Find the questions for the preliminary round of the Mathematics Olympiad for junior high school

A total of 28 students from Year 7 Class 5 participated in the Math and Science Interest Group, of which 5 more people participated in the Math Interest Group than in the Science Interest Group, and 9 students participated in both interest groups. Q: How many students participate in the Math Interest Group?

A cylindrical glass container containing water has an inner bottom radius of 10 cm and a height of 12 cm for the water inside the container. Insert a glass rod with a radius of 2 cm vertically into the water and ask how much the water in the container will rise?

2.With the continuous development of Internet technology, the role of the Internet in people's daily life has become more and more important. According to the statistics of a municipal telecommunications company, as of June 2003, the number of individual registered users in the city has reached 40.96 million, and the annual growth rate has increased by 55% in the first two years.

There are 45 students in a certain class, and the number of people who can play chess is double the number of people who can play Go, and the number of people who can or can't play both types of chess is 5, and the number of people who can only play Go is required.

Please use a one-dimensional equation to solve.

The school selects 10 students from 30 candidates to form the student council, and a class has 4 candidates. It is assumed that every candidate has the same chance of being selected.

Students in Class 5 of Grade 7 are arranged in several rows for physical education class, and if there are 8 students in each row, there will be 2 more students; If there are 9 students in each row, there is a difference of 5 in the row, and there are many students in the class.

Let's do that first.

When a store buys an item, the purchase rate is lower than the original, and the profit margin has increased by 8%, what is the original profit margin?

A factory worker travels, each car does 22 people, then the remaining one person, if you remove a car, the average separation of people has no remaining, how many employees, how many cars?

s=1÷1/1980+1/1981+1/1982+……1/2000+1/2011

then What is the integer part of s?

2x+1）⁴﹢=ax⁴﹢¹bχ⁴﹢cχ³﹢dχ²﹢eχ+f a+b=？

This is the Olympiad question I just took and I didn't do it, and it's very difficult.

ab is a positive integer, and we can get that a is the smallest and 1. Therefore, the minimum power of 2 to the nth power is 16, which means that the n-1 power of n greater than or equal to is (5a+b 2) is also an even number, indicating that b is divisible by 2. 2 to the nth power (16, 32, 64, 128, 256, 512, 1024, 2048...)

axb=(1x6，3x2，6x4，12x8，25x6，51x2，102x4，204x8...

Since we know that b is divisible by 2, we only need to see if the number in parentheses can be divisible by 3, so as long as we judge whether the factors in it are divisible by 3 if the numbers add up, it is obviously possible. So it can be concluded that ab is divisible by 6.

The 1st and 3rd floors are unreliable! The 1st floor will only count to 100 The 2nd floor is good, borrow the proof that b can be divisible by 2, and then just prove that it can be divisible by 3 at the same time:

n must be greater than 4, that is, it must start at least from the 4th power of 2, that is, 16, and you can put 2 to the nth power.

Regarded as 16 times 2 to the power of m, this m is greater than or equal to 1, which is the premise;

That 2 n = 2 m * 16 = 2 m * (10 * 1 + 6) = 10 * 2 m + 6 * 2 m

At this time, a=2 m b=6*2 m

ab=6*2^(m+1)

This is definitely divisible by 6.

is multiplication, and 2 m is the meaning of 2 to the m power.

I think it's almost an adoption.

If b is less than 10, it is not true, and the tenth power of 2 = 1024 = 10 * 100 + 24

There are x people in the solution.

x(x-1)＜159

then there are those who are eligible.

x = 13, there are 3 second handshakes.

When x = 12, there are 27 second handshakes.

Not on topic. So there were 13 people in the meeting, and there were 3 second handshakes.

Choose b because A2 + B2 >=2AB

In this case, 1 2 (a 2 + b 2 ) ab this is not possible.

The area should be < = ab 2, and the equal sign is obtained when ab is vertical.

B, I don't know what the level of learning is in the junior high school competition, I said mine.

s=1 2sin@*a*b @代表ab边夹角角度,0

The Leaning Tower of the Competition has a total of 8 floors, composed of more than 200 stone pillars (no more than 250), there are 12 on the top floor, 6 layers in the middle, the number of roots in each layer is the same, the number of stone pillars in the bottom layer is only half of that of each layer in the middle, and the number of stone pillars in each layer and the bottom layer in the middle are multiples of 5, find the exact number of stone pillars in the leaning tower.

An elderly couple said, "The square difference between the ages of the two of us is 195A pair of young people said:

Coincidentally, the square difference in the ages of our husband and wife is also 195A middle-aged couple also came over and said, "The square difference between the ages of the two of us is also 195," please think about it, how old are these three couples?

Grandpa often asks some strange questions", Ning Ning said, "In the summer, my grandfather and I were enjoying the shade on the top of a 10-meter-high building, and my grandfather held the glass in his hand and said, I threw the cup into the sky, and when the cup fell 10 meters, it didn't break, is it possible?" ”

Is there something very soft like thick cotton or sponge lying downstairs? ”

No, it's a normal concrete floor'

That's why this cup is special."

No, it's an ordinary cup."

Do you know what this is?

A1Let the number of stone pillars at the bottom be x, then the middle six layers are 2x each, a total of 12x can get 12x+x+12<=250,x<,, first assume x=15, then 12x+x+12=207, in line with the title. So 207.

2.Young couples 22,17, middle-aged couples,31,34, older couples 98,97 The solution can be listed as x 2-y 2=195,195=5*39=3*65=1*195

When x-y = 5, 3, 1, x+y = 39, 65, 195

Solve Equation 3Probably, it should be on top of a ten-meter-high building. The height must be greater than 10 meters after being thrown into the sky, so the cup has not yet hit the ground when it falls 10 meters, and it is still falling.

You still choose me, really, no one will have it, and I am also sincere.

See if it's if:

Table of Contents: 2005 Beijing Junior High School Mathematics Competition Questions.

2006 Beijing Junior High School Mathematics Competition.

2007 Beijing Junior High School Mathematics Competition.

2008 Beijing Junior High School Mathematics Competition.

2009 Beijing Junior High School Mathematics Competition.

2005 Tianjin Junior High School Mathematics Competition.

2007 Tianjin Junior High School Mathematics Competition.

2008 Tianjin Junior High School Mathematics Competition Questions.

2009 Tianjin Junior High School Mathematics Competition Questions.

2005 Shanghai Junior High School Mathematics Competition.

2006 Shanghai Junior High School Mathematics Competition.

2007 Shanghai Junior High School Mathematics Competition.

2008 Shanghai Junior High School Mathematics Competition.

2009 Shanghai Junior High School Mathematics Competition.

2005 Jiangsu Province Junior High School Mathematics Competition Questions.

2006 Jiangsu Province Junior High School Mathematics Competition Questions.

2006 Jiangsu Provincial Junior High School Mathematics Competition.

2006 Huanggang City, Hubei Province Junior High School Mathematics Competition Questions.

2007 Huanggang City, Hubei Province Junior High School Mathematics Competition Questions.

2008 Huanggang City, Hubei Province Junior High School Mathematics Competition Questions.

2009 Huanggang City, Hubei Province Junior High School Mathematics Competition Seventh Grade Qualifier Questions.