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BALESTIER HILL SECONDARY SCHOOLPRELIMINARY EXAMINATION 201 6SECONDARY 4 EXPRESS

MATHEMATICSPaper 1

Thursday

Tho number ofmarks is given in bractets [ ] at thc end ofeadr qucstion or pert qucstion.Thc total oftho marks for thid paper ls t0.

For Examlne/s use:

/80

4048t01

2 hours18 August 2016

Additlonal Materials:Nit

READ THESE INSTRUCTIONS FIRST

Writc your namc, class and regist6r numbcr on alt thc work you hand in.Write in dark blue or black por.You may usc a pcncil for any diagrams or graphs.Do not use staples, paper clips, lrighlighters, glue or correction fluid.

Answer all questions,If wirrking is needed for any question it must bc shown in the spacc bclow that question.Ornlaslon of esscntial workilg wlll result ln lors of mrrks.You are expeoted to uso a scicntific calculator to cvaluatc cxplioit numcrioal cxprcssions.Ifthe dcgrce ofacourncy is not spcoificd in tho qu6tion, and ifthc answer is not cxact, givc thcanswer to three significant figures,Oive answers ip dogrees to one dccimal placc,For rr , use either your calculator value or 3. 142, unlcss the qucstion rcquirce thc answer in tcrms offi.

.i. .": l

'[his qucstion papcr conslsts of!! printed pages (lnctudlng this page).

[Turn over

2

Mathematlul Formalae

Compound lnleresl

Mensurallon

Trigonomelry

Std,tistlcs

Totat amount =rC*ft1"

Curvcd surfacc area of a @ic = r r I

Surfacc arca of a sphare = 4 t 12

Volumcofa "on"-

!or'h3

Volumc of a sphcrc = 1rr rt

Area of hiangle ABC= !absinC

Arc lcngth = rB, *no" A

2i,

in .uai"n,

Scctor arca - f r', . *here d is in radians2

abcsinl sinB sinC

a'=b7+c'-2bcasA

M"rn = x/'E,f

Standard dcviation =(Drr\'-t r/JET

fionlmr':For

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DANYAL EDUCATION

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3

Aoswer atl the qu$tlon8'

':Evaluate 4",101, *.t.r c a=:2.13' 6=!,altac=3'8lr' write

:,.; . .Nb+c .. ...

, S * fiist 6 digiti o1r your caloulstol.dtsplay"

Emlrfrr'sFor

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z (a)

Ansier(a) . 'I2'l

(b) Writo your answer to pgrt (a) oorrect tro 3 sigpificant figures

Answdr . (b) trl

Givon that g$ = 2 x ! x 5, find thc smallcst integcr n such thdt 90n is a

perfcot squarc,Iti-La - !iisi+i:;'.1='::i;1' ,

ffimfisl.,i.r

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(b) TheHCFandLCMof2nrmbcrsareg0and3TS0respeotively.Finaolci

"r.U*t, givcn that thcy are not 90 nor 3780' '

Answer (a)

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lE PRBUM EMM 2016

Awwer (U-d

4M8i/01 BT6s lE PRBU'T PAM 2016

Ansv'er (c)

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3

4.

Factorise thc following expreissions oouplctely'

(O 4x'-2lx-18,

Awwer (a)

(bl 6a-5b+l!;ab-3

Anrwer @)

(c) 'x' + 2x - y1 +.2y

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3 interior angles of a polygon arc 139o, 147o, and 164., Thc onainirig interioranglcs src xo. Civen that the sum ofthc intcrlor anglcs ls 28800, find the valuoofr.

Exonlnr's &dhut's

6

(a) Thc tcopcraturc at a parti@lar toum is .roC at 0800. It risca at a constantratc atrd rcachcsyoC at 1500. Find an expression in tcrms of.r and.y forthc tcmperaure at 1230.

Ans+er (a)

Exomlmr

Anstter ' [3]

"c al

Dany buys a $25 000 sailboat via hiro puroliasc, Sho pays a 35% downpaymentand tho romalnirtg amount by monthly installmcnts for 5 ycars. tfthc intcrcstrato is 67o per arrnunr, calculate hcr monthly installmcnt.

