2022 Kangaroo Math Junior Test

Q4. Various symbols are drawn on a piece of paper (see picture) . The teacher folds the left side along the vertical line to the right. How many symbols of the left side are now congruent on top of a symbol on the right side ?

3 points

Q5. Karin places tables of size 2 × 1 according to the number of p articipants in a meeting. The diagram shows the table arrangements from above for a small, a medium and a large meeting. How many tables are u sed in a large meeting ?

3 points

Q7. The midpoints of both longer sides of a rectangle are connected with the vertices (see diagram). Which fraction of the rectangle is shaded ?

3 points

Q8. Sonja‘s smartphone displays the diagram on the right. It shows how long she has worked with four different apps in the previous week. This week he has spent only half the amount of time us ing two of the apps and the same amount of time as last week using the other two apps. Which of the following pictures could be the diagram for the current week?

3 points

Q9. In the multiplication grid displayed , each white cell should show the product of the numbers ∙ x x+1 in the grey cells that are in the same row and column respectively. One number is already y entered. The integer 푥 is bigger than the positive integer 푦 . W hat is the valu e of 푦 ?

3 points

Q10. There are 5 people to choose from on a ballot paper. After counting 90 % Alex Bella C lint Diana Eddy of the votes the intermediate result looks as shown in the table. How many of the 5 people cannot win the election anymore? 14 11 10 8 2

3 points

Q11. F ive squares and two right - angled triangles are placed as shown in the diagram. The numbers 3, 8 a nd 22 in the squares state the size of the area in m². How big is the area (in m²) of the square with the question mark ?

4 points

Q12. 2022 tiles are placed in one long row . Adam removes every sixth tile. Then Beate removes every fifth of the remaining tiles. Subsequently Cora removes every fourth of the remaining tile s . How many tiles are left ?

4 points

Q13. The diagram shows three big circles of equal size and four small circles. Each small circle touches two big circles and has radius 1. How big is the sha ded area ?

4 points

Q14. A bee called M aja wants to hike from honeycomb X to honeycomb Y. She can only move from one honeycomb to the neighbouring honeycomb if they share an edge. How many , different ways are there for Maja to go from X to Y if she has to step onto every one of the seven honeycombs exactly once ?

4 points

Q15. The sum of two positive integers is three times as big as their difference. The product of the two numbers is four times as big as their sum . How big is the sum of the two numbers ?

4 points

Q17. A rabbit and a hedgehog enter a race against each other. The circular raceco u rse is 550 m l o ng. The starting line and the finish line are the same. The speed of the rabbit is a constant 10 m/s, the speed of the hedgehog is a constant 1 m/s . They start at the same time , but the hedgehog tr ies to cheat by going in the opposite direction. When the two meet, the hedgehog turns around immediately and follows the rabbit. How many seconds after the rabbit does the hedgehog reach th e finish line ?

4 points

Q18. The grandchildren ask their grand ma how old she is. The grandma invites them to guess the age. The first child says 75, the second says 78 a nd the third says 81. It turns out that one child is wrong by 1 year, one by 2 years and one by 4 years . How many possibilities are there for the age of the grandma?

4 points

Q19. There are three paths running through our park in the city (see diagram). A tree is situated in the centre of the park. What is the minimum number of trees that have to be planted additionally so that there are the same number of trees on either side of each path ?

4 points

Q20. The diagram shows a square 푃푄푅푆 with side length 1. The point 푈 is the midpoint of the side 푅푆 a nd the point 푊 is the midpoint of the square. The three line segments , 푇푊 , 푈푊 a nd 푉푊 split the square into three equally big areas . How long is the line segment 푆푉 ?

4 points

Q21. Once I met six sisters whose ages were six consecutive integers. I asked each one of them: How old is the oldest of your sisters ? W hich of the following numbers cannot be the sum of the six answers ?

5 points

Q22. She has already formed the first two digits (see picture). How many matches will be left in the box when she has finished the number ?

5 points

Q23. One square is drawn inside each of the two congruent isosceles right - angled triangles. The area of square 푃 is 45 units . How many units is the area of square R?

5 points

Q24. In a certain city the inhabitants only communicate by asking questions. There are two kind s of inhabitants: the ‚positive‘ that only ask questions that are answered with ‚yes‘ and the ‚negative‘ that only ask questions that are answered with ‚no‘. We meet the inhabitants Albert and Berta and Berta asks us: „Are Albert and I both negative?“ What kind of inhabitants are they ?

5 points

Q25. Twelve weights have integer masses of 1 g , 2 g , 3 g , …, 11 g and 12 g respectively . A vendor divides those weights up into 3 groups of 4 weights each. The total mass of the first group is 41 g, the mass of the second group is

5 points

Q26. The d iagonal s of the squares 퐴퐵퐶퐷 a nd 퐸퐹퐺퐵 are 7 cm and 10 cm long respectively (see diagram) . The point 푃 is the point of intersection of the two diagonals of the square 퐴퐵퐶퐷 . How big is the area of the triangle 퐹푃퐷 (in cm²)?

