60, q = 1.10, r = 160 P1P1P1 (b) I = 11(400) 15(00) 110(150) 160(50) = 16.3 (c) Q Q13 = (d) = Negeri Sembilan SPM 013

61 No Solution and mark scheme Sub Marks 14 (a) Full Marks // (b) Draw a line correctly Draw all the lines correctly Correct region R (c) (i) 350 (ii) Profit P = 1x + 15y Maximum point ( 0, 450 ) Maximum profit = 1 ( 0 )+15( 450 ) = RM (i) PR (8)(18.4) kos = (ii) 0 sin PRQ sin107 0 PRQ 0.97 (b) Q P 10 R QPR = ' PQP (5.03) Negeri Sembilan SPM 013

62 No Solution and mark scheme Sub Marks = Full Marks ' 0 0 QP R QR sin QR = sin Luas P ' QR = 1 = sin Negeri Sembilan SPM 013

63 Graf Q7 log10 y Plot lg y against x (Correct axes and uniform scales) P points are correctly plotted N or 5 or 4 points correctly plotted 1.6 Line of best fit x Negeri Sembilan SPM 013

64 Q14 y R x Negeri Sembilan SPM 013

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