(b) Beatrix boug'ht a applcs 6t D doltars pcr dozcn. Shc sold all tho applcs at cccnts aach. Find an oxprcssion in tcrms of a, b, utd c for hcr prollt indollam.

Anstter (b) S

A bcakc contains 7.2 cm3 of chemlcal I and 12 on! of chemical B. Flnd theratio of chcmical I : chemicd B in its simplcst form.

8.

t21

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Jason invcsts $30 000 into bonds that gavc a rchrrn of4,87o po annumcompound intercst. Find the amount ofintcrcst accrucd at thc end of4 ycars.

5

t31Ansyer $

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4048/tl DHSS 46 PRELIM EXAM 2016

Answer

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6

DANYAL EDUCATION

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Thc tabla below shovrrs tlrc o6argci for Ubcr and Comfort Taxi scrvioes in

i;;;;;tlwilctr scrvice is ohJaper for a 2l km.joumcv at 8 pm on a

irlJf.[ry, *fr.tt thc total ttuuetting timt is-25 minutes' inclusive of 4 minutes

oi".itlittg ti,net Show your working olearly'

Basc Cost

Distalrcc Cost

s3.00

$Q.50 pcr km

$0.25 per minutc

Nil

$3.20

$022 cvcry 400 m (uP to l0.km)$0.22 ovcrY 350 m (ater l0 kni)

50.22 wery 45 s waiting time

257o of metered fare

Tinrc Cost

Peak HourSurchargo(bctwcat 6 Pmand midriight)

'l::"

aii.':. ...;illtr.l:

*;!r,1*6r,r,_,

.,i,i.+

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BITSS 4E PRBUM EXAM 2016

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{018/01 BI]SS IE PRELIM

Answer A) m

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IA l-rex spots Mr Tco 60 m away and attacks, aoceleradiri Z at ! m!.s2 to its top

rp"uO of iS m/s. At the samc time, Mr Teo flees in ttrb opposite direction'

quickly rcactring his top specd of5 m/s.

(e) Sketch the vclooity-timc graph of theT'rexfor 0 < / < l0 in ttre answer

sPacc bclow.

Answer ' (a)(m/,

Mr Teo

10 Timc (s) t,

(b) . Find the distsoce Mr Tco.can travel before he is caught and eaten'

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DANYAL EDUCATION

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UseMake c the subiect of the fo rnula a= @-

Emfrhsr't Exmh.t\ l3 6ivcn that i - 8x + 3 can bc writtcn in the form (, - o)' + b, findtho vatucs

ofa and 6.

An$oer a=_ , b=_ l2l

l5 Thc mean, nfedian, and modal height of 4 men are 177 cm,l76 cm, and172 crn rcspectivoly, Write down the heights of cach man in asc.cnding order.

Answer_ ,_t2l

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t2 (a) Solve tlre inequnlity l* z.Ef sl -,

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Answer (a)

(b) Represent your answer in (a) on the number line in the space betow.

Answer (b)

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It is givcn thaty is invcrscly proportional to thc cube root of.r. Find thcpcrccntagc decrcasc in y when x is incrcased by 500%.

t4

Answer % t3l

BHSS,IIi I'REI.IM E,YAM 20I6 4048/0r BHSI;18 PIII|LIM EXAM 2016 4048/0t

DANYAL EDUCATION

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Tho linc 2y + 5x - I 0 = 0 intersects the 'r-axis and th€ faxis at points z{ and B

respeotivelY.

Aruwer. (a) A(

u( _ ,) r,r

(b) Writb down the gradi-ent of the line'dB'

Answer (b) lu

(c) Find the length of tlre line '48'

Answer k) units tll

(d) A ooint c lies on thc *-axis such that the arca of rianglc lBc = l0units2.

\irIi;; G"*'coordinates of 2 possible positions of point C'

) r,r

Anser (d) x= --

u

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BI+SS 4E PRBW EXAM 10I6{04E/0 r 8H85 4E PRBUM E)UM2016

404U01

12

i,l Solve thc following pair of simultaneous equations'

3x+5Y=-g

2x-9Y+8=39

Answer x=

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DANYAL EDUCATION

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Consider the number pattcrn below.

3,7, lt,15, 19, ..

(n) Write down an expression for thc /h tcfm.

