Spm Trial 2012 Addmath a Pahang

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PEPERIKSAAN PERCUBAAN SPM TAHUN 2012MARKING SCHEME FOR ADDITIONAL MATHEMATICS FORM 5 PAPER 1 NO. MARKING SCHEME MARKS FULL MARKS1 a) p, qb) 2c) many to many11132 -11f (-6) = 2 (-6) + 1 @ fg (-2) = 11 2 -2 - 6 -++ g(-2) = -6 @ fg (x) =113 -2 +1]1

+ x x3B2B133) 3 ( 25+ x, 3 x5 = ) 3 ( + x2y or y = 6 25+ x2B124k = - 50 ) 1 )( 1 ( 4 ) 4 (2 k1 42+ + x k x3B2B135213 - x ( ) ( ) 0 3 1 2 + x x3B2B136and x31 5 x5 ) )( 14 3 ( + x x1 ) )( 14 3 ( log5 + x x3B2B13-321http://www.chngtuition.blogspot.com731 - x81x - 5+ x31x - 5log2 1]1

+ xChange base: 2 log 2x) - 5 ( log 2224B3B2B148 a) p=2b) 9c)1 a 11139 a) -8 P 2 - ( - 6 ) = -14 - ( p 2 ) @ 2 - p214 - 6 -+ b) 126[ ] ) 4 ( 6 ) 6 ( 2277 + Sd = -10 ( - 6 ) = -42B12B2B1410128( )

,_

21164S21 r3B2B1311 h =5 and h=15h =5 or h=1540 3 32 35 8 16 h 5 16 - 21 - + + + + h3B2B1312 r =1 1http://www.chngtuition.blogspot.com21t 5) ( 1 ) 4 ( 43 rr + or 5) 8 ( 1 ) ( 42 + t1B1313 b~ ~6 a 4 PR QP QR + 2B121429013 11 i j +% %3 ( j i 7 3 + ) - 2( j i 5 2 + )3B2B13153 +x xy3 1 + xyxm = 1 21 2x x y y = 1330 33 6 or c = 33 B2B1316a)t t21Cot = n ta1b)21 t 2 B11317a)3b) 60 ,131.81 , 228.19 , 300 ( 2 cos 3 + )( 1 cos 2 ) = 03 ( 1 cos 22 ) + cos + 1 = 013B2B14http://www.chngtuition.blogspot.com18 a) rad 2 b) 32cm r =4 or 8 ) 2 ( 4AB S 2r = ( 8 r ) 213B2B1419 k = 17h = - 84 x + h = 0h xdxdy+ 44B3B2B1420 5 = 1]1

