Đề thi Toán quốc tế IMSO năm 2009

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Notice: Individual students, nonprofit libraries, or schools are permitted to make fair use of the papers and its solutions. Republication, systematic copying, or multiple reproduction of any part of this material is permitted only under license from the Chiuchang Mathematics Foundation. Requests for such permission should be made by e- mailing Mr. Wen-Hsien SUN ccmp@seed.net.tw

IMSO 2009 IMSO2009

Short Answer Yogyakarta, 8-14 November

Page 2 of 6

6th INTERNATIONAL MATHEMATICS AND SCIENCE OLYMPIAD FOR PRIMARY SCHOOL

IMSO 2009

SHORT ANSWER PROBLEMS

DIRECTORATE OF KINDERGARTEN AND PRIMARY DEVELOPMENT

DIRECTORATE GENERAL OF PRIMARY AND SECONDARY EDUCATION MANAGEMENT

MINISTRY OF NATIONAL EDUCATION

Yogyakarta, 8 – 14 November 2009

IMSO 2009 IMSO2009

Short Answer Yogyakarta, 8-14 November

Page 3 of 6

1. A big square is formed from twenty five small squares. Some of the small

squares are black. To make the big square symmetric about both diagonals, at least … additional small squares are needed to be colored black.

2. If , then =….

3. In a training program, an athlete must eat 154 eggs, during a period of time from

November 8th till November 14th. Every day in this period he must eat 6 more eggs than the previous day. The number of eggs he eats on November 13th is …

4. ….

5. In the following grid, the area of the shaded region is … unit square.

6. Danny wants to create a set of cards of sizes from a sheet of paper of size . The number of cards that can be made by Danny is at most … . 7. Mrs. Anna has 4 children: Alex, Brad, Christine, and Dennis. Alex is not the

youngest, but he is younger than Dennis. If Brad’s age is the same as the mean of the ages of Alex and Dennis, then the oldest one is … . 8. In a math test, a correct answer will be marked 5 points and a wrong answers

points. Tom answered all of the 35 questions and got a total score of 140. The number of questions Tom answered correctly is … .

IMSO 2009 IMSO2009

Short Answer Yogyakarta, 8-14 November

Page 4 of 6

A B

C D P

9. The following shape is made from horizontal and vertical lines. The lengths of

some of the lines are given. The perimeter of the shape is … unit.

10. Use numbers 2, 3, 4, 5, 7, and 8 exactly once to form two three-digit numbers P

and Q. If is a positive number; the smallest possible value of is ... . 11. The natural numbers bigger than 1 are arranged in five columns as given by the

following figure. The number 2009 appears in the … column and the … row.

I II III IV V

2 3 4 5

9 8 7 6

10 11 12 13

17 16 15 14

12. The integer 8 has two properties:

 If the number 1 is added, we get the number 9, which is a square number,

i.e., 9 = 33.  Half of it is 4, which is also a square number, i.e., 4 = 22. The next natural number which has the same properties is … . 13. The next natural number which has the same properties is … . ABCD is a trapezoid

(trapezium) with AB parallel to CD. The ratio of AB : CD is 3 : 1. The point P is on CD. The ratio of the area of triangle APB to the area of trapezoid ABCD is …:…. 14. I have some marbles and some empty boxes. If I try to put 9 marbles on each

box, then there will be 2 empty boxes. If I try to put 6 marbles in each box, then there will be 3 remaining marbles. I have … boxes.