Đề thi Toán IKMC năm 2022 Cấp độ Ecolier, Khối 3-4 (Có đáp án)

 KÄNGURU DER MATHEMATIK 2022 
 17. 3. 2022 
 Level: ẫcolier, Grades 3 - 4 
Name: 
School: 
Class: 
 Time: 60 min. 
 24 starting points 
 each correct answer to questions 1. – 8.: 3 points 
 each correct answer to questions 9. – 16.: 4 points 
 each correct answer to questions 17. – 24.: 5 points 
 each questions left unanswered: 0 points 
 each incorrect answer: minus ẳ of the points for the question 
 Please write the letter (A, B, C, D, E) of the correct 
 answer in the square under the question number 
 (1 bis 24). Write clearly and carefully! 
 1 2 3 4 5 6 7 8 
 9 10 11 12 13 14 15 16 
 17 18 19 20 21 22 23 24 
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 8. John uses some building blocks to form a work of art. 
 What does John see when he looks at his work of art from above? 
 (A) (B) (C) (D) (E) 
 - 4 Point Examples - 
 9. Five cars are labelled with the numbers 1 to 5. They drive in the direction of the arrow. 
 1 2 3 4 5 
 First the last car overtakes the two cars in front of it. 
 Then the now second to last car overtakes the two in front of it. 
 In the end the car that is now in the middle overtakes the two in front of it. 
 In which order do the cars now drive? 
 (A) 1, 2, 3, 4, 5 (B) 2, 1, 3, 5, 4 (C) 2, 1, 5, 3, 4 (D) 3, 1, 4, 2, 5 (E) 4, 1, 2, 5, 3 
10. The members of a family of kangaroos are 
 2, 4, 5, 6, 8 and 10 years old. 
 Four of them are 22 years old when added together. 
 How old are the other two kangaroos? 
 (A) 2 and 8 (B) 4 and 5 (C) 5 and 8 (D) 6 and 8 (E) 6 and 10 
11. Mosif has filled a table with numbers (see diagram). 
 When he adds the numbers in each row and in each column together, the result 
 should always be the same. He has however, made a mistake. 
 In order to get the same result every time he has to change one single number. 
 Which number does Mosif have to change? 
 (A) 1 (B) 3 (C) one of the two 4s (D) 5 (E) one of the two 7s 
12. Aladdin’s carpet has the shape of a square. 
 Along each edge there are two rows of dots (see diagram). 
 The number of points is the same along each edge. 
 How many dots in total does the carpet have? 
 (A) 32 (B) 36 (C) 40 (D) 44 (E) 48 
13. In a classroom the children sit in rows. 
 In each row there are the same amount of children. 
 In Robert‘s row there are 2 children to the left of him and 3 children to the right of him. 
 In front of Robert there are 2 rows, behind him just one. 
 How many children in total are in this class? 
 (A) 8 (B) 15 (C) 18 (D) 20 (E) 24 
19. A pyramid is built from cubes (see diagram). 
 All cubes have side length 10 cm. 
 An ant crawls along the line drawn across the pyramid (see 
 diagram). 
 How long is the path taken by the ant? 
 (A) 30 cm (B) 60 cm (C) 70 cm (D) 80 cm (E) 90 cm 
20. A road leads away from each of the six 
 houses (see diagram). 
 A hexagon showing the roads in the 
 middle is however, missing. 
 Which hexagons fit in the middle so that 
 one can travel from A to B and to E, but 
 not to D? 
 (A) 1 and 2 (B) 1 and 4 (C) 1 and 5 (D) 2 and 3 (E) 4 and 5 
21. Ahmed and Sara move from point A in the direction 
 shown with the same speed. 
 Ahmed walks around the square garden and Sara 
 walks around the rectangular garden. 
 How many rounds does Ahmed have to walk to meet 
 Sara in point A again for the first time? 
 (A) 1 B) 2 (C) 3 (D) 4 (E) 5 
22. Five girls eat plums. 
 Laura eats 2 plums more than Sophie. 
 Bettina eats 3 plums less than Laura. 
 Clara eats one plum more than Bettina and 3 less than Alice. 
 Which two of the girls eat the same amount of plums? 
 (A) Alice and Bettina (B) Alice and Laura (C) Alice and Sophie 
 (D) Clara and Laura (E) Clara and Sophie 
23. The big cube is made up of three different kinds of 
 building blocks (see diagram). 
 How many of the little white cubes are needed for this 
 big cube? 
 (A) 8 (B) 11 (C) 13 (D) 16 (E) 19 
24. Under cards with the same colour, the same number is always 
 found. If the three hidden numbers in one row are added, one 
 obtains the number to the right of the row. 
 Which number is hidden under the black card? 
 (A) 6 (B) 8 (C) 10 (D) 12 (E) 14