NO: CLASS:NAME:----ff--

2

ADMIRALTY SECONDARY SCHOOL

Matftemadcgl Formulee

Cornpound ialeresl

Mensuratlon

Tdgonomety

Sfaa,slics

l+ r100

Curved eurfaco etea of a cooo = zfl

Curved eurfecs aree of ai $phelie * 4rEra

rotarAmount = p[)

AnSUBJECT

CODE/PAPER

LEVEUSTREAM

DATE

TIME

DURATION

lnstructlons to candidatgs:

Elementary Mathematics

4048/01

Secondary 4 Express

16 August 2016

0800h - 1000h

2 hour

Volurne of a cone = !*'1,3

AVolume of a sphere =: r{'J

Aroa ol trlangle ABC = f,rc sin a

Arc length * rA, where A ts ln radians

Sector area *lr'O,where 0 ls ln radians2

1, Write your name, class and index number.

2. Answer-ALL questions.

3. Calculators should be used where appropriate.lf the degree of accuracy is not specified ln the question, and if the answEr isnot exaci give the answer to three significant figures. Give answerc ln degreesto one decimal place.For a , usE either your calculator value or 3.142, unless the question reguiresthe answer in terms of r.

4. EsEential workings must be shown. Omission of essential worklngs andlltegible handwrlting will result in loss of marks.

DO NOT TURN OVER THIS PAGE UNTIL YOU ARE TOLD TO DO SO.

This question PaPor consists of lZ printed pages including this cover page.

abcsinA sinB sinC

a" = bn +c'-ZbccogA

,u"n = #stiandard deviation = Ef_ [EfJ'

PRELIMINARY EXAMINA 2016

.K

DANYAL EDUCATION

43

1 Expriss nf,W aso fuction in its slmplost form'

Answer; ......,.,...h...,,..,.."'...'mh t31.

During the Great Singaporo Saie,'all pricos in tho shop wero reduoed by 27%. Tha cost pricc of

ail6ecookeris$is. riDauraiollingpriccof*rccoolccrbiforethcsateifitsprofitduringfre

salo is 407o on thc oost Price

4 John makcs 3 ctay pots. Each pot io fircd indcpondcntly' Thc probabitity that a pot cracks

iuhilc boing fncd is 0.03.

(r) Calorlatc dc poUatility that all ofJobo's pots oraik while bcing fired'

An*ten

(b) Calo'lato thc frobabitity that at toast I ofJohn's pots craok whito bcing fircd.

(c) IfJohn makes S0 pots, oalculate thc numbo ofpots that arc likely to craok

Answen

5 h ftG e4uations bclow, & md. c yrs*te tbc. prioc pq. kilogram' in dollars, of becf urd

dri*co, rcspcctiwty,, wc*s arur lnno. W .liat was the pricc per kilograrn of bcof u&cn it was

eqtrat tb thc piico pcr tClogrmr of cltickcn?

b =2.35+O.25xc = 1.75+0.40*

Aaswcr all the questions.

'Ansver'.

ffi

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Answer: $. t2l Arcwer; $,........,..... tzl

.2 In onc woek Jamal watohcd lalwision for 26 hows. In ttrat wcctc' hc tvatctred tclwisioa for

t . iro ,*rut r*gth of timo on Monday, Ttresday, wcdncsday and rhursday. on Friday, satrnday

and Sunday, he watohed tolcvision for twioc as tong as on Monitay. itow tong did hQ spord

watohiDgtgtavisiononsahrrday?Writoyourarrswoinhoursandminutes.

DANYAL EDUCATION

5

6 Ths following dot diagram represgnts the number of durians collected from each durian tee.

012345Number of dr:rian collcctcd

(a) State the number of durian trees.

Answer: (a) trl

,: (b) Find ttro nredian nunrber ofdurians collocted.

Ansu,er: (b)...,...,....... tll(c) Find the snrallest nunrber ofdurian trees, which produces 4 durians, to be added to the

dot diagranr such that tlre nrodal numbor of duriars becomes 4.

Answer: (c)... tll(d) Find the smallost nunrber ofdurian trees, wlrioh producos 5 durians, to bc added to the

dot diagram suoh that tlre median number of durians becomqs 4.

