Chong Boon Secondary SchoolPrelimlnary Examinatlon 2016Secondary 4 Exprees / 5 Normal AcademicMathematics 4016/01

4048101

Paper {

30 Augqst 2016 (Tuesday) 2 hourc

Candidate Namo: Class:

lndex No:

Contpound intcrut

l,hwuratiott

Trigorcnelry

Srarirriat

MUhemslicol Fornuatae

o=b_csio,A sin8 sinC

a' = bz + c' - 2bccns A

rTotal amount - ,(,. ,ft)'

Curvcd surface arca ofa cone = ,r{

Surfaca arca ofsphcre - 4nl

Volurne of conc = lru lrr3

Volumc ofsohere lart'3Arcs of &{8C - !tcsilrt

2

Arc length - 74, where d is in radian

SactorE ca- !,'O.rnh.te d is in radian2

READ THESE INSTRUCTIONS FIRST

Do not opon thlg booklet untll you arc told to do so,

Candidatgs an$/t/et on the Question Paper.

Wrlte your name, class and candidatg numb€. on the cover 8heet.\rvrlte ln dsrk blue or black pen.You may u8e s soft pencll for any dlagrams or graPhs.Do not use staples, peper clips, highllghters, glue or correctlon fluid.

Answer all questlons.lf worklng ls needed for any question it must be shown with the answer.Omission of sssenlial worklng will resull ln losE of marks.Calculstors should be used where appropriate.lf the degree of accuraoy is not spoolflsd ln the guestion, and if the answsr ls not exacl glve lhoanswEr to lhr€e slgnltioant flguree. Glve answers h dogrees to one decimal place.Forr, uge elther lhe calculator value or 3.142, unlsss th6 quEstlon rcqulre3 lhe sn8u,., ln tetm8 ofE.

Th€ number of marks b giv€n in brack3ts [ ] at the end of €ach question or part question.Tha tolal of lhe marks for this paper ls 80.

For Errmlne/r Ua,

80

"*'-#sra^dsfd deviatio. = Ef_lE+l

Thls document cons&ls ol 2!l glntad p.gos lnoludng tha oov.r pago,CBSS .tE5N Mclhcm.0c! Pr.lim 1010t01tot16

40{o10'uol1a2

DANYAL EDUCATION

h tro dilgrsm, /OC i,rr ri$rt-an$od tsiangtc tod DEf is parallcl to flGE' Givcn tut

,io /[li's0, lrnSo GB'I- 6T ud ari$ ACB - 4*'Answcr dl tho qucstions

I

20t5i +3'(a) calculatc T.or4-ffi

' Writo down tho first four digits of your'answcr

Anwer (a).'.""""""""""""' tll

(b) Writo your answor to part (o) cofioct to 3 significant figuros'

2.' Thc first five torms of a soqucnco aro -2' 4'-8; 16'-12' "'

. (a) Writo down thc noxt trlo tcrms in tho soquonco'

ln*ter (a) ' ".......... [ll

(b) Find an oxprossion, in tcrms of rr ' for thc

't th tcrm of tho scqucncc'

4.

II.

HG

F

B c

3. A factory manufac'tures micrdchips'

In.a partibular month, thc factory pro4uscd (xl0' microchips. on inspcctioq l.5xl0rt ofthoso

microchips wcro found to bo in good conditioh and tho rcst rryob fautty,snd had to bo dircardod'

(a) Find the numbcr of microohips that worc faulty Givc your answor in standard form'

Caloulato

@) aunglaAEF,

(hl auirdcADE,

(c) anglo CGB.

Attwt (a) ."""I1l

Answer (b) ....'.'tll

Arcver (a) -......................... ttI

(b) . Find the ratio of tho number of miorochips in good oondition to tho total numbor of

nfcrochiPs Produced.

4016/01ro/16 1

.i,i.J; .j. ,;.ril

rili+$I{[iiilij

iri.g#;CBss 4E5N Mathomatios

4048/01ro/16

3 CBSS 4E5N Mathomatlcs Preum4048rc1r9n6

DANYAL EDUCATION

5. Tho lino gruph bclow shows tho prolits that company A has mado over a fcw years.

Profits of CompanyA

ffi,nthousands

450

400

350

300

250

200

t50

6. Expandanttsimpliff xex-4y)-2(x-y)r.

Answer tzl

7. Thc encrry E injoules stored in an elastic band varies as the square ofils extension dcm.(a) Thc valuc oft is 100 when thc cxtonsion ofthc olastic band is at a partioular value.

Find ths ncw value ofE wheo the odensioo of thc elastic band is doubled.

Arlrl,ter (a) .., joules [2]

(b) Whcn thc clastic band is oxtondcd by 3 cm, the cnorgy stored is 243 joulcs.

What is thc oxtonsion whcn thc stor4"daergy is 108 joules?

Atuver (b) --..,,,.,............,,... crn [2]

404.OiO1lot18

. 2005 2006 2007

Ycar

Explain onc way in which the graph is misleding.

2008 20t5

I

L

\

I

i

I

4glWAltUt't64048n1/o|1A

Answer

CSSS 4E5N Mathematlcs PrelimDANYAL EDUCATION

8. g - {5 : x is an intogor such that I 5r 5 l0}'

A - {x i xis aPrimo numbcr},

3; {x: x is nn odd number},

(a) List thc clemcnts in lnB .

Anwcr (a) ...-...t11

O) List the clcmonts in luB

(c) Findthovaluc n(.tvaf

g. ABCD isa quadrilateral such thatlE is riarallct to DC. BA- BD ard BD bisccts anglclDC.

(a) Explain why triangle lBD is equilatoral.

...r..........rit....