Ansiver (a)

(b) l-lence, evsluate thc 75rh tcrm.

Ansrer (b)

(c) Explain clearly why 240 is not a tcrm in thc pattcrn.

Ansa)er (c)

(d) Consider another number pnttern bclow.

6,2t,44,75, I 14, ...

By comparing the 2 number pattcrru, find an cxprcssion for the rth termof the 2d pattern.

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RHSS 'IE PIIDLIM $XAM 2OT6

Ansver (d)

4048/01 BHSS 4E PRDUM DXAM 2016

Annt'er (c)

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19 In thc diagrun, OAQB is tho sector of a circlo with radius 14 om and anglc

AOB = 1,3 rad. C is thc centrc of I airalc PQR itscribed in thc sector.

o

A

P

14 on

o

(n) Show that thc radius of thc circlc PQR is 5.28 cm.

Anewer (d)

(b) Find thc pcrimctcr ofthc shaded region.

Awwer ft)

(c) Find the aroa ofthc shaded rcgion.

t2)

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DANYAL EDUCATION

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.15Zit (e) CoflsrructatiarUlelBCiuctrthat,{r=8-.*, AC ='llo,q andangle

ABC =75" ' Tho lino '48 has been drawn tbr you'

Answer (a)'azJ

BA

(b) Bv oonstruoting 2 pcrpendioular bisactorq diaw a oirole that

"ii*r*riUo foiritt,e, B,arrdC.Labol ttrc ccntp of thc olrolo O'

Answer (h) Ondtasran tll

(c) Measurc and writs down thc radiui of thc cirole'

Awwer .(c) cm tll

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RTTS{} 4E PREUM il(AM 20 I 64048/0r BHSS 4E PREUMEI1'M2016

404&01

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EndolPqetDANYAL EDUCATION

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Mathematical FormuleeCandldate's Name Class Reglster Number

BALESTIER HILL SECONDARY SCHOOLPRELIMINARY EXAM]NATION 201 6SECONDARY FOUR EXPRESS

MATHEMATICSPaper 2

22 August 2016

4048t02

2 hours 30 mlnutes

For Exrmincrts Uce

/ 100

Compound lnteresl

Mensurallon

Trlgonomelry

Statlsilcs

Total amount = f1t*fr)'

Cuwed surfaoe area of a oona' n r I

Surfacc area ofa spficre = 4z r'

Votumcofacone = Lor'h3

Voltrme of a soh o" - !ort'3

Aroaof trianslc ABC- LabsinC"2Arctcngth= r0, whcrc d isinradians

ISector area = !r'e . whcre d is in radians

2

READ THESE INSTRUCTTONS FIRST

Write your name, class and register number in the spaccs providcd at thc top of this pagc, witingpapers and graph paper,Writc in dark blue or black pen.You may use a pencil flor any diagrams or graphs.Do not use staples, papcr clips, highlighters, glue or correction fluid. abc

Answer all qucstions.If working is ncodcd for any qucstion it must bc shown with thc answcr.Omlsslon of csscntlat worklng wllt result in loce of marks.You aro cxpeoted to uso a scientifio caloulator to cvaluatc oxplioit numcrioal cxprcsslons.Iftho degreo ofaocuracy is not spccilled ln thc quostion, and ifthc answor is not cxact,givc the answer to thrc€ slgnificant figurcs.Givc answors in dogrecs to onc decimat placc.For r, usc either your calculator valuc or 3.142, unlcss thc quostion rcquiros tho answerin terms of r.

The number of marks is given in brackets I J at thc cnd of each question or part question.Thc total number of marks for this paper is 100.

sin,l sin B sinC

ar = b2 +c2 -LbccosA

Moan - zfxLf

Standard deviation -T,T

(Lft\,-[r/J

paper consists of t2 printcd pngcs (lncludlng thls covcr pagc)This questlon

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RHSS 4E PREIJM E)AM 2016 40,t8/02

Monday

Additlonal materials:Writing paper (6 sheets)Graph paper (1 sheet)

DANYAL EDUCATION

3

ALLwoRKINGsMUSTBEsHowNCLEARLYoNTIIEWRITINGPAPER.Answor all the quostions.

6a'7a-' 4b"'

, leaving your answer in positive index notation. t3l

h tho figure TA andTB uatangents to ir circle with centre O.

