Đề thi Toán Kangaroo năm 2009 Full cấp độ

 Lietuvos Respublikos švietimo ir mokslo ministerija
Keng¯uros konkurso organizavimo komitetas
Matematikos ir informatikos institutas
Leidykla TEV
 KANGAROO 2009
 Nipper
 1 and 2 grades
Time allowed: 50 min
Calculators are not permitted
3-point questions
1. The following construction is made from the
 identical wooden tiles (as shown in the pic-
 ture). From how many tiles?
 A)12 B)8 C)9 D)10 E)11
2. What is the sum of all digits of the number 2009?
 A)7 B)11 C)12 D)18 E) 209
3. 5 girls have their birthday on the same day. Their birthday cakes are shown.
 Vida Nida Rita Gita Zita
 Which of the girls is the eldest one?
 A)Vida B)Nida C) Rita D) Gita E) Zita 9. The doctor prescribed 60 tablets for Ann to be taken one tablet each day.
 Ann took the first tablet on Monday. On which day of the week will Ann
 take the last tablet?
 A) On Monday B)OnTuesday C) On Wednesday D) On Thursday
 E) On Friday
10. Diana’s mother bought 6 identical packets of chalks. Diana spilled the content
 of 2 packets – there were 18 chalks on the floor. How many chalks did Diana’s
 mother buy?
 A)26 B)54 C)24 D) 108 E)9
11. Tom is 2 cm taller than Peter and 5 cm taller than Paul. How many centimeters
 is Peter taller than Paul?
 A)7cm B)3cm C)10cm D) Paul is higher than Peter
 E) Impossible to determine
12. Diana has drawn 6 flowers and Ann has drawn 4 hearts. Barbara has drawn
 3 times less flowers than Diana and 2 hearts more than Ann. Which of the
 pictures below is drawn by Barbara?
 A) B)
 C) D)
 E) None Lietuvos Respublikos švietimo ir mokslo ministerija
Keng¯uros konkurso organizavimo komitetas
Matematikos ir informatikos institutas
Leidykla TEV
 KANGAROO 2009
 Minor
Time allowed: 75 min 3 and 4 grades
Calculators are not permitted
3-point questions
1. 200 · 9 + 200 + 9 =
 A) 418 B) 1909 C) 2009 D) 4018 E) 20009
2. Where is the kangaroo?
 A) In the circle and in the triangle, but not in the square
 B) In the circle and in the square, but not in the triangle
 C) In the triangle and in the square, but not in the circle
 D) In the circle, but neither in the square nor in the triangle
 E) In the square, but neither in the circle nor in the triangle
3. There are five brothers in a family and each of them has one sister. How
 many brothers and sisters together are there in this family?
 A)6 B)7 C)8 D)9 E)10
4. There is a number 930 on the display (see the picture). How many little
 square lights must be switched in order to obtain number 806?
 A)5 B)6 C)7 D)8 E)9
5. Mom has bought 16 mandarins. Karol ate half of them, Eva ate two and
 Dana ate the rest. How many mandarins has Dana eaten?
 A)4 B)6 C)8 D)10 E)12 13. One side of the rectangle is 8 cm long, while the other is half as long. How
 long is a side of the square, the perimeter of which is the same as that of the
 rectangle?
 A)4cm B)6cm C)8cm D)12cm E)24cm
14. Thomas made a wall from small cubes (see the
 picture). How many cubes did he use?
 A)6 B)12 C)13 D)15 E)16
 15. Three squirrels Anni, Asia, and Elli collected 7 nuts. They all collected a
 different number of nuts, but each of them found at least one. Anni collected
 the least number of nuts and Asia most of all. How many nuts did Elli find?
 A)1 B)2 C)3 D)4 E) It is impossible to determine
16. Which figure cannot be formed from the two dominoes
 iliustrated on the right?
 A) B) C) D) E)
 5-point questions
 17. A farmer has 30 cows, some chickens, but no other animals. The total number
 of legs of the chickens is equal to the total number of legs of the cows. How
 many animals altogether does the farmer have?
 A)60 B)90 C) 120 D) 180 E) 240
18. Ann and Peter live on the same street. On one side of Ann’s house there are
 27 houses and on the other side there are 13 houses. Peter lives in the house
 that is exactly in the middle of the street. How many houses are in between
 Ann’s and Peter’s house?
 A)6 B)7 C)8 D)14 E)21
19. A secret agent wants to guess a 6-digit code. He knows that the sum of
 the digits in the even positions is equal to the sum of the digits in the odd
 positions. Which of the following numbers could be the code?
