Trích đề thi hoc sinh giỏi 7-8 Úc 2003

Trích đề thi hoc sinh giỏi 7-8 Úc 2003

Xin chép tiếp một số câu hỏi trong đề thi học sinh giỏi 7-8 ở Úc 2003 tôi mới vừa có đuợc:

1. A triangle is called scalene if no sides are the same length. Find the number of scalene triangles whose vertices are the vertices of a given cube.

2. In a mathematical competition consisting of 12 problems, 8 marks are given for each correct response, 0 mark for each incorrect response and each no response is awarded 3 marks. Vicki scored 35 marks in this competition. Find the largest number of incorrect responses she could have had ?

3. The numbers from 1 to 15 are arranged in a triangular fashion, one such arrangement is shown.
1
6 7
2 13 4
5 11 3 15
12 8 14 10 9
If they are arranged so that the sum of the numbers along each side of the triangle is the same and is as small as possible what is that sum?

4. Steve has a broken calculator. When just turned on, it displays 0. If the key + is pressed it adds 51. If the key ?" is pressed it subtracts 51. If the key x is pressed it adds 85. If the : is pressed it subtracts 85. The other keys do not function. Steve turns the calculator on. The number closest to 2003 that he can get using this calculator is

5. A 10cm x 10cm x 10cm cube is cut into 1cmx 1cm x 1cm cubes. As many of these cubes are needed are glued together to form the largest possible cube which looks solid from any point on the outside but is hollow inside. What could the maximum number of smaller cubes left over be?

6. How many numbers less than 10 000 have the product of their digits equal to 84?

7. A 3 x 3 square is divided up into 1 x 1 unit squares. Different integers from 1 to 9 are written in these 9 unit squares. For each two squares sharing a common edge, the sum of the integers in them is calculated. What is the minimum possible of different sums?



Được phan2 sửa chữa / chuyển vào 16:58 ngày 14/08/2003