Đề thi Toán quốc tế IMSO năm 2004

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Mathematics Short Answer Problems

International Mathematics and Science Olympiad (IMSO)

for Primary School 2004

Jakarta, November 29 - December 3, 2004

Instructions:

* Write down your name on every page.

* Answer all 25 questions.

* You have 60 minutes to work on this test.

* Write your answer in the boxes provided.

Mathematics IMSO Primary School 2004

1

Name : ........................................................................ Country : ........................................................................

1. A pole is 156 cm high. It casts a shadow of length 234 cm. Find the length of the shadow cast by a 104 cm-high pole.

Answer:

2. The square ABCD is divided into 9 smaller squares as shown in the figure. The perimeter of ABCD is 360 m. Find the perimeter of one smaller square.

Answer:

3. A farmer has some goats and chickens. He counts 110 legs and 76 eyes. How many goats does he have?

Answer:

2

Name : ........................................................................ Country : ........................................................................

4. The table shows Andi’s grades for Test 1 and Test 2 in Mathematics, Language and Science.

In which subject does he show the best improvement in terms of percentage, from Test 1 to Test 2?

Answer:

5. Complete the magic square so that the vertical sums, horizontal sums and diagonal sums are all equal.

6. Nasir draws 5 straight lines on a piece of paper. What is the maximum number of intersection points can Nasir make?

Answer:

3

Name : ........................................................................ Country : ........................................................................

7. Ade and Tomi are talking about money. Ade says, ”If you give me 1, 000 rupiahs, our money will be equal”. Tomi says, ”If you give me 1, 000 rupiahs, my money will be twice as much as your money”. How much money do they have altogether?

Answer:

8. A swimming pool is 10 m long and 4 m wide. The shallow end is 1 m deep. The bottom slopes evenly to the other end, where it is 2 m deep. Find the volume of the pool in m3.

Answer:

9. In the figure below, the number assigned to the edge connecting two circles describes the sum of two numbers in the circles.

Fill all circles with the appropriate numbers following the above rule.

4

Name : ........................................................................ Country : ........................................................................

10. The figure below shows paths in a garden. ABCDEF is a regular hexagon with center O. H is the midpoint of side AB. What is the shortest way to go from H to E along the paths?

Answer:

11. In a birthday party, all the children are given candies. If each child gets 5 candies, there would be 10 candies left. If each child gets 6 candies, 2 more candies are needed. How many candies are there?

Answer:

12. A natural number has the following conditions:

* When this number is divided by 4, the remainder is 3.

* When this number is divided by 3, the remainder is 2.

* When this number is divided by 2, the remainder is 1.

Find the smallest number that satisfies the above conditions.

Answer:

5