Đề thi Toán Kangaroo năm 2010 Full cấp độ

 Lietuvos Respublikos švietimo ir mokslo ministerija
Keng¯uros konkurso organizavimo komitetas
Matematikos ir informatikos institutas
Leidykla TEV
 KANGAROO 2010
 Nipper
 1 and 2 grades
Time allowed: 50 min
Calculators are not permitted
3-point questions
1. Which of the numbers indicated below is the smallest one?
 A)2− 0 + 1 − 0
 B)2− 0 + 1 + 0
 C)2+ 0 + 1 + 0
 D)2+ 0 + 1 − 0
 E)2+ 0 − 1 + 0
2. There are two bear cubs, a small car, and two balls on Dominick’s shelf.
 Which of the pictures represents his shelf?
 A)
 B)
 C)
 D)
 E) 8. Birute has created beads by stringing small beads on the thread following a
 certain simple rule:
 What does the covered part of those beads look like?
 A) B) C) D) E)
 9. Find the largest odd number among that written below.
 A)3· 1 + 2 · 4
 B)3· (1 + 2 · 3)
 C)3· (1 + 2) · 4
 D) (3 · 1 + 2) · 4
 E)3· (1 + 2 · 4)
10. Vytautas celebrated his birthday in the hall with 9 four-seated tables. After
 Vytautas and all his guests have taken their seats, still there were 7 vacant
 seats. How many guests have come to Vytautas birthday?
 A)29 B)28 C)27 D)25 E)24
11. Mother gave Marta 20 euro. She bought a pack of milk, a kilogram of
 bananas, a loaf of bread, two packets of butter, and for the rest money she
 bought lollipops.
 2 € 5 € 2 € 250ct€ 150ct€
 How many sweets has Marta bought?
 A)3 B)4 C)5 D)6 E)7
12. Twelve pairs of dancers take part in the contest of dances. Johny has counted
 that 18 dancers danced waltz. How many pairs have not danced waltz?
 A)7 B)6 C)5 D)4 E)3 Lietuvos Respublikos švietimo ir mokslo ministerija
Keng¯uros konkurso organizavimo komitetas
Matematikos ir informatikos institutas
Leidykla TEV
 KANGAROO 2010
 Minor
Time allowed: 75 min 3 and 4 grades
Calculators are not permitted
3-point questions
1. There is a maze on the picture for a cat
 and a mouse. The cat can reach the
 bowl with milk, mouse can reach the
 cheese, but cat and mouse will never
 meet. How does the hidden part of the
 maze look like?
2. A 40 minutes lesson started at 11:50. Exactly at the middle of the lesson, a
 bird flew into the classroom suddenly. When did that happen?
 A) 11:30 B) 12:00 C) 12:10 D) 12:20 E) 12:30
3. Which of the numbers indicated below is biggest one?
 A)2+ 0 − 1 + 0 B)2− 0 − 1 + 0 C)2+ 0 − 1 − 0 D)2− 0 + 1 + 0
 E)2− 0 − 1 − 0
4. In this restaurant, first course costs 4 Lt, main course 9 Lt and dessert 5 Lt.
 The menu, which is first course + main course + dessert, costs 15 Lt. How
 much does someone save if he orders the menu instead of the three separate
 courses?
 A)3Lt B)4Lt C)5Lt D)6Lt E)7Lt
5. Six coins are lying in a triangle. You have to
 move some coins to place them in a circle as
 you can see in the second picture. How many
 coins must be moved at least?
 A)1 B)2 C)3 D)4 E)5 13. In the figure there are nine regions inside the circles. Put
 ?
 all the numbers from 1 to 9 exactly one in each region
 so that the sum of the numbers inside each a circle is 11.
 Which number must be written in the region with the
 question mark?
 A)5 B)6 C)7 D)8 E)9
14. John starts a chainletter. He sends a letter to his mate Peter. Peter has to
 send the letter to 2 other people. Everyone who receives this letter, has to
 send it also to 2 other people. After 2 rounds in total 1 + 2 + 4 = 7 persons
 have received the letter. How many persons in total have received this letter
 after 4 rounds?
 A)15 B)16 C)31 D)33 E)63
15. Children were measuring length of the sand playground by steps. Ana made
 15 equal steps, Betty 17, Denis 12 and Ivo 14. Whose steps were the longest
 ones?
 A)Ana B) Betty C)Denis D)Ivo E) Impossible to determine
16. Both rows have the same sum.
 1 2 3 4 5 6 7 8 9 10 199
 11 12 13 14 15 16 17 18 19 20 x
 What is the value of x?
 A)99 B) 100 C) 209 D) 289 E) 299
5-point questions
17. The product 60 · 60 · 24 · 7 equals
 A) the number of minutes in seven weeks
 B) the number of hours in sixty days
 C) the number of seconds in seven hours
 D) the number of seconds in one week
 E) the number of minutes in twenty-four weeks
18. Every cell of the 4×4 table contains a playing card
 (their suits are shown in the picture). One lead
 allows switching the positions of any two cards.
 How many leads will be played at least so that
 each row and each column will contain all suits?
 A)1 B)2 C)3 D)4 E)5 Lietuvos Respublikos švietimo ir mokslo ministerija
Keng¯uros konkurso organizavimo komitetas
Matematikos ir informatikos institutas
Leidykla TEV
 KANGAROO 2010
Time allowed: 75 min Benjamin
Calculators are not permitted 5 and 6 grades
3-point questions
 1. Knowing that 
 + 
 + 6 = 
 + 
 + 
 + 
, determine which digit is hidden by 
.