E

(a) Striting your rgasons olearly, find

(D aagleBAT,

(iD anglcAOB,

(iii) anglcl8B,

(lvl ang)a ADB

(v) anglcEBlV.

(b) Find the radius of the oircle given that the length of BT k 12 cm'

3

( -sr''\I (r) Sime[ry[-:-. J

x+l(b) Express +x-6

7

3-2xas a singlc fraction in its siriplost form.' t31

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(c) Solle the eqnation *-#;0' leavhg your ailwFnl concct t'o 4

significaot ligurcs.

2 Rcctangular tilcs mcasuring * om by (r-r) t, arc uscd h linc tho insido edgc 9fa iectangular'scction of a watl mcasuring_3-60 9In.bJ 100.s,.A11 thc tilcs atc

pr".J rftiuty, with the shortcr sidc paralel to the lcngth of the wall soction.

writc down an oxprcssion in tcrms of r for thc numbcr of tiles thot will fitaoross the length ofthe wall scction.

writ€ down an oxprcssion in torms of r for thc numbor of tilcs that will fitaeross the widtb of the wall scotion.

Given that a,total of 96 tiles are necdc4 fonn en equatlon and show thal it

rpduoos to 5r' -8k+90 = O.

Solve the equation.5tl-8lr+90=0' Explaio whf y9u would rejcct one of

O. r,r**s irna hcnce find thc length of ttre shorto sidc of the tilc'

$*liiiili:

f{i:+iil.

13l

(a)

(b)

(c)

(d)

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BHSS ID PRELIM EXAM 20161018/01 BHSS 4E PREIJM EXAM 2016

4048/02

l

4DANYAL EDUCATION

4

5

300 students from school z and J20 studcnts from school g took an English tcst.Their tcst results are rooorded in the ctmulative frcquency graph bclow.

6

Ir thc diagram, OlB is a trianglo and C is a point on lB such that AC : C B = 2 :lThc sido OB is produccd to point D suoh that OB : BD = 3:2 .

oo E

(o) Given that d=s ard7f,=A, cxpress as simply as possible in terms of nand/or b,

5

Enslish Test Results for Schqol,{ rnd Schoot 8

:50

300

A

250

B'd03E

200

lLI-g r50)taO

t00

AB,

ftoc

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(tr)

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t0 20 30 40 50 60 7o 80 90 t00

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School I

I'

----- School I(a) Find tlre median mark for School I and School g.

(b) Find the interquartile range for School I and School B.

(c) Given that_the passing mark is i0, find tho percentage ofstudcnts who passcdth€ tost ln School,4.

(d) Find the value o'f x if 6z.s% of the students from school B icorcd less than.rmarks.

(c) Conrpare the results ofthe studcnts ftom thc 2 schools in 2 ways.

Givcn that E is a point on Ol such tfrot 6 = f a,

"*prus E in terms of a

Showthat 6=n-1,3

antl b.

(d) Writc down 2 facts about the points C, D, and B.

(e) Find

(l) arca of hiangle IECarea of hiangle OEC'

qrca of rianglc IECaroa of fianglc O,{8 t2l(it)

,Jrr.9's,/r' PREUM tlxAM x016t04,/02 BHSS 'IE PRELIM EXAM 2016 J048/02

I

DANYAL EDUCATION

7

6 Answer thc whote of thls guestion on a rheet of grtpb poper'

Th9 variables * lndl arc connected by the cquation ,= {:.i-')

Tho table lolow shows sorne values ofx and thclr oorrcspondingy values'

,. I 1.5 2 2,5 3 4 5 6

v 3.5 1.72 0.875 0,38 0.05s a -0.58. 4.74

v >2x+7

(a) Find the valuc ofa, oorreot to 2 decimal placos'

(b)Usingascslcof2c{ntorEpr€scntlrrnitonthehorizontalaxisand4omto' . ,*ro* I unitontheverlicalaxis,drawthcgraphof /=i(}.r+. ,

f*

.l<;<6.

(i) using youi graph, write down thesolution of ttre cquatiim ;(l-i-')=Ofor lSxS6.

