SULIT PROGRAM GEMPUR KECEMERLANGAN SIJIL PELAJARAN MALAYSIA 08 NEGERI PERLIS SIJIL PELAJARAN MALAYSIA 08 MATEMATIK TAMBAHAN Kertas Peraturan Pemarkahan Ogos 47/(PP) UNTUK KEGUNAAN PEMERIKSA SAHAJA Peraturan pemarkahan ini mengandungi 6 halaman bercetak [Lihat halaman sebelah 47/ 08 Program Gempur Kecemerlangan SPM Negeri Perlis SULIT
SULIT 47/ (a) PR = PO + OR or OQ = OP + PQ (i) PR = a + 9b N (ii) OQ = a + 6b N (b) OT = OP + PT = OP + k PR = a + k *( a + 9 b) = (* k) a + *9kb OQ = λot or OQ = λtq or OT = λtq Collinear *(a + 6 b) = λ (* k) a + *9kb *(a + 6 b) = (* k)λ a + *9kλb * = λ(* k) or *6 = *9kλ * * λ= or λ= * k *k Equate the coefficients of a and b and solve simultaneous equations for k * * = (* k) or *6 = *9k *k * k k = N 6 5 47/ 08 Program Gempur Kecemerlangan SPM Negeri Perlis SULIT
SULIT 47/ h( x) = ax + x + 5 h( x) = a x + x + + 5 a 4a 4a h( x) = ax + + 5 4a 6a At maximum point, 00 x = = 00 P = 00, a = N 4a 400 Height of the highest pole = + 5 6 400 = 0m N OR h( x) = ax + x + 5 At maximum point, 00 x = = 00 P b x=, x= = a a 4a = 00, a = N 4a 400 Height of the highest pole, hx ( ) 400 = (00) + (00) + 5 = 0m N 5 5 [Lihat halaman sebelah 47/ 08 Program Gempur Kecemerlangan SPM Negeri Perlis SULIT
SULIT 4 47/ πx+ πy = 6π P and πx πy 4π + = P x= 8 y or y = 8 x P *(8 y) y 4 + = or x + *(8 x) = 4 Solve the quadratic equation ax + bx + c = 0 for b 0 Factorisation ( y )( y 5) = 0 or ( x )( x 5) = 0 OR Formula ( 8) ( 8) 4()(5) y = or () x = () ( 8) ( 8) 4()(5) a, b, c must correct y =, 5 or x =, 5 N cm and 5 cm N 7 7 4(a) x x Ahmad Luqman 5.+ 48. + 5.0 + 47.+ 45.0 + 5.4 = or 6 5.+ 48. + 5.0 + 47.+ 45.0 + 5.4 = 6 x Ahmad = 49.7 or x Luqman = 49.4 N 4666.98 σ *(49.7) 6 Ahmad = or 4698.4 σ *(49.4) 6 Luqman = σahmad =.665 N and σluqman =.54 N 5 47/ 08 Program Gempur Kecemerlangan SPM Negeri Perlis SULIT
SULIT 5 47/ 4(b) Luqman N Luqman s achievement is more consistent N 7 5(a) Use cos( A B) = cos Acos B sin Asin B cos x cos x sin xsin x or 4 4 4 4 cos x+ x 4 4 LHS = RHS N (b)(i) y 0 x Shape of positive cosine graph at least cycle P cycles for 0x π P Modulus of cosine graph for 0x π P (Maximum =, Minimum = 0) (ii) y = x or Implied N 5π Sketch the straight line with *gradient or *y-intercept and straight line involves x and y must be correct. of solutions = 5 N 8 [Lihat halaman sebelah 47/ 08 Program Gempur Kecemerlangan SPM Negeri Perlis SULIT
SULIT 6 47/ 6(a) Find δ y δx δy 6xδx + (δ x) = or δx δx δy 6x δx δx = Use limit δx 0 δy lim * = 6x δx δx 0 dy 6x dx = N (b) Solve dy * 0 dx = *6x = 0 x= 0, y = (0, ) N (c) d y d 6 0 x = (0, ) is minimum point N 7 7(a) dy = x dx or dy x dx = y 6 = *( x ) y = x+ N 47/ 08 Program Gempur Kecemerlangan SPM Negeri Perlis SULIT
SULIT 7 47/ 7(b) Find the area of rectangular shape OR Integrate 4 d x + x A = 6 OR A x = + x 6 4 Use limit 0 x into * + 4x 6 A = 9 * A * A * *9 8 N x= y 8 P Integrate ( y 8) (y 8) dy OR Use limit 6 (y 8) into* 4 8 N 4 (c) Use π x dy and integrate with respect to y 6 Use limit y into* 8y 4 y π 8y 4π N 0 [Lihat halaman sebelah 47/ 08 Program Gempur Kecemerlangan SPM Negeri Perlis SULIT