 A)2 B)3 C)4 D)5 E)6
 2. The number 4 is next to two mirrors so it reflects twice
 as shown. When the same thing happens to number 5,
 what do we get instead for the question mark?
 A) B) C) D) E)
 3. Kangu goes directly from Zoo to School. He counts each flower on the way. Which of the
 following number can not be his result?
 Zoo School
 A)9 B)10 C)11 D)12 E)13
 4. A ladder has 21 stairs. Nick and Mike are counting stairs one – from bottom to top, another
 — from top to bottom. They met on a stair that was called the 10th by Nick. What number
 will Mike give to this stair?
 A)13 B)14 C)11 D)12 E)10
 5. Ann has connected all the upper points to all the lower
 points. How many lines Ann has drawn?
 A)20 B)25 C)30 D)35 E)40
 6. A fly has 6 legs, while a spider has 8 legs. Together, 2 flies and 3 spiders have as many legs
 as 10 birds and
 A) 2 cats B) 3 cats C) 4 cats D) 5 cats E) 6 cats
 7. There are seven bars in the box. It is possible to slide
 the bars in the box so there will be room for one more
 bar. At least how many bars have to be moved?
 A)1 B)2 C)3 D)4 E)5 16. An ant walks along the lines of a grid. She starts and finishes at
 the point A. There are no other points where the ant comes twice.
 She must walk along the indicated segments. What is the smallest
 possible number of square cells within the pass of the ant?
 A)8 B)9 C)10 D)11 E)13 A
17. Using next picture we can observe that 1 + 3 + 5 + 7 = 4 × 4.
 What is the value of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17?
 A)14× 14 B)9× 9 C)4× 4 × 4 D)16× 16 E)4× 9
18. Ivona has drawn a flower with 5 petals. She wants to colour the
 flower, but she has only 2 different colours – red and yellow.
 How many different flowers can Ivona get if she has to colour =
 each petal using one of these 2 colours?
 A)6 B)7 C)8 D)9 E)10
 24
19. What fraction of the square is shaded?
 1 1 1 3 2 2
 A) 3 B) 4 C) 5 D) 8 E) 9
 4
20. Three identical dice are glued together. See picture. The sum
 of dots on opposite sides of a dice is always 7. What is the
 sum of dots on the sides which are glued together?
 A)12 B)13 C)14 D)15 E)16
5-point questions
21. The picture shows a balanced mobile. We neglect weights
 of horizontal bars and vertical strings. The total weight
 is 112 grams. What is the weight of the star?
 A)6 B)7 C)12 D)16 E) We can’t know
22. A pizza-shop offers a basic version of pizza with mozzarella and tomatoes. One or two
 toppings must be added: anchovies, artichokes, mushrooms, capers. Moreover, for each
 pizza three different sizes are available: small, medium, large. How many different types of
 pizza are available at all?
 A)30 B)12 C)18 D)48 E)72
23. To decide who will have the last piece of Leni’s birthday cake Leni, Sarah, Hannes, Petra
 and Arno form a circle clockwise in this exact order. They count clockwise: KAN-GA-
 ROO-OUT-GOES-YOU – each syllable counts one child and the one who is caught by the
 YOU is out of the game. They repeat until there is only one child left. Leni can choose
 who starts. Who will she pick to secure the last piece of cake for her best friend Arno?
 A) Leni B) Sarah C) Hannes D)Petra E)Arno Lietuvos Respublikos švietimo ir mokslo ministerija
Keng¯uros konkurso organizavimo komitetas
Matematikos ir informatikos institutas
Leidykla TEV
 KANGAROO 2010
Time allowed: 75 min Cadet
Calculators are not permitted 7 and 8 grades
3-point questions
 1. How much is 12 + 23 + 34 + 45 + 56 + 67 + 78 + 89?
 A) 389 B) 396 C) 404 D) 405 E) Other answer
 2. How many axes of symmetry does the figure have?
 A)0 B)1 C)2 D)4 E) Infinitely many
 3. Toy kangaroos are packed for shipment. Each of them is packed in a box which is a cube.
 Exactly eight boxes are packed tightly in a bigger cubic cardboard box. How many kangaroo
 boxes are on the bottom floor of this big cube?
 a
 A)1 B)2 C)3 D)4 E)5 b
 4. The perimeter of the figure is equal to a
 A)3a + 4b B)3a + 8b C)6a + 4b D)6a + 6b E)6a + 8b 2b
 a
 b
 5. Eleanor draws the six vertices of a regular hexagon and then connects some
 of the 6 points with lines to obtain a geometric figure. Then this figure is
 surely not a
 A) trapezium B) right-angled triangle C) square
 D) equilateral triangle E) obtuse-angled triangle
 6. If we type seven consecutive integer numbers and the sum of the smallest three numbers is
 33, which is the sum of the largest three numbers?
 A)39 B)37 C)42 D)48 E)45
 7. After stocking up firewood, the worker summed up that from the certain number of logs he
 made 72 logs besides 53 cuts were made. He saws only one log at a time. How many logs
 were at the beginning?
 A)17 B)18 C)19 D)20 E)21