2024年4月2日发(作者：郑州中考数学试卷翻译真题)
Känguru der Mathematik 2018
Level Felix (Grade 1 and 2)
Austria – 15. 3. 2018
– 3 Point Examples –
1. Alice draws lines between the beetles. She starts with the beetle with the fewest points.
Then she continues drawing to the beetle with one more point.
Which figure is formed?
(A) (B) (C) (D) (E)
2. The same amount of kangaroos should be in both parks. How many kangaroos have to be moved from the left park
to the right park for that to happen?
(A) 4 (B) 5 (C) 6 (D) 8 (E) 9
3. Which beetle has to fly away so that the remaining beetles have 20 dots altogether?
(A) Beetle with 4 points (B) Beetle with 7 points (C) Beetle with 5 points (D) Beetle with 6 points (E) no beetle
4. Peter has drawn this pattern:
He draws exactly the same pattern once more.
Which point is on his drawing?
(A) A (B) B (C) C (D) D (E) E
5. Theodor has built this tower made up of discs. He looks at the tower from above.
How many discs does he see?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
– 4 Point Examples –
6. This diagram shows two see-through sheets. You place the sheets on top of each other.
Which pattern do you get?
(A) (B) (C) (D) (E)
7. In order to get to his bone, the dog has to follow the black line. In total he turns 3-times to the right and 2-times to
the left.
Which path does he take?
(A) (B) (C)
8. Lisa needs exactly 3 pieces to complete her jigsaw.
Which of the 4 pieces is left over?
(D) (E)
(A) A (B) B (C) C (D) D
(E) C or D
9. Charles cuts a rope into 3 equally long pieces. Then he makes one knot in one of the pieces, 2 in the next and in the
third piece 3 knots. Then he lays the three pieces down in a random order.
Which picture does he see?
(A) (B) (C)
10. How many of the hands pictured show a right hand?
(D) (E)
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7
– 5 Point Examples –
11. The number of spots on the fly agarics (toadstools) shows how many dwarfs fit under it. We can see one side of the
fungi. The other side has the same amount of spots. When it rains 36 dwarfs are trying to hide under the fungi.
How many dwarfs get wet?
(A) 2
(B) 3 (C) 4 (D) 5 (E) 6
12. You are forming two-digit numbers using the digits 2, 0, 1 or 8. They have to be bigger than 10 and smaller than 25.
Every number is made up of two different digits.
How many different numbers to you get?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
13. Alice has 3 white, 2 black and 2 grey pieces of paper. First she cuts every piece of paper that is not black into two
pieces. Then she halves every piece of paper that is not white.
How many pieces of paper does she obtain in total?
(A) 14 (B) 16 (C) 17 (D) 18 (E) 20
14. Susi makes this pattern using ice-lolly sticks. Each stick is 5 cm long and 1 cm wide.
How long is Susi’s pattern?
(A) 20 cm (B) 21 cm (C) 22 cm (D) 23 cm (E) 25 cm
15. The road from Anna’s to Mary’s house is 16 km long. The road from Mary’s to John’s house is 20 km long.
The road from the crossing to Mary’s house is 9 km long.
How long is the road from Anna’s to John’s house?
(A) 7 km
(B) 9 km (C) 11 km (D) 16 km (E) 18 km
Känguru der Mathematik 2018
Level Ecolier (Grade 3 and 4)
Austria – 15. 3. 2018
- 3 Point Examples -
1. As seen in the diagram, 3 darts are flying towards 9 fixed
balloons. If a balloon is hit by a dart, it bursts and the dart
continues in the same direction it had beforehand.
How many balloons are hit by the darts?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
2. Susanne is 6 years old. Her sister Lisa is 2 years younger. Brother Max is 2 years older than Susanne.
How old are the 3 siblings altogether?
(A) 15 (B) 16 (C) 17 (D) 18 (E) 19
3. The diagram shows a wooden block with 5 screws. 4 of which are equally long, one
screw is shorter.
Which is the shorter screw?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
4. Leonie has one stamp for each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Using them, she stamps the date of the kangaroo-
competition.
How many of the stamps does Leonie use to do that?
(A) 5 (B) 6 (C) 7 (D) 9 (E) 10
5. On the right you can see a picture of ladybird Sophie.
Sophie turns.
Which of the pictures below is not Sophie?
(A) (B) (C) (D)
6. Lucy folds a piece of paper exactly half way and then cuts out a figure:
Then she unfolds the paper again.
Which of the five pictures can she see?
(A) (B) (C) (D)
7. Mike sets the table for 8 people: The fork has to lie to the left and the
knife to the right of the plate.
For how many people is the cutlery set correctly?
(A) 5 (B) 4 (C) 6 (D) 2 (E) 3
(E)
(E)
8. Using these tiles Robert makes different patterns.
How many of the patterns shown below can he make?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
- 4 Point Examples -
9. Diana shoots 3 darts, three times at a target board with two fields.
The first time she scores 12 points, the second time 15.
The number of points depends on which field she has hit.
How many points does she score the third time?
(A) 18 (B) 19 (C) 20 (D) 21 (E) 22
10.
