2024年袋鼠数学竞赛Level-D (7-8年级) 真题+解析.docxVIP

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Cadet

3points

1(Germany).Whichofthefollowingstringscannotbetransformedintothestringontherightwithoutcutting?

(A)(C)(

(A)

(C)

(B)

(D)

Solution:OnlyforB,tworingsareformedthatmustpassthrougheachotheranditisimpossibletodothiswithoutcuttingthestring.

2(Slovenia).Ashapeismadeofequal-sizedpentagonaltiles.Whichofthefollowingtilescanbeplacedinthespaceintheshapetoproducetwoclosedcurves?

(C)(B

(C)

(B)

(E)

(D)

Solution:Notethatalltilesarerotatedby180。.Nootherrotationcanmakethetilefitasthepentagonaltilehasexactlytworightangles.

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3(Spain).Thefirstdiagramshowsarhombus.Theareaofthefirstdia-gramisincreasedbyaddingtworight-angledtriangles,asshown.Bywhatpercentagehastheareaincreased?

(A)20%(D)40%(C)30%

(A)20%

(D)40%

(C)30%

Solution:Theinitialfigurecanbedividedintofourrighttrianglesofthesamearea,andtheinitialfigureintosixtriangles,thustheproportionin6/4,thatis3/2=1.5,thereforeithasincreasedby50%.

4(Uganda).Whatisthevalueof?

(A)12(B)30(C)48(D)60(E)120

Solution:===20×3=60

5(Germany).Juliocutsoffthefourcornersofaregulartetrahedron,asshown.Howmanycornersdoestheshapethatremainshave?

(A)8(C)11(E)15

(B)9

(D)12

Solution:Atetrahedronhasfourcorners.Threesidesmeetateachvertex.Everycutcornertherforgivesthreenewcorners.Soifallfouroldcornersarecutoff,4×3=12newcornersarecreated.

15116(Netherlands).Riahasthreecountersmarked1,5and11,asshown.Shewantstoplacethemsidebysidetomakeafour-digitnumber.

1

5

11

Howmanydifferentfour-digitnumberscanshemake?

(A)3(B)4(C)6(D)8(E)9

Solution:Youcanmake