Answer: (d) IU

ABobject,{ and B shown above are eactr made up ofa solid cube with length ofr unit. Borh bave

a trianglc prism cut out from it, Find the differencc between thc total surface area ofobjectsA wtd B in terms of:.

Anster',

6

7

oaoa)

oooaoaaaooo

t3l

DANYAL EDUCATION

78

o

10 Thc total uca of oa& irf So foffowing shapca is '{' Tho aroa of ftc shadcd part of iach shapo is

,t{. For caoh oftho following shryc; frnd 'hs

valus of &'

(e)

8 . (a) There aro 3 terms,XSa,llary rrlfiaf '

0) Find ttro higficst oolnmon faotor of thc tcrms'

Answer: (aXi)'-"

(iD Find the lowest common multiple of tho tcrms'

I

M

Answer. (axi|'.'.".... t1l

(b) Givou thar 19g = 2 x 3, x I I , .find thc smallcst intcgcr valuc t such thrrt l98t is a p€rfect

cube.

Awwen (b) l2l

(a) Simpliff 35)c3 +"lx-'

Answer. (a)..........,,.,..,,,.,.,.., tlJ,

(b)' If (ax+2)(Dr+7)= llx'+cx+14 for all values of x, and a+b=8, find the t,vo

possible values for c.

The rtiagram above shows a scdor of a circ.ib centre O: IAOB'=90'

Answer; (oi,t=

(b)

(c)

AB=BC=CD

Thc diagram abovcshows a rcgular hoxogoo

tr

0

Answen (a)t=..

Answer O) &=

tll

.j.

lrii:lrh:ill'trl:lEjir.r.Ai:..

.

iiii:ij,lilf,i::.,.,..1:1inj ;{(il.i' .:i :.

iji#,iffi,,

tr1

tu.

tll

DANYAL EDUCATION

I

I I Two satollites circle around the Earth. Tlrc distance from tlro centrc of thc Earth is:

1.53 x 107 m for Satellite A

9.48 x 106 m for Satellite B

(a) Caloulate tlre minimum dlstancc in whioh the satcllites could be apart. Give your

answer in standard form.

Anster: ..............rn l2l

(b) Calculate tlre mnximum distsncc in whioh the sarcllitcs could be apart. Cive your

answer in standard form.

Atrrlter: ...,.. ....m l2l

I 2 In the tiangla PQR, PQ - 5 am, QR = 7 an and PrR = 9 crn. Decide whether the triangle is acute

angled or obtuse anglod. Explain using calculations to support your decision. Explanation by

accurate drawing is not accepted.

Answer:

I2l

l0

l3 (a) Kim knows that one angle ofur isosceles triangle is 48o. He says that one ofthe otherangles must be 660. Explain why Kim is wrong.

Answer:(al

t21

(b) ln fte diagram below,lB is parallel to CD.

a

l)

A

Find thc value oft.

Arsx,eri (b)................ pl

(c) Robert says it is possible to draw a regular potygon with interior argles of 130.. Explain

why Robert is moog

Answer: (c) ... ....... .

t2)

c

DANYAL EDUCATION

-+!.YI ft'{tf:n!!,:.

(i) Lisl the oloments in (l t-r B)'

Ansten (aXD.., tu

(iD Find the value of n(Aa B)

IU

(iii) Given that C c A,it(C)= 3 and I n C = l' list tho possiblc olcmcnts h stt C'

Answer'. (aXiii)... ;... .. '. . . tU

(b) On tlre Venn diagram below, shado ttre set (l u B)' ' t

I2'l

B

12

15 Sikdch tho gra@ to sho'w cfrch relafiorship

(a) Tha siromfercnco of a sirclc C, plottcd against its diamctcr' d'

c

0) ' tAc arca of a ckclq l, plottod dgainst its radiug r'

(c) Tlrc lengflr, i, of a reotanglc with arco 30 crh2 plottcd against its width' pf'

ll

la (a) a={r:xisaninleger,Zsxsl4|'' .t. .,i=(r:risaPrimcnumbor)

B = {i: r is a multiPto of 3)

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A

L

W

Anwer: (a)(ii).........:..''.;....,......

d

,r

DANYAL EDUCATION

16 The weights of 20 fishes fiom Shop A is recordcd in tho tablE below.

'eieht (x kc) Freouencv

1Sx<2 2

23x<3 alSt <4 8

4Sr<1 b

(s) Civen that thc nrean weight offishes is 3,5 kg calculate the value ofa and ofD.

