Đề thi Toán Kangaroo năm 2011 Full cấp độ

 Lietuvos Respublikos švietimo ir mokslo ministerija
Keng¯uros konkurso organizavimo komitetas
Matematikos ir informatikos institutas
Leidykla TEV
 KANGAROO 2011
 Nipper
 1 and 2 grades
Time allowed: 50 min
Calculators are not permitted
3-point questions
 1. What is the sum of the digits of the number 2011?
 A) 202 B)31 C)4 D)13
 2. Kate’s doll is wearing a gown, has two pigtails and holds one flower in her
 hand. Which picture portrays the doll?
 A) B) C) D)
 3. As winter season has passed, 12 pairs of ski boots remain unsold at the
 sporting goods shop. How many ski boots remain in the shop?
 A)6 B)12 C)24 D)4
 4. One piece is missing in the puzzle on the right.
 Which of the pieces below is the missing one?
 A) B) C) D) 11. Ned folded a rectangular piece of paper in half and cut a
 figure out of it, as shown in the picture, and then unfolded
 the part of that piece that remained. Which of the following
 could be the result?
 A) B) C) D)
 12. Mr. Smith has three daughters, of whom the youngest is 5 years old. The
 middle daughter is 4 years younger than the eldest one and 6 years older
 than the youngest one. How old is the eldest daughter of Mr. Smith?
 A)10 B)11 C)9 D)15
5-point questions
 13. At the florist’s all the flowers are displayed in three buckets. There were
 16 flowers in one bucket, 11 flowers in the second bucket and 17 flowers in
 the third bucket. The flowers are sold only in bouquets of five. Suddenly
 the shop-keeper saw that she is not able to compose such a bouquet. How
 many flowers remain unsold?
 A)1 B)2 C)3 D)4
 14. To get her toy, little Ann has to follow the path marked by the consecutive
 signs ,,,,,,,,.
 Which toy belongs to Ann?
 A) B) C) D) Lietuvos Respublikos švietimo ir mokslo ministerija
Keng¯uros konkurso organizavimo komitetas
Matematikos ir informatikos institutas
Leidykla TEV
 KANGAROO 2011
 Minor
Time allowed: 75 min 3 and 4 grades
Calculators are not permitted
3-point questions
 1. Basil wants to paint the word KANGAROO. He paints one letter each day.
 He starts on Wednesday. On what day will he paint the last letter?
 A) Monday B)Tuesday C) Wednesday D) Thursday E) Friday
 2. A caveman wants to balance two set of stones.
 20 kg 17 kg
 8kg
 26 kg 12 kg
 Which stone should he put on the right side to have both sides equally
 heavy?
 A) B) C) D) E)
 5kg 7kg 9kg 11 kg 13 kg
 3. A toy is in a square as seen on the picture. A child moves
 the toy from one square to the next. He uses the following
 order first to the right, then upwards, then to the left, then
 downwards, and then to the right. Which of the following
 pictures shows where the toy will be at the end?
 A) B) C) D) E)
 4. Simon got up one hour and a half ago. In three hours and a half, he will
 take the train to grandmother’s. How long before the train departure did he
 get up?
 A) 2 hours B) 3 hours and a half C) 4 hours
 D) 4 hours and a half E) 5 hours 12. The sheet is folded along the thick line. Which
 letter will not be covered by a gray square?
 A)A B)B C)C D)D E)E
13. Ann, Bob, Cleo, Dido, Eef, and Fer each roll a die. They
 all get different numbers. The number Ann rolled is twice
 as much as Bob’s. The number Ann rolled is three times as much as Cleo’s.
 The number Dido rolled is four times as much as Eef’s. What number did
 Fer roll?
 A)2 B)3 C)4 D)5 E)6
14. In a quiz show there are the following rules: every participant has 10 points
 at the beginning and has to answer 10 questions. For a correct answer 1
 point is added and for an incorrect answer 1 point is taken away. Mrs. Smith
 had 14 points at the end of this quiz show. How many incorrect answers
 did she give?
 A)7 B)4 C)5 D)3 E)6
15. At each square of the magic maze there is a
 piece of cheese. Mouse Ron wants to enter
 and go out taking as many pieces of cheese as
 he can. He cannot step on any square twice.
 What is the largest number of pieces of cheese
 he can get?
 A)17 B)33 C)37 D)41 E)49
16. During a party each of two identical cakes was divided into four equal
 pieces. Then each of these pieces was divided into three equal pieces. After
 that each of the participants of this party got such a piece of cake and three
 more pieces were left. How many people were at this party?
