RI(JC) H2 Maths Promo 2008

RAFFLES JUNIOR COLLEGE JC1 Promotion Examination 2008 MATHEMATICS 9740 Higher 2 September 2008 3 hours Additional mate.ials : Answer Paper List of Formulae ([,4F15) READ IHESE INSTRUCTIONS FIRST Write your name, exam number and CT group on all the work you hand in. Write in dark blue or black pen on boih sides of the paper. You may use a soft pencil for any diagrams or graphs. Do not use slaples, paper clips, highlighters, g{ue or correction fluid. Answer all the questions. Give non exact numerical answers correct to 3 significant figltes, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question You are expected to use a oraphic calculator. Unslrpported answers from a graphic calculator are allowed unless a question specifically Where unsupported answers from a graphic calcu{ator are not allowed in a question. you are requked to present the mathematical steps using mathematical notations and not calculator You arc reminded of the need for clear presentation in your answers At the end of the examinaiion, fasten all your work securely iogether- The number of marks is qiven in brackets [] at the end of each question or part queslion Can do the 11 hole question. Can do part ofqucstio[ only. /. o RJC tES 2008

,y'' Find {ir gll )- ct J3'dr. Hence find Jr3'.r d.,c. The functiors f and g are defined by [::r-+:] : , x€R, r+ 2, g.,"+-x' , r€R,.r<d. (i) Sketch the graph of f. (ii) Fiod l-1 , the inve6e tunction of f. (iii) Fiod the largest value ofd so that the composite function lg exists. Two concentric circles have radii R and ,", where R > r. R increases at a constant rate of I cm per minutc and the arca between the lwo circl€s remdirs consLlnt at 25cm?- At the instad when R = 5 cm. find the exact rate of increase of (i) the area of the srnall€rcircle, (ii) r. State precis€ly a sequence of 2 8€om€tric transformations on the graph would .esult io the graph of), = g(4 r.). Ill tU t3l of y = g(x) that I2l The graph of-y = g(Jr) has asFptotes t =2at:dt=4 n. It aLso has a maximum potnl whose Jc coordinate is 3. Given that g(jr) : g(4 - r) for all real values ofr in the dornain of g' sketch one possibl€ graph ofy = g(ir)- fYour sketch shoutd demonstrote .karu all the appropriate features of the grcph tlldt lhov that the given conditions are satisfed.l t3l (N) Find J', ller dr. (b) Find Jj.cos(") dr. tlt Ill t3t I2l 12t t3t t2t (ct U.erhesubstrurio" " '^il ro rrnd lhe exacl *rr.ot Jt-f.a, . t{2 MA 9740/5/2008 RJC tC I Pomotion Exad I4l

l A sequence ofreal numbers Jrr,J.r,Jrr,... satisfies the recurrence relation Prove algebraically that, if th€ sequence converges, then it converges to eith€r Derenrine rhe rdnge of rhe tuncrion ,,r,- rF-" .;^ l. r . r 2. (u (i0 I or 2. [21 IU (iii) 'l hc diagram belolv shows a porrion of thegmpn.,., =,/{l]l r I, for,.:0.-\t ) When rr = 1.001, by considering x,,,, -.r, ;r.., > x. fbr all integen a ) l. The above diagram shows the points l(0, coordinates (r, 0), whe