(b) Given furthcr that anglo DBC = 80", find rcflox anglo BCD.

t21

'ul

(a) Two cylindcrsl ad 8 havc diamctcn 6x cm and l2r cm respcctively.

Initially, cylindorl contains imtcr to a hcight of 45 cm and rytindct I is cmpty. If all

ttro wator froml is poured into a, calculatc tho hcigtrt of rirrator in B.

10. Factoriso di foltowiry complctoty

@1 3aib+c)-b-c,

(b) 5r'-2os'

il.

c

i r....

lnswar (a) .......cm [2t

@) A smalt trafiIo nurlro ig gcomotricalty cimitar to a largc onq 8d tho diamctsrt of tho two

mrrkor uo !4 om and 28 om rccpoctivoly.

0) WriE doum thc ratio of lho btat surftco rroa of tho rmalt marts to that of thc largo onc,

Ann* p)fi).-:...'......' : .........-... [l]

(li) Find tho wcight oftho largc markor, in kitograms, if rho small onc weighs 0.8 kg'

Anwer p)(ii) ,,..,,.ke121

4016/01/O/t8.r04E/01/o/16

4016/01/O/16 ICBSS 4E5N Mathematlcs Prsllm4olan1to116

hnter P)

CBSS 4E5N MathemallcE PrelimDANYAL E

DUCATION

12. (u) Exprass y = xt +zx-B in tho tbrm of y= (x+ pl(x+ql

Anwer (a) ....... tll

(b) Flence,sketch y =ar a2r-3

Auwar (b)

v

.r

13. (a) Express y'+lly-15 intheform(y+a)'+0.

(b) [Ionce rolvo tho oquatioo y2 + I I y - I 5 = 0, giving your answer cortect to two

decimal places.

Answer (b) .....,.......,.and... ...,..,.,. l2l

14. Two storcs advertiss tho eame sofa set during the Grcat Singapore Sale.

$1500 + 7% GsT*t21

*GS? : Goods and Sentices Tax

(e) Which store solls tho sofa set at a lowor prioe? Justify your answer

Arunter (a) 5torc................ offers a lower price

(b) Catculatc the amourt of GST charged on the sofa sct h Store 8.

- Deposit of$220plus 12 nrontbly instalmcnts of$t20

- Prlce lncludcs 7ole GST*

t21

0

I 4016t01totl64p48l01tOl16

STORE,4 STORES

CBSS.[EEN Melh€mstlcs Prcllm 4016101tO11640d.A|01totls

CBSa 4E5N Mathgmodcs Prcllm 10

DANYAL EDUCATION

nin . .r"..i'i-,,+rf,4'.

16. Tho graph chow dio c'hargor of an olodi{oiaq Mr Lim' to carry out rcpoirs'

G. (o) Two of the intcrior anglcs of a pentrgon riro (r + Eo)o and^(3r + t 0f' whilc tttct-'

rcmaining intcrior anglos arc I l0o Gach' Find thc valuc ofr'

Answcr (a) x * ..-........."."""""' t2l

(b) Thcrliagramshowsthrcosides AB.BCutdCDofarogularpolygon' AngloCDD-l8n'

A

(t) Find the extorior angle ofthe polygon'

Answer (b) fi).;.......................'.' IU

(ii) Catculato tho numbor of sides of the polygon'

4016/01/on6/lo48m1/O/16

(a) If Mr Lim ohargcd $ 100 tor a particular ropair, how long did it takc?

(b) Anothor olcctriciaq Mr Batg chugcs $30 porhour, but dtics not havo a fixcd chargc'

Ihrw a tinc on tho grld to c;Prtsont Mr Bala'r chargcs' tl1

(c) For a ropair that is sxpectcd to tako 3'5 hours, whict oloctrician would charBo lcss?

ao16/01/o/'164048/01/Or16

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J

5w.\ ,J

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Ees-s +gsN Mathematica Ptellm 11 EBss ieSN utathamatie Prelim12DANYAL E

DUCATION

17. A bag contains 4 balls, numbered 1,2,3 aad4.

Two balls are taken from the hag at rsndom, one afle( tho olher, without rcpl&ccmcut.(e) Draw tho possibility diugrum to represent the outcomes.

Anwer (a)

tlI

(b) Find, in ils simplsst form, the probability that

(l) tlre product of the two numbers is a square number,

Answer ft)(i) ......... tU

(ll) ono numbor is odd and aoothor number is ovon,

Anotcr (b)(ii) tll(lll) tho sum oftho nunlbors is morcthln 5,

Answar (b)(iii)...........,........,.....,,........ t I l(lv) ono of lhe numbors is I

Answer (b) (iv)..........-..-..................... t I l

4o4ol01tona

18. A rectangular garden rvith a flower b€d is as shown bolow. The arca ofthe garden is I 5 mz

Garden

Flower bed

(a) If a flower bed occupies 237o of tlre garden, frnd the area of the flower bed.

(b) Given the length of the gardcn is (x + 2) m, find its width in terms of r.

(c) Given thut the width of thc gard"n i, I n , write an equrtion in .r ancl use ir to find thex

lengtrh ofthe garden.

Answer (c) .......m [2]

1018tO1lot1gDANYAL EDUCATION

19, Tho fotlowing tangranl oonsists of7 picccs that arc cut from ir squaro' It consisb of:

,{ : Two large congruont trianglcs

B :Two small oongruant trianglcs

C: Ono Parallelogram

D: One squarc

E : One medium trianglc

Tho total arca ig 56 cm2. Calculato thc aroa of

(a) parallelogram C,

,lnswer (a) '... cmt [2]

(b) squaro D,

Lnwor ft) .... cml 1t1

(c) triangte E.