(d) By drawing a tangent, fmd tbc gradicot of the graph il x = 2 '

(O By drawing an appropriate graph, fiud the range of vqlucs of 'x for whiotr

9-+T

1 The diagram below shows a field,4BCDE on level lromd' wbere C is due south of

A,

A

111.8 m

l13.l

B

1063

D90.6m

(r) Givcn that tbc boaring of E fiom I is I 16'6", and the bcaring of D ftom E is

186.3",

(i) 4rorr551 nngle CED=38.7o.

00 Findtb;kngtho-fcE-

(iiii Findtbetotalarcaofthc naa.lacos''

(b)JohnstmdsotDaodfliosadroneinaslrsightlinotoE.Giventhatthedrone\-' ;"tt itt Atght Aon oo gorma at point b and ascends at 3 mls Bt a ?5o

mSlo,0nd

(i) thelcng0of8fl

(ii) thc hoight oftho drooe whcn it is direotly above B'

(ili) tho flieht time ofthc drone whcn it is directly above B'

(tv) ftcsPcodofthodrone.

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4048/0x BHS'4E PREUM 'EXAM 20t6404u02

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DANYAL EDUCATION

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Choosing whrre to go for thcir tcrtiary cduoation is an important choicc for manystudents. lrr making their ohoiccs, studcnts usually tako lnto considcrAtion scvcralflactors such as the location ofthe school, the quality ofacadernic lcaming, and thefacilities tlrat the school has.

To hclp hor ohooso whioh school to go to, Cascy uscs a scoring systcm to assign avaluo to cach of the factors, After rescarching cach sohool, sho camc up with thefollowing table, scoring each factor fiom I to 5, with 5 bcing thc bcst and I beingthc worst.

Acadcmics FacilitiesReoublio Polv 4 5

Sincaporo Polv J ) 4Temasek Poly 5 3 3

(a) Write down a 3x 3 matrix A to reprcscnt theinformation givcn in thctable. tll

represents.

Casoy does not think that all 3 factors are equally importhnt. Shc assigns aweightage of 0.5 for thc locaticin, 0.3 fgr thc acadcmie, and 0.2 for thcfacilities. Writc down a 3 x I matrix C to represent this information.

(d) Hence, evaluate AC and stat6 what caoh ofthc olcmcnts rcproscnts.

(c) Statc the school that Cascy will sclcct based on hcr crltcria.

r0

9 In E gamc of ohanct, tho expectcd vatuc is tho probability-waightcd av'cragd of allpossiblc values. For cxamplg in.a gamc whorc thc player randomly draws I ofeither a red or blue batl, if he wins $2 for drawing the red ball ond loses $l fordrawing thc bluc ball, thcn thc cxpoctcd valuo of playing thc garne once is

(i)ta-(Jt-r)=j, mcaning that, in thc Ions run, aftor ptaving trrc gamc

multipte timcs, thc playcr can cxpcct to win, on avcrag6, $0.50.

Considcr a gamc whcrc you arc givon a bag with 2 black balls and 3 white balls. Ifyou draw a black ball, you win $1. lfyou draw a whitc ball, you losc $1. Thc ballsarc drawn without replaccmcnt, and you may stop at any time you wish, aftcr whichthe gamc is rcsel

(a) Amclia plays tho gamc and she decides to follow the strategy of quittingimmcdiatcly if shc docs not draw tho black ball in thc first try.

(l) Writc down thc probability that she draws a black ball in thc first try.

(il) Caloulate the cxpccted valuc for Amclia's stratcgy.

(b) Bcnson plays thc gamc and he deoidcs to follow the strategy of continuallydrawing until be successfully draws I black ball.

0) Calculatc the probability that Benson draws the black ball on th€ secondtry.

(ll) Calcutate thc probability that Benson draws the blaok ball on tlre thirdh'y.

(lil) Calculatc thc probability that Benson drsws the black ball on the fourthtry.

(lv) Calculate thc expected valuc for Benson's strategy.

