Olympiada 2015 E St Demotikou

I 2015

26 2015

www.cms.org.cy

PAPERS IN BOTH GREEK AND ENGLISH

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CYPRUS MATHEMATICAL

OLYMPIAD 2015

ENGLISH VERSION

CYPRUS MATHEMATICAL SOCIETY 36 Stasinou street, Off. 102, 2003 Strovolos

Nicosia, Cyprus Tel. 22378101, Fax: 22379122

Email: [email protected] -Website: www.cms.org.cy

16th CYPRUS MATHEMATICAL OLYMPIAD

Sunday, 26/04/2015

EXAMS PAPER 5th , 6th Grade E, ST Dimotikou

TIME: 60 minutes

Fill carefully the answer sheet, by choosing only one answer to each question. The selection must be made by shading the right answer.

Every right answer is graded with 4 points. For each wrong answer 1 point will be lost.

If a question is answered by shading more than one answer, the answer will be considered wrong. The correction will be electronically, so any mark will be taken wrong.

You can use the space next to the questions to make extra notes.

It is recommended that you complete the answer sheet in the last five minutes of the exam, with your final answer.

Choose only one of the five proposed answers (A, B, C, D or E) and fill the box for right answer.

Example of filling the table of answers: 1. Find the result 2+3=? (A) 6 (B) 5 (C) 4 (D) 3 (E) 2 These fillings are correct and these are incorrect 1. 1. 1. 1.

1. 1.

A B C D E A B C D E

A B C D E A B C D E

A B C D E A B C D E

5th&6thGrade16thCyprusMathematicalOlympiadApril2015(E&StDimotikou)

CyprusMathematicalSociety Page1

1. Whichofthefollowingfractionisgreaterthanandlessthan?

. . .

.

.

2. Whatisthedifferencebetweenthelargest3digitnumberandtheleast4digit

number?.1 .2 .10 .11 .100

3. Whichofthefollowingnumbersisaprimenumber?

.3874 .1572 .6975 .45231 .Noneofthese

4. Whatisthesumofthe25%of80andthe75%of120?

.110 .100 .200 .40 .905. If 673and 327,whatisthesum ?

.1000 .1002 .1001 .2000 .9996. Whatisthevalueoftheexpression1 1

1

1

?

.3 . . .

.Noneofthese

7. Thiseasbought4sandwichesand5juicesandpaid14.Efterpibought5sandwiches

and6juicesandpaid17.Howmuchdoesasandwichandajuicecost?. Sandwich1,Juice1. Sandwich2,Juice2. Sandwich1,Juice2. Sandwich2,Juice1. Sandwich3,Juice1



8. Inthefigurebelow,isasquareandisaparallelogram.Whatisthelengthoftheside,ifyouknowthattheareaofthetriangleis9squareunits?

.1 .2 .4 .6 .89. Howmany2digitintegersarecommonmultiplesof6and8?

.2 .3 .4 .5 .610. Whatisthevalueof ?

. . .2 .2014 .4028

11. Inthefigurebelow,weformasquareusing16circles.Wecolorthe12outercircles

black,asshown.Ifwehave144circlesthatformasquare,howmanycircleslyingintheoutersurroundingwillbecoloredblack?

.44 .48 .42 .50 .52



12. Apatternisshownbelow.Whichofthefollowingnumbersisnotpossibletoexpressthenumberofshadedsquaresinashapeofthepattern?

13. Wedefinetheoperation 5 .If3 31holds,whatisthe

valueof?.8 .7 .6 .9 .10

14. Inastorearefrigeratorcosting80,issoldwithprofit25%.Insalesthisrefrigeratoris

soldwithareductionof25%.Acustomerwillbuytherefrigeratorattheprice:.70 .75 .80 .85 .90

15. Inthetablebelow,thenumbersthatareoutsideofitshowthesumofeachrowand

columnofthenumbersinthetable.Whatisthevalueof ? 15 25 20

20 ; 18

.19 .21 .22 .24 .Noneofthese

.104 .125 .404 .904 .204

Shape1 Shape2 Shape 3



16. Howmanydegreesisthemeasureoftheangle?

.30 .35 .40 .45 .50

17. Inthefigurebelowthereare27smallcubeswithedgeof1.Thesesmallcubesform

abigcube. Ifthecubesthataremarkedandareremoved,howdoesthesurfaceareaofthenewshapewillbechangedinrespecttothebigcube?

.Decrease

by4.Decreaseby

3.Remainsthe

same.Increaseby3

.Increaseby4

18. Inthefigurebelowvarioustrianglesandsquaresareformed.Howmanymorearethe

squaresthanthetriangles?

.6 .5 .4 .3 .2

19. If4 6 8and8 100,whatisthevalueof9 12?

.125 .175 .160 .150 .210



20. Anumberiscalledperfectifitisequaltothesumofitsdivisorsexcludingitself.Forexample,6isaperfectnumber,sinceitsdivisorsexcludingitselfare1, 2, 3and6 1 2 3.Whichofthefollowingnumbersisperfect?

.8 .18 .28 .38 .4821. Thesideofasquareis16.Wejointhemidpointsofeachsideandasecondsquareis

formed.Thisprocedureiscontinueduntil4squaresareformed(includingtheinitialone).Whatisthesumoftheareaofthese4squares?.240 .120 .116 .480 .Noneof

these22. Inthefigurebelow,isasquareandthetrianglesandareequilateral.

Howmanydegreesisthemeasureoftheangle?

.7,5 .10 .12 .12,5 .15

23. Inthefigurebelow,thelengthofthesideofthesquareis12.isthe

midpointofandisthemidpoint.Whatistheareaoftheshadedquadrilateral?

.54 .63 .72 .36 .108



24. ThefollowinggraphshowsthepathofMarytogotoherschool.

Whichofthefollowingstatementsisdefinitelywrongbasedonthegraph?

. Between8 10minutesshetraveledagreaterdistanceinrelationtotheinterval10 12minutes.

. Atthe6thminuteshestoppedbecauseshemetafriendandspokefortwominutes.. Atthe3rdminuteshegottiredandstoppedforthreeminutestorest.. Duringfirstthreeminutesshetraveled100meters.. Between3 6minutestheroadwasuphill.

25. isthemidpointofwhichisasideofthesquare.isthemidpointof.is the areaof the triangle, is the areaof and is the areaof thetriangle.Whatisthevalueof ?

.3 .4 .5 .6 .7

Timeinminutes (m)

Distancefro

mhe

rhou

sein

meters(m

)

OLYMPIAD 2015_COVER___ CYPRUS MATHEMATICAL SOCIETY

_2015_-___2015_-_ _EnglishBlank PageBlank PageBlank PageBlank PageBlank PageBlank PageBlank Page

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