Đề thi Toán Kangaroo năm 2006 Cấp độ Minor, Benjamin, Cadet, Junior, Student

 Minor (3and4grades) 117
 Questions of Kangaroo 2006
 MINOR (grades 3 and 4 )
3-POINT QUESTIONS
M1. Betty keeps drawing three different figures in the ?
 same order. Which figure should be the next?
 AB CD E
M2. What is the value of 2 · 0 · 0 · 6 + 2006?
 A 0 B 2006 C 2014 D 2018 E 4012
M3. How many cubes have been taken from the block?
 A 4 B 5 C 6 D 7 E 9
M4. Kate’s birthday was yesterday. Tomorrow is Thursday. What day was Kate’s birthday?
 A Tuesday B Wednesday C Thursday D Saturday E Monday
M5. Ivo was playing “Darts”. He had 10 arrows. For each throw at the centre he gained two
 additional arrows. Ivo made 20 throws. How many times did he hit the centre?
 A 6 B 8 C 10 D 5 E 4
M6. Four people can sit at a square table. For the school party the students put together 7 square
 tables in order to make one long rectangular table. How many people could sit at this long
 table?
 A 14 B 16 C 21 D 24 E 28
M7. In his purse Stan has a note of 5 euros, a coin of 1 euro and one coin of 2 euros. Which of
 the following amounts Stan can not pay without change?
 A 3 euros B 4 euros C 6 euros D 7 euros E 8 euros
M8. A kangaroo enters a building. He only passes through triangular rooms. Where does he leave
 the building? Minor (3and4grades) 119
M13. Six weights – 1g, 2g, 3g, 4g, 5g and 6g – were sorted into three boxes, two weights in every
 box. The weights in the first box weigh 9 grams together and those in the second box weigh
 8 grams. What weights are in the third box?
 A 5g and 2g B 6g and 1g C 3g and 1g D 4g and 2g E 4g and 3g
M14. Between two points four routes are drawn. Which route is the shortest?
 ABCD
 E All routes are equal
 8
M15. In the picture you can see a number flower. Mary pulled out all
 the leaves with numbers which give remainder 2 when divided by 58 18
 6. What is the sum of the numbers on the leaves that Mary pulled
 out?
 A 46 B 66 C 84 D 86 E 114 48 28
 38
M16. Four crows sit on the fence. Their names are Dana, Hana, Lena and Zdena. Dana sits exactly
 in the middle between Hana and Lena. The distance between Hana and Dana is the same as
 the distance between Lena and Zdena. Dana sits 4 metres from Zdena. How far does Hana
 sit from Zdena?
 A 5m B 6m C 7m D 8m E 9m
5-POINT QUESTIONS
M17. You can move or rotate each shape as you like, but you are
 not allowed to flip them over. What shape is not used in the
 puzzle?
 ABC DE
M18. John is building houses of cards. On the picture there
 are houses of one, two, and three layers that John built.
 How many cards does he need to build a 4-layer house?
 A 23 B 24 C 25 D 26 E 27
M19. The structure shown in the picture is glued together from 10 cubes.
 Roman painted the entire structure, including the bottom. How many
 faces of the cubes are painted?
 A 18 B 24 C 30 D 36 E 42 Benjamin (grades 5 and 6 ) 121
 B5. Choose the picture where the angle between the hands of a watch is 150◦.
 A B C D E
 B6. On the left side of Main Street one will find all odd housenumbers from 1 to 39. On the right
 side the housenumbers are all the even numbers from 2 to 34. How many houses are there
 on Main Street?
 A 37 B 38 C 28 D 36 E 73
 2
 B7.
 With how many ways one can get a number 2006 00
 while following the arrows on the figure?
 A 12 B 11 C 10 D 8 E 6 0 0 0
 666 6
 B8. One half of one hundredth is
 A 0.005 B 0.002 C 0.05 D 0.02 E 0.5
 B9. We need 9 kg of ink (in kilograms) to paint the whole
 cube. How much ink do you need to paint the white
 surface?
 A 2 B 3 C 4.5 D 6 E 7
B10. Which of the following nets has a cube in the right picture?
 ABCDE
4-POINT QUESTIONS
B11. What is the perimeter of the star (in centimetres) if you know that
 the star on the picture is formed by four equal circles with radius
 5 cm, one square and four equilateral triangles?
 A 40 B 80 C 120 D 160 E 240
B12. What is the difference between the sum of the first 1000 strictly positive even numbers and
 the sum of the first 1000 positive odd numbers?