20, ABCD is atra@um in which tfu lcngth of BC.is I tutib'

v

B

xA o D

Ifl is tho point (-+ o); a is dro point (- r, l) u,a U'" tto" ofthc rapozium is 48 squarc units'

frnd

(a) tho coordinatos of tho Point C,

Answer (a) (...............'.,.......'........) ttt(b) thc longth ofl,,

Anster p) ..'. units [l]

(c) thc coordinatcr of dtc point 4

hnrer (c) (..............,,.................) t:t

(d) sin OiA , ocprorsing your answcr as a fractiorr-

Answ* (d)..-.......... ;.. ;............,. t U

4016/01/O/16/t048/01/Or16

c

BA

D

B

I

EL

CBSS leSru Mattrematics Prelim4UE/01/o,18

'15 CBSS 4E5N Mathematlcs Prcllm16

DANYAL EDUCATION

21. The diagram shows a pattern formod by four identical circlEs insido a larger circle.

Tho radius of the largcr circlc is twice thc radius of the smaller circlcs.

Find thc shaded ar€s ifthc radius ofthc largcr circlo is J cm.

Answer ....,...,........,..,,.... om' 15;

40,4,U0ltOnA

22. (a) The data below shows tho marks of class 4A in their recent Mathematics common test-

Calculatc thc interquartile rangc.

(b) Thc cumulativc frcqucncy graghcohort in thc rccent. Mathematics

Awver (a) .......tl]

Iepres€nB the marks Ofthc wholc Seeondary Fourcommon t6st

250

200

150

100

50

aa

F{odz

Mtks

Use thc greph to estimate the passing mark if only 42% ofthe cohon passed theMathematics common tcst.

At $ter (b)...,..................,...... t I l

4016t01to1164048101tona

CBSS.+EgN Malhamalis Prellm 18DANYAL EDUCATION

(cl Hore arc two statomonB comparing thc martrs ofthc cohort and Class 4'4"

'-' ro, .u.t one, writc down whcthcr you agec or disagrcc-

Oiuo . ,ouron fo, eaoh answr' stating oloarly tro shtistical data rrs€d'

(i) On avcragc, Class 4A did bcttor than tho wholo Socondary Four cohort in thc

Thc diagrsm belilw shou! part a map ofso Mainland atut o holiday rcsort, sand Islan4 wttich

aro coonoctcd by a clblc car oyrtcrn Ttrc scalo is l; I 5 000'?jt.

Mathematics common tcst'

Annuer | ,,.,..'.""""""' bccauso """"""""1"""""""'

.................................... tll

(ii) Tho Mathcmatics mffks of the studonls ln Class 4A havc a widor sprcad than tho wholc

Socondary Four cohort in thc common tcst'

Ansver I bccausc """""""""""'""""""'

tu

Tho actual diitanpo bcturcon Bay Front Station on

IsLtd.is 1260 Dctrcs' It wilt uko t2 mlnr$os dr atho Mainland and Sard Island Station on Sand

oontinuous rido tom BayFroot Stntionto

l2l

6

Surd Islaod Stclon"(e) Calculitc ttrc spccd ofthc cablo car, Givc ytrur answcr in mctros pcr second'

Ansu'or ft) ...' m/s f2l

Ttro lvlaritime Musewt, C is on a bcaring of 03ff from lgz triw\ A, arld 600 mctrcs from thc

UtdarvoerWorl4 B,

O) Mfik ddt cnd labol tho position of C on thc map abovo'

(c) Cilculatc thc actual distanco, in kilomctros, tictweon A o;nd B'

lwwer (c)........r...............' km t2lENDOFPAPER

(.

MAINI,AND 6 *r*n r,.*

. B: IJnderttaterWorld

SAND ISLANI),L'.Aquqium

f SandlafandStatlon

4046/01/O/10

19 4048n11O116

MERMAIDSEA

N

DANYAL EDUCATION

Chong Bqon Secondary SchoolPreliminary Examlnation 20{ 6Secondary 4 Express I5 Normal (Academic)Mathematlcs 4016102Paper 2 4O4S1O2

30 August 2016 (Tuesday) 2 hour 30 mlnutes

Candidate Name;

Additional Materlals: Writing PaperCover PageGraph Paper

READ THESE INSTRUCTIONS FIRST

Do not opon thls booklet untll you are told to do so.

Write your name,.class and candidate number on all the work your hand ln.Writ6 ln dsrk blue or blad( pen on both sldes of th6 paper,You rhay u8c a sof, pencll for any dlagrame or graphs.Do not uso staples, paper cllps, hlghlighterg, glue or oonedion tluld.

Class:

lndex No:

Compowd Interest

Mensfirdtion

TrigonoMetty

Srarrilr'cr

Muhematlcol Formulrc

Toral amounr= rO*fi),

Curvod surface area of a conE - ra.,

Surfaco area ofa sphere = 4ra-r

abcsir,l -.irs = rirC

ar =bz +cr -2bcosA

61

1

Volumcofacone = | ,.'h3

Volume of a sphere - f ro''

IArea of triangle,y' BC - :absrlC

'I

Arc longth = r0 , wharo d is in radians

Sector orea = !r'0 , ntn "

d is in radians

Ansuer all quosuons.lf worklng ls needed for any quo8tion lt must be shown lvlth th€ answEr.Omlsdon of essentlal worting wlll roeult ln losE of marks.The uee ol an approved sclenllfic calculstor 18 expected, where appropfiate.lf thc d€gre€ of aocuracy b not spocltl€d ln the question, and lf the snswEr is not ex8ct, glve theanlrrvcr to thr€o slgnmcant flgures, Glvo anstrors ln degrees to ons dcclmal plac€.Forr, u$c elthor the calculetor valuo or 3.142. unloss tho quostlon rcqulres the answar ln t6ms otz.

