Soal IMSO Matematika 2006 | Info Ops IMSO2006 Math
INTERNATIONL MATHENATICS AND SCIENCE OLYMPIAD
FOR PRIMARY SCHOOLS (IMSO) 2006
Mathematics Contest in Taiwan
Name:111
1
School: 111111
Grade: 1111
number: 11111
Short Answer: there are 12 questions, fill in the correct answers in the answer
sheet. Each correct answer is worth 10 points. Time limit: 90 minutes.
1. At a sale, Sam bought a radio valued at $500. If he received a discount of
5%, what was the price he paid?
2. In how many ways can the number 2006 be expressed as the product of two
factors, each of them greater than 1?
3. Chien-Ming Wang is a Taiwanese pitcher for the New York Yankees, and is
scheduled to pitch in a game on Wednesday starting at 6:00 pm New York
time. If Taipei time is 13 hours ahead, when will a live broadcast on local
television begin?
4. In Pingtung, the average minimum temperature during a week was 30°C.
The minimum temperature on the first six days of that week were 27°C,
29°C, 32°C, 33°C, 29°C and 32°C. What was the minimum temperature on
the last day of that week?
5. How many positive integers greater than 5000 can be formed with the digits
2, 4, 6, 7 and 8, if no digit is used more than once in a number?
6. The Student Council has 36 members, and the ratio of the number of boys
to the number of girls is 3:1. How many more girls should be added to the
Student Council so that the ratio of the number of boys to the number of
girls will be 9:5?
7. The first digit of a 6-digit number is 1. We move this 1 so that it becomes
the last digit of the number, without disturbing the order of the other five
digits. For example, 123456 will become 234561. If the new number is
exactly 3 times the original number, what is the original number?
8. In the diagram, the net of a cube is shown on the right,
and four cubes are shown on the left. Which of the four
cubes may be folded from the net?
(a)
(b)
(c)
(d)
9. Two polygons are overlapping such that
2
3
polygon lies outside the larger polygon, and
of the area of the smaller
8
9
of the area of the larger
polygon lies outside the smaller polygon. When not overlapping, the total
area of the two polygons is 120 cm2. What is the area of the overlapping
part of the polygons?
10. In the diagram below, a square piece of paper is divided into 16 identical
boxes in a 4×4 array, each filled with a different letter. The piece of paper is
folded four times according to the following instructions
(1) After the first fold, the upper half covers the lower half.
(2) After the second fold, the left half covers the right half.
(3) After the third fold, the lower half covers the upper half.
(4) After the fourth fold, the right half covers the left half.
Which letter is in the box on the 10th layer from the top?
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
11. The Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, 21, 34, ... . Each term after
the first two is obtained by adding the last two terms. What is the greatest
value of the ratio of two neighboring terms of the Fibonacci numbers?
12. The sum of six positive integers is equal to their product. What is this
common value?
FOR PRIMARY SCHOOLS (IMSO) 2006
Mathematics Contest in Taiwan
Name:111
1
School: 111111
Grade: 1111
number: 11111
Short Answer: there are 12 questions, fill in the correct answers in the answer
sheet. Each correct answer is worth 10 points. Time limit: 90 minutes.
1. At a sale, Sam bought a radio valued at $500. If he received a discount of
5%, what was the price he paid?
2. In how many ways can the number 2006 be expressed as the product of two
factors, each of them greater than 1?
3. Chien-Ming Wang is a Taiwanese pitcher for the New York Yankees, and is
scheduled to pitch in a game on Wednesday starting at 6:00 pm New York
time. If Taipei time is 13 hours ahead, when will a live broadcast on local
television begin?
4. In Pingtung, the average minimum temperature during a week was 30°C.
The minimum temperature on the first six days of that week were 27°C,
29°C, 32°C, 33°C, 29°C and 32°C. What was the minimum temperature on
the last day of that week?
5. How many positive integers greater than 5000 can be formed with the digits
2, 4, 6, 7 and 8, if no digit is used more than once in a number?
6. The Student Council has 36 members, and the ratio of the number of boys
to the number of girls is 3:1. How many more girls should be added to the
Student Council so that the ratio of the number of boys to the number of
girls will be 9:5?
7. The first digit of a 6-digit number is 1. We move this 1 so that it becomes
the last digit of the number, without disturbing the order of the other five
digits. For example, 123456 will become 234561. If the new number is
exactly 3 times the original number, what is the original number?
8. In the diagram, the net of a cube is shown on the right,
and four cubes are shown on the left. Which of the four
cubes may be folded from the net?
(a)
(b)
(c)
(d)
9. Two polygons are overlapping such that
2
3
polygon lies outside the larger polygon, and
of the area of the smaller
8
9
of the area of the larger
polygon lies outside the smaller polygon. When not overlapping, the total
area of the two polygons is 120 cm2. What is the area of the overlapping
part of the polygons?
10. In the diagram below, a square piece of paper is divided into 16 identical
boxes in a 4×4 array, each filled with a different letter. The piece of paper is
folded four times according to the following instructions
(1) After the first fold, the upper half covers the lower half.
(2) After the second fold, the left half covers the right half.
(3) After the third fold, the lower half covers the upper half.
(4) After the fourth fold, the right half covers the left half.
Which letter is in the box on the 10th layer from the top?
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
11. The Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, 21, 34, ... . Each term after
the first two is obtained by adding the last two terms. What is the greatest
value of the ratio of two neighboring terms of the Fibonacci numbers?
12. The sum of six positive integers is equal to their product. What is this
common value?