 A 1 B 1002 C 500 D 1000 E 2000
B13. A paper in the shape of a regular hexagon, as the one shown,
 is folded in such a way that the three marked corners touch
 each other at the centre of the hexagon. What is the obtained
 figure? O
 A Six corner star B Dodecagon C Hexagon
 D Square E Triangle Cadet (grades 7 and 8) 123
5-POINT QUESTIONS
B21. A rod of length 15 dm was divided into the greatest possible number of pieces of different
 integer lengths in dm. The number of cuts is:
 A 3 B 4 C 5 D 6 E 15
B22. A river goes through a city and there are two A B
 islands. There are also six bridges how it is
 1 5
 shown in the attached image. How many paths 3
 there are going out of a shore of the river (point
 A) and come back (to point B) after having spent
 2 4 6
 one and only one time for each bridge?
 A 0 B 2 C 4 D 6 E More than 6
B23. Which set of three numbers represents three dots with the same space in between, if you plot
 them on a number line?
 1 1 1 1 9 1
 A ; ; B 12; 21; 32 C 0.3; 0.7; 1.3 D ; ; E 24; 48; 64
 3 4 5 10 80 8
B24. Ann calculated the sum of the greatest and the least two-digit multiples of three. Bob calculated
 the sum of the greatest and the least two-digit numbers that are not multiples of three. The
 number of Ann is greater than the number of Bob by how much?
 A 2 B 3 C 4 D 5 E 6
 3
B25. Belinda is building squares with matches adding small 2
 squares that it already has built according to the sche- 1
 ma of the figure. How many matches does she have
 to add to the 30th square to build the 31st?
 A 148 B 61 C 254 D 120 E 124
B26. The natural numbers from 1 to 2006 are written down on the blackboard. Peter underlined all
 numbers divisible by 2, then all numbers divisible by 3, and then all numbers divisible by 4.
 How many numbers are underlined precisely twice?
 A 1003 B 668 C 501 D 334 E 167
B27. What is the smallest number of dots that need to be removed from
 the pattern shown, so that no three of the remaining dots are at the
 vertices of an equilateral triangle?
 A 2 B 3 C 4 D 5 E 6
B28. Three friends, Alex, Ben and Charlie, were together 15 times in the swimming pool. Alex
 bought the tickets for all of them 8 times, and Ben –– 7 times. Charlie pays his share by using
 30 coins, all of the same value. The right way to distribute the coins is
 A 22 to Alex and 8 to Ben B 20 to Alex and 10 to Ben
 C 15 to Alex and 15 to Ben D 16toAlexand14toBen
 E 18toAlexand12toBen
B29. On the faces of a cube are written letters. First figure represents one possibility of its net.
 What letter should be written instead of the question mark in the other version of its net?
 D F
 BCEF D ?
 A
 A A B B C C D E E Impossible to determine Cadet (grades 7 and 8) 125
 C7. The solid in the picture is created from two cubes. The
 small cube with edges 1 cm long is placed on the top of a
 bigger cube with edges 3 cm long. What is the surface area
 of this solid?
 A 56 cm2 B 58 cm2 C 59 cm2 D 60 cm2 E 64 cm2
 1 3 1 
 C8. A bottle that can hold 3 litre is 4 full. How much will it contain after 5 has been poured
 out of it?
 1 3 1
 A  B  C 0.13  D  E It will be empty
 20 40 8
 C9. Two sides of a triangle are each 7 cm long. The length of the third side is an integer number
 of centimeters. At most how many centimeters does the perimeter of the triangle measure?
 A 14 cm B 15 cm C 21 cm D 27 cm E 28 cm
C10. A rod of length 21 dm was divided into the greatest possible number of pieces of different
 integer lengths in dm. The number of cuts is:
 A 3 B 4 C 5 D 6 E 20
4-POINT QUESTIONS
C11. If it’s blue, it’s round.
 If it’s square, it’s red.
 It’s either blue or yellow.
 If it’s yellow, it’s square.
 It’s either square or round.
 That means:
 A It’s red B It’s red and round C It’s a blue and square
 D It’s blue and round E It’s yellow and round
C12. Three Tuesdays of a month fall on even dates. What day of a week was the 21st day of this
 month?
 A Wednesday B Thursday C Friday D Saturday E Sunday
C13. Alex, Hans and Stan saved money to buy a tent for a camping trip. Stan saved 60 % of the
 price. Alex saved 40 % of what was left of the price. This way Hans’ share of the price
 was 30 euros. What was the price of the tent in euros?
 A 50 B 60 C 125 D 150 E 200
C14. Several aliens are travelling through the space in their rocket STAR 1. They are of three
 colours: green, orange or blue. Green aliens have two tentacles, orange aliens have three
 tentacles and blue aliens have five tentacles. In the spaceship there are as many green aliens
 as orange ones and 10 more blue ones than green ones. Altogether they have 250 tentacles.
 How many blue aliens are travelling in the rocket?
 A 15 B 20 C 25 D 30 E 40
C15. If kangaroo Jumpy pushes himself with his left leg, he will jump on 2 m, if he pushes with
 the right leg, he will jump on 4 m, and if he pushes with both legs, he will jump on 7 m.
 What the least number of jumps should Jumpy make to cover a distance of exactly 1000 m?
 A 140 B 144 C 175 D 176 E 150