2009 Kadett Test | Test and Chat

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2009 Kadett (Grade 7 - 8)

Questions: 30 | Answered: 0

Q1. Which of the following is an even number?

3 points

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Question 1

Q2. At a party there were 4 boys and 4 girls. Boys only danced with girls and girls only danced with boys. At the end of t he evening each person was asked how many people they had danced with. The boys gave the answers 3, 1, 2, 2 and three of the girls answered 2. Which answer did the fourth girl give?

3 points

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Question 2

Q3. The star shown in the picture is made by fit ting together 12 congruent equilateral triangles. The perimeter of the star is

3 points

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Question 3

Q4. Harry delivers newspapers in Long street. He must deliver a paper to every house with an odd house number. If the first house is number

3 points

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Question 4

Q5. ° und 10°. What is the size of the smallest angle in the acute angled triangle?

3 points

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Question 5

Q6. The product of four different natural numbers is 100. What is the sum of the four numbers?

3 points

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Question 6

Q7. In a park there are some cats and dogs. The number of cats feet is double the size of the number of dogs noses. The number of cats is …… ??? …… . of the number of dogs.

3 points

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Question 7

Q8. In the diagram QSR is a straight line. – QPS = 12° and PQ = PS = RS. How big is – QPR?

3 points

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Question 8

Q9. A lift can carry either 12 adults or 20 children. What is the maximum num ber of children that could travel in the lift with 9 adults?

3 points

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Question 9

Q10. Which of the following is made using more than one piece of string?

3 points

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Question 10

Q11. For how many positive whole numbers does a² und a³ have the same number of digits?

4 points

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Question 11

Q12. What is the minimum number of dots that must be taken away from the picture so that no three of the remai ning dots lie on a straight line?

4 points

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Question 12

Q13. Nick measured all 6 angles in two triangles. One of the triangles was acute angled and the other obtuse angled. He noted four of the angles to be: 120°, 80°,

4 points

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Question 13

Q14. What fraction of the largest square is grey?

4 points

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Question 14

Q15. On the island of the truth tellers and the liars, there are 25 people standing in a line. The person at the front claims that everybody standing behind him is a liar. Everybody else claims that the person sta nding in front of them is a liar. How many liars are standing in the line? (Truth tellers always tell the truth and liar always lie.)

4 points

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Question 15

Q16. In the diagram opposite there is an object with 6 triangular fac es. On each corner there is a number (two are shown). The sum of the numbers on the corners of each face is the same. What is the sum of all 5 numbers?

4 points

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Question 16

Q17. In the equation = T ¥ W ¥ O each letter represents a certain F ¥ O ¥ U ¥ R digit (the same letter represents the same digit each time). How many different values can the expression T ◊ H ◊ R ◊ E ◊ E have?

4 points

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Question 17

Q18. We want to paint each square in the grid with the colours P, Q, R and S, so that neighbouring squares always have different colours. (Squares which share the same corner point also count as neighbouring.) Some of the squares are already painted. In which colour(s) could the grey square be painted?

4 points

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Question 18

Q19. The diagram opposite shows a regular nonagon. What is the size of the angle marked X?

4 points

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Question 19

Q20. A pattern is made out of white, square tiles. The first three patterns are shown. How many tiles will be needed for the tenth pattern?

4 points

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Question 20

Q21. A beetle walks along the edges of a cube. Starting from point P it first moves in the direction shown. At the end of each edge it changes the direction in which it turns, turning first right then left, then right etc. Along how many edges will it walk before it returns to point P?

5 points

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Question 21

Q22. How many 10 digit numbers are there which use only t he digits 1, 2 and 3 (not necessarily all) and are written in such a way that consecutive digits always have a difference of 1.

5 points

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Question 22

Q23. The fractions und are shown on the number li ne. In which position 3 5 1 should be shown? 4

5 points

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Question 23

Q24. A cube is cut in three directions as shown , to produce eight cuboids (each cut is parallel to one of the faces of the cube). What is the ratio of the total surf ace area of the eight cuboids to the surface area of the original cube?

5 points

ABCDE

Question 24

Q25. All factors of a number N (with the exception of 1 and N itself) are written down one after the other. It turns out that the biggest factor is 45 times as big as the smallest factor. For how many numbers N is that true?

5 points

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Question 25

Q26. A square is cut into 2009 smaller squares. The side length of each smaller square is a whole number. What is the min imum possible side length of the original square?

5 points

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Question 26

Q27. In the quadrilateral PQRS PQ = 2006, QR = 2008, RS = 2007 und SP = 2009. At which corners must the interior angle definitely be smaller than 180°?

5 points

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Question 27

Q28. I have a 6 cm × 6 cm square and a certain triangle. If I lay the square on top of the triangle I can cover up to 60% of the area of the triangle. If I la y the 2 triangle on top of the square I can cover up to of the area of the square. What 3 is the area of the triangle?

5 points

ABCDE

Question 28

Q29. Friday writes different positive whole numbers that are all less than 11 next to each other in the sand. Robinson Crusoe looks at the sequence and notices with amusement that adjacent numbers are always divisible by each other. What is the maximum amount of numbers he could possibly have written in the sand?

5 points

ABCDE

Question 29

Q30. In triangle ABC the interior angle B equals 20° and C 40°. The length of the angle bisector through A is 2. What is the difference of the side lengths of BC and AB?

5 points

ABCDE

Question 30

2009 Kadett Test | Test and Chat