(c) Thc optimal stratcgy for the gamo is to stop aftcr drawing a black ball in thcfirst or sccond try, or to stop after drawing 2 blaok batls, or to draw all theballs, whichovor comcs ftrst. By oomplcting thc partiat probability trcc bclow,or othcrwiso, dctcrmino thc cxpcotcd valuo ofthis stratcgy.

l.l 2rd 3rd

Black

Black

Black

(b) Civen that B = , evalrrate AB and statc what each of thc olcmcntsiilttI

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1018/02

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DANYAL EDUCATION

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l0 .A hot air balloon .oonsists bf an cnvelop Taac- o{ nyfo. q with a bastcit suslendcd

'- i**tU n..ieo alr insiaotrre cnvctope iratcs the bailoon buoyant siaco the hot air

[it "f"**..a*tt y than the abnosphoe outsidetheballoon

T[rc shapc of tha c,uvclope Ttr F .1'oaerco *

,1 ]T131"-.T:prgl3"gcn.ftrqrrnm- nic Oasarir below sbori,s thC oross-seotioh ottbe cnvelopc,4B,gDE Thc

;"8; &-;i u,;fi*isptrero ano co-oc is l0 q the radirs' r' of thc narrow end of

ih; A;h;* is 6 q qnd the hcight of thc covelopo is 15 m'

12

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coblo

(a) Calculate thc volunro of air insidc tho onwlopa'

DIt$s 48

(b) By fioding. thc surface area of tho cnvolopc' qalorlato thc mass of thc\-'

illrcrppe ii rc, givon that thc rtixrsity of tl[o nflon is 102 g/mr'

t41

t31

(c) T[oamount oflift geircratcd by the hotairbaloon dopon& on thc differcnoot-' io-o*rrty bctwed th; h;ge air an! tho annosphuo' rirultipliS by thc

ilri..'Jr.il" ttsted air, Given Otat t5c density of air in t1c atuospherc is

i;ofid{ilJtu. a-titv "itrt u*tuato..ro6"c is 0'949 kglmr' 99l-culatc

the amount of tin genorateJii tt i. t ot uir u.floon in kilograms at l00oc. I2l

(d) Given tlrat the rest of the equipmant (cables' basftct' fucl tanke' otc') has.alu,, #ffi; ffi40i, 6 iii,_-o t r rouit um number of peoplc that can ride

thehot airballoou ifo"ttpttson weighs 75 kg on averago' l2l

il48/01

basket

'ii;ih$#+rj

PRELIMqtaM

End ofPaPer

4E fiaMDANYAL EDUCATION

- -z(-z.r:'l'*o.s[l?)-2a'+0.5b \ / \5/-Ml

(or B2)

3Ja+c -2.13+1.8n

= -0.5 lB74 - A I

I (a)

l(b) -0.519 - Bl

2(a) 10 -- Bl

2(b) 3780=21 x3'x5x7 .-:MlThc numbcr5 arer l B0 and 1 890 - A l, A l (OE)

270 and 1260540 and 630

4x1 -2lx-lB= 4r +3 x-6 -- Bl, Bl3(a)

3(b) 5D+ I oaD - 3 = 3 (za - t) + so(za - t\-- B', Br (OE)

6a-

= (za - r)(: + sa)

3(o) x' +zx - y';zi=(r*yfir-r) *i(** y\ - Ml, Ml

= (r+ y)(r - y+2) - Al

4 (r- z)(r to) = zsao

z=lB -Mll39o +147" +"164o + l5x = 2880o - Ml

x=1620 -Al1$,

= $361 88. I s

Intercst=$36t88,15-$30000 -- Ml

4.8 \-tl 00, -Mt

a

+

= $6188. l5 -- Al

Amount = $30000

6

-dt.. ,-'".: .:..

. Balance =0.65x$25000= $16250 - Ml

,n,.,rr, = ('u"oxuxt)

100

= $4875 - Ml

lnstaltment

I=$352.08 -- A

7(a)rate =

y-17

-Mt

ta,rpcratu'! = r. [1-) P r)

=5x+9y -AIt4

7(b) abcost=

12

salcs =31 - Ml100

profltac ab

-Al

I 7.2:12

72;120 -Ml3:5 - Al

(or 82)

I cost(ubcr)=11 0. .MI

= $19.75

cost (comfort) = 1.25 x

[, 2.to z(ulu.,J.t,r,)(#).(r,)[ry)] - "'

= $20.98 - Ml

Spccd (m/s)

25

6

I6.25(s)

t..i..