SULIT 8 47/ 8 (a)(i) Use 0 r 0 r C r (0.65) (0.5) Write P( X = 8) + P( X = 9) + P( X = 0) P 0.66 N (ii) σ = 960(0.5)(0.65) 8.4 N (b)(i) 40 50 Z = 5 Find the probability in the correct region PZ ( * 0.667) 0.5 // 0.59 // 0.54 N (ii) Find the probability in the correct region P( Z 0.667) P( Z ) 0.95 // 0.964 // 0.96 *0.95(7) 6 N 0 9(a) x 5 6 9 0 log0 y 0.7 0. 0.5 0.09 0.6 0. N (b) Plot log0 y against x (Correct axes and uniform scales) 6 *points plotted correctly N Line of best fit (Refer graph on page 5) N 47/ 08 Program Gempur Kecemerlangan SPM Negeri Perlis SULIT
SULIT 9 47/ 9 (c)(i) y ( ) h log = log q x + log P 0 0 0 Use * m= log0 q q =.9 N h (ii) Use * c = log0 h = 7.96 N (iii).95.00 N 0 0 (a)(i) p = 4 N (ii) Use m m = JK m = KL KL m JK = y 5 = * ( x ) or y *4 = * ( x 6) y = x+ 6 or equivalent N (iii) 6 0 A = 5 *4 4 5 (* 84 + 0) (0 + 0 4) 0 N [Lihat halaman sebelah 47/ 08 Program Gempur Kecemerlangan SPM Negeri Perlis SULIT
SULIT 0 47/ 0 (b)(i) Use distance formula for WJ or WK WJ x y = ( ) + ( 5) or WK = ( x 6) + ( y 4) OR WJ = WK or Implied x y 4x y 74 0 + + = or equivalent N (ii) stitute x = 0 into the locus of *W and use b 4ac ( ) 4()(74) 604 0 Locus W not intersect the y-axis N 0 (a) θ Use r sin OR other valid method 40 (7) sin 4.79 // 4.788 N 80.4 (b) A = 7 80 * A + * A 0.4 OR A = *4.79 80 9.78 + 8.9 8.6 // 8.7 N 47/ 08 Program Gempur Kecemerlangan SPM Negeri Perlis SULIT
SULIT 47/ (c) 0.4 A = (*4.79) 80 OR A 40.4 80 = (7) (7) sin 40 A = * A = * A * A 4 * A (* A ) 4 4.0 4.4 N 5 0 (a) x 60 N y 50 N 0x+ 0y 500 N x y N 4 (b) Draw correctly at least one straight line from the *inequalities involves x and y Draw correctly all four *straight lines Note: Accept dotted lines Region shaded correctly (Refer graph on page 6) N N (c) Minimum point (0, 0) N stitute any points in shaded *region into 8 000x+ 4 000y 60 000 N 0 [Lihat halaman sebelah 47/ 08 Program Gempur Kecemerlangan SPM Negeri Perlis SULIT
SULIT 47/ (a)(i) ACB = 58 P AP + 4 = sin 58 sin 85 5.94 // 5.944 N (ii) PQ = + 4 ()(4) cos 7 8.6 N (b) A = ( + *5.94)(4)sin 7 OR A = ()(4)sin 7 * A * A 4. 4.5 N (c)(i) 7 Note: A' C' B' obtuse angle N (ii) A' C' B' = N 0 47/ 08 Program Gempur Kecemerlangan SPM Negeri Perlis SULIT
SULIT 47/ 4(a) stitute t = 5 and v = 0 5m+ 5n= 0 or 5m+ n= 0 Differentiate dv a = dt mt + nt w.r.t t a = mt + n stitute t = and a = into dv * d t m+ n= Solve simultaneous equation to find m and n m = N n = 5 N 5 (b) *( t + 5 t) 0 0t 5 N (c) Integrate *( + 5 )d t t t t 5t s = + Use * st= * st= OR *( + 5 )d t t t () 5() () 5() + + 5 6 // 6 // 5.67 N 0 [Lihat halaman sebelah 47/ 08 Program Gempur Kecemerlangan SPM Negeri Perlis SULIT
SULIT 4 47/ 5(a) 900 00 0 P = 5 000 N I6/5 I8/6 (b) Use I6/5 = 00 08, 47, 56, 5 N (All correct) N (Only correct) (c)(i) W = 600 : 400 : 00 : 00 or Implied (seen) P I 8/5 *600(*08) + *400(*47) + *00(*56) + *00(*5) = *600 + *400 + *00 + *00 0.7 // 0.67 N (ii) P8 00 = *0.7 900 000 7 40 N 0 47/ 08 Program Gempur Kecemerlangan SPM Negeri Perlis SULIT
SULIT 5 47/ Graph for Question 9(b) 0.6 0.5 0.4 (, 0.7) 0. 0. (5, 0.) (6, 0.5) 0. 0 4 6 8 0 4 0. (9, 0.09) 0. (0, 0.6) 0. (, 0.) 0.4 [Lihat halaman sebelah 47/ 08 Program Gempur Kecemerlangan SPM Negeri Perlis SULIT
x = 60 SULIT 6 47/ y (Factory T) Graph for Question (b) 80 70 60 50 y = 50 40 0 (0, 0) R 0 0 0 0 0 0 40 50 60 70 x (Factory S) PERATURAN PEMARKAHAN TAMAT 47/ 08 Program Gempur Kecemerlangan SPM Negeri Perlis SULIT