Đề thi Toán quốc tế IMSO năm 2012

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Mathematics Short Answer Problems

_________________________________________________________________

9th International Mathematics and Science Olympiad (IMSO) for Primary School 2012

_________________________________________________________________

Instructions:

* Write down your name and country on the answer sheet.

* Write your answer on the answer sheet.

* You have 60 minutes to work on this test.

* Use pen or pencil to write your answer.

“Smart, Skilled, and Creative In a Joyful Competition for Excellence”

City Montessori Inter College,

RDSO Campus, Manak Nagar, Lucknow, India

27 Oct. – 2 Nov 2012

International Mathematics and Science Olympiad 2012

SHORT ANSWER PROBLEMS

(1) The radius of a circle is increased by 100%. Find the percentage increase in the area?

(2) Three committees meet today. Of these three committees, one meets every 11 days, a second meets every 15 days, and the third meets every 21 days. What is the number of days before they all meet on the same day again?

(3) A nonzero number is halved and the result is squared. This yields a number which is twice the original number. What is the original number?

(4) The hypotenuse of a right triangle has length 10 cm, and the other two sides have lengths y and 3y respectively. Find the area of the triangle, in cm2.

(5) In the diagram below, ABC is an equilateral triangle of side length 7 cm. The arcs AB, BC and CA are drawn with centres C, A and B respectively. Find the

total length, in cm, of the three arcs. (Using 22

7  )

(6) Carmen selects four different numbers from the set {1, 2, 3, 4, 5, 6, 7} whose sum is 11. If l is the largest of these four numbers, what is the value of l?

(7) When my age is divided by 2, 3, 4 or 6 there is always a remainder of 1, but when divided by 7 there is no remainder. How old am I if my age is under 100?

(8) If 7 is subtracted from a three-digit number x, the result is a multiple of 7. If 8 is subtracted from x, the result is a multiple of 8. If 9 is subtracted from x, the result is a multiple of 9. When x is divided by 10, what is the remainder?

(9) In a class of 25 children, 12 wear glasses and 11 wear braces. If 7 wear both glasses and braces, what is the number of those who wear neither?

(10) IMSO, MOSI and SMIO are some arrangements of the letters I, M, S and O. How many different arrangements are there such that the letter I is not next to the letter O?

(11) A boy saved 1 dollar in the first week, 4 dollars in the second week, he saved 3 dollars more than he did the previous week. What was the total number of dollars that the boy had in the first ten weeks?

A

C B