The number of marks ls glven ln breckots I I al the end of each guestion or parl questlon.The total of the marks for this paper is 100.

For Examlnor'i U8o

100

vre-=ff

stsndard Deviation= trH

CESS 4E5N MathemetiB Prollm 4016rc,/on64015102t0t16

Th/E doemont aonslsts of I ptioacd pagos (lnahtcllng the aow pago) end :l bbnk p.gas.DANYAL EDUCATION

Answor all tho qucstions.

A triangular prism is rcmovcd from a cuboid as shown in ttro diagram'

rcm

l8

cm

(e) A cafc rctlg thpc tpoo of bubblc tca Thc nnmbcrof orp of bubblo tcr sotd on Friday'

saardrv and Sundrvdrtt"; ilitttt;ak of tho Juoo h;Idays and thc scllini pricc of onc

cup oftiro vuious tlpc of bubbtc toe arc at follow:

t,

l. (a)

(b)

cm

.MilkTca Jasn'rinel',Iilk Tca -Fantasv lco-blcndcdr6

Friday 20 30; l(Srturdsy 38 46) 28

Sunday 24 52 40

Scllhs prico $1.50 $2.50 $3.00

(D Evaluatc tlro matrix P - BS.

0tl) Stato what thc oiomcnb of P rcProsont

(iv) Bvatuatc.firc matrix T - (l I 0P'

(v) Stato whatT rcPrcsonts'

During thc sccond wcek, thc cafc had a promotion by oftcring a 2096 discount on all thrac

typcs of bubblo tea.

(l)Writodownanow3xlmatixDtofcprrsontthoncwsctlingpriocofonccupofthcthrcc tyPcc of bubblc toa,

(ll) undor this promotion, tho numbcr of oupo of b.ubblo.toa sold inorcasod by Sooh for all-' u;Ar. iind tho total amount of monoy colloctod on tho sccond rrycck'

9x' 6{1. (c). SimpliS lyo' y'

(b) Simolito 8-2r -12+ x-r'

(c) Solvothe incquatitY3-2x 2x+5 ^

- <-+ t.53

(d) (i) **"" *-;} as a singlo fi'action in its simplcst form'

(li) Solvothocquation210

x-2 . 4-x7

4016/0?0/164{r48/0ZO/16

(D Writo down a 3 x 3 niatrk B to ropnoscnt tbe quantity of bubblo tca sold snd a

3 x I matrix S to roprosent tho seliing prico of ono oup of the threc types of bubblc tca - -ttl

The cross-sectiooal aroa oftho triangular prbm is 5'625y ar?'

(i) Form two oqriations in terms ofr andy'

(ll) Solvo your simultErco$ oquations to flnd tho valuo ofr and ofy'

(lir) Calculato tho volumo of the triongular prism as a pcrccntago of thc volumc of tho

cuboid.

t2ll2t

t21

tlltutt1

tl1

solvcthccqu&tion t5-3x-lOxr-o,givingthdanswcrsoorrccttofourdccimalplaocs. [3] o)

tu

t21P. No(h U

20

T

pl

t2l

t2'l

t21

t31

tel

a)t21

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t3l

154 m V

(a) Caloulato

(i) w,(ll) tho arqa of tho triangular fiold TW,@ficf,,llotha noE ost squaro metsq

(il$ anglo TW,

(tv) thoboaringof lfrom U.

'(h) An ant is resting at I spot, S, along 77, whcrc St/is tho shortcst distrncc ofthc 8nt from

'"' ;;il r. &iiihrt tr,i t Jigi,t of tlo fligpoh rt is 20 m, catcutato thc anglo of olovation

off from S.

4016/0?o/16404AlO2lOl16

=4

13

-)-

. ii+ ..

.-,.itlirl.:'

CBSS 4E5N Mathomstica P16llmCBSS 4E5N Mathematlca Prellm

In tho diagram, ?url rcproscntg"a horizontal triin$tarfiold and 11P roprosonts a vortical flagtlolo.

Uir.io r-r.*i r, ,/is dus cast of rand anglo UTV-64"

DANYAL EDUCATION

S. (a) ItisgivontLnt @ =(;.')

o) ri"a lFEl.

0D Givcn ttrat P is thc point (6, -15), find the coordinatos of tho point Q.

(iii) tt is given tlrat 8.1 is parollel to PQ and it io ono quuter us long as Pp,

Express 13 as a column voctor.

C

In tho diagram, Od - c, Ob - aand lhe point C d ividas Oi in tho ratio of I : 3.

Thc points D and E lios on OB rlul, CB rospcctivcly suoh ,f,", I - I nd BC - SEC.oB4(i) Express cach ofthe lbllowing, as simply as possible, in tcrms ofc andlor d,

@l ot,(b) 6,(cl oi,

I(ll) Show that PE = - (4c - d).J

(ilD Wrim down two thots about thc points,{, D and E

CBSS /tEsN Mslhcmatics Prellm 4010to2lona404UOAO|1A

Expross 9000 os a product of its primc factors.

9ir.q O"t_gOOOt -y', whcrc & andp are integea and p is as small as possible,fnrdthc value of &urd ofp,

Thc lowestcomrnon multiplc of two numbcrs is 9000.The highest common factor ofthoso two numbers is 500.Both numbers are greater than 500.

Find the two numbers.

(b) r is a positive integer.

(i) Writc down an o<prcssion for thc next odd nurnber g,reater than 2r, + l.(ii) Find rnd simplirt an opression for dre ditrerence betwccn the squares of those

two odd numbers.

(iii) Hence o<plain whytho difference bctween the squaros oftwo consecutive oddnuinbcrs h alnnys a multiplo of8.