(b) Find the standard deviation.

Ansvsr. (b)................. tz'l

(c) Meanwhile, in Shop B, dro nrean and standard deviation ofthe fiehes are as follows:

Mean: 4.4 kg, Standard deviation: 1.2 kg,

Which shop is morc consistent in producing fishes of similar weight? Explain your

answer

Anster', (a).

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l4

17 Tbe equation of lineA is y=2y14.It intersects anothcr line,h which has a gradient

of-3,atpoint M(a,2).

Lt

x

(a) Find the value ofa.

Answer'. (a)

(b) Hcncc, find thc cquation ofLr.

Answer: (b).,...

v

trl

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l3

DANYAL EDUCATION

t

I c

I \ /I \

I \/ ,/ \

I \/ t \

/ / \ Car

/ I \

l5

IE Thc diagram shows thc distanoo-timc graph ofa car and a motorcyole'

Distarrce

TownB 80

Towa A1700 1800 .1900

,rl "rwhattimedidthcmotorcyc o**"Xur

ru,

(b) Find the speed ofthc car in kmfir at l8X0 h.

tu

Answer: (b)......'.'......... .. lsn/h 12)

G) Find the acceleration in km/h2 of the motorcyclo at l615 h'

Answer: (c)...."...'....'...., lo/h2 tll

(d) . Find tho averago spood of tho motoroyclo in km/h for the wholc joumcy.

l6

19 ABCD isa prallclognm whoso diagarsls, lc aad BD, intcrscct at o. E is E point on l8 such

:frrat AE - 2EB. DE itr&rlccb lC Et F.

(a) Oivoo that d- a ndd[-n, cxpross thc fOllowing vcoJors in tcrms ofaandb,

giving cach ofyour answers in its simltcst form.

oftAnswer: (a)(i)".....'........".'... tll

(lD6tllAnswer: (aXiD...

60

40

20

1600

(b)1

Show that p6 =: (a + 5b).

(c) Givcn that ilA-

=:oA , show that D, E and .F" lic on tho same straight litrc'

An$ren ;. . ... .... .. .

(d) Findthonumorical valucof

(l) Aroa of AIEFAroaofACDF

Arcaof ADOF

k ^.t

LAN

Answer (dxi)....

t2t

tll

Answer: (d).. .. ... km/h tzl

(lD

Answer: (dxii).. lu

tzt

DANYAL EDUCATION

l7

2A A, B and C arc the three corners of a horizontal triangular field. The points A andB are 300 m

apart andBis due east 0f,,4. The pointCis such frrat ICAB =40"and ICBA=60". The

paint A is shown in the diagram below.

(a) Using a scale of I cm to represent 25 m, construct the triangle ABC.

(b) On your scale drawing, draw the perpendicular bisector of line BC ndthe angle

bisector of I.CBA

(c) P is a point inside tlre triangle,4EC such itrat it is equidistant from AB and BC and

equidistant from ^B and C. Mark a possible location of P.

(d) Measure and state the bearing of P from 8.

Nortlr

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xA

End of Paper

An*ter: (d). o tllDANYA

L ED

UCATIO

N

%rGNAIVIE: NO: CIASS:

ADMIRALTY SECONDARY SCHOOL

2

.&n

ifgtrreiledcat FormUlae

Compound lnlercsl

Mensuralbn

Trtgonometry

Stallslics

rotarAmount " r(l "fi)'

; Elementary Mathematics

:4MB|O2

: Secondary 4 Express

:18August2016

:0900h-1130h

: 2 hour 30 minutes

Curved surface arsa of a cone * rilt

Curved ourface ereE of a sph€ro - 4zrrSUBJECT

CODE/PAPER

LEVEL/STREAM

DATE

TIME

DURATION

lnstructions to candidates:

Volume of a cone =!rn'h

Volume of a sphere -**'

Aroa of tdanglo ABC - I bc sin n2

Arc length E rA. wh6r€ d ls ln radlang

Ssctorarea -lr'0,where g ls ln radlans2

1. Write your name, class and lndex number.

2. Answer.g!! questions.

3. Calculators should be used where approprlato.lf the degree of accuracy ls not specified in the questlon, and lf the answer is notexact, glve the answer to three slgniflcant flguree. Glve answgftl in d€grBes to onedeclmal place.For a, use elther your calculator value or 3.142, unless the question requlres theanswer ln terms of a.

