2023 Kangaroo Math Kadett Test

Q3. A dark disc with two holes is placed on top of a dial of a watch as sh own. The dark disc is now rotated so that the number 8 can be seen through one of th e holes. W hich of the numbers c ould one see through the other hole now ?

3 points

Q4. John throws 150 coins onto a table. 60 of them show „head“ , the oth ers show „ tail “ . He wants the same amount of coins to show „head“ as „ tail “ . How many coins that show „head“ does he have to turn over ?

3 points

Q5. Kristina ha s a piece of see - through foil on which some points and lines are drawn. She folds the foil along the dotted line. W hat can she see now ?

3 points

Q6. A grid should be cut along the black lines into several identical shapes. No piece is to be left over. In to which of the following shapes is it n o t possible to cut this grid in this way ?

3 points

Q8. Werner wants to label each side and each corner point of the rhombus shown with exactly one number . He wants the number on each side to be equal to the sum of t he numbers on the co rner points of th at sides . W hich number is he going to write in the place of the question mark ?

3 points

Q9. Anna ha s five circular discs that are all of different size s . She wants to build a tower using three discs where a smaller disc always has to lie on to p of a bigger disc. How many ways are there for Anna to build the tower ?

3 points

Q10. Evita wants to write the nu m bers from 1 to 8 with one number in each field . The sum of the numbers in each row should be equal. The sum of the numbers in the four columns should also be the same. She has already written in the numbers 3, 4 a nd 8 (see d iagram ). W hich number does she have to write in the dark field ?

3 points

Q11. Dorli writes down three consecutive natural numbers in increasing order. She replaces the digits using symbols and gets : □ ♦♦ , ♡ ∆∆ , ♡ ∆ □ . W hat would be the next bigger number in this notation ?

4 points

Q13. Some edges of a cube are coloured in red so that each sides of the cube has at least one red edge. What is the minimum number of red edges that the cu be has ?

4 points

Q14. The digits 0 to 9 can be formed using matchsticks (see diagram ) . How many different positive whole numbers can be formed this way with exactly 6 matchstick s ?

4 points

Q15. The side lengths of a square are 1 cm l o ng. How many points on a plane surface are there that are exactly 1 cm away from two co rner points of the square ?

4 points

Q16. Some kangaroos and three beavers are standing in a circle. No bea ver stands directly next to another beaver. There are exactly three kangaroos that are standing next to another kangaroo . W hat is the biggest possible number of kangaroos in the circle ?

4 points

Q17. Tom, John a nd Lily have each shot 6 arrows on a disc with three sections (see d iagram). The number of points of a hit depends on the section that has been hit. Tom has 46 points and John has 34 points. How many points did Lily get ?

4 points

Q18. Max and two of his friends are standing in a line. The number of people in the line is a mult iple of 3. He realises that the re are the same number of people in front of him as there are behind him. His two friends are both behind him: one is in position 19, th e other one in position 28 of the line. In which position of the line is Ma x?

4 points

Q19. Two rays starting in S form a right angle . More rays starting in S are drawn within the right angle so that each angle 10°, 20°, 30°, 40°, 50°, 60°, 70° a nd 80° i s enclosed by two rays . W hat is the minimum number of rays that have to be drawn ?

4 points

Q21. The diagram shows a grey rectangle that lies within a bigger rectangle which sides it touches. Two corner points of the grey rectangle are the midpoints of the shorter sides of the bigger rectangle. The grey rectangle is made up of three squares that each hav e an area of 25 cm 2 . How big is the area of the bigger rectangle in cm 2 ?

5 points

Q22. S now W hite organises a chess tournament for the seven dwarfs lasting several days. Every dwarf has to play every other dwarf exactly once. On Monday Grumpy play s 1 game , Sneezy plays 2, Sleepy 3, Bashful 4, Happy 5 a nd Doc 6 games . How many games does Dopey , the 7th dwarf , play on Monday ?

5 points

Q23. The show n triangle 퐴퐵퐶 is isosceles with ∡ 퐴퐵퐶 = 40° . The two angles indicated ∡ 퐸퐴퐵 a nd ∡ 퐷퐶퐴 are equally big . How big is the angle ∡ 퐶퐹퐸 ?

5 points

Q25. Elisabeth wants to write the numbers 1 to 9 in the fields of the diagram shown so that the product of the nu mber s of two fields next to each other is no greater than 15 . Two fields are called „ next to each other “ if they share a common edge . How many ways are there for Elisabeth t o label the fields ?

5 points

Q26. Several mice live in three houses. Last night every mouse left their house and moved directly to one of the other two houses. The diagram show s how many mice were in each house yesterday and today. How many mice used the path tha t is indicated with an arrow ?

5 points

Q27. Bart wrote the number 1015 as a sum of numbers that are made up of only the digit 7. In total h e uses the digit 7 , 10 times. Now he wants to the write the number 2023 as a su m of numbers that are made up of only the digit 7. He uses the digit 7, 19 times in total. How often does he have to use the nu mber 77 ?