5.:

I 0(a)

I

I

I

IIII

DANYAL EDUCATION

dist fiojnMrTeo uuur 6.25, = (60+(Q(o.zs))-28,12s = le'375

time to caPhre= U.,t*ffi='#- -Ml

-Ml

-Al

dist by t-rcx aftor 6.25s = 0.5

otal dist bYMrTcn=6x7474l

-78.125 -Ml

II

i*zrffer'o 3't+5<z-'

2x+12<9x+t5 AND 3.r+5 <14-2r7r > -3 AI'ID 5* 3 9

-1 A.r>-i ANDI<l= -Bl"Bl

-1 L-a <x1l:75

i+2.ff*-,

a=4

v=l'whenx=a,y=b

b=L{a

. k=b{tr$r,y=w

whcor= 6o

nt;y=frb

r/o

-Ml

o/o decroase= xl00

.k

-Ml

,rtb

2.x-9Y+8=39

,ftitr)-rr+8=3e -Mr:18-toy-.ny+?4=ll7

'-37 Y = 111

Y='3 -AlI=

k+5y--

-s - s(-g)

3

Lu,;

lo(b)

ffihffis"'

-31

0 r15

ra-o)-

- i.,,*,',S;*ilti" :

ffiir

-B1

-Bl

-BlDANYAL EDUCATION

r8(d) (ln-t)(,r+t)

= 4n2 +3n-l(or 82)

-Mt-Al

I 9(a)sin0,65 = -i-14-r

r = 5.28

-Ml..Al

r9(b)oP=oR= 5'28 --Ml

tan0.65

PtR= r-1.3 - Ml

perimotcr = (s.2811 " - r.:1. z(ffiJ

=23.6 - Al

ie(cio Pc R = (2\(o sl(*#) l', s) = 36,ctzzq

crn = (o.s)(s.za)' (z- r.:) = 2i.670328

-Ml

*Mtshaded area = 36 .67224 - 25.670328 = I I .0 -- A I

20(aj

Conect triangle- Bllines -Bt

(b) constructioncircle

) onof circlc -Bt

BI

(c\ 5.6 cm - Bl

DANYAL EDUCATION

2(a)-Bl360

x-3

2(b) 300

x -BI

2(c) ,($.,(lllJ-,=* -M,360 *199=56r-3 x

360r+300(x - 3) = so(r)(, -:)360r +300x-900 = 50.r'l - l50x50.r'!-810x+900=0

5.r'-8lx+90=0 *Al

-Ml

2(d) Sr'1-8Lx+90=0

(x- ts)(sx- o) = o

--Al

ncicct f| sincc (r-3) cannotbcncgative, -- Bl

Lcngdr ofshortor sidc - 12 om - Bl

..Ml

r=15 or 115

I (a)

-MI/-3r')' 6a-1 9ait- | +_\ zbo ) 4b-t 4b8

6a-2

W4b"?-,oa

-Mt9an

x4b8

36a6 b-l= zuda

.Istl

-at2btl

-Ml.r+ I 1,+l 7

-+-=

2x1 +x-6 3-2x 2x-3

-Ml

..AI

T-T{/O;Nx+l-l(x+21(,+z)(2,-t)

-6x - 13

@-r40;n

,(2,+ r)-(r -+,)(,-:)=o -- Ml2x'+x-(x4-4rr+ttu)=o

6.v'-12.r+3=0 -Mt

x l-4x___=0.r-3 2x+l

,_ -(-rz)n,F4{{oxr)2(6)

=0.2929 or -1,707 -Al,AlDANYAL EDUCATION

j(rso"-os')=56o (isocoles triangle) -BlBAr

l,a =$t -xo-900-680- 112. (z zumoftia"sl") -Al*Ofrl=9t (tangenr.l mdius) -Ml

.riea = !fw) = 56" (z tt af,ffie - 2l at cirqm&r€oce) - Bl

= l80o-560= l24o (oyclicquadrilateral) -Bl

3(av) =90" (l in -Ml

t",rg4.= tuii* -Ml

radius = l2tan34o = 8.09 om * Al

B1B1Schooi B:

Sohool marksmarlcs

4(b)