4. Essentlal worklngs must be shown. omlssion of essentlal worklngs and llleglblehandwritlng wlll result ln toss of maits.

DO NOT TURN OVER THIS PAGE UNTIL YOU ARE TOLD TO DO SO.

abasln A sln B sln C

az =b" +c' -zbc'catA

uu", = E3LT

standerd devratron = Ef _ (Eflt

PRELIMINARY EXAMINATION 201 6

00

Thls question paper conslsts of 12 prlnted pages lncludlng thlo oover page.DANYAL EDUCATION

43

Answer all the questions.

1 (a) Tho oxchango rgte betwcch Sterling pounds (f,) and Singaporc dollars ($) was

fl-$2.10.(i) Tania went on a holiday to Engldnd. she changed $1500 to sterling poutls and

this is inclusive of l% commission paid in dollars. How much stcrling pounds did

shc reccivc?

(ii) Tania spent f,500 on her holiday, shc oonverted the rernainin$ sterling pounds

back into Singripore dollars. She paid [10 as commission !o makc thc exchange.

using the same cxchange rate, calculate tho amouD! in dollars, Tania reoeived-

6) In l{January 2014, Alicc invested $10 000 of her savings ib il baDk that pays

compound intercst at thg rate ot),.5% pcr annum, Finf ft.. in&rast fiat Alicc has

carncdby3ldDocember20l6' 121

3 A 6hop sels two types of shirts, dry-.fit aill cotton. Each type is sold in three different sizes -srnall, mcdium and large. Thc sales in two succcssivc weeks are given in thc tablc below:

FIRSTWEEK SECONDWEEK

Sdall Medium Large Small Mcdium Luge

Dry-Fit 7 26 ll l5 32 9

Cotton t2 l6 17 25 t0

t2l

l2lTho infonnation for thc first week's sale can be represented by tho matrix C =

Thc information for thc sccond weok is repisentcd by a matrix D.

(t ze tt\1,, ,o ,u,J

(a) WritcdownthematrixD.

/r\(b) Givcn *"=lrl *a s-cR.calc,late S. Dcsc,ribc what is represcnted bj, thc

t,l(c) It is givcn that/ is inverscly pioportional to tho oubo root of.x and thaty - 3 when

.x= 64.

(i) Find the expression ofy in terms of*'

1i) Find the value ofY whenx = 8000.

2b +l(a) Given tbat a = 7pt,

(i) find the valuo of a when 6 = !

(ii) ' cxPress & in tenns ofa'

. 2x+8 _ 5 -U.(b) Solvetheoquatiou;-148 4_ x

(c) SolvetheinequalitY-5 <!:1 '3'

(d) (i) Solve thc equatioo (x + l)r = !. cino yo* answers oorreot to 2 dccimal plaoes'

(,i) Thesolutions of 1.r+]), = 1 aroalsothe solutionsof x'+ Bx=C, whoreB and

2'4C are integers' Find the valucs of8 and C'

IU

l2lIU

clements in.S.

(c)' oivan thal G = (1 l) and g = 65, calculate Q' Dcscribe what is represented by the

elements in @.

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1

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.,.i

-ri-rx;r1 i::,

{itiriiliI/iltY,1: i:$, "

'i.

ffiffi

t.zl

30

DANYAL EDUCATION

5 6

36 cm

ttjn

IThe diagram above shows a containcr which is made by attaching a holtow hemispherc

of internal rsdius 23 cm to thc rim of a hoilow cylinder with thc samc intcrnal radius

and a height of, cm.

Thc containcr is suspended from O by four wiros, cach of length 36 crn, fastened

symnrctrically to thc rim ofthe cylinder.

Givcn that 43.7 litrcs of watcr is nceded to complctely fill the container, calculate the

value of lr.

