2010 Kadett Test | Test and Chat

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2010 Kadett (Grade 7 - 8)

Questions: 30 | Answered: 0

Q1. How much is 12 + 23 + 34 + 45 + 56 + 67 + 78 + 89?

3 points

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Question 1

Q2. How many lines of symmetry does this figure have?

3 points

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Question 2

Q3. A fly has 6 legs and a spider has 8. Together 2 flies and 3 spiders have as many legs as 10 birds and.......

3 points

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Question 3

Q4. For transport, games are packed in several equally sized, cube shaped boxes. Every eight of which are packed in a bigger cubic box. How many of the small boxes are on the bottom level of the bigger box?

3 points

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Question 4

Q5. The perimeter of the figure pi ctured on the right is..............

3 points

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Question 5

Q6. Martina draws the six cornerpo ints of a regular hexagon and then connects some of them to obtain a geometric figure. Which of the following figures cannot be generated?

3 points

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Question 6

Q7. I write down seven consecutive whole numbers. The sum of the smallest three is 33. What is th e sum of the biggest three numbers?

3 points

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Question 7

Q8. Herbert has cut firewood. After he has made 53 cuts, he realises that he has 72 pieces of wood. How many pieces of wood did he have to start with?

3 points

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Question 8

Q9. In the box are seven blocks. It is possible to slide the blocks around so that another block can be added to the box. What is the minimum number of blocks that must be moved?

3 points

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Question 9

Q10. The sum of the first hundred positive odd numbers is deducted from the sum of the first hundred positive even numbers. What is the result?

3 points

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Question 10

Q11. Grandma has baked a cake for her grandchildren. She does not know if today 3, 5 or all 6 grandchildren will come. Into how many pieces does she have to cut the cake in order to be su re that all grandchildren present will get the same amount of cake?

4 points

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Question 11

Q12. Which of the following two-digit numbers is the smallest which cannot be made by adding three different single-digit natural numbers?

4 points

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Question 12

Q13. In the quadrilateral ABCD AD = BC, ∠ DAC = 50°, ∠ DCA = 65° and ∠ ACB = 70°. How big is ∠ ABC ?

4 points

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Question 13

Q14. In order to sew together three short strips of cloth to get one long strip Cathy needs 18 minutes. How much time does she need to sew together a really long piece consisting of six short strips?

4 points

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Question 14

Q15. Andrea wraps a band around a piece of wood. She then turn s the wood around as pictured. What does th e wood now look like?

4 points

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Question 15

Q16. A square is split into 4 smaller squares. All small squa res should either be coloured in white or black. How many ways are there to colour the big square? (patterns ar e the same if they can be – as shown in the picture – transformed into one another by rotation.)

4 points

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Question 16

Q17. In a box are 50 counters: white ones, blue ones and red ones. There are eleven times as many white ones as blue ones. Th ere are less red ones than white ones, but more red ones than blue ones. By how much is the number of red counters less than the number of white counters in the box?

4 points

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Question 17

Q18. In the figure ABCD is a rectangle and PQRS a square. The area of the grey part is half as big as the area of ABCD. How long is the side PX?

4 points

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Question 18

Q19. What is the smallest number of straight lines with which a plane can be divided into exactly 5 sections?

4 points

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Question 19

Q20. Which of the numbers a, b, c, d and e is biggest if a – 1 = b + 2 = c – 3 = d + 4 = e – 4?

4 points

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Question 20

Q21. 23 24 25 26 27 28 29 30 Information über den Känguruwettbewerb: www.kaenguru.at Wenn Du mehr in dieser Richtu ng machen möchtest, gibt es die Österreichische Mathema tikolympiade; Infos unter: www.oemo.at

5 points

ABCDE

Question 21

Q22. In the figure there are nine regions inside the circles. The numbers 1 to 9 should be written in the regions so that the sum of the numbers in each circle is exac tly 11. Which number has to go in the region with the question mark?

5 points

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Question 22

Q23. At the Lumpimarket only exchanges can be made. A cock is worth 4 hens, 3 cocks are worth 1 goose and 2 hens and 5 cocks are worth 5 turkeys. Mister Gaga č goes to the market with a load of hens in order to buy a goose, a turkey and a cock. What is the least amount of hens he has to take with him?

5 points

ABCDE

Question 23

Q24. A paperstrip is folded three times in the middle. It is then opened again and looked at from the side so that one can see all 7 folds from the side at the same time. Which of the following views is not a possible result?

5 points

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Question 24

Q25. On every one of 18 cards either a 4 or 5 is written. The sum of the numbers on all cards is divisible by 17. On how many cards is the number 4 written?

5 points

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Question 25

Q26. The numbers from 1 to 10 are wr itten 10 times each on a board. Now the children play the following game: One child deletes two numbers off the board and writes instead the sum of the two numbers minus 1. Then a second child does the same, and so on until there is only one number left on the board. The last number is

5 points

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Question 26

Q27. In Tautostadt there are only nobles and liars. Each sentence that is spoken by a noble is true. Each one that is spoken by a liar is false. One day some of th em meet in a room and three speak as follows: The first one says: „ There are no more than three in this room. We are all liars.“ The second one says: „ There are no more than four in this room. We are not all liars.“ The third one says: „In this room we are five. Three of us are liars.“ How many people are in the room and how many of them are liars?

5 points

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Question 27

Q28. A kangaroo who is interested in geometry has a collection of 1 × 1 × 1 dice. Each die has a certain colour. It wants to make a 3 × 3 × 3 cube out of the dice so that small dice that meet at the very least on one corner are always of a different colour. What is the smallest amount of colours it needs to use?

5 points

ABCDE

Question 28

Q29. The big equilateral triangle consists of 36 small equilateral triangles which each have an area of 1 cm². Determine the area of ABC.

5 points

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Question 29

Q30. In the figure α = 7°. All lines OA 1 , A 1 A 2 , A 2 A 3 , … are equally long. What is the maximum number of lines that can be drawn in this way if no two lines are allowed to intersect each other?

5 points

ABCDE

Question 30

2010 Kadett Test | Test and Chat