2020 ACJC Promos (w/Suggested Answers)

BP-3 ANGLO.CHINESE J UNIOR COLLEGE JC1 PROMOTIONAL EXAMINATION Higher 2 /1 00 CANDIDATE NAME TUTORIAU FORM ',-l INDEX NUMBER Paper 1 Candidates ansv{er on the Question Paper. Additional Materials: List of Formulae (MF26) 5 October 2020 3 hours READ THESE INSTRUCTIONS FIR.ST Write your index *umber, class and rrame on allthe work ynu hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams ar graphs, Do not use staples, paper clips, glue or conection fluid. Answer all the questions. Write your answers in the spaces provided in the Question Paper. girr.,on-*iact numerical answers correct to 3 significant fQuies, or 1 decimat place in the case of angles in degrees, unless a different level of accuracy is:specified in the,question" You are expected to use an approved graphing calculator. Unsupported arlswsil$ from a graphing caleulatsr are allowed unless a quesiion specifically states otherwise. Where u nsupported answers f rom a $ra,phing calculator are.not a llowed in a questior"r, you are required to presentthe mathernalicalsteps using mathematical notations and not calculator commands. You are reminded of the need for clear presentation in your answers' The number of marks is given in brackets [ ] at the end of each question or part question. The total numher of marks for this paper is 100. Questisn Marks I 13 2 l4 3 l5 4 /5 5 lv $ 7 t8 I 18 I /8 {0 t11 {T 112 tI0 13 172 This document consists 3 ,flngtr-ffq \trr;r,t Srrntrr ff c{lc$c of 26 printed pages. [Tlunr river I {l 12 ffi

BP-4 2 t The dia$afil belolv shows tho graph of /-f (x) rvith asym-ptotes r=0, r=4 and I = 3', T,he curve has aminimum point at (*1,0) an*i u maximlm point at {2,*3). y = f(x) t, rl: E Sksfch ths graph qt' stnting cle*rrly tl* qquations of fllly asynptotes, the th$ irxss. crossos t3l ,filsL+slJWE$8.iUNiORt0il^EG;Ee0?0 r,r? MATHET\riATiCSe?58trC1 4 I I t I I I I t i t I ,} i I I ' .rc* *[ t .11 s 'r*' f(t)

BP-5 1 Users $f targets,trr rseqt sach week. Those who nleet &eir aan be vouchers. A 60, or 1 00 coins. In aparticularmonth,23g5 qpinsweremadeintotal. Of lhtsc, S0Yowere successful spins and a totai of I I? 640 coins were 1voo. 25% of the spins that won 40 coins, 35% of the $prn.! that wcn 60 soins wer* made ,in the last t41' weCk Sind 3 ASTCLO-CHrNrSHJUNiSRf;flLLf;CH20?S H2MATF{EtlrArrc$e75&/01 lTurn over 5

BP-6 4 3 = 0, where &is a real constant. (r) l?l ti*} T,hc,ta&gent'tn Sat,tlre paiat where of ,L H2 MATHEI4ATIC$ 97$&ll1nt'rcr-o"*]{D:g$E JuNtoR cotrgce zozu 6

BP.7 3 wher* c5rS",A$ fi $eftl* dtagragr, statixg4 cl early th* eoor*lifl ntes 11rl*l ralL4l tl l Solve the eqtmfion I.l c l{=;, teavilr$ youf aft sw,q iU'W{ry{*'$f a' rr : : : i :riirl ,t, Hence solve the -,requalitY [d t r::*.,. -.,. I l4*rg t: *Acl*-*pfla$q.-lUt*ionC.ilr-l-EGE2s2s 1."l2MAYrl[MArlC$ *75#01 7 flf'rtra *v*r

BP--8 6 Skgt$h fi16,graph of G gi,ven by the oquation yz *\x+a)'-1" u.htr$ Er>(}" st*ting clearly the equations sf'a43, $s)-.$rptptCIs *md the e*mrdilrates, tf ary: tunring point"s. I?] Hen*e'sketch ths er;uatiiins CIf ilsy ;l$yulpl*to*, ,v.axl{i., where cleady the cr*sses the rnltlJ &NfiLu.ctjLlltrE$E.lUhllORC*ttrG;,?CI20 l{tMA:?}{€MAT}C$S75&'01 B

BP-9 "l 7 The eurye q ;s tt forgted'',o$to,the'eufiro Cr mth equation (&y*,I)r -is-0: = | , ,.> l. Desuribe a sequ{i:ncc of transforeations which transfurms the curve ( onto the c'urve c2. t}l Al-\iGt0-cHlNEsE iufiiloR*p.f-L-rBE ?020 :H2 l'{ATHEtulArlC$S7$&l01 I [Turil **er

BP-"10 * fi T"he diagram be-low*korve a trapexitr$r O,{C&, whero 0} : n, $ii= b a;;1l i5C =c - lu rf "t le, Bffqgnsjrlerixffi;,are-*.of'trj*figl*p tlr'*.&wrvine, prove thatth*:+rea nf tlre trap*zitrn igr I+Zr ;:l** t{' ANGTA-0H{}i[€$EJuf.ll0,qSOI{-ESE.:01{} I.12tulATH=l\1AIlC$SZSBjlql 10 t-

BP-11 !) :show that l*.h{' + }ax ul" =tlqll{}'" t.}l Given fu*herthat 3*-,3b = r, iul* z, ltf : 3, la.ul - 5, find the xea oll trapsziwl'olt,'f' exactly, til ,${6Lo"(X-I}lEsf,j,JNiOhcOrLEG[2020, HzMATFtEMAttcssTS&o{ [Tuf,n:*r*f 11 i:

BP.1 2 10 I The;functions f and g are defined as f,ollows: f :xpr 7{x*a'f *1, ;reR, x<} g:xr+1+/t-e*', x)0, Whersa and & are real constants. (i) State thesmallestvaiueofa such that f;-I exists: tu [31 For {he re'st odthi$ question, lr:4, {iS Explain,if f-t ax.ist*, fl$d,if it rloss, {ind f;.I {:r}, and *tate itr:dorn{g, ANGLO-CHINES€ juNIOR COLLEGc ?020 il? MATHEMATICS s758l0r 12