Free Tuition Listing @ 99Tutors.SG $2s 1 sA2 2 sA2 3 sAL 4 sA2 5 sAL 5 ,sAL 7 sA2 8 sA2 9 Serangoon Garden 20L7 sA2 1.0 sA2 LL S:A2 L2 ,sAz 99Tutors.SG | Page 1 Free Tuition Listing @ 99Tutors.SG 99Tutors.SG | Page 2 BP/2017 13 Free Tuition Listing @ 99Tutors.SG tuUlo€lttttoe Sdroo, tMel, Rrmd) 2017 4EAM ACS (Barker Road) Prelim Asswer ail the questions t The equation uf a cuwe is y - 2x2 -6x+ k, whete kis a constaut' which y < 0 (D tn the case whep ,t = -20, find tre set of values of r for ' tzl thecurve' (ii) lnthecasewheu k =tO,show thattheline y +2x-8 isa tangentto FI in u' 2 $ Given thar u = i', express 4' -2'd = 3 as an equation t2l places' (ii) Hence {ind the iralue of x, oorcct to 2 decimal t3l < t21 (iii) Explain why the oquation 4' -2n1 = /c has no solution if & -l ' 3 Thecquation 3r2 'If5=0 hasrcotsGandP' (r) Find the valu€ of a' + Pt ' tsl t3I 2cos2 r' I - sin {cosr+ r as A quadraflcnuedt ' expresrsion in cot x. 4 (i) Express -:---H:F-::":: asa t3l sin x(3sin.r + cos r) (ii) Heuce, usiilg G) polve the equation I + 2cos2 x = for 0' < x< 360?. t4I r*{ ,Sec 4 (FqPressJ minali sn 20t 7 PtelirnirurY fu Additla*d nmrtler,tattcs 4047 PaWr 7 99Tutors.SG | Page 3 Free Tuition Listing @ 99Tutors.SG BPt2017 t4 Angrto-Cfn'nese Scfioal (@t@ Road) A fteshly baked bread, wirh an inicial rempem&re of 75'C, is lefi to cool orr the raek. The temperatrrre, io'C of the bread r rrinrtes after it has been placed on the rack is gtveri by ? =27 + lce-"', wher€ k atd. n are positive consEuts. [} Calculate the value of /r. trl (ii) If thebread has cooled doua by20'c after r0 minuteq find the value ofa- Lzl (iii) Find the least tirne takcn, to rhe nearesf minutg for the bread to have a tanperature of less than30'C. t3l (iv) Explain with the skech for f = 27 + lce-"', why tlre temperarure of the bread can nsv€f, reach 27'C, trI 4Ji -z'.li arrgle BAD = 30". Given that the leagth of AD is twice th€ i€ngth ot BC and that ' area of the trapezium [s 25 +sJE- cmz, find withoutthe use of a calculator, the Iengthof lD in the fonn 15 . "^fZ*t t4l part The diagmm shows of a straight line, passing through (2, r) and (8, 1 3) , drawn ro f@reseot the equation 3y = 4x' + at, whiere a and , arc conshnts. Find tlre ralue of a and t. (s, t3) t41 4 freli ml n ary fxaminalion Nl 7 I I 99Tutors.SG | Page 4 AtiditiondtLr,{rre*rr"*ini'!rtr'1, I I BP12017 15 Free Tuition Listing @ 99Tutors.SG Attg{o.Chlnese Scltool (B sks Roadl I ta) Given that the first 3 tetms in the expansion of (a - rxl + 3x)tr in ascending powers of x is 2+29x+ Df +..- Find the values of the constals a, b a*d n. tsI (b) O Writedopn the ge,neral termin the binomial exparsion of 1rt .' -l1ro2f' t1I (ii) Write down the power of x in this general term, trI (iii) Hence, ot otherwise, detetmine the coefficie,nt of x-ts in ttre binomial expansioir of (x2 * *. # t2l 9 A cune has equationyl rn( ,n" normal to the curue at the point (a, D) is ' i \5*2rll+;! ). paraltit'to the line lty uSx-25 = 0. Given that where a) l,find the values of a and D. tsl 10 The diagrarn shows pafilof the graph of y =lzx+ 4l + 1 . I -lz** 4l + I (i) FiaiC the coordinafes of P and of Q- t3l A Iine of gradiant a passes through the point (0,3). (ii) tn the case where ;m = -1, find the x-coordinates of the points of interscction be*ween the lineai:dtteeraph of y: l2.r+ al+l t3I (iii) Detennine the set bf vatues ofzz for which the line intersects the graph of y =px+al+ I at two points. sa Wirninary Breffiffiatton ZAfi I Affiiorral rt@rarnaries &47 fumy'i 99Tutors.SG | Page 5 I I BPt2017 t6 Free Tuition Listing @ 99Tutors.SG Angl o - Chl ne s e Sfim,l (U*q Roadl Il Aparticle stafts from rest and moves in asbaight line, so that t seconds afler leaving O, its velocity,vmlsis given by u= 23-ZeT . (D Calculate ttre initial accelerationof theparticle. t2l (ii) Calculate, to 2 decimal places, the displacanent of the particle from O when /= 10. t4l (iiD Ddennine, withexplanation, whether theparticlewill retrrn to O. lrI 12 In the diagrambelow, the line AE is tangeat to &e circle at 