12 Points 15 Points ?
Albert places these 5 figures , , , , on a 5x5-grid.
Each figure is only allowed to appear once in every column and in every
row.
Which figure does Albert have to place on the field with the question
mark?
(A) (B)
11. Tom wants to completely cover his paper boat using the shapes
12. The two colours of this picture are swapped.
Then the picture is turned.
Which of the pictures below is obtained?
and .
What is the smallest number of shapes he needs for that?
(A) 5 (B) 6 (C) 7 (D) 8
(C) (D) (E)
(E) 9
(A) (B) (C) (D) (E)
13. Felix the rabbit has 20 carrots. Every day he eats 2 of them.
He has eaten the 12th carrot on a Wednesday.
On which day of the week did he start eating the carrots?
(A) Monday (B) Tuesday (C) Wednesday (D) Thursday (E) Friday
14. A rose bush has 8 flowers on which butterflies and dragonflies are sitting.
On every flower there is at most one insect sitting on it. More than half of the
flowers are occupied.
15.
The number of butterflies is twice as big as the number of dragonflies.
How many butterflies are sitting on the rose blossoms?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
(A) 17 km (B) 23 km (C) 26 km (D) 33 km (E) 35 km
16. Tobias glues 10 cubes together so that the following object is formed:
He paints all of it, even the bottom.
How many cubes then have exactly 4 faces coloured in?
(A) 6 (B) 7 (C) 8 (D) 9 (E) 10
The map shows the roundtrip that Captain Bluebear
covers during his journey. Three distances are given on
the map.
He sails from island to island and starts at the island
Berg. In total he covers a distance of 100 km. The
distances between the islands Wüste and Wald is equal
to the distance between the islands Berg and Blume via
Vulkan.
How big is the distance between Berg and Wald?
- 5 Point Examples -
17. The big rectangle consists of various squares of different sizes.
Each of the three smallest squares has area 1.
How big is the area of the big rectangle?
(A) 65 (B) 71 (C) 77 (D) 87 (E) 98
18. In order to slay a dragon, Mathias has to cut off all of its heads. As soon as he has cut off 3 heads, a new one
grows back immediately. After Mathias has cut off 13 heads the dragon is dead.
How many heads did the dragon have initially?
Start
(A) 8 (B) 9 (C) 10 (D) 11 (E) 12
19. The rooms in Kanga’s house are numbered. Eva enters the house through the
main entrance. Eva has to walk through the rooms in such a way that each room
that she enters has a number higher than the previous one.
Through which door does Eva leave the house?
(A) A (B) B (C) C (D) D (E) E
20. The symbols
It is known that
stand for one of the digits 1, 2, 3, 4 or 5.
Which symbol stands for the digit 3?
(D) (E)
(A) (B) (C)
21. A belt can be joined together in 5 different ways.
How many cm is the belt longer if it is only closed in the first hole instead of in all 5 holes?
(A) 4 cm (B) 8 cm (C) 10 cm
(D) 16 cm (E) 20 cm
22. A decorated glass tile is mirrored several times along the boldly printed edge. The first mirror image is shown.
spiegeln
What does the tile on the far right look like after the third reflection?
(A) (B) (C) (D) (E)
23. Lea should write the numbers 1 to 7 in the fields of the given figure. There is only one
number allowed in every field.
Two consecutive numbers are not allowed to be in adjacent fields. Two fields are
adjacent if they have one edge or one corner in common.
Which numbers can she write into the field with the question mark?
(A) all 7 numbers (B) only odd numbers (C) only even numbers (D) the number 4 (E) the numbers 1
or 7
24. Each of the four balls weighs either 10 or 20 or 30 or 40 grams.
Which ball weighs 30 grams?
(A) A (B) B (C) C (D) D (E) It can be A or B.
Känguru der Mathematik 2018
Group Benjamin (Grade 5 and 6)
Austria – 15. 3. 2018
- 3 Points Examples -
1. As seen in the diagram, three darts are thrown at nine fixed
balloons. If a balloon is hit it will burst and the dart continues in the
same direction it had beforehand. How many balloons will not be
hit by a dart?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
2. Peter places three
building blocks on a table, as
shown.
What does he see when he is
looking at them from above?
(A) (B) (C)
(D) (E)
3. If you hit the target board, you score points.
The number of points depends on which one of the three areas you
hit. Diana throws two darts, three times at the target board. On the
first attempt she scores 14 points and on the second 16 points.
How many points does she score on the third attempt?
(A) 17 (B) 18 (C) 19 (D) 20 (E) 22 14 Points 16 Points ???
4. A garden is split into equally sized square-shaped lots. A fast and a slow snail crawl in different directions along
the outside edge of the garden. Both start at the corner S. The slow
snail crawls 1 m in one hour and the fast one crawls 2 m in one hour.
In which position will the two snails meet for the first time?
(A) A (B) B (C) C (D) D (E) E
5. A star consist of a square and four triangles. All
sides of the triangles are equally long. The perimeter of the square is 36 cm. What is the perimeter of
the star?