4(9) ofstutlents =

n*.-.ao=ffi xrcvtc=746/o -Al

hrSbcr. -Blife tesults ofshrdents.fiom Soho<il I is less sprcid because tfreir interquartile range is

mediau scoreAom A on average

lower. -Bl

EDJV = 180'-90o-56o = i4' (zs on a suaigbt lind) - At

-BlSchool 8:

.r = 64 marks - Al

DANYAL EDUCATION

5(ai) AB.OB-at=b-q --Bl

5(aii) 'r-AC=:AB

J

2- 2=:b--a3- 3- -Bl

5(aiii ) &=o,q*ft2. 2

= a+-b--a- 3- 3-t2

=-a+-3- 3o -Bl

5(aivtOD

5

3OB

{=ab

J-- Bl

5(b) CD=OD-oC5. I

= -D--A-3- 3-.t

= b--a' 3-

,,ab3-

s(c) ED= EO+OD

5 d+1b- 3- -BlI

5(d) They aro collinear. - B I

ao=Jco -- Br (oE)

5(ci) .AEC AE 4

OEC OE 5-Bl

5(eii ) AEC AEC AOC_=_x_OAB AOC OAI]

42x-I 3

B

11 -At

--Mt

=4.34

Soalc - BlPlot-BlCtrvc-Bl

x= 3.1

Correct gradient line on graph - Blm=-1.25 - Bl

6(c)

-- AlDraw graph of..-AI

6(a)

6(b)

6(c)

6(d)

DANYAL EDUCATION

cEP = xe - t86.3" - 63.4" -7 r'6"" =38.7" .-Bl

' cE 90.6

-4

Sio102.6 sin38.7

CE=141.4139

=l4l ..Bl

II.-4005335+75ffi.899+5998.049 - Ml, Ml' Ml

-175u283r175fi) -Al

ti.t)0063xsin86.2')t.o)(sinztarcS

=450+38.7" +48.8e= 132.5" -Ml-Ml

BED

BD=

= 180.335

=180 -Al

*rr.=ffi -Mlhcight = 180.335tan 25o

= 84.09159

=84.1m -Al84.091s9flisltttimb=---

= 28.0305

=28.0 s -Bl

distancc *r"*oO-H=198.977 -Ml

r98.977speed= -:--=:

= 7.09858

= 7'10 m/s - Al

80)

-BlA=145324533

The elements represent th€ lotal score ofeach school respectively' :- B I

AB= -Bl10

11

0.5

0.3

0.2-Blc

Tho clomcots reprosent thc wcighted scores ofoach school respootivcly' -Bl

2;7

AC= 2.9 -Bl4

DANYAL EDUCATION

9(ai)-- Bl

2D=-,5

9(aii) ,, =(,?)(r.(9t-,1

-BlI

5

7, '.)

D=-X-'543

t0 -Bl

e(b0

e(bii) 322D=-X-X-'54 3

=-!. - Br5

9(biii) 32D=-X-'54I=-l0 -Bl

,-l"t3

9(biv)

.r:.."

(3) r,l. (*) r,t. (f) c,r. (*) (-42t r

;0

55-- Bl

E.V.=

.. i'...'li.: il1fl ,

9(c)

.H (*) (l (*) r'r,r. (:) (*) (i) r,x,x-u -Ml

, , = (J)t'). (i)r,).(i)(i)(3Xj)r.r

=?+o+o- I - I

5 l0l0=f -Ar

5

I 0(a) Let thc height ofthe cone bc x + 5.

t =6 --Mlx 15 t0

x=7.5 -Al

'.,"," = [,j[f t a t, ot' . [j)( ") 1,

o)' p s. 4 - [,f p) g)' (t s)

2000 1250=+n+-rt-yurf33=3120.6487

=3120 mt - Al

*Ml

r0(b)T.S.A r) (r o)' +(z)(ro)(Jro,-rzs) - t{ta(.tr;f;

=950.1746

=950 m' -Mlmass=102x950.1746 --Ml

=96917.8092 e

= 96.9178

= 96.9 kg - Al

l0(c) tin = (r .zor - o.ear) (trzo.an) -- Ml

=795.7654

=796 kg - Al

r 0(d) . 795.7654-96.9r78-400f, Ot DeODIC =

-

75

= 3.9846

e3 --Al

-Mt,' ,:1. DANYAL EDUCATION