7. Answer thc wholc of thb questioo otr r rhcet ofgroph papcr.

The variablcs x and r/ afe connectcd by thc equttion y = 6 - t8

4

x

(c) Usc your Eraph to fiod tho two solutio* o, , - { - 1 = O8.r

6, (r) 0)

00

(rii)

ttl

tll

(b)

tzl

l2t

tu l2t

tll

t2l

trl

D

o

tt)

ttI

ttl

tlI

t2I

Soma corrcsponding valuos ofx andy aro givcn in the table below.

x 0.6 0.8 I 4 5 6 7v - 0.71 0,92 3 2.08 0.83 - 0.70

(r) Calculate the value of/c. tll(b) Using a scale of 2 cm to I unit, drarv a horimntal x-axis fbr 0 t.r s 7,

Ueing r scalc of 4 cm to I unitr dmw a vortioal 1'a1is fe1 - I s y s 4.

On your axcs, plot tho poaoB gavoo in tho table nnd join them with a smooth ourve, t3l

(d) By dnwing a t&ngcnt" find thc gradieot ofthe curve at (5, 2.08).

(e)

tzt

tzt

Bydrawingasuitablostraightlineonyourgrapt,sofe f-t'- !n*=O for 0s.r<7.[3]

CBSS 4E5N M.lhomeuos Prellm &1WOUO|164UgtUtOl16 05

n

DANYAL EDUCATION

c

(a) anglaEAD'

(b) anglo EBD,

(c) onglc BED,

(d) reflcxwtglc BOD.

A point, P, is to be ma*ed on the diagnrq on thc aamc sidc of'{D as 6', ruoh that

6nq,lc BPD' 50"

(il) Does the point P lic on thc ciroumfcronce oftho circlo, lnsidc tho circlo or

outside thc circle? Givo a rcason for your aoslvcr'

D' c

40 om

,(

9. (a) Thc tim6 h&Gn by lo0 Etrdd8 toar sohool I to oomplctc lho 2.4 km run is shown in thc

tsbtobolor.

fimo (rhinutos) 6<t <9 9<t<12 12<t <15 .15 3, <18 t83r<21

Frcquoncy 3 36 47- t2 )

(l) What pcroontagb oftho studona ran fasto than t2 km/h? 121

0l) Catculatc an estlmetd.of

-(r) trcmpatl.limo, tU

(b) drc $ndard d;viation. tll

(ltl) Explain why tlrc mcan timo and standard doviation calculatod in part (aXl) and (ii) -- -tllErc cttimatc.

Thc mcan timo for lq) shilonts from school I to complctc tho 2.4 km run was 12.l minutos

and ttro standrrd doviation wsg 2.2 minutcs,

(lv) Makc two comporisorrs bctwccn the times for both schools' t?l

E8. (a)

(b)

Tho,diagramshowsacfucloABCDBwithcarrroo.clisitangonttothociroloalthopointE.iit" Jioil.tot,lo is extcndcd to mcct tho tangcil at r'

- - --irief" DEf = no , anglc ETD = 25o and anglo BCD - I 40o'

(i) Findt2l

tlltrltll

tll

(b) A bag conhins cight idontical rod flags and tw'olvo idcntical grocn flagr'Turo tlags arc soloctod at rudom without roplacomcnt.

(l) Draw ttroc diagrrm to show tho pmbabilitios of tho possibto outcomos' I2l

A gamc ir playcd by sotccthg two fla$ at random frcm ttt6 bEg r;vithout roplaoemcnt'

If tro rcd 0ryr aro aoloctod intho lirct attompl 100 points will bo awardcd

Ifonc flag of-cach oolour is solcotod, both flagr arc roplaocd ard a sccond attompt is givcn.

If tuo rcd=flagr'arc sctootod in ttrc sccond attomp! 75 polnts witl bc awardod'

Fin4 as a fraotion in its simplost ftirnr5 tho probability of

($ borng awwdad lo0 Poin$, tll

tu(lii) bcingawardcdT5 Pointr.

Tho diagram shows tho covcngo of a car wlndscrccn wrpa LBCD. 'lB and DC aro arcs of

oir"tor int "

o *ith radii 25 crn and 40 cm rcspcctivoty, Thc pcrimotor of ABCD is 121 cm.

0) Showthat angloloi = 1.4 radians. 12)

(ir) Calculato tic arca ofUre windscrocnthattro carwipciwipcs through' t2l/rc1erozo/164048'0?0/184A161mUOl16

1048t021o1'16 78bqSs lesN Malhcmetics Prellm

CBSS 4ESN Mathomatlcs ProllmDANYAL E

DUCATION

. volume ofenvolope:2800 mr

o mass of envelopg; 63.5 kg

r mass of emptl passonger basket: 60.2 kgo mass ofgns burners: 22.7 kg. mass of two 75.7-titrc fuel tanks t'ull of

prop&no; 123.4 kg

envelopo

passenger

basket

gss burnoosttachcd totwo fueltanla full ofpropane

.10. I-lcro is sonrc inlbrntotion nbout a hot air balloon.

In this question the hot air balloon can be modelled as a sphcrical envclope with gas bumersottached to two cylindricol fuel tanks full ofpropane. A cylindrical basket is arached to holdpassengers.

4- cnvelopc

.gas-burners.- -

passengcrbaskot

(n) Show that the radius of thc sphorical cnvclopo is 8.744 m, corect to tlroc decimal places. [2](b) Calculato tlro gurf'ace aroo ollho onvolopo. t2l

Uscful iufornutiou

. Donsity of propurc: 493 kglm'

o 1000 kg is cquivalent to 9,81 kN

(c) Culoulato thc mass. in kilograms, of an 6mpty tbel tank. I4j(d) Tho hot air balloon componenB oonsisting oftho onvolopc, baskot, gas burncrs, two fucl

tanks full ot'propsna and passcngom 0!n woigh at most 7l I kg in ordcr for lhc buoyant forcoto be oble to complctely liti fic hot air bslloon offthc ground.

