Đề thi Toán Kangaroo năm 2008 Full cấp độ

 126 Kangaroo 2008
 Questions of Kangaroo 2008
 NIPPER (grades 1 and 2)
3-POINT QUESTIONS
N1. Now it is 2008. What is the total sum of these digits? 2008
 A 0 B 6 C 10 D 16 E 20
 Birželis Liep a Rugpjū tis
 P 6 12 18 24 30 P 5 11 17 23 29 P 6 12 18 24 30
 A 1 7 13 19 25 31 A 6 12 18 24 30 A 1 7 13 19 25 31
 T 2 8 14 20 26 T 1 7 13 19 25 T 2 8 14 20 26
 K 3 9 15 21 27 K 2 8 14 20 26 K 3 9 15 21 27
 P 4 10 16 22 28 P 3 9 15 21 27 P 4 10 16 22 28
 Š 5 11 17 23 29 Š 4 10 16 22 28 Š 5 11 17 23 29
N2. Which of these figures differs from the rest four?
 ABCDE
N3. Mary has written all the numbers from 1 to 30. How many
 times has she written digit 2?
 A 10 B 12 C 13 D 19 E 27
N4. Emily celebrated her birthday on Thursday, and her
 sister Liepa 8 days earlier. Which weekday was that?
 A Wednesday B Thursday C Friday
 D Tuesday E Sunday
N5. How many points are there in the three unseen sides of dice?
 A 9 B 10 C 11 D 12 E 13 128 Kangaroo 2008
5-POINT QUESTIONS
N13. Anthony paid 6 litas for 15 buns. How many litas did John pay for 5 buns more?
 A 7 B 8 C 9 D 10 E 20
N14. What time is it now, if after 6 hours and 30 minutes the clock will
 show 4:00?
 A 10:00 B 10:30 C 2:30 D 22:10 E 21:30
N15. Tom bought a chocolate heart (see the picture) to Mary on her birthday.
 How many grams did the chocolate weigh, if each square weighs 10 grams?
 A 180 B 170 C 150 D 140 E 160
N16. How many different letters are there in the word
 MATHEMATICS?
 A 12 B 11 C 7 D 10 E 8
N17. A trip of the pupils to the zoo took 135 minutes.
 How many hours and minutes does it make?
 A 3h 5min B 2h 15min C 1h 35min D 2h 35min E 3h 35min
N18. A wooden block has 8 vertices. One vertex is cut off now (see the picture).
 How many vertices has the block now?
 A 8 B 9 C 7 D 10 E 11 130 Kangaroo 2008
4-POINT QUESTIONS
 M9. The storm made a hole on the front side of the roof.
 There were 10 roof tiles in each of 7 rows. How
 many tiles are left on the front side of the roof?
 A 57 B 59 C 61 D 67 E 70
M10. Carol is playing with two equilateral triangular cards shown.
 She puts one card beside or on the top of a part of the other
 and both on a sheet of paper. Then she draws on the paper
 around them, following the contour. She cannot get only
 one of the shapes. Which one is it?
 AB C DE
M11. John multiplies by 3, Pete adds 2, and Nick subtracts 1. In what order can they do this to
 convert 3 into 14?
 A John, Pete, Nick B Pete, John, Nick C John, Nick, Pete
 D Nick, John, Pete E Pete, Nick, John
M12. Gabi is taller than A´ ron and shorter than Tama´s. Imre is taller than Kristo´f and shorter than
 Gabi. Who is the tallest one?
 A Gabi B A´ ron C Kristo´f D Imre E Tama´s
M13. Anna made the figure on the right out of five cubes. Which of the
 following figures (when seen from any direction) cannot she get
 from the figure on the right side if she is allowed to move exactly
 one cube?
 ABC DE
M14. Which of the figures is shown most often in the sequence?
 A B C D and E All of them are shown equally often
M15. How many two-bed rooms should be added to 5 three-bed rooms ia a hotel to host 21 guest?
 A 1 B 2 C 3 D 5 E 6 132 Kangaroo 2008
 BENJAMIN (grades 5 and 6)
3-POINT QUESTIONS
B1. Which number is the smallest one?
 A 2 + 0 + 0 + 8 B 200 : 8 C 2 · 0 · 0 · 8 D 200 − 8 E 8 + 0 + 0 − 2
B2. By what can be replaced to get: · = 2 · 2 · 3 · 3?
 A 2 B 3 C 2 · 3 D 2 · 2 E 3 · 3
B3. John (J) likes to multiply by 3, Pete (P) likes to add 2, and Nick (N) likes to subtract 1. In
 what order should they perform their favourite actions to convert 3 into 14?
 A JPN B PJN C JNP D NJP E PNJ
B4. To make the equality 1 + 1♣1 − 2 = 100 correct, we should replace ♣ by
 A + B − C : D 0 E 1
B5. Carol is playing with two equilateral triangular cards shown.
 She puts one card beside or on the top of a part of the
 other and both on a sheet of paper. Then she draws on
 the paper around them, following the contour. She cannot
 get only one of the shapes. Which one is it?