4 (a) A, B, C aad D arc four points on a circle with ccnfo O.

/.ADB = 38' and ZOBC =56".

D

Find, stating rcasons,

(i) reflex IAOB.

(il\ zAcB ,

(lit\ tcDB.

(b) Diagranr I shows a thin mctal in thc form of a scctor of a circlc of radlus 20 orn and

IAOB= 120", The metal is then bent to form a right circular cone as shown in

Diagram ll.

Dagrarn I

o

Dhgrlnr Il

(i) Convert 120'into radian.

(li) Find the length of arc ,4pd.

(lii) Firrd the votumc of the cone.

5 (a)

(b)

h

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t)

cThc figure above shows a solid triangular prism whcre the cross section idBC atd DEF

arc equilateral bianglcs. It has a oyllndrical hole in the ccnbe and a squorc basc BCFE

of aroa 36 m2. Thc volumo of tho cylindcr is 75.36 m3.

I can ofpaint covcf,s 9 m2 ofthe arca. Find the numbcr ofoans ofpaint to purchase to

paintthc€ntire solid. t6I

AP

B

II

tllttIt4l

DANYAL EDUCATION

I7

6

ABDlandACEarcstraightlnes'/EAC=0"'BD-12crnandCE=4crr.'AB-rornand

AC*?t-5 cm.

7 (a) P

A 24oo ic D

PQi is a right-qngled ilangle in whi th LPRQ = x" QR = 2a crn and PR - 25 cm'

The point,s lies on pR produoed. Writo doivn, as a ftactiorl the value of

(l) coszPfiS.

(li) tan(90-r)'.

(b) The'diagram sholan fou pointsl,B,CandDon the grouhd withDat a bearing

of 039'ftour,4. . Poiut I is 70 m due south of ,4. Point c is. on the l]lnle AD such thal it

is60mfrom,{. BDis150m.

60

A150 rt

70m

(il FndzADB.

(ii) Thero is a trcc 8t poitrl C. A boy mcasures fte anglo of elevation of the top of the

tre€ from point I an<l fiads that it is 23' - Find thc height of the tree'

cm

t1l

tzl

D

lzl

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t4t

tuazl

G)

(d)

(c)

i.in'it

AreaofAIEC AB"AC(e) showthat ffi MDE= AD" AE'

'' Area of AIBC = ]. using the rcsuh in part (a)' form on cquation inr and(b) Itisgiven *o, T;AMEE -J'"-".

show that it simpli.fies to 2x' - l9x + 6 = 0'

Solvo this cquation, giving your answcrs corrc'ct to 2 dcoimal placcs'

State with a rcason, which of these solution does not apply to &{8C'

Giva that 0.=25" ,find tho length BC'

B

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|a

DANYAL EDUCATION

8

I

In the diagranr,ABCGandD8F0aro squarcs and AGF=90'. X and I/ arc the

intcrsection with the lincs CC and 8D and the lincr BF wrd lD respcctivoty.

l0

9 Tho numbors I to 100 ate arranged in a grid as shown. A I-shapcd finamc is upright in

various positions on thc grid to onolosc 5 numbcrs. Tho number at thc centcr of thc top row

givcs the T-number,Tha T-number of thc f-shapcd ftame bclow shown is f-15.

Iil2t3l4l,l6t7l8t9t

(r) Statc thc largcst possiblc T-numben

(b) Find the sum ofthe numbers in I-15..

(c) Copy tho diagram bctow and writc on it, in terms ofx, alt thc numbcrs in I-x.

(d) Exprcss tho sum, in tcrms ofr, ofthc numbcrs cncloscd in I-x.

(e) Find the T-numba which has a sum of468.

(0 Find thc dilfcrcncc bctwecn thc sum qf thc numbcm in 7-x and f-6+l\

5

65758595

4

24!44454

64748494

23t2 13

22 2132 3342 4352 53

62 6!?2 7382 8392 93

6 789r0t7 l8 19 2027 28 29 3037 38 39 4041 48 49 5057

'8 59 60

67 68 69 7077 78 79 8087 88 89 9097 98 W t00

2636465666768696

tt1

tlltzl

(a) Prove that ABCF is congruent to A,LAD

(b) Civen that IBFC = 2O' , find IDBF .