Calculate, in kN, tho maximunr woight of Passengers allowcd. l2l

CBSS 4EON Malhemallos Prellm 40161021011A404UOAO|1A I

I

DANYAL EDUCATION

2016 4E 5N Preliminary Examination Paper I Marking Schemc 7b 243 = kQrT

h =27

108 =27d2

dz =4d =2an

MI

AI

8a BI8b l,2.3,5, 7,9) BI8c 4 BI

9a

lB.lD - &EDA (base ls of iiror. A)

-4DC (DSbtrcts 4{DC)

= L{BD (alL /s)Since all 3 angles of AASD ue equel, A.{AD is cquilateral.

B2 Award Blfor anylwocorreclcottditionsslqted

9b zScD llgoo-8;ao-60o

=40o (Zsuo d A)Errrcqrfu. IBCD-l2V

BI

l0a 3o(D+c)-(E+c)

= (3c - l)(6 + c) BIt0b 5(r!4rr)

- 5(r + 2s)(r - 2r) BI

llaHcight of B =

n x(3x.1-' 145,r x (6r)'

= 11.25 cm

MI

AI

l tbi l4z;282-l:4 BI

il bii 2'x 0.8d.4 ks

MIAI

l2t y - (x + 4)(x -21 BIt2b 82 Atard I

markforlhe correctshape andI nnrkforall thelnterceptsandmhrimumpoint

Qn Mark Remark

la 2.400 BIlb 2,40 BI

2a 64,-t28 BI

2b (-2)' BI

3a 5.85x10m BI

3b l:40 BI

4a

4b 690 BI4c lllo BI

BI5

yeam aro

years u0shown

ofyears

Verticaldoes not start

Effect B2Award BItor,ilN.adingI€atw.qrd Bl lottluefieaolcl$tteaut ontha grafi.

Exoggerates llro dillerencesbctween tho 2015 End 2008This doss not ollow I goodcomparison or fair comparison oftho Drofit made over lhe yearc

Profits could bo vory low or vcryhigh from 2009 o 2014. Thotrend is misroprosonted.Rots ofgdn in profits appearsteopef

6 r(2r -4y) - 2(r - ylz * 2x7 -442- ?(r3 - 2,v+ y2)

=Zxz -4ry-2x2 +44y-Zyz

= _2y2

MI

AI

7s E-kdzlo0 = kd'. 100k=-d'

Whcn d is doubled

E = k(zd)'

e =ffeafE = 4OOjoules

MI

AI

t3. s.7)

I

DANYAL EDUCATION

.i;'ti'; .:;

': r:ir'

-15

sl)'-rsl2)4

,z *11, -15 = y2 +l7l

= (,'i)'-*,i * ('*

Ml(csf)

AI

tl'4stttdctttsurcdtlu.hrndaa.solvebrotrlyam&wr,,

(,. ri)'

[,.'])y- 1.23 or -12.23

454

,tr

orcna*

wtorSanswer olthe prices

tEx$1500Prico ofLCD TV (Storo A) -

i00

Pricc orLCD rv (s,"," B) =;ilf11,**"0: $1660

Storc A offers better deal sinoe the cost oftho TV sot is lower at Storo A

4

1AmorurtofGST= -:= x $1660 = $ 108.60 (2 dccimal placos)

4r+420=5404x =120r= 30

+3x110= EO+80)+ +15a

BI= 1E0 - 2xlE = 144"IntoriorI

BI

BI

3

82

B1

6 l,-=-12 2.

4

81 .

BI

l6c

t7r

ITbr 2l126

BI

l7bii BI

lTbiii 4t12. 7

lTbrv BI

v

I4

-t

Gl,-e)

'82r'1,*a

ffiil,tritar{.i.E!:l

BIl4b

M1

Ar

3

DANYAL EDUCATION

I8r Arca = 23ol0x15 mr

,11xr5100

-1.45m2

MI

AI

l8b l5r+2

BI

159x+2 r

9(x+2) = 15x

9r+18 - l5r6x -lBr-3

Length-213-5-

MI

AI

:9a nroaote;so+4= l4cmlArea of B = 14 + 4 = 3.5 cm2

Area of 28 = area oiC = 3.5 x 2-7 cm'

MI

AIr96 Aroa of2B - area of D = 3.5 x 2

n7 cm' BIrft Aroa of 28 - aroa of E - 3.5 x 2

-7 cm' BI

2Aa c 0.41 BI?0b .6Tlfr-.[]_=5unitszgc

Ix(8+/D)x4=488+ AD =24AD.=16

D fl2.0)

MI

AI

2(rd 4

5

Bt

2t 8 shadod rogions =Largc circlo - 4 semicirclos - square + 4 scmicircles - squaro

Largecircle-2squarcs

n5'-ozlzQ.s)lz25n-2i<5225r - 50- 28.5 cml (to 3 signitioant tigures)

lvLz

MIM1AI

Msthod I

Shaded area half logfa = quadrsnt -

ooi"n x(z.s1t-L 12.51t

0u4.9087 -O3,125E0L7837Shadcd aroa of leaf = 2 xl.7 837 =3.567 4

Shadcdarsag = 1 *n5r- lxrx1..S,- lxixl,.st +A1.5674

O=D1.5674Totrl Shadad aroa = 8 x 3.5674D=O28.5 cmz po 3 frgures)

A

Arca of thisuruluded region =area ofleaf

Total Area ofshaded rcgion - 4 x (area ofquadrant - area oftriangle)

-n( I,,r*s'-**s')=uf o-ns1-25n- 5028.5 oml (!o 3 significant figues)

MI

MIMI

MI

AI

M2

MI

MIAI

Method a

I Method 3

22a 25 marks BI22b l3 BI22ci I a$c€ becauso Class 4A's mcdian mark (,+4).is higbar tha$ thc cohort's

(12)BI

22aii I agree because thc intarquartile range ofthc mathematios marks ofClass A is higher than the cohorl

BI

23a Spccd=1260+ 12x60= 1.75 m/s

MIAI

23b B2 iv,atd Inark for

6

I

DANYAL EDUCATION

-{ .a.

