2009_Maths2U_TrialHSC_Neap_Solutions

2009_Maths2U_TrialHSC_Neap_Solutions - 2 HSC...

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@: HSC Trial Examination 2009 Mathematics Solutions andmarking guidelines NeapTrialExams are licensed to be photocopied and used only within the confines of the school purchasing them, for the purpose of examining that school's students only. They may not be placed on the schoolintranet or otherwise reproduced or distributed. The copyright of Neap TrialExams remains with Neap.No Neap Trial Exam or any part thereof is to be issued or passed on by any person to any party inclusive of other schools, non-practising teachers, coaching colleges, tutors, parents, students, publishing agencies or websites withoutthe express written consent of Neap. [email protected] eenrssrosooo+s POBox214 StLeonardsNSW 1590 Tel:(02)9438 1386 Fax:(02)9438 1385 rENMssoeFM
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HSC Mathematics Trial Examination Solutions and marking guidelines Abbreviations: CFPA = correct from previous answer IU = ignore units IR = ignore rounding CNE = correct numerical expression, i.e. correct substitution into a correct formula ISE = ignore subsequent errors Question I Sample answer (b) (a) QJa -D2 -QJ\-r)=12-art + | -zJi + | = 14 _6rt (5a-l)(5a+1) _-(5a+ l) 2(l -5a) 2 -5a-l =- 2 "t*(#)= rog,oro Syllabus outcomes and marking guide P3, H9 . Givescorrectanswer .... 2 Makesoneminorerror.. ....... 1 P4 . Givescorrectanswer .... 2 . Factorises one expression correctly. . . . . 1 H3.H9 . Givescorrectanswer .... 2 . Usesoneloglawcorrectly ...... 1 P4 . Givescorrectanswer .... 3 Obtains (AB)2 =24.17 . Rounds4.9incorrectly .... ..... 2 Substitutes into the cosine rule. Demonstrates correct rounding to one decimalplace.. ........ 1 H4 . Givescorrectanswer .... 3 . Calculatesthe interest for both options correctly ........ 2 . Calculates the final value of the investment correctlyforeitheroption ...... 1 (c) (d) -l (AB)2 = 42 + 5.22 - 2 x 4 x 5.2 x cos(1.1 ) = 24.1104 (to four decimal places) AB = 4.9 (to one decimalplace) Option 1: Interest = $20 000(1.005)36 - $20 000 = $3933.61 Option 2: lnterest = $20 000(1.062)3 -$20 000 = $3955.41 Option 2 gives more interest. (e) Copyright @ 2009 Neap IENM $ Og.FM
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HSG Mathematics Trial Examination solutions and marking guidelines Question 2 (ii) !s""tnra*=!tunn* + C (iii) [1r,* t r'4r= l{*o +2xz + l)dx J' J 1. 2t =tx"+jx'+x+C =€*1+x+c )J y =lognx ,I y =- x le y-3=1G-e-) e I v=ix-l+3 J3 e t tt=ix+2 e (i) 6y=x2- 10x+ 13 6y+12=x2-llx+25 6y + 12=(x-5)z 6(y+2)=(x_ 5)z (ii) 4a= 6 a= rt (iii) 6(Y + 2) = (x - 5)2 veftex = (5, _2) ^ (- l\ tocus = \r,__) Syllabus outcomes and marking guide H5,H9 . Gives correct answer (ignore + Q. . .... 1 H5,H9 . Gives correct answer (ignore + C;. H5, H9 . Gives correctanswer(ignore+ C).. . . . . 2 . Multiplies out bracketsbefore integrating ..'...1 P5, H3,H9 . Gives correct answer in anyform ' . . . . . 3 . Correctly determines gradient and v-J.. . Correctly differentiations or determines y-J.. P3 . Correct demonstration by anymethod. . . H5 . Gives correct answer 5 Bothpoints conect (orCFPA) . . . . . . . . . 2 Eitherpointcorect(CFPA) ..... I P5 . Givescorrectanswer(CFPA) ....... ... I (a) (i) [or'.a*=3e2'+ C Sample answer X=e3,y=3 I fllT = -3 e (b) H a (iv) Range: y2-2
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E HSG Mathematics Trial Examination Solutions and marking guidelines Question 3 (a) (i) !'=8-2x (ii) t' = -2sin2x (iii) !
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