(c) Prove that LGXDis similar to AOYF.

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t21

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DANYAL EDUCATION

IO Angwer thc wholc of thls qucstion on a sheet ofgraph papcr'

Thc variables.r and y aro connccted by the equation y =' - Z +!'rThc tablo below strows some conesponding vahics ofr ondy, ooncct to I decimal place.

ll

, I 1.5 ) 3 4 5 6 718v :1.0 4.8 4.0 m 4.0 4.6 5,3 6.1 I z.o

(r) . Calculete tlre valuc of nt'

..-(b) Ur..F "

scale of 2 cm to represert I unit on baoh a,xis, draw a horizontalnaTns for

0(x38 and a verticalyaxis for 05y37. Ptot thc points givcO in Oo tablo srd

. draw thc graPh of Y = x-2+!-'i

(c) Use your graph to find the value of'x whony = 3'9'

(d) By drarfling a tangcnL find thc gradient of thc curvc at thc point whcro x = 5.5.

I(e) Plot the line y=:.x+4 on the samo axes for 03'138' Hcnoc solvc thc cquatioo-5

5x-1b+9=.r+20.x

t2

ll A globri{ woaltb rcport rclcased by Cicdit Suipse in Ootobo 2013 shows the wealth per adult

who are aged11 and abovc for a populatign of 4 inillion. It also states that the mean wealth

pcr adult was us$281,764. The gap bctwcen thc median and the mean is one of the biggest

in the rich wori4 according to thc Credit Suissc rclort

Cumutatlve Fregugncy Gtaph of Wealth Per Adult

oIbao3Eoot,oIeIU

4500

4(xI0

3500'

3000

2500

zo00

1500

1000

500o 1OO 2OO 3OO 4OO sgo 600 7OO 8OO 90O 1OOO 1100

Wetlth Psr Adutt IUSD'$00)

(a) Find the median weallh per adult. Explain what oould be the possible cause of thc

diffcrence in the value fdr.mcan and median.

(b) Find thc interquartile range of wealth per adult. Explain what the interquartile range

would represent.

(c)Giventhatthcprobabilityofthcpopulationoamingmorethar.rxthousanddollarsis0.2,

find the valuo of.r.

End ofPaPer

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12)

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DANYAL EDUCATION

8ai) a.....81i0 33alb)2'xJxll,,,..,.Ml1452.........At

9a)

5xt....Alb)

abx2 +lax+Zbx+1415

= ab.....Ml

7a+2b = c..,.....M1

a=3 b=5c=31 or 41...,,.A1

Minimurdist=1.53x 107 - 9.48xld...Ml

- 5.kilx 16..........,n'

b)Maxinrundistc 1.53 x I 0? + 9 A8 x 106... Ml

= 2.47 8 x I 01 ...........A1

roal j,........ar

b) *""'""ar

c)

Shadod. Arcs =; rz - |r, sin9l....Jufi

1 w'-Lr'2

-'0-:)4

I4

By pythagras thooror1

ra - JVfr . s.00........Mt

Sinoo PR'9om whiolr ie longcr thaa 8.60, ir

will be a obtugo anglod trianglc.....B I

l3a)Angle - 180 - 48 x 2 = 84..,.,M I66 is ono of0re possible answcr but not a defuritcone.,..,Blb)72= w+40w =32....Ju11t =180-72-2x32

= 44,.....A1

........8tii)1,,,....81iii)2,5,7,11(Auy 3 but not atl 4)......b)Qorrcct shading of AUB....:BlCorrcct shading of (AUB)|...... ...Bt

.,.8t

S.A forobjcctA = fu' - *fi , qx 2 +4.r+3r -5.r

l9

7)

= 6xz +Lr-L2,.....M1

S.A forobjectB = 612 -! x3x4x2+4x+3x +Sx

=6xz +12*-12.....M1Diffcronoe= 10x.,....11

l8

for

u!32.........ar'4002)4x +2(3x) = 26.....M1

x -2.6h.........Mt2x = 5hl2min........Al

3)100%----$25

14go7o - - - - L

xl4(-....Ml100

$35

73%.----$35l00o/o - - - -947 .91....... Al

4a) 0.000027......... Al

6; I - (o'97)'..-'.".ut

0.08't327 ..........Atc)0.03x80=2.4

a3........A1

6a) 16..........81b)2......,...8rc)2..........Bld)7... . .. .,..8 r

5)2.35 + 0.25t = 1.75 + 0.40x..........M1

x=4b =2.35+0.25(4)