5 points

Q28. A regular hexagon is split into four quadrilaterals and a smaller regular hexagon. 퐴푟푒푎 표푓 푡 ℎ 푒 푑푎푟푘 푠푒푐푡푖표푛푠 4 The ratio = . 퐴푟푒푎 표푓 푡 ℎ 푒 푠푚푎푙푙 ℎ 푒푥푎푔표푛 3 퐴푟푒푎 표푓 푡 ℎ 푒 푠푚푎푙푙 ℎ 푒푥푎푔표푛 How big is the ratio ? 퐴푟푒푎 표푓 푡 ℎ 푒 푏푖푔 ℎ 푒푥푎푔표푛

5 points

Q29. Jakob wrote six consecutive numbers on six little pieces of white paper, one number per piece of paper. He stuck those six pieces of paper on the front and back of three coins. Then he threw the coins three times. After the first throw the numbers 6, 7, 8 were on t op (see diagram) which Jakob then coloured in red. After the second throw the sum of the numbers on top was 23 and after the third throw the sum was 17 . How big is the sum of the numbers on the three white piec es of paper ?

5 points

Q30. A rugby team scored 24, 17 a nd 25 p oints in their 7 th , 8 th a nd 9 th game of the previous season . The average number of points per game was higher after 9 games than after their first 6 games. Their average after 10 games was more than 22 points. What is the minimum nu m ber of points they have scored in their 10 th game?

5 points

2023 Kadett (Grade 7 - 8)

Q1. The diagram shows a grid made of vertical and horizontal lines. W hich part was cut from the grid ?

Q2. W hich of the following shapes cannot be cut into t wo trapeziums with one single straight line ?

Q3. A dark disc with two holes is placed on top of a dial of a watch as sh own. The dark disc is now rotated so that the number 8 can be seen through one of th e holes. W hich of the numbers c ould one see through the other hole now ?

Q4. John throws 150 coins onto a table. 60 of them show „head“ , the oth ers show „ tail “ . He wants the same amount of coins to show „head“ as „ tail “ . How many coins that show „head“ does he have to turn over ?

Q5. Kristina ha s a piece of see - through foil on which some points and lines are drawn. She folds the foil along the dotted line. W hat can she see now ?

Q6. A grid should be cut along the black lines into several identical shapes. No piece is to be left over. In to which of the following shapes is it n o t possible to cut this grid in this way ?

Q7. The diagram shows the starting position, the direction and the distance covered within

Q8. Werner wants to label each side and each corner point of the rhombus shown with exactly one number . He wants the number on each side to be equal to the sum of t he numbers on the co rner points of th at sides . W hich number is he going to write in the place of the question mark ?

Q9. Anna ha s five circular discs that are all of different size s . She wants to build a tower using three discs where a smaller disc always has to lie on to p of a bigger disc. How many ways are there for Anna to build the tower ?

Q11. Dorli writes down three consecutive natural numbers in increasing order. She replaces the digits using symbols and gets : □ ♦♦ , ♡ ∆∆ , ♡ ∆ □ . W hat would be the next bigger number in this notation ?

Q12. The diagram shows 5 equally big semicircles and the length of 5 distances . How big is the radius of one semicir cle ?

Q13. Some edges of a cube are coloured in red so that each sides of the cube has at least one red edge. What is the minimum number of red edges that the cu be has ?

Q14. The digits 0 to 9 can be formed using matchsticks (see diagram ) . How many different positive whole numbers can be formed this way with exactly 6 matchstick s ?

Q15. The side lengths of a square are 1 cm l o ng. How many points on a plane surface are there that are exactly 1 cm away from two co rner points of the square ?

Q16. Some kangaroos and three beavers are standing in a circle. No bea ver stands directly next to another beaver. There are exactly three kangaroos that are standing next to another kangaroo . W hat is the biggest possible number of kangaroos in the circle ?

Q17. Tom, John a nd Lily have each shot 6 arrows on a disc with three sections (see d iagram). The number of points of a hit depends on the section that has been hit. Tom has 46 points and John has 34 points. How many points did Lily get ?

Q19. Two rays starting in S form a right angle . More rays starting in S are drawn within the right angle so that each angle 10°, 20°, 30°, 40°, 50°, 60°, 70° a nd 80° i s enclosed by two rays . W hat is the minimum number of rays that have to be drawn ?

Q20. The sum of 2023 consecutive integers is 2023. W hat is the sum of the digits of the biggest of those numbers ?

Q23. The show n triangle 퐴퐵퐶 is isosceles with ∡ 퐴퐵퐶 = 40° . The two angles indicated ∡ 퐸퐴퐵 a nd ∡ 퐷퐶퐴 are equally big . How big is the angle ∡ 퐶퐹퐸 ?

Q24. An ant walks along the sides of an equilateral triangle (see diagram) . I ts velocity is

Q26. Several mice live in three houses. Last night every mouse left their house and moved directly to one of the other two houses. The diagram show s how many mice were in each house yesterday and today. How many mice used the path tha t is indicated with an arrow ?