 A)24 B)21 C)18 D)27 E)13
5-point questions
17. Four girlfriends Masha (M), Sasha (S), Dasha
 (D) and Pasha (P) sit on a bench. First Mas-
 ha exchanged places with Dasha. Then Dasha
 exchanged places with Pasha. At the end the
 girls sat on the bench in the following order
 from left to right: MSDP. In what order from
 left to right did they sit in the beginning?
 A)MSDP B)MDPS C) DSPM D)SMDP E)PMSD
18. How many times a day (24 hours) a digital watch with
 four digits shows the same digit in the four positions? (In
 the picture there is an example with two different digits.
 A)1 B)24 C)3 D)5 E)12 Lietuvos Respublikos švietimo ir mokslo ministerija
Keng¯uros konkurso organizavimo komitetas
Matematikos ir informatikos institutas
Leidykla TEV
 KANGAROO 2011
Time allowed: 75 min Benjamin
Calculators are not permitted 5 and 6 grades
3-point questions
 1. Basil wants to paint the word KANGAROO. He paints one letter each day. He starts on
 Wednesday. On what day will he paint the last letter?
 A) Monday B)Tuesday C) Wednesday D) Thursday E)Friday
 2. A motorcyclist rode a distance of 28 km in 30 minutes. At what average speed (km/h) did
 he drive?
 A)28 B)36 C)56 D)58 E)62
 3. A square of paper is cut into two pieces using a straight line. Which
 of the following shapes cannot be the result of the cut?
 A) Square B) Rectangle C) A right-angled triangle
 D) Pentagon E) An isosceles triangle
 4. Hamster Fridolin sets out for the Land of Milk and Ho- Entrance
 ney. His way to the legendary Land passes through a
 system of tunnels. What is the highest number of pum-
 kin seeds he can collect if he is not allowed to take the
 same path or intersection twice?
 A)12 B)13 C)14 D)15 E)16 Exit
 5. In Crazytown, the houses on the right side of Number Street have odd numbers. However,
 crazytowners don’t use numbers containing the digit 3. The first house on the right side of
 the street is numbered 1. What is the number of the fifteenth house on the right side of the
 street?
 A)29 B)41 C)43 D)45 E)47
 6. Which of the following pieces do I need to complete the cuboid?
 A) B) C) D) E) 13. Move four of the numbers on the left into
 the cells on the right so that the addition
 17 167
 is correct. Which number remains on the +
 left?
 30 +
 A)17 B)30 C)49 D)96 E) 167
 49 96
14. Nina used 36 identical cubes to build a fence of cubes around
 a square region (part of it is shown in the picture). How many
 cubes will she need to fill the region?
 A)30 B)49 C)64 D)81 E) 100
15. Square floors are made of white and black tiles. Flo-
 ors with 4 and 9 black tiles are shown in the pictu-
 re. There is a black tile in each corner and all tiles
 around a black tile are white. How many white tiles
 are needed for a floor with 25 black tiles?
 A)25 B)39 C)45 D)56 E)72
16. Paul wanted to multiply an integer with 301, but he forgot the zero and multiplied it by 31
 instead. The result he got was 372. What result was he supposed to get?
 A) 3010 B) 3612 C) 3702 D) 3720 E) 30720
17. In a tournament FC Barcelona scored three goals and had one goal scored against it. It won
 one game, drew one game and lost one game. What was the score of the game FC Barcelona
 won?
 A)2:0 B)3:0 C)1:0 D)2:1 E)0:1
18. We are given three points that form a triangle. We want to add one point to make a
 parallelogram. How many possibilities are there for the fourth point?
 A)1 B)2 C)3 D)4 E) It depends on the initial triangle 1
19. The numbers 1, 2, 3 or 4 should be written at each of the 8 marked
 points in the picture in such a way that the ends of each line should
 have different numbers. Three numbers have already been written.
 How many times does 4 appear in the picture? 2
 A)1 B)2 C)3 D)4 E)5
 3
20. Daniel wants to make a complete square using only pieces like the one in the
 picture. What is the smallest number of pieces he can use?
 A)8 B)10 C)12 D)16 E)20
5-point questions
21. There are 10 pupils in a dance class. Their teacher has 80 jelly beans. If she gives each of
 the girls in her class the same number of jelly beans, there are 3 jelly beans left over. How
 many boys are there in the class, if in it there are at least 2 girls?
 A)1 B)2 C)3 D)5 E)6