= $3.35.....,.,{l

DANYAL EDUCATION

2t

20

o(t 8ngl6

3607.2.. ...-n4t

s0drawSincc n rs Dot an intcgo, ir ts not possible to

..8 I

b)

c)

l0+a+b=20a+b =10........M|1.5 x2+2.5a+3.5x8+ 4.5b

= 3.520

2.5a+4.5b =39.-...M|a=3,b =7.....41b)0.%9.....82

c)

Shop A,...81. Ithas a srnallcr standard

deviation...,.Bl

I2.=2x + 4........M\

x=-1.....41l7b)2.= -3(-l) + c

c = -1,..,.,.,-l'Ily = -3x-1.....A1

tgai) iC = z io = -2s.........et++++

ii\ Cb = AB = AO+ OB = -g+ b .""""""'Alb)

44jDE = DA+ AE

ie =Ifu =!(b - e).-.......Mt

it= io*dA=b*,s

;. fis = p * q *lu -le = Ju *

!s-..-...Al

{4fDF = DA+ AF

4= b+a--a5-

..........41

= b+Lo- 5-

Hrn", iF =ltt-*nl=lie

,,,(i) =I o'

aiilfi .................nr

lea) r645:Iat

b)sP""q:#- ""'t'= pOnVs........nt

c)0....B!d)

ewsncca=fi"'.'.vr' :rot Al

c) DANYAL EDUCATION

t3

2016 - 2

l4

tb)

,4 = P(r +#)" = rooootr +ffif= t01 68.9.........-M t

lai)

Anrt chansed - 99 ,lsOO = $l+ 85.....:.Ml" r00

Pounds - l4B5 - tlol.l+ ........e,t. 2.t0laii)tlefr - 707.14 - 500 - f207.14f, to cxchangc - 207 .14 - l0 - f,197,14 .....M1Amt of $ - 197 .14 x 2. l0 = $4 t 4 .....A I

/ = 10768.91- I0000..........At- $768.91

.At

-i: t2,.'...,41- v8000

lcl)kv=w

^kV64

k = 12,,...,..M1

12;.y=.$..I cii)

3

5

d=- 5lr-lSab - a = 2b + 1.............M1

Sab-2b=a+lb(Sa-2)=a+t

b= o+l ............A1

5a -2

2b)2x+8 5 -

---=6

3(.r'-4') 4-x2(x+4) - 5

=6.........M13(*+a)(*-4) 4-x2 * 5

=6....-..Mt3(.r-4) x-42+(5x3)3(.r - 4)

t'7 =18(x - 4\..........M1

* = 4!..........A1l8

=!........At7

2ai)

]rrr *,'=62aii)

2b +l

4x-1< 6.....,..M1

Ir<-4

2c)-5s4'-3<3-,,-l0s4r-3_! <,

4

-l'*'1......,n

x +! = *t.t 1g0...,.....M I

x = -2.38, - 4.62.........11

2dr)

2di')

(r+1)'=l'2'43a)

D=

3b)

........8tl5

l'7

32925 l0

u.lr, =i,' *7**9 -1=ox2 + 7 x + I I = 0.........M1

B=7, C=-11.........41

.9 I

I

7 26 Ilt2 30 16

(7 +26+ll12+30+16)

..Ml

=(I) "It reprcscnb the sum ofdry fit shirts and cottonshirts rcspcctivoly3c)

e=('{I)= @4+58),...Ml

=102..,.....41It roprcscnts thc sum ofall fry fit ind cotton ..

shirts

4ai),7AOB=38 xZe760

( Z d. crrffa - 2 Zat ciroum) .......M1Rcflo( ZAOB - 360 -76 - 2860(Zat apt) .... Al4aii)ZACB=380

(Z in ftc safirc sogmcnt) .,.. Al4aii0

268A = 180-- 76 - j20 (isos A ) .....M12

ZCDB- 180 - 56 - s2 - 38;340Z in opp scg) ....At

4bD

120 *2n =2.0944s2.09 rad......Al3604bii)Aro APB = r0 - 20 x 2.0944= 41.8879 = 41.9 cm ......A1

Vol of Container =|t!*\+ *'n

43.7x 1060 = 3

r x23' + r x23 x h......Mt.

