Đề thi IKMC lớp 5 - 6 năm 2023

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ĐỀ THI IKMC LỚP 5-6 NĂM 2023

1. Holger writes the numbers up to 40 in the table in the same way as shown. Which of the pieces A to E can he then cut from the table?

A. B. C. D. E.

2. Matchsticks are arranged to form numbers as shown. To form the number 15 one needs 7 matchsticks. To form the number 8 one needs the same amount. What is the biggest number that one can build using 7 matchsticks?

A. 31 B. 51 C. 74 D. 711 E. 800 3. Which of the shapes cannot be split into two triangles using a single straight line?

A. B. C. D. E.

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4. Nine steps of a staircase arranged in a cylindrical order starting at the bottom and leading all the way to the top can be seen. All steps are equally high. How many steps cannot be seen?

A. 9 B. 10 C. 11 D. 12 E. 13

5. Anna has five discs of different sizes. She wants to use 4 of them to build a tower. She always has to place a smaller one on top of a bigger one. How many ways are there for Anna to build the tower?

A. A B. B C. C D. D E. E

6. Four ribbons M, N, P and Q are wrapped around a box. In which order were they wrapped around the box?

A. M, N, Q, P B. N, M, P, Q C. N, Q, M, P D. N, M, Q, P E. Q, N, M, P

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7. Alice has four jigsaw pieces. Which two can be fitted together to form a hexagon?

A. 1 and 2 B. 1 and 3 C. 2 and 3 D. 2 and 4 E. 1 and 4 8. A dark disc with three holes is placed on top of a dial of a watch (see diagram). Then the disc is rotated around its centre. Which numbers can be seen at the same time?

A. 4, 6 and 12 B. 1, 5 and 10 C. 2, 4 and 9 D. 3, 6 and 9 E. 5, 7 and 12

9. Jan sticks these three pieces of paper

on top of a black circle Which picture can he not obtain？

A. B. C. D. E.

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10. Franziska writes down three consecutive two- digit numbers．They are in increasing order.

Instead of the digits she uses symbols and writes , , . What does Franziska’s next number look like？

A. B. C. D. E.

11. A terrace is covered with square tiles of different sizes．The smallest tile has a perimeter of 80 cm ．A snake lay down along the edges of the tiles（see diagram. How long is the snake？

A. 380 cm B. 400 cm C. 420 cm D. 440 cm E. 1680 cm

12. The picture of a digital watch can be seen in a mirror

Which picture of the watch can be seen in the mirror 30 minutes later？

A. B. C. D. E.

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13. Maria, Peter, Richard and Tina play football in the classroom. While doing so a window pane broke. When the head mistress wanted to find out who broke the window pane she got the following answers: Maria: “It was Peter.“ Peter: “It was Richard.” Richard: “It wasn’t me.” Tina: “It wasn’t me.” Later is became clear that only one child spoke the truth. Who broke the window pane?

A. Maria B. Tina C. Peter D. Richard E. It cannot be determined．

14. The sums of the numbers in the white and in the grey fields should be equally big． Which two numbers have to be swapped so that the sums are equally big？

A. 1 and 11 B. 2 and 8 C. 3 and 7 D. 4 and 13 E. 7 and 13

15．The big rectangle is made up of five small rectangles（see diagram）． Lukas wants to colour in the small rectangles in red，blue and yellow．Two rectangles next to each other should be coloured in different colours． How many ways are there for Lukas to do that？

A. 3 B. 4 C. 5 D. 6 E. 7