Juj pahang 2014 add math spm k2 set 2 skema

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Bahan Pecutan Akhir Add Math SPM

Text of Juj pahang 2014 add math spm k2 set 2 skema

  • 1. 2No Solution and Mark SchemeSubMarksTotalMarks12 4y xy x 3 3 x 2y 3x 3 2y32xy 224 04 3 2 3 2 0y xy xy y y y 224 03 34 02 2y xy xx xx x 2y 1 y 3 0 x 2 x 9 01@ 322@9yx 2@91@ 32xy 1111152(a) 2 24 2 3 281 273 38 3 665x xx xx xx 1117

2. 3(b)2 22 2242323log 16log 1log 2log 216216644xxxxxxx 11113(a) 232220500 1.05200000T araa27(b)(ii) 11400000200000 1.05 4000001.05 21 log1.05 log 21 14.2115.2116nnnTnnnn 2008 4152009 419.52010 423.342011 427.572012 431.852013 436.172014 440.532993.62 77415 1.01415 1.01 11.01 12993.62a r orS 5 3. 44(a)(b) 2sin 2sin cos1 cos 2cos 1sin 1 2coscos 1 2costanx x xx xx xx xx Proven / TerbuktiBentuk tan x (di graf) P1Period (di graf) P1Straight Line (di graf) P11xy P1No Of Solution = 2 N12572 4. 55(a)(b) 2333y x xy x x 223 3 01 011, 21, 2dyxdxxxx yx y 22 61, 6 min1, 6 maxd yxdxdyx imumdxdyx imumdx Maximum point is 1,2 x 0.02 2 2, 3 2 3 9dyxdx 9 0.020.18yy 4376(a)Find the coordinates of B(6,0) or coordinates C( 0,4)Find midpoint of BC 3,2Gradient of BC =23 .Gradient of the line perpendicular to BC = 232m The equation of perpendicular bisector to BC is : 32 323 52 22 3 5y xy xory x 7N1 7N1K1N1 5. 6(b)Area of triangle ABC 214 0 6 4 0 2 2 6 0 4 42124 28226areaunit No Solution and Mark SchemeSubMarksTotalMarks7(a)(b)(c)x11.522.533.5log10 y1.501.220.930.660.340.10Graf = Rujuk LampiranPlot 10 log y against x and correct axes and uniform scales.6 points plotted correctly N1Line of best fit N1* If table not shown but all points are correctly plotted , award N1 mark. 10 10 10 log y 3log k x log p(Can be implied)(i) 10 3log k 0.56k 0.65K1K1P1N1K1N1N1K1 6. 7(ii) 10 log p 2.04p 109.65(iii) 10 1.3823.99loy yy8(a)(b)10tan659.041.0312 1.031631.518CDCD 11.661.03112.02ABAB2 2 10 611.66OBOB 11.66 65.66BD AC Perimeter of shaded region31.518 5.66 5.66 12.0254.858 2510(c )Area of sector2 111.66 1.031270.09 Or3K1N1N1 7. 8Area of right angle triangle16 10230 Area of shaded region70.09 3040.09 9(a)(i)(ii)(b)Use the triangle law for PS or QR99OP PS OSy PS xPS x y 5 33 5OQ QR ORx QR yQR y x ST=m9y xRT=n5x 3y3710K1N1N1N1N1 8. 9Use the triangle law to find TQ : 4 9 5 3 5 34 9 5 3 5 34 5 5 9 3 31 5 9 1 5 3 311 5 9 45 3 37242 6717ST TQ SQ RT TQ RQTQ x m y x TQ x y n x yx m y x x y n x ycomparem n m nm n n nm n nm nn 10(a)2dyxdx2(1) 2 T m Equation of tangent2 2 12y xy x 310(b) Area of triangle Area under the curve 11 221 1201301311 0343x dxxx 4N1K1K1N1K1 9. 10Area of shaded region = 2 4 113 3 unit(c) 212212 2212(2) (1)2 12 212y dyyyunit 311(a)(i)(ii)(b)(i)n 8, p 0.8, q 0.2 8 0 8 8 1 7 8 2 60 1 22 0 1 20.8 0.2 0.8 0.2 0.8 0.20.7969P X P X P X P XC C C 250 0.8 0.26.325 npq 110, 4100 120100 110 120 1104 42.5 2.50.9876P XP ZP Z 5510 10. 11No Solution and Mark SchemeSubMarksTotalMarks12(a)(b) 2232322 18 284 182 18 2829 2830, 0, 029 283v t tdva tdts vdt t t dtts t t cs t cts t t 2, 018at A ta ms 212 18 28, 028initialv t tv tv ms 2210(ii) 100100 11042.50.00621P XP ZP Z 0.006214802.98n AP An sn An ABilangan helaian yang ditolak ialah 3 11. 12(c) 222 18 28 09 14 02 7 02 7v t tt tt tt 3(d)distance s 3 23 22229 28322 9 2 28 231253tts t t tss dt 3 27227 9 7 28 731163ttss The distance is2 7 21 12 25 163 367t t s s sss 32 7 12. 1313(a)1010116 100250290QQ 210(b)10/ 0810/ 08115130 100149.5II2006 2008 20102006 100 115 10/ 08 I2008 - 100 1302010 - - 1002(c)I w Iw110 13 1430116 25 2900130 40 5200x 10 103x120 12 1440100 10970 + 103 x10970 10120100103xIx 4 13. 14(d)08081599120 1001332.5QQ 214a(i) 2 2 2 10.5 12.5 2 10.5 12.5 cos8014.86QSQS 2 10(ii)00sin sin 3514.86 9.5sin 0.897263.79116.21RRQRSQRS 2b(i)1RQ'QP 14. 15(ii)*2sin sin 8012.5 14.86sin 0.828455.94'1(10.5)(10.5) sin 68.12251.15Find PQSQQPQSArea of PQQcm 0 110.5 12.5 sin 80264.63'64.63 51.1513.48Find area of PQSArea of PQ S 515(a)(b)(c)1.8x 2y 2403x 2y 600y x 50Rujuk Lampiran(i) Jambu batu sebanyak 66 pokok(ii) Maximum point = (100 ,150)Maximum total fees = 120 ( 100 ) + 180 (150 )= 39000 15. 16Soalan 7(a)2.01.81.610.51.522.530.23.50.40.60.81.01.21.4XXXXXXlog10 y20 16. 17Soalan 15(b)40206080100120x201406080100120140y160160180R(100, 150)040180