14. The line EB is the angle bisector of angle,{dC and cuts the cirple at D- The chord .4C is the argle bisector of anfie BAD and cuts thecirple at C. The chords BC arrd AD ate produced to meet at F. The line segments AD and FD xe e+El. (r) Prove fiat angle DAC: angle DAE, t3l (ii) Prove that trianglex- ADg and BAE are similar. l2l (iii) Prove that C is a mid-point of BF. t2l (ir) Hence, using (ii) and (iifl, show that AF x AE = 4CD x DE . V1 toellminq &wriration ZA't 7 .9ec 4 (Express/ 99Tutors.SG | Page 6 Additiortal tufeithernaties 4Ul F'aW t Free Tuition Listing @ 99Tutors.SG Ansrrer aII the questions (s] [ Given that lg0y + 2) - 4xL - /, exprffis y in terms of x. t3l (b) Soirr theequatioa Zlogn(8- 2*\- log:(r- Z)=3-Ioge(r+ x) IsI The diagriam shows 6r wtter wheel whichrotates at 3 revolutious per minute in au anticloc}s,ise dircctibnAt *re start of dre revolution, a poiut P on the rim of &e wheel is at the heiglrt of 3 rh above the strdace of the water. The radius of the water wheel is 4 trt" The height, ft m, of poiut P above the water surface is given I h = dsi(l}+c , wherel is thetime iri seconds. (i) Sute tre valugs ofs,&and c. t3l G) Fiod the time;f, whercpoint P first emage ftom the water. l3I show u* ti) ft{"*(2r+II=gk(4r+4}. IZT Cu) Hence, o, oth|*ir, evaluate a*. llz*u [4] On*$gwy Uarninelton 2A t 7 Se6 A{*ger} e&tltupll Wt{rcsnatics PaW ? 4047 99Tutors.SG | Page 7 BPt2017 t8 Free Tuition Listing @ 99Tutors.SG AtE,bl0hircce School (Aar*er Roadl The cubic polynomial (x) is such *rat tbe coefficient of.t' is 4 anil the constant ternr is -3. Whea rt I is a fictor of (r), the qrndratic factor is pi + qx+ r. tt is given that (,r) Ieaves a rclmailrder of -2O when divided by r - I . (r) Ffud dre values of P, q and r. t3] (ir} Solve (x):0. t2l Gii) Hence solve the equation (-r) = Q. tll \' : \1 - 4x +t It is given that x'-4 G) Findthe values of a,b and c. t3l (ii) Hencg using partiat ftactions and the values of a,h and c obtained in part (i), x3 _x:a|+t** find f t6l (r) ;'If,fu g sufves constants, 1i; Findthe value of a and of k. "127 (ii) On the same axes, sketch the two cutYes, for x > 0. tzl (2*+ wtren *= 8re value ' (b) Giveothaty= hnr)zand*fr., S -uE+DJ5 ;,find of a and of D. 141 dl loa 1 Sec 4 [E4press) P relblrii raty Erraitl rrat fr 7 I I Additiorral tielhettettcs P apet 2 4847 99Tutors.SG | Page 8 I I BP/2017 19 Free Tuition Listing @ 99Tutors.SG Anglo.Chtnese Scftoo/ (turlrcr Road) A curvehas the equation jr = f(r),where f(x) = 1'x-1) for x > 0. 5x+ 3 (i) Find an expression for f'(.r). t2l (if, Explain why thelcurve hes no sbtionary points. tu (iiil Show with full urprkings, deternaine whether tlre gradient function of the curve is ar incrcasing or decreasing function for r > 0. Th6 pornts (I, 10) and (?, l0) are on the circumference of a circle whose centr€i G lies above'tlre x-axis, The liue y = I is tangent to the circle. ' (i) F.inil the coordinates of C. t3l (ii) Find theeguatioriof thecirclein theform x'+ y' + px+W+ r =0, wtwe p,q and rareinteger$. (iii) ffud the quatiois of the hngeuE b the circle parallel to they-axis. tI The abovediagram sbonrs a troughof 3m long and lm deep with ABCD horizontal. Its cross section is an isosdeles triangle of base 2m with its vstex downwards. The empty trough is filleil with water at the rate of 0.03 m3/s. (D #ti" A"pttt of th$water at time ! seeonds is tr m, show that the volume of water is 3lr2 m3. ttI Gi) Henoe, find the rdte at which the water leivel is rising after the water has been runningfor25s. I4l rLa *t Frcffnlrnry &arnreitian fl? 7 Sac 0 {furesel Addifurlelt eraffu,?Baf,bs tuW 2 4847 99Tutors.SG | Page 9 Free Tuition Listing @ 99Tutors.SG BPt2017t10 ArpltChiaese Sclrool (8erker Road) IO !:rr-3 The diagram shows part of the curve ard two pmallet lines Or? arfr. PQ. The line OR interseots the curue at the poiut ,R (2,2) aod the lirte PQ is a tangent to the curveatthe poir,t O. O Fiud thecoordinatcs of P and of Q. t4I (ii) Find the atez:.of thesbadd region OPOR t6l (i) Find the coordioates af B arr.d D.