Mathematics Newspaper Competition for Primary School Students (Grade Five) in 2005

The fifth grade textbook of the primary school mathematics newspaper's initial evaluation activity for outstanding young readers

(Time: 9: 00 on March 9, 2005 ——10: 30)

First, fill in the blanks:

1, A, B and C pass the ball to each other, starting from A (as the first pass), so after five passes, the ball just returns to A, so there are () different ways to pass.

Five pairs of sports shoes with the same specifications in four colors, red, blue, yellow and black, are piled up in a big cloth bag at random. If you take shoes with your eyes closed, at least take out a pair of shoes from your bag. In order to ensure that there are two pairs of sports shoes of the same color.

3. Please fill in "×" or "∫" in the box of the following formula to make the formula hold:

9 mouths, 8 mouths, 7 mouths, 6 mouths, 5 mouths, 4 mouths, 3 mouths and 2 mouths 1=2/35.

There are always () different filling methods.

Three students, Xiao Zhao, Xiao Zhang and Xiao Wang, estimated the number of books in Max's schoolbag. Xiao Zhao said: "There are at least 10 books in the schoolbag and at most 15 books." Xiao Zhang said, "There are less than 10 books in the schoolbag." Xiao Wang said, "There are at least 1 book in the schoolbag and at most 15 books." But michaels said, "Only one of you three is right." In this way, there are () books in the wheat bag.

5. As shown in figure 1, select 1 from the blank squares of1(all the other nine squares are cut off), and fold them into a cubic carton with five squares written with "I wish you progress in your study". * * * There are () different selection methods.

6. The difference between two four-digit numbers is 2005, so the maximum sum of two four-digit numbers is () and the minimum is ().

7. All students in a class have a basketball shooting practice, and each student has to throw 10 balls, and each ball gets 1 point. The scores are shown in the right table. It is also known that among the students in this class, those who scored more than 3 points scored an average of 6 points, and those who scored less than 8 points scored an average of 3 points, so there are () students in this class.

8. One day, four pairs of painters went to the countryside to sketch, and they always drew 44 paintings. Among them, four female painters A, B, C and D painted 2, 3, 4 and 5 paintings respectively; The number of paintings drawn by four male painters is: A drew the same number as his wife; The width of B, C and D is twice, three times and four times that of the wife. Then the husbands of A, B, C and D are (), (), () and () respectively.

Second, fill in the blanks

1. The main traffic arteries of a city are shown in Figure 2. Each blue dot in the figure represents the intersection of the road, the connecting line between the blue dots represents the road, and the number marked next to the connecting line represents the maximum number of cars that can pass per minute (for example, 60 represents the maximum number of cars that can pass per minute). How many cars can you pass at most every minute from A to B?

The distance between a and b is 2400 kilometers. A starts from A and B at the same time and runs back and forth between A and B. A runs 300 meters per minute and B runs 240 meters per minute, and stops exercising after 35 minutes. When did A and B meet for the first time, the closest to A? What's the nearest distance?

Third, the operation questions

1, as shown on the right, there is a chess piece (indicated by ★) in the square in the upper left corner of the rectangular chessboard of 2004× 16.

Xiao Bing and Xiaoyan play chess according to the following rules:

1. The soldiers go first, and then they move the pieces in turn;

2. A chess piece can walk several squares vertically or horizontally (diagonally), but at least 1 square is required;

3. Each square allows chess pieces to pass or stay once;

4. which side has no squares to go, which side will be considered as failure.

Both of them are trying their best to win, and one of them will win. Excuse me: Who is sure to win? Briefly describe the strategy of winning.

2. What is the maximum surface area of a square centimeter of 35 pieces of 3×2× 1 cuboid wood? What is the smallest square centimeter?

Fourth, question and answer.

1, garden path, winding path leading to a secluded place. As shown in Figure 4 (Sorry, I really can't draw that picture, but I remember this topic is the final exam of the 5th China Cup). This small path is paved with white square slates and blue and red triangular slates. Is the total area of triangular slates in the inner ring larger or the total area of the outer ring larger? Please provide a justification for the answer.

2. A square piece of paper with a side length of 20 cm is cut at a 45-degree angle 5 cm from the apex (as shown in Figure 5) to form a small square in the middle. How many square centimeters is the area of a small square?

There are five points on the plane, and the distance between each two points is different. Please connect the nearest two points with a straight line. How many triangles have these lines formed? Why?