5ai)

h -252.122 e 252 cn......41

5aii)

h= J:6' -zl' =27.6941.......M1Vcrtical Dist - 27.69 + 252.122 + 23

-302.82 = 303 cm ...-.......A1

S.A of Cvlfudrical holc: 2m x 6

5b)

S.A of Prism - 36x3+ j, 6x 6sin 60x 2

= 139. 1769 cmz.,........M1

Cylindrical hole B.A - Af = 12.56 cnfDANYAL E

DUCATION

.-^ l:5'

,nn, *ebc =f,ABx ACs.I(.l.....-Bt

,too tlot =iADx Alsino.,....Bt

ATeaLABC -ABxAC,Area MDE ADxAE .

6b),lrea AABC IArea.L,4DE

x(Zx-5) =!.........ut(x+t2)(2x-5+4) 3

3x(2x - 5\ = (x +12)(2x -l)5xz * l5x = Zxr - x.+ 24x - lz.-... "' -lv{l

4x2 -38x+12=0Lxz -lgx+6 = 0.....':.ll6o)

-br:lTGix='--1;:-(- *

,,,,.812(7)

ler.6rj=-,,,,,,.,814

=9.17 or 0.31.........,A2

6d)x = 0.33 does not apply 6eoausc AC= 2x '5 wlllglve a negativc valuc6G)

Bc - s.r73' + (2 \ 9.t73 - sr - 2Q .t73)Q x

f.i73 - 5) cos25 ..'....',....M1

BC = 6.35

r6

- p.yn 6-75.36 cmz .....M1

S.A of Prism with holc

= 139.1769 - 12.56x2+75.16- 189.4169 cm2.......M1

No. of csns = 189,4169 + 9 .,..,..M1

=21.046=72 .........:...41

4biD2rr * 41.8879t- 6..67 crn -.......M1

h = @ffi = t8.856 cm.....'...M1

Vol ofConp

= t -' h ) ! d6.6667)t (l 8.856)......M t

332 gll.$$ * 81 I ryn' ..........A1

cos ZpiR^s = -!r..,.....n

tan(90 -.t) = 4 ...,.........A17

7bi). 70 150

sirZ{DB =

si"(180-39)"7o eLnl4l - r'

^D8..,..,....,MrI50l7 .l = LiDB...,.Al7biO

tanzl = L.......^Ut50

H =25.5..,...41

,MI

8a)

BC = BA (sidcs ofsquarts)IBCF - ZBAD-900 (linsqusre)

cc+GF-AG+GD(C6=AG, GF

By SAS, MCF - MAD............-BI

........81

=GD)....81

8b)ICBF = ZABD (ABCF = LBAD)ICBF = 180 - 90 - 20 = 700..........M1

IDBF =70 x 2 - 90 = 500...........A.I

8c)ZXGD - Z YGF - 900.......81

(sumof linABDA)ltuG * ZYFO'2e .........81

By AA, AG)(D is similar to AGYF

9a)T - 69 .........B1eb)5o6 - trf+l5-t-16+25+35+45 = 50 ..,...B1

9o)l-l x x+l

y+ l0x+ 20t+30

Corrcct column ..... Bl Correct row ..... Bled)Sum=x- l+x+t* I tr+ l0+r+20+x+30- 6r + 60.......B19e)459 = gi+ 60x - 68....... Ble0Differonce = 6 (x + l) + 60 - (5x + 60) = 5 .91

I la)usD 100 000 .........-BlThe wcalth is only held by a few very rich people

whioh.cause the mcsn to go up ........'..81llb)I QR= l60k - 20k.;........M1= 140k.........A1It reprcsenb the income gap betu,een the rich and

the poor........Blllc)No. of population = ffi x a0000/r =3200k......M1

Wealth pcr Aduh - USD 25q !qq,--.Al-

DANYAL EDUCATION