Đề thi Toán Kangaroo năm 2012 Full cấp độ

 Lietuvos Respublikos švietimo ir mokslo ministerija
Keng¯uros konkurso organizavimo komitetas
VU Matematikos ir informatikos fakultetas
VU Matematikos ir informatikos institutas
Leidykla TEV
 KANGAROO 2012
 Nipper
 1 and 2 grades
Time allowed: 50 min
Calculators are not permitted
3-point questions
 1. How many animals are in the picture?
 A)3 B)4 C)5 D)6 E)7
 2. Which piece fits in the empty place?
 A) B) C) D) E) 8. Grandmother made 11 cookies. She decorated 6 cookies with raisins and
 then 7 cookies with nuts. At least how many cookies were decorated with
 both raisins and nuts?
 A)2 B)3 C)5 D)7 E)11
 9. 13 children are playing hide and seek. One of them is the “seeker”. After
 a while 9 children have been found. How many children are still hiding?
 A)3 B)4 C)5 D)9 E)22
 10. Father hangs the laundry outside on a clo-
 thesline. He wants to use as few pegs as
 possible. For 3 towels he needs 4 pegs, as
 shown. How many pegs does he need for 9
 towels?
 A)9 B)10 C)12 D)8 E)18
 11. Today Betty added her age and her sister’s age and obtained 10 as the sum.
 What will the sum of their ages be after one year?
 A)5 B)10 C)11 D)12 E)20
 12. The clock shows the time when Stephen leaves his school. School lunch
 starts 3 hours before school ends.
 At what time does lunch start?
 A)17 B)16 C)12 D)11 E)10
5-point questions
 13. A dragon has 3 heads. Every time a hero cuts off 1 head, 3 new heads
 emerge. The hero cuts 1 head off and then he cuts 1 off head again. How
 many heads does the dragon have now?
 A)4 B)5 C)6 D)7 E)8 Lietuvos Respublikos švietimo ir mokslo ministerija
Keng¯uros konkurso organizavimo komitetas
VU Matematikos ir informatikos fakultetas
VU Matematikos ir informatikos institutas
Leidykla TEV
 KANGAROO 2012
Time allowed: 75 min Minor
Calculators are not permitted 3 and 4 grades
3-point questions
 1. Basil wants to write the word MATHEMATICS on a sheet of paper. He
 wants different letters to be coloured differently, and the same letters to be
 coloured identically. How many colours will he need?
 A)5 B)6 C)7 D)8 E)9
 2. In four of the five pictures the white area is equal to the grey area. In which
 picture are the white area and the grey area different?
 A) B) C) D) E)
 3. Father hangs the laundry outside on a clo-
 thesline. He wants to use as few pegs as
 possible. For 3 towels he needs 4 pegs, as
 shown. How many pegs does he need for 9
 towels?
 A)9 B)10 C)12 D)8 E)18
 4. Iljo colours the squares A2, B1, B2, B3, B4, C3, D3 ABC D
 and D4. Which colouring does he get? 1
 2
 3
 4
 A) B) C) D) E)
 AABBCCDD A B C D A B C D A B C D
 11 1 1 1
 22 2 2 2
 33 3 3 3
 44 4 4 4
 5. 13 children are playing hide and seek. One of them is the “seeker” and the
 others hide. After a while 9 children have been found. How many children
 are still hiding?
 A)3 B)4 C)5 D)9 E)22 13. Among Nikolay’s classmates there are twice as many girls as boys. Which
 of the following numbers can be equal to the number of all children in this
 class?
 A)30 B)20 C)24 D)25 E)29
14. In the animal’s school, 3 kittens, 4 ducklings, 2 goslings and several lambs
 are taking lessons. The teacher owl found out that all of her pupils have 44
 legs altogether. How many lambs are among them?
 A)6 B)5 C)4 D)3 E)2
15. Therewerealotoffruitsonthetable:pears, apples, mandarines and plums,
 totally 496 fruits. Amount of pears was three times less than one of apples,
 amount of apples was five times less than one of mandarines, and amount
 of mandarines was seven times less than one of plumes. How many plums
 was there?
 A) 350 B) 315 C) 455 D) 385 E) 420
16. There are coins on the board. We want to have
 2 coins in each column and 2 coins in each row.
 How many coins need to be removed?
 A)0 B)1 C)2 D)3 E)4
5-point questions
 .
17. A grasshopper wants to climb a staircase with many 3 .
 steps. She makes only two different jumps: 3 steps
 2
 up or 4 steps down. Beginning at the ground level, at
 1
 least how many jumps will she have to make in order
 to take a rest on the 22th step?
 Ground
 A)7 B)9 C)10 D)12 E)15
18. Frank made a domino snake of seven tiles. He put the tiles next to each other
 so that the sides with the same number of dots were touching. Originally
 the snake had 33 dots on its back. However, his brother George took away
 two tiles from the snake (see the picture). How many dots were in the place
 with the question mark?
