(for students at grades 7 and 8, Gymnasium)

Transcription

1 Kanguru Sans Frntières Kanguru Maths 009 Level: 7-8 (fr students at grades 7 and 8, Gymnasium) pints questins: ) Amng these numbers, which ne is even? Β) C) D) Ε) ) At a party there were 4 bys and 4 girls. Bys danced nly with girls and girls danced nly with bys. Afterwards we asked all f them, hw many dance partners they each had. The bys said:,,,. Three f girls said:,,.what number did the furth girl say? 0 Β) C) D) Ε) 4 ) In the figure, the triangle cnsists f 9 identical equilateral triangles. The perimeter f the uter big triangle is 6 cm. What is the value f the perimeter f the shaded inner hexagn? 6 cm Β) cm C) 8 cm D) 4 cm Ε) 0 cm 4) Harry is a pstman. One day he has t deliver packages t Kanguru street delivering ne package t each dd numbered huse. The first huse he visited was number and the last ne was number, while he visited all the huses in between with dd number in their address. In hw many huses did Harry deliver a package? 9 Β) 0 C) 7 D) 8 Ε) ) The area f the big square is. What is the area f the black little square? 00 D) 900 Β) 00 Ε) 000 C) 600 6) What is the remainder f the divisin f by ; 4 Β) C) 6 D) 7 Ε) 8 7) In a garden there are cats and dgs. All the cats tgether have duble number f legs than the nses f all dgs tgether. Then the number f cats is twice the number f dgs Β) the same as the number f dgs C) half f the number f dgs D) the 4 f the number f dgs Ε) fur times the number f dgs Kanguru Mathematics Level: page f

2 8) In the triangle ΑΒΓ, the angle BA is equal t. In additin AB = Α = Γ. Hw many degrees is the angle ΒΑΓ? Β) 7 C) 64 D) 69 Ε) 74 A Γ B 9) Due t restrictins in weight, in an elevatr it is nly permitted t enter adults maximum r 0 children maximum. It is understd the elevatr can enter mixed adults and children. If 9 adults entered the elevatr, what is the maximum number f children that can enter? (Fr practical reasns we assume that all adults have the same weight, all children have the same weight and adults weigh as much as 0 children). Β) 4 C) D) 6 Ε) 8 0) Which f the fllwing links requires mre than ne piece f rpe t cnstruct?,, 4 and Β), 4 and C), and D) all Ε) nne f them 4 4 pints questins: ) Hw many natural numbers frm t 0 inclusive, have the prperty that their square and cube have the same number f digits? nne Β) C) D) 4 Ε) 9 ) What is the smallest number f pints in the figure ne needs t remve s that n f the remaining pints are cllinear? Β) C) D) 4 Ε) 7 ) Nick drew an acute and an btuse triangle. The fur f the angles f the tw triangles were and 0. Hw many degrees is the smallest angle f the acute triangle? Β) 0 C) 4 D) Ε) we cannt find it 0, 80, 4) What is the area f the shaded regin, if the length f the uter square is? 4 Β) π C) π + 6 D) π 4 Ε) Kanguru Mathematics Level: page f

3 ) In an island there are inhabitants. Sme f them always say the truth and the rest always say lies. One day, these peple std in a queue. Every ne f the last tw in line said that the persn in frnt f him is a liar. The first ne n line said that the ther tw are liars. Hw many f the peple n this island are liars. nne Β) C) D) Ε) we cannt find it 6) The prduct f fur distinct natural numbers is 00. What is their sum? 0 Β) C) D) 8 Ε) 0 7) In the equality f prducts Α Β Γ Ε = Α Ζ Η Θ Ι Κ every letter represents a different number frm the digits 0,,,,, 9. Hw many different values culd the prduct Α Γ Η Κ have? Β) C) D) 4 Ε) 8) We want t clur the squares in the grid using clurs A, B, C and D in such a way that neighburing squares d nt have the same clur (squares that share a vertex are cnsidered neighburs). Sme f the squares have been clured as shwn. What are the pssibilities fr the shaded square? A B C D Α Β) Β C) C D) D Ε) there are tw different pssibilities 9) Andreas, Vasilis, Yiannis and Demetris have bks in their bags. One f them has ne bk in his bag, anther ne has tw, anther has three and the last ne has fur bks in his bag. Andreas, Vasilis and Demetris have tgether 6 bks. Vasilis and Yiannis tgether have 6 bks. Vasilis has in his bag less bks than Andreas. Wh is the ne that has nly ne bk in his bag; Andreas Β) Vasilis C) Yiannis D) Demetris Ε) we cannt find it 0) The first three patterns are shwn. Nt including the square hle, hw many unit squares are needed t build the 0th pattern in this sequence? 76 Β) 80 C) 84 D) 9 Ε) 00 pints questins: ) Din calculated the value f the expressin and Dina calculated the value f the expressin What is the sum f the values f bth Din and Dina? 004 Β) 008 C) 009 D) 407 Ε) nne f the previus ) Hw many fur-digit numbers cmpsed nly f digits,, exist, in which any tw neighburing digits differ by? (Repetitin f digits is allwed). 6 Β) 7 C) 8 D) 9 Ε) mre than 9 Kanguru Mathematics Level: page f

4 ) In a straight rad we mark the distances in Km frm a tree. A sign shws Km frm the tree. What is the psitin f the sign that shws 4 Km frm the tree? Km and anther shws at α Β) at β C) at γ D) at δ Ε) at ε α β γ δ ε 4) Jhn and Demetri had the same cube. Jhn painted the uter surface f his cube. Demetri made three cuts f his cube in rder t make eight smaller cubids and then he painted the uter surface f the eight smaller cubids. Hw much mre paint did Demetri used cmpared t Jhn? the same Β) ne and a half times mre C) duble D) triple Ε) quadruple ) We place a square f dimensins 6 cm x 6 cm n tp f a triangle. The shaded cmmn regin cvers the 60% f the triangle. The same regin cvers the f the square. What is the area f the triangle? 4 cm Β) 4 cm C) 6 cm D) 40 cm Ε) 60 cm 6) Csta wrte n a cmputer the prducts f the cnsecutive numbers,, 4, 4,..., Then he added all these numbers. What is the last digit f the number he fund? 0 Β) C) 4 D) 9 Ε) ther digit 7) Tasia drew a strange windmill. He began drawing lines passing thrugh the same pint and then she cnnected them with sme smaller 4 lines. In this way triangles were established with a cmmn vertex. What is the sum f the f the marked 0 angles f the triangles? D) 60 Β) Ε) ther answer 40 C) 8) Five friends, Anna, Viky, Yianna, Danae and Elli cmpared their height. We bserve that Anna is the shrtest f all Danae is taller than Viky but shrter than Elli Which f the fllwing is definitely wrng? Yianna is taller than Anna Β) Yianna is taller than Elli C) Viky is shrter than Danae D) Viky is taller than Elli Ε) Elli is taller than Viky Kanguru Mathematics Level: page 4 f

5 9) We write the natural number,,, 4,, cnsecutively in three clumns f squares, as shwn in the figure. In places where there is X, the square remains empty. The empty squares are in triples diagnal. What is the number in the 00 th square f the middle clumn? 97 Β) 99 C) 00 D) 99 Ε) nne f the previus X X 4 X X 9 X 0 X 4 X 0) The prduct f three natural numbers is equal t 40. The secnd f the numbers is seven times the first ne, and the third f the numbers is smaller than the secnd. What is the sum f the three natural numbers? 9 Β) C) 8 D) 4 Ε) we cannt find it Kanguru Mathematics Level: page f