-tJ'o

--_-+

2..

Eo

ao=ooo

?

3tU2E\

...

a!

t.

?

zFz

@..1

sloofAaoo'oo.=o

oo. l,!J

AXn;NEgE9Ise

oooo

FsA.

azchFL2,U t$

I EB.-&II

iaG

s:L

DANYA

L ED

UCATIO

N

Choug Boou Sccoudury School2016 O PrsUrn Elcmcutrry Mrlhcmatlcs Paper 2

Marking Scheme

+ BI

b

IS - 70oos 640 = 30.685

,lngte ol etev uio, =,--,[#i) = r.,,BI

MIAI

Sorne usE 3sf for calculationCommon mistake-

as TS.

3 8r

/20 30 16\

n =lra +o za l,

\24 s2 40)

1.50

2.50

3.00

s- BI

not statematrices B and S will not gginBI

.50 2.50

It

(zo to r6\fl.so\ ft53\

l;: ; ;i[;:r'[il, AI

Rcjccl/zo ro ro\

I m +o za [r.s z.s :;

\u s2 40)

lll Amount collectcd ftom tho salcs ofthe 3 bubble teas foi&i-Sttlnd.Suq resoectivelv. BI Do not accept cos( price, each

day

3 lv r=(r r r)

'r53'

2s6

286AI

No braoket * no-mark

thc 3 Rejcct if I days is not stated

bi

f l.2o\o- lr.or l

lr*JAI

ok

I

(20+38+24)x1.5x1.20+ (30 + 46 + 52) x 1.5 x 2.00+(t5+28 +40) x 1.5 x 2.40- $(147.60 + 384 + 302.40) - 9r3,.{

MI

AI

Acccpt morix methodRojcct:

fr$.6'\|

307.2 l(r r r) o.

\143.2)ft s3.6\

L;r.;J= ("+t 'r

No Al if answer left as (834)Some mixed up days with typesoftoa.

4 a9rt 6x' 3v'

-+-=1ryo- y' l6xzB2

2correct-BlAcceptx{, q*l$ll.S

bz(t- r)

G:;F;)2

3+rMIA

I

Many had (x-4)(x+3) *fromcalculator

reject

I

Geoerat commcnts:Although thoro uo 2 to 3 moro chollonging quostiirns, most are still qf O lovol standard with strrdonts achioving afull tange of marks.

I tick ) I rurk (s)<copt gr&ph based on P2 & Cl)ll A * accuracy ofanswor (t-2 occurrencog minus I mark, )2 occuroncot minus 2 marks)

o notin3sforldpo rounding offwhqn answer is exact

ll Unit ) trcorect or no units (>2 occur.renccs minus i muk)Many split tho pages tbr.workings when they ehould continue on thc n6xt psgs

x* )ta BI worc notot I

-x 18xo5.625/ o,e.eblc to form tho 2 oquatloos.

BI

il r= 10,/- l6 B2Somc carclcss mistalccs whcnsolving

ill

l.i' *too?.- 5

xlo(Jl7c or lffi ,1gg"/.x+ y 26 8424

-te.2%Osn)

MI

AI

Many cdlculato tho oxactvolurnes and aro ablc to g?t thc@rect answor.Thoec who got it wrong clcarlydo not know how to furd volumcof prism.

bxe

=-1.3839 or 1.0839(4dp\

MI

M

No working to show sub8titutiooofvalucs ) o rnarkSomo did not loavo in 4dp andlost2 marks

al uv=@= 138.43 = l38a (3sf)

M2AI

No rnark awarded when asumeright anglc.Some studcnt's calculator arc inRadian mode, rcsulting in loss ofmarks *neod to rcmindstudentsllA not in'3sf

ll

IArea of trianglo =; x 154 x70sin64o = 4844.4

' -484ui (nearesl ut"1

MIAI

No Al if not in ncarcst m'

ltl

l54z +118.432 -7oz

or

zrvu*sm"(ryJl) or2xl54x118.43

4844.4

x l54x 138.43

*27.032-27.0o (ldp)

MI

AI

llA: not in ldp

0k

2

DANYAL EDUCATION

oqufualcot &aotion.

Comrnon ontr, dful not ohango

incquatity sign uAcq dividine bY

'-vc"

Manygavoarsrvdas -2

toto

8<x7

MI

AI

r(: -z.r)s s(zx+ t t)

3-2J -

-s5 3

7o.e.x>

.- 46316x

AI

Marry rmabto to marrEgP dlc "-vc" rign.No Ml if oross-nrillrod dirccdY'

El if corrcc.t final answcrdi

2 _. 19r-2 (2+x\2-x)

=t##-#:,e "MI

MIA1

dccimals or fraction

No working no MlAl

cannot havofactorization

2x2 -8+ x+7

2x'-x-15=0(z.t+ s[.r- l)= o

x--2.5 or 1

=4

ll

MlAIai

+24r -26tnlts5

AI

M1

ll

,D-[_1J.(-,',1

-(,1a=?4.e)

OP+d0

BIDo not accGpt

24iiiRJI E

64 24

No voctorSooc gEvo 3e * dilfficultY

0

BIbia

+

BI+

AI

MIbii

--a+ct|(-c+la)

3d 4d)

a--'cB5

'1(-"*

I (snorun)

or 6E=3d--d+OC+CE

1---ll+c+:CB

5

Minug lm if show

* vcctor cqnnot ditide vcctorNo Al if did not show collincar

DA

il=sfr'P2Q8,20t0

ifAINoP2Q4Iftcf2|t ,'

B2lll Sinco DE=ID7 andD is a oommon Point,t.