(A) 144 cm (B) 120 cm (C) 104 cm (D) 90 cm (E) 72 cm
6. A big spot of ink covers most of a calendar page of a certain month.
Which day of the week does the 25th day of that month fall on?
(A) Monday (B) Wednesday (C) Thursday (D) Saturday (E) Sunday
7. How many times do you have to roll an ordinary die in order to be certain that at least one
number is rolled twice?
(A) 5 (B) 6 (C) 7 (D) 12 (E) 18
8. A figure is made up of three squares. The side length of the smallest square is 6 cm. How long
is the side length of the biggest square?
(A) 8 cm (B) 10 cm (C) 12 cm (D) 14 cm (E) 16 cm
- 4 Point Examples -
9. Alice subtracts one two-digit number from another two-digit number.
Afterwards she paints over two digits in the calculation.
How big is the sum of the two painted digits?
(A) 8 (B) 9 (C) 12 (D) 13 (E) 15
10. In the diagram the circles represent light bulbs which are connected to some
other light bulbs. Initially all light bulbs are switched off. If you touch a light bulb
then that light bulb and all directly adjacent light bulbs switch themselves on. What
is the minimum number of light bulbs you have to touch in order to switch on all
the light bulbs?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
11. Four equally big squares are partially
coloured in black.
In which of the four squares is the total
area of the black parts biggest?
(A) A
D
(B) B (C) C (D)
(E) The total area of the black parts is always equally big.
12. The four smudges hide four of the numbers 1, 2, 3, 4, 5. The calculations
along the two arrows are correct.
Which number hides behind the smudge with the star?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
13. A lion hides in one of three rooms. On the door to room number 1 a note reads: „The lion is not here“. On the
door to room number 2 a note reads: „The lion is here“. On the door to room number 3 a note reads: „2 + 3 = 5“.
Exactly one of the three notes is true. In which room is the lion?
(A) Room 1 (B) Room 2 (C) Room 3
(D) It can be in any room. (E) It is either in room 1 or room 2.
14. The two girls Eva and Olga and the three boys Adam, Isaac and Urban play together with a ball. If a girl has the
ball she throws it either to the second girl or to a boy. Every boy only throws the ball to another boy, however not to
the one where the ball has just come from. The first throw is made by Eva to Adam. Who makes the 5th throw?
(A) Adam (B) Eva (C) Isaac (D) Olga (E) Urban
15. The faces of a die are either white, grey or black. Opposite faces are always a different colour. Which of the
following nets does not belong to such a die?
(A)
(B)
(C)
(D)
(E)
16. From a list with the numbers 1, 2, 3, 4, 5, 6, 7, Monika chooses 3 different numbers whose sum is 8. From the
same list Daniel chooses 3 different numbers whose sum is 7. How many of the numbers were chosen by both
Monika and Daniel?
(A) none (B) 1 (C) 2 (D) 3 (E) It cannot be determined.
- 5 Point Examples -
17. Emily wants to write a number into every free small triangle. The sum of the numbers in
two triangles with a common side should always be the same. Two numbers are already
given. How big is the sum of all numbers in the figure?
(A) 18 (B) 20 (C) 21 (D) 22 (E) it cannot be calculated
18. Instead of digits Hannes uses the letters A, B, C and D in a calculation. Different letters stand for
different digits. Which digit does the letter B stand for?
(A) 0 (B) 2 (C) 4 (D) 5 (E) 6
19. Four ladybirds each sit on a
different cell of a 4 x 4 grid. One is
asleep and does not move. On a
whistle the other three each move to
an adjacent free cell.
They can crawl up, down, to the right
or to the left but are not allowed on any
Initial
account to move back to the cell that
position
they have just come from.
Where could the ladybirds be after the fourth whistle?
After the first
whistle
After the
second whistle
After the third
whistle
(A)
(B) (C) (D) (E)
20. The five balls weigh 30 g,
50 g, 50 g, 50 g and 80 g.
Which of the balls weighs
30 g?
(A) A (B) B (C) C (D) D (E) E
21. Three different digits A, B and C are chosen. Then the biggest possible six-digit number is built where the digit A
appears 3 times, the digit B 2 times and the digit C 1 time.
Which representation is definitely not possible for this number?
(A) AAABBC (B) CAAABB (C) BBAAAC (D) AAABCB (E) AAACBB
22. The sum of Kathi’s age and the age of her mother is 36. The sum of the age of her mother and the age of her
grandmother is 81. How old was Kathi’s grandmother when Kathi was born?
(A) 28 (B) 38 (C) 45 (D) 53 (E) 56
23. Nick wants to split the numbers 2, 3, 4, 5, 6, 7, 8, 9, 10 into some groups so that the sum of the numbers in each
group is equally big. What is the biggest number of groups he can build this way?
(A) 2 (B) 3 (C) 4 (D) 6 (E) another number
24. The figure shown on the right consists of one square part and eight rectangular parts. Each
part is 8 cm wide. Peter assembles all parts to form one long, 8 cm wide rectangle. How long is
this rectangle?
(A) 150 cm (B) 168 cm (C) 196 cm (D) 200 cm (E) 232 cm
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