5 points

Q27. The p rodu c t of the digits of a number 푁 is 20 . W hich of the following numbers ca nnot be the product of the digits of the number 푁 + 1 ?

5 points

Q28. Consider the five circles with midpoints A , B , C , D and E respectively , which touch each other as displayed in the diagram. The line segments , drawn in, connect the midpoints of adjacent circles. The distances between the midpoints are 퐴퐵 = 16 , 퐵퐶 = 14 , 퐶퐷 = 17 , 퐷퐸 = 13 a nd 퐴퐸 = 14 . W hich of the points is the midpoint of the circle with the biggest radius ?

5 points

Q29. Eight t eams tak e part in a football tournament where each team plays each other team exactly once. In each game the winner gets 3 points and the loser no points. In case of a draw both teams get 1 point . In the end all teams together have 61 points . What is the maxi mum number of points that the team with the most points could have gained ?

5 points

Q30. A hemispheric hole is carved i n to each face of a wooden cube with side s of length 2 . All holes are equally sized, and their midpoints are in the centre of the faces of the cube. The holes are as big as possible so that each hemisphere touches each adjacent hemisphere in exactly one point . How big is the diameter of the holes ? 3 3

5 points

2022 Junior (Grade 9 - 10)

Q1. What is ? ( 2 + 0 ) ⋅ ( 2 + 2 )

Q2. 9

Q3. An equilateral triangle with side length 12 has the same perimeter as a square with side length x . W hat is the value of x ?

Q4. Various symbols are drawn on a piece of paper (see picture) . The teacher folds the left side along the vertical line to the right. How many symbols of the left side are now congruent on top of a symbol on the right side ?

Q5. Karin places tables of size 2 × 1 according to the number of p articipants in a meeting. The diagram shows the table arrangements from above for a small, a medium and a large meeting. How many tables are u sed in a large meeting ?

Q6. I am smaller than my half and bigger than my double. The sum of me and my square is 0 . W hich number am I ?

Q7. The midpoints of both longer sides of a rectangle are connected with the vertices (see diagram). Which fraction of the rectangle is shaded ?

Q9. In the multiplication grid displayed , each white cell should show the product of the numbers ∙ x x+1 in the grey cells that are in the same row and column respectively. One number is already y entered. The integer 푥 is bigger than the positive integer 푦 . W hat is the valu e of 푦 ?

Q10. There are 5 people to choose from on a ballot paper. After counting 90 % Alex Bella C lint Diana Eddy of the votes the intermediate result looks as shown in the table. How many of the 5 people cannot win the election anymore? 14 11 10 8 2

Q11. F ive squares and two right - angled triangles are placed as shown in the diagram. The numbers 3, 8 a nd 22 in the squares state the size of the area in m². How big is the area (in m²) of the square with the question mark ?

Q12. 2022 tiles are placed in one long row . Adam removes every sixth tile. Then Beate removes every fifth of the remaining tiles. Subsequently Cora removes every fourth of the remaining tile s . How many tiles are left ?

Q13. The diagram shows three big circles of equal size and four small circles. Each small circle touches two big circles and has radius 1. How big is the sha ded area ?

Q14. A bee called M aja wants to hike from honeycomb X to honeycomb Y. She can only move from one honeycomb to the neighbouring honeycomb if they share an edge. How many , different ways are there for Maja to go from X to Y if she has to step onto every one of the seven honeycombs exactly once ?

Q15. The sum of two positive integers is three times as big as their difference. The product of the two numbers is four times as big as their sum . How big is the sum of the two numbers ?

Q16. The rectangle 퐴퐵퐶퐷 is made up of 12 c ongruent rectangles (see diagram ) . 퐴퐷 How big is the ratio ? 퐷퐶

Q19. There are three paths running through our park in the city (see diagram). A tree is situated in the centre of the park. What is the minimum number of trees that have to be planted additionally so that there are the same number of trees on either side of each path ?

Q21. Once I met six sisters whose ages were six consecutive integers. I asked each one of them: How old is the oldest of your sisters ? W hich of the following numbers cannot be the sum of the six answers ?

Q22. She has already formed the first two digits (see picture). How many matches will be left in the box when she has finished the number ?

Q23. One square is drawn inside each of the two congruent isosceles right - angled triangles. The area of square 푃 is 45 units . How many units is the area of square R?

Q25. Twelve weights have integer masses of 1 g , 2 g , 3 g , …, 11 g and 12 g respectively . A vendor divides those weights up into 3 groups of 4 weights each. The total mass of the first group is 41 g, the mass of the second group is

Q26. The d iagonal s of the squares 퐴퐵퐶퐷 a nd 퐸퐹퐺퐵 are 7 cm and 10 cm long respectively (see diagram) . The point 푃 is the point of intersection of the two diagonals of the square 퐴퐵퐶퐷 . How big is the area of the triangle 퐹푃퐷 (in cm²)?

Q27. The p rodu c t of the digits of a number 푁 is 20 . W hich of the following numbers ca nnot be the product of the digits of the number 푁 + 1 ?