1 1 3 - 4 10 - 3 - 5 10 - = 541 1 1) 3 x 101]1

3B2B1321 a) 36.6(16.8 X 2) + 3 b) 52B11322a) 88P = 40320b) 4320=66P X 23P 23P13B2B1423 BJ'L =154)32)(53)(32( 1http://www.chngtuition.blogspot.com =4519 =4544534512+ + = )52)(31)(32( )31)(53)(31( )32)(53)(32( + + BJ'L + LJ'B+ BL'J3B2B1424n = 820pq n2 196.8 = n (0.4)(0.6)P=0.4 or q=0.63B2B13250.2580=0.5 0.1612 -0.0808 0.08083B2B13( ) f zz0 1.4 m0.16120.08080.5 0.1612 -0.0808http://www.chngtuition.blogspot.com3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING No. QuestionPERATURAN PEMARKAHANTOTAL MARKS1224 3 5 or 2 3 3 5 or 4 3 2 3 3x y x y xyx y x y xy+ + + +5 34 yx OR 5 43 xy * 2 *5 3 5 32 3 3 54 4y yy y 1 1 + 1 1 ] ] OR * *25 4 5 42 3 3 53 3x xx x 1 1 + 1 1 ] ]23 8 5 0 y y + + ( ) ( ) 3 5 1 0 y y + + or 2(8) (8) 4(3)(5)2(3)y t OR22 9 10 0 x x + ( ) ( ) 2 5 2 0 x x or 2( 9) ( 9) 4(2)(10)2(2)x t 5 , 13y y 5 , 22x x 11111162(a)242 p or ( ) 2 4 4 k + 10 p 4 k (b)4 4 x y ( )144yf y (c) ( )12 2 f g 11111161 SULIThttp://www.chngtuition.blogspot.com3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING 3 y = 32x - 2y = - 2 cos 32 x- 222yx(a) Draw cosine shape Negative cos 1.5 cycle Amplitude 2(b) Equation : 322y x Draw line 322y x No of solutions : 3111111174 (a) 2 or 2 a r ( ) ( )782 2 T 256(b) ( )10102 2 12 1S 106428.532 cm S RM 64. 2911111162 SULIThttp://www.chngtuition.blogspot.com3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING 5(a)12DEBm 192y x +(b)19 2 62 x x + ( ) 6, 6 B(c) ( ) ( ) ( ) ( ) 0 2 6 1 9 2 6 1,3 3E + + _ ,( ) 2, 8 E(d) ( ) ( ) ( ) ( )2 2 2 26 6 0 9 x y x y + + 4 2 3 0 x y + 1111111186 (a) 4 m (b) (i) 10 112+ Median 10.5 (ii) 22078 fx or 323x 22078 3218 3 _ , 1.291 (c) New median 13.5 111111173 SULIThttp://www.chngtuition.blogspot.com3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING 7 a)2yx114 99 85 68.75 53 38.89b) Plot 1 point and use a correct scalePlot all points correctlyLine of best fitc)2yhx kx (i) h m 5 h (ii)int k y 128 k (iii)931 y 1111111111108(a)4cos7AOD 55.15 AOD 0.963 AOD rad(b) ( )*4 0.963 BD 2 27 4 or 5.745 AD AD Perimeter ( )*4 0.963 5.745 3 + +12.597 cm(c) ( ) ( )* 1Area 5.745 4 or 2AOD ( ) ( )2 * 1Area sector BOD 4 0.9632111111114 SULIThttp://www.chngtuition.blogspot.com3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING Area ( ) ( ) ( ) ( )* 2 * 1 15.745 4 4 0.9632 2 3.786 cm211109(a) (i) DE DA AE +uuur uuur uuur (ii) CG CA AG +uuur uuur uuur8 4 DE q p +uuur% % 5 2 CG q p +uuur% %(b) (i) 4 BE q p +uuur% % 4 BF nq np +uuur% %(ii) 5 2 CF mq mp +uuur% %(c) BF BC CF +uuur uuur uuur( )4 4 5 2 nq np q mq mp + + +% % % % % Sub 2 m n in 4 5 n m 49n 89m 11111111111010(a)23 3 x x x + ( ) ( ) 3 1 0 x x + + ( 1, 2) P ( 3, 0) Q 1115 SULIThttp://www.chngtuition.blogspot.com3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING (b) Area ( ) ( )12 22 or 2 332 3x x 1 1 ]Sub limit 0 and 2 3*31 in 2 3x x 1 1 ]Total area ( ) ( )2 31 32 22 2 3x x 1 + 1 ]196 unit2(c) ( )22 23 y x x Volume ( )02 3 439 6 x x x dx + +4 53332 5x xx 1+ + 1 ]Use limit 0 and *3 in 04 533332 5x xx 1+ + 1 ]8.1 unit211111111011 (a)(i) 0.3 and 0.7 p q ( ) ( )2 462( 2) 0.3 0.7 P X C 0.3241 (ii) ( ) 3 P X < ( ) ( ) ( ) ( ) ( ) ( )2 4 1 5 0 66 6 62 1 00.3 0.7 0.3 0.7 0.3 0.7 C C C + + 0.7443(b) (i) ( ) 0.55 P z < 29.12 %11111116 SULIThttp://www.chngtuition.blogspot.com3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING (ii) ( ) 0.4 P z k > 0.253 z 38.20.2534k 39.21 k 1111012(a)12/106.501005.00I 130(b)116.67PI or 120QI or 125RI Note: all correct 2, one or two correct 1.116.67(30) 120(50) 125(70) 130(20)30 50 70 20I + + ++ + +122.65(c)12100 122.6540P RM 49.06(d) 12/ 08115120100I 1381121111111013(a) ( ) ( )134 8 9 sin2 QPS 70.81 QPS (b) ( ) ( ) ( )2 28 9 2 8 9 cos 70.81 QS + 9.883 cm QS 11117 SULIThttp://www.chngtuition.blogspot.com3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING (c) Use 109.19 QRS sin sin109.196 9.883SQR 35.82 QSR (d) Area ( ) ( )19.883 6 sin35.822QSR Area PQRS ( ) ( )19.883 6 sin35.82 342 +51.35 cm21111111014a) (i) 35 x y + (ii) 30 60 1200 x y + (iii) 12 2 120 x y + b) Draw one line correctlyDraw all line correctlyShaded the region R correctlyc) (i) 10(ii) Use point ( ) 5, 30 Profit ( ) ( ) 850 5 1150 30 +RM 387501111111111108 SULIThttp://www.chngtuition.blogspot.com3472/2 ADD MATHS SPM TRIAL 2012 SCHEME OF MARKING 15(a) ( ) ( )23 0 18 0 15 v +15 ms-1(b) 6 18dvtdt 3 t -112 ms v (c)23 18 15 0 t t +