 A)81∗∗61 B)7∗727∗ C)4∗4141 D)12∗9∗8 E) 181∗2∗ Lietuvos Respublikos švietimo ir mokslo ministerija
Keng¯uros konkurso organizavimo komitetas
Matematikos ir informatikos institutas
Leidykla TEV
 KANGAROO 2009
Time allowed: 75 min Benjamin
Calculators are not permitted 5 and 6 grades
3-point questions
 1. Among these numbers, which is even?
 A) 2009 B)2+ 0 + 0 + 9 C) 200 − 9 D) 200 × 9 E) 200 + 9
 2. Where is the kangaroo?
 A) In the circle and in the triangle, but not in the square
 B) In the circle and in the square, but not in the triangle
 C) In the triangle and in the square, but not in the circle
 D) In the circle, but neither in the square nor in the triangle
 E) In the square, but neither in the circle nor in the triangle
 3. How many integers are there between 2.008 and 20.09?
 A)17 B)18 C)19 D)16 E) More than 19
 4. The smallest number of digits to be erased in the number 12323314 in order to get a number
 that reads identically from left to right and from right to left, is equal to
 A)1 B)2 C)3 D)4 E)5
 5. There are three boxes: white, red and green. One of them contains a bar of chocolate, the
 second contains an apple, and the third is empty. Find the chocolate, if it is known, that the
 chocolate is either in the white or in the red box, and the apple is neither in the white nor
 in the green box.
 A) White B)Red C) Green D) Red or green E) Impossible to determine
 6. KLMN is a square and KLP is an equilateral triangle. N M
 P
 What is the measure of ∠LQM?
 A)95◦ B) 105◦ C) 115◦ D) 125◦ E) 135◦ Q
 KL
 7. A bridge is built across the river. The river is 120 meters wide. One quarter of the bridge is
 over the left river bank and another quarter of the bridge is over the right river bank. How
 long is the bridge?
 A) 150 m B) 180 m C) 210 m D) 240 m E) 270 m 16. In the picture a “tower” is formed of three structures –
 square, rectangle, and equilateral triangle. The perimeter
 of all the three structures is the same. The side of the
 square is 9 cm long. How long is marked side of the
 rectangle? ?
 A)4cm B)5cm C)6cm D)7cm E)8cm
 9cm
 17. We want to fill up a 40 × 40 × 60 box with rigid cubes all of the same size. Which is the
 minimum number of cubes that allows us to do that?
 A)96 B) 96 000 C)12 D) 12 000 E) 768
 18. Today is Sunday. Francis begins reading a book of 290 pages. He reads 4 pages each day,
 except Sundays, on which he always reads 25 pages. How many days will it take him to
 read the book?
 A)15 B)46 C)40 D)35 E)41
 19. Andrija, Branimir, Celestin and Davor have won the first four places at the fencing tourna-
 ment. If you add the number of places won by Andrija, Branimir and Davor, you will get
 number 6. You will get the same number if you add the number of places won by Branimir
 and Celestin. Who won the first place, if Branimir is ranked higher than Andrija?
 A) Andrija B)Branimir C) Celestin D)Davor E) Impossible to determine
 20. Oliver takes 2009 equally sized square pieces and places them all side by side in the form
 of a full rectangle. How many different rectangles can he have?
 A)1 B)2 C)3 D)5 E)10
 5-point questions
 21. There are 4 statements about the positive integer M:
 M is divisible by 5; M is divisible by 11;
 M is divisible by 55; M is less than 10.
 It is known that two of these statements are true, and the other two are false. Then M can
 be equal to:
 A)0 B)5 C)10 D)11· 55 E)55 1
22. The picture shows a solid formed with 6 triangular faces.
 At each vertex there is a number. For each face we
 consider the sum of the 3 numbers at the vertices of
 that face. If all the sums are the same and two of the 5
 numbers are 1 and 5, as shown, what is the sum of all
 the 5 numbers?
 A)9 B)12 C)17 D)18 E)24
 23. The rooms of a hotel are numbered with three digits. The first indicates the floor and the
 next two the number of the room. For example, 125 indicates room 25 of the first floor. If
 the hotel has a total of 5 floors numbered from 1 to 5 with 35 rooms per floor, how many
 times will the digit 2 be used to number all the rooms?
 A)60 B)65 C)95 D) 100 E) 105 Lietuvos Respublikos švietimo ir mokslo ministerija
Keng¯uros konkurso organizavimo komitetas
Matematikos ir informatikos institutas
Leidykla TEV
 KANGAROO 2009
Time allowed: 75 min Cadet
Calculators are not permitted 7 and 8 grades
3-point questions
 1. Which of these numbers is even?
 A) 2009 B)2+ 0 + 0 + 9 C) 200 − 9 D) 200 × 9 E) 200 + 9
 2. There were 4 boys and 4 girls at a party. The boys danced only with girls and the girls
 danced only with boys. Afterwards we asked all of them, how many dance partners each of
 them had. The boys said: 3, 1, 2, 2. Three of the girls said: 2, 2, 2. What number did the
 fourth girl say?
 A)0 B)1 C)2 D)3 E)4
 3. The star in the picture is formed from 12 identical small equilateral
 triangles. The perimeter of the star is 36 cm. What is the perimeter
 of the shaded hexagon?
 A)6cm B)12cm C)18cm D)24cm E)30cm
 4. Harry delivers folders in the Long Street. He must deliver a folder to all the houses with an
 odd number. The first house has number 15, the last one has number 53. How many houses
 does Harry visit?
 A)19 B)20 C)27 D)38 E)53
 5. The area of the big square is 1. What is the area of the black little
 square?
 1 1 1 1 1
 A) B) C) D) E)
 100 300 600 900 1000
 6. The product of four different positive integers is 100. What is their sum?
 A)10 B)12 C)15 D)18 E)20