D{ - 5Df (o.0.).andz( D &B aro collinoar.

BI6 al

havo

wtthpBIii=30

9Q00t =k-t and

Not good dosPlto quostion

siririlar to Practico Exam

MIAI.lll

5fi)-2'x5rfih numbors aro 1000 and 4500.

27x

+9 EL +lIruso (zr+t): -(zz +r)',Ml for conoot cxPansion but no

MIAI

It

(zz+:)'-(za+t)'

- 4n2 + l2tt + 9- (4n' + 4z + l)

=82+8 or 8(r+l)

8lttoso taking rmall - larg!

cxccpt

'nl Sirco lto dtfrofloco is 8(n +l) whcro (r +l) ic en intcgor'

it lr alunyr a mulflplo of 8.

Notrccommprded to drawbcyond 0tr37.NoCl- If c.urvo docg not Pass through

all tho gints- Doublo linos- Not smootl

at corfcct

b

s[roothouruo atl plotod pQ

ffi

.." r; ,.

i;'liJ;|;.li:ti:i.

...,.:ii

o

Solno wrotq -l0z i inooncctansricr

Somodid not lcavo in coordinato

ok

firm ,'l| nn A I

i-i

il

4c

i. -;:i okBI

bok

c

DANYAL EDUCATION

(j.r - 0.81 and 5.87(acccpt 0.8 < .r < 0.9 & 5,8 s.r < 5.9) B2

A fow took the x.intcrtopU asanswers

dDraw langent at., = 5, grad = - 1,09(acoept gr8dicnt tiom - I .29 to -0.875)

MIAI

No mark iftangent doeinotlouch curv€ at xo 5 onlyTugontwrong I no AlOrad frorn curve I ostimatc,not cxact to givc in 3sf

er-l .03(aocopts 1<r<l.l)

Suitablc straight line : y = -* 1 3Draw lino correctly

MIMIAI

Poor. A fcw werc able to dmwtho lirrc but did not ststc thcsolution.

I aia

LIED =9tr bt I in wnt - ciralal

IEAD - 180 - 90 - 32 - 26(Zs un ol trtangb)

-32oOR /.&lD - 32o (Z i,t

"tr. srg)

MI

AI

Minus I m if >l roason notshtcd o, wrong reisonok

b ZEBD -32" (Z.e tu sameseg) ./et Averago

0 IBED - 180 - 140 (Zs ttr opp sq) - 4' AI Avorago

drdlq lNDaLxl4|a (lat ctl -2Zal circud)= 2800

AI Avorago

all Sinco anglo BPD - 50> 40 , P is inside the circlo.(no rcason )no mark)

AI Purr, not ablc to wc 40which isangles in the samc sogncnt

bi2x(40 -25) + 250 + 400 = l2l650=91AngleAOB * 1.4 (shown)

MI

AI

Good.Do not accept vgrify meth; subin 1.4 as this is a "show"question

llf,x

+Or x t .l - )x25r x .l .4 = 682.5 onl MIA

I

ok

I at

r -?:!1r.12*'nt2

% fastdr thnn 12 ln,lh=t+16 *l(tr)%-39%100

BI

AI

Many calculaM 6l%. tntcrpretcurvo incorroctly,

ll0 Mean = 12.7 min BI Aaacpt 12.72; should bo 3sfsince it's an ostima(o.

iib S.D. = 2.35 min (3sl) ok

lllTimo given is grouped data & mid-value, which is anestimate, is used lbr calculotion of mean & SD

BIPoor as many oxplanstions wasnot clcsr, Mid-valuo oe. Must bostated.

tv

Mean time tbr sch B < mean time tbr sch Alon averagc, studonB tiom sch B arE fasterS.D. of sch B < S.D. of sch A*timirrgs of studcnts from sch B is morc consirtqnt

AI

AI

Some compared but noconclusion i 0 mHigher moan + bctGr. mustchcck contsxt of question

bl 'K:'-,##.rqu

gteenred

82I

mirtakc

Minw1m

Mnus I m whon porition of"coloud'& "prob" aroiotorohangod

ll BI

ill P(75 ptsl =t2

+12 8

I9t4 672

9025-x- xl9 20 95

BIMany

multiplying

l0 a1-'=rtoo

,= dE!99i1

- 8.i44,

MI

AI

Ifverify, ie sub r = E.7rt4 I 0m

bs.t.-qdglla)l

-960.7$-gew, (tsllMIAI

not

c

M = Dr/ -4$x(".r.i#)nass 7 5.7 l luel = 37.32O1 kg

Moss of ompty fud tsnk -! * lzt.q - z * st,nzo t) = z4.37sg yr

M2

MIAI

M I for convsrsion of ltr to- mf,1000m

Poor

llA : 24.4 whon answer is exact

d

I,al Wkgbo max. mass of passengors.61.5 + 60.2 + 22,7 + 123,4 + ty s 7 I t

W <441.2k9

W s4l'2 xg.8t kNt000

Maxwt =4.3281'12 kN

MI

AI

Bt - 44t.2kg

Many did not use inequalitywhich is ok but finisl answermust be exoct.No mark if round of to 3sf

r<rooprl=*x#-# ok

Good.

DANYAL EDUCATION