 AB C D E
B6. Numbers 2, 3, 4 and one more unknown number are written in the cells of
 2×2 table. It is known that the sum of the numbers in the first row is equal to
 9, and the sum of the numbers in the second row is equal to 6. The unknown
 number is
 A 5 B 6 C 7 D 8 E 4
B7. At a pirate school, each student had to sew a black and white flag. The condition was, that
 the black colour had to cover exactly three fifths of the flag. How many of the following flags
 fulfilled this condition?
 A None B One C Two D Three E Four
B8. Before the snowball fight, Paul had prepared a few snowballs. During the fight, he has made
 another 17 snowballs and he threw 21 snowball at the other boys. After the fight, he had 15
 snowballs left. How many snowballs had Paul prepared before the fight?
 A 53 B 11 C 23 D 19 E 18
B9. This is a small piece of the multiplication table and another ´ 4 3 ´
 one, in which, unfortunately, some numbers are missing.
 What is the number in the square with the question mark? 5 20 15 35 63
 A 54 B 56 C 65 D 36 E 42 7 28 21 30 ? 134 Kangaroo 2008
B17. Rebeka wanted to put all her CDs on a shelf, but one third of them did not fit there. Those
 CDs that did not fit on the shelf were put into three cases. She put seven CDs into each, but
 there were still two more CDs, which did not fit into those cases, so she left them on the desk.
 How many CDs does Rebeka have?
 A 23 B 81 C 69 D 67 E 93
B18. Which of the “buildings” A–E, each consisting of 5 cubes, cannot be
 obtained from the building on the right, if you are allowed to move
 only one cube?
 AB C DE
B19. Points A, B, C and D are marked on the straight line in some order. It is known that AB = 13,
 BC = 11, CD = 14 and DA = 12. What is the distance between the farthest two points?
 A 14 B 38 C 50 D 25 E Another answer
B20. Two years later my son will be twice as old as he was two years ago. And three years later
 my daughter will be three times as old as she was three years ago. What is right?
 A The son is one year older B The daughter is one year older
 C They are of equal age D The son is two years older
 E The daughter is two years older
5-POINT QUESTIONS
B21. The five signs @, ∗, #, &,  represent five different digits. Which digit does  represent, if
 @ + @ + @ =∗, # + # + # = &, ∗+& =?
 A 0 B 2 C 6 D 8 E 9
B22. 3 friends live on the same street: a doctor, engineer, and a musician. Their names are: Smith,
 Roberts, and Farrel. The doctor has neither sister, nor brother. He is the youngest among his
 friends. Farrel is older than the engineer and is married to the sister of Smith. The names of
 the doctor, engineer, and musician are as follows:
 A Smith, Roberts, Farrel B Farrel, Smith, Roberts C Roberts, Smith, Farrel
 D Roberts, Farrel, Smith E Smith, Farrel, Roberts
B23. Suppose you make a trip over the squared board shown, and you visit
 every square exactly once. Where must you start, if you can move only
 horizontally or vertically, but not diagonally?
 A Only in the middle square B Only at a corner square
 C Only at an unshaded square D Only at a shaded square E At any square
B24. The picture shows the plan of a town. There are four AB
 circular bus routes in the town. Bus 1 follows the route
 CDEFGHC, which is 17 km long. Bus 2 goes ABCF GHA, C D
 and covers 12 km. The route of bus 3 is ABCDEF GHA, H
 and is equal to 20 km. Bus 4 follows the route CFGHC.
 How long is this route?
 G
 A 5km B 8km C 9km D 12 km E 15 km F E 136 Kangaroo 2008
 CADET (grades 7 and 8)
3-POINT QUESTIONS
C1. How many pieces of string are there in the picture?
 A 3 B 4 C 5 D 6 E 7
C2. There are 9 boys and 13 girls in a class. Half of the children in this class have got a cold.
 How many girls at least have a cold?
 A 0 B 1 C 2 D 3 E 4
C3. 6 kangaroos eat 6 sacks of grass in 6 minutes. How many kangaroos will eat 100 sacks of
 grass in 100 minutes?
 A 100 B 60 C 6 D 10 E 600
C4. Numbers 2, 3, 4 and one more unknown number are written in the
 cells of the 2 × 2 table. It is known that the sum of numbers in the
 first row are equal to 9, and the sum of numbers in the second row is
 equal to 6. The unknown number is
 A 5 B 6 C 7 D 8 E 4
C5. The triangle and the square are of the same perimeter. What is the peri-
 meter of the whole figure (a pentagon)?
 A 12 cm B 24 cm C 28 cm D 32 cm
 E It depends on the lenghts of triangle sides
 4cm
C6. The florist had 24 white, 42 red, and 36 yellow roses left. How many identical bunches can
 she make at most, if she wants to use all the remaining flowers?
 A 4 B 6 C 8 D 10 E 12
C7. A cube has all its corners cut off, as shown. How many edges
 does the resulting shape have?
 A 26 B 30 C 36 D 40 E Another answer