 ?
 A)2 B)3 C)4 D)5 E)6
19. Gregor forms two numbers with the digits 1, 2, 3, 4, 5 and 6. Both numbers
 have three digits, each digit is used only once. He adds these two numbers.
 What is the greatest sum Gregor can get?
 A) 975 B) 999 C) 1083 D) 1173 E) 1221 Lietuvos Respublikos švietimo ir mokslo ministerija
Keng¯uros konkurso organizavimo komitetas
VU Matematikos ir informatikos fakultetas
VU Matematikos ir informatikos institutas
Leidykla TEV
 KANGAROO 2012
Time allowed: 75 min Benjamin
Calculators are not permitted 5 and 6 grades
3-point questions
 1. Basil wants to paint the slogan VIVAT KANGAROO on a wall. He wants different letters to
 be coloured differently, and the same letters to be coloured identically. How many colours
 will he need?
 A)7 B)8 C)9 D)10 E)13
 2. A blackboard is 6 m wide. The width of the middle part is 6m
 3 m. The two other parts have equal width. How wide is
 the right-hand part?
 A)1m B)1,25 m C)1,5m D)1,75 m E)2m
 ??3m
 3. Sally can put 4 coins in a square built with 4 matches (see picture). At least
 how many matches will she need in order to build a square containing 16
 coins that do not overlap?
 A)8 B)10 C)12 D)15 E)16
 4. In a plane, the rows are numbered from 1 to 25, but there is no row number 13. Row
 number 15 has only 4 passenger seats, all the rest have 6 passenger seats. How many seats
 for passengers are there in the plane?
 A) 120 B) 138 C) 142 D) 144 E) 150
 5. When it is 4 o’clock in the afternoon in London, it is 5 o’clock in the afternoon in Madrid
 and it is 8 o’clock in the morning on the same day in San Francisco. Ann went to bed in
 San Francisco at 9 o’clock yesterday evening. What was the time in Madrid at that moment?
 A) 6 o’clock yesterday morning B) 6 o’clock yesterday evening C) 12 o’clock yesterday
 afternoon D) 12 o’clock midnight E) 6 o’clock this morning
 6. The picture shows a pattern of hexagons. We draw a new pattern by connec-
 ting all the midpoints of any neighbouring hexagons. What pattern do we get?
 A) B) C) D) E)
 7. To the number 6 we add 3. Then we multiply the result by 2 and then we add 1. Then the
 final result will be the same as the result of the computation
 A) (6 + 3 · 2) + 1 B)6+ 3 · 2 + 1 C) (6 + 3) · (2 + 1) D) (6 + 3) · 2 + 1 E)6+ 3 · (2 + 1) 15. The perimeter of the figure below, built up of identical squares, is
 equal to 42 cm. What is the area of the figure?
 A)8cm2 B)9cm2 C)24cm2 D)72cm2 E) 128 cm2
 16. Look at the pictures. Both shapes are formed from the same
 five pieces. The rectangle measures 5 cm × 10 cm , and the
 other parts are quarters of two different circles. The differen-
 ce between the perimeter lengths of the two shapes is
 A)10cm B)15cm C)20cm D)25cm E)30cm
 17. Place the numbers from 1 to 7 in the circles, so that the sum
 of the numbers on each of the indicated lines of three circles
 is the same. What is the number at the top of the triangle?
 A)1 B)3 C)4 D)5 E)6
 18. A rubber ball falls vertically through a height of 10 m from the roof of a house. After each
 4
 impact on the ground it bounces back up to 5 of the previous height. How many times will
 the ball appear in front of a rectangular window whose bottom edge has a height of 5 m and
 whose top edge has a height of 6 m?
 A)3 B)4 C)5 D)6 E)8
19. There are 4 gearwheels on fixed axles next to each other, as
 shown. The first one has 30 gears, the second one 15, the
 third one 60 and the last one 10. How many revolutions does
 the last gearwheel make, when the first one turns through one
 revolution?
 A)3 B)4 C)6 D)8 E)9
 20. A regular octagon is folded in half exactly
 three times until a triangle is obtained, as
 shown. Then the apex is cut off at right
 angles, as shown in the picture. If the
 paper is unfolded what will it look like?
 A) B) C) D) E)
 5-point questions
 21. Winnie’s vinegar-wine-water marinade contains vinegar and wine in the ratio 1 to 2, and
 wine and water in the ratio 3 to 1. Which of the following statements is true?
 A) There is more vinegar than wine
 B) There is more wine than vinegar and water together
 C) There is more vinegar than wine and water together
 D) There is more water than vinegar and wine together
 E) There is less vinegar than either water or wine