High school math competition, high school math competition how to learn by yourself

It's only a freshman in high school, and it must be for the purpose of the national league. In this case, you should first realize the importance of giving it a try. That is, the 120-point paper that is slightly more difficult than the one.

To improve this aspect, we must first ensure that all the knowledge of the entire high school stage is learned. For students of the new textbook, calculus, determinants, etc., are also necessary. For books, I recommend the mathematics compendium of Zhejiang Education Press, as well as the mathematics textbooks of Hua Luogeng School, which are also very good.

If you try it for the second time, you have to focus on it. Algebra, Geometry, Number Theory, Combinatorics. Four aspects, four major questions. In general, it is safer to choose to break them one by one. The small series of books at ECNU is considered very good.

Then go buy a copy of the classic question types of previous competitions to practice.

It's still necessary to do more questions. A few books are recommended for you.

The competition questions are basically a reverse push process, with the two heads pushing to the middle. It is also necessary to know the method of reversal and induction.

Everyone can go to the preliminaries, but the number of people who go to the semifinals is very small. If it is a rural middle school, it is almost impossible to enter the semi-finals, and if it is a key middle school, there are some people who enter the semi-finals. Prerequisites:

According to the "Implementation Rules of the National High School Mathematics League (Trial)", the National High School Mathematics League is open to all high school students and adheres to the principle of voluntary participation.

Students who participate in the National High School Mathematics League can voluntarily choose whether to participate in the "National High School Mathematics League Additional Test"; Students who intend to win the first prize in the competition area and intend to participate in the National Middle School Mathematics Winter Camp must participate in the first test of the league and the additional test (second test) of the league, and the total score of the two tests will be used as the standard for determining the first prize and the campers of the winter camp.

Registration Period

The provincial-level competition area shall organize the registration work in accordance with the notice of the Organizing Committee of the National High School Mathematics League, and each school shall register at the teaching and research department (or mathematics society) of the local (municipal) education bureau.

The registration time is based on the actual situation of each place, and different regions have different registration times, which are subject to the notice of the local educational institution. Generally, the deadline for registration is one month before the test. For the latest registration information, please pay attention to: National High School Mathematics League Exam Dynamics.

The self-study method of the high school math competition is as follows:

1. First of all, choose a set of Olympiad competition textbooks of appropriate difficulty according to the knowledge points of the high school curriculum, and carefully complete this set of textbooks.

2. After completing the textbooks, basically master the knowledge points of high school mathematics competitions. Note that the time is controlled within one year, and it is suitable to be completed in one year.

3. During the summer vacation from the first year to the second year of high school, I began to make special high school competition textbooks with different topics, and at the same time began to make regular ones.

Competition questions, past past questions.

4. During the sophomore year of high school, you should complete a set of competition question bank books and all direct questions in recent years. During the winter and summer vacations, if conditions permit, you can participate in the training of high school mathematics competitions organized by some universities.

5. In the second half of the second year of high school, some training should be added specifically for the "second test", such as ensuring that the first question of geometry must be won, and the first question is usually combinatorial mathematics, so if you have enough time, you can specialize in learning the knowledge of combinatorial mathematics, and the "inequality" series of knowledge should be focused on training.

6. The most important thing is to do a lot of questions on a set of competition tutorials and be familiar with the question types of the competition. You can study in the order of the textbook, and refer to the supplementary materials while studying the textbook, so as not to miss some knowledge points. After familiarizing yourself with the textbook, it is also important to use the skills.

For the college entrance examination knowledge and problem-solving skills, it is necessary to integrate them, and if you really can't learn the overall knowledge structure, you must also learn the basic usage.

2^8+2^11+2^n =2^8（1+8+2^（n-8））2^8（9+2^（n-8））

2 8 is already a perfect square number 16 2

9+2 (n-3)) when 2 (n-8)=16 i.e. n=12 is the perfect square number 5 2

Then n=12 is a perfect square number of 16*5=80, and there is only one natural number n, which can be borrowed from the explanation in the question to prove that the found n is unique.

n=12 first extract the common factor 2 8 for the original formula, the original becomes (2 8)*(1+2 3+2 (n-8)), the first part is already a square number, as long as 1+2 3+2 (n-8) is also OK, guess, 12 is just right.

There are two steps to this problem, one is to prove that 32 is feasible, and the other is to prove that 31 is not feasible.

The first step is to directly verify that the following strategy is feasible.

The second step can be described with a geometric model, which can be more concise, and examine the grid point 3 in r 3, and each point tried is equivalent to verifying the points (22) on the three lines that have verified the point and are parallel to the coordinate axis.

If only 31 test points are taken and 8 planes perpendicular to the z-axis are examined, the least number of test points on z=1 may be assumed.

If there are no more than 2 checkpoints on z=1, then at least 64 points on the plane should be covered by the points on the top 7 layers, which is a contradiction. So there are 3 checkpoints on the plane.

There are at least 25 points on z=1 that are not on the line generated by these 3 points (denoted as class A points) and need to be covered by points in the plane of the above 7 layers (the 25 points that meet the conditions are counted as class B points), and the remaining 3 free points are denoted as class C points.

The straight line generated by Class A points covers up to 64-25+3*7=60 points;

The straight line generated by class B points covers up to 25*(8+6)=350 points;

The straight line generated by the C type points covers up to 3*21=63 points outside the z=0 plane (all the points on z=0 have been counted).

These points don't add up enough to cover all 512 points.

I calculated that the probability was 22 512, which means that the guarantee that the lock must be unlocked is to account for 22 of these 512 times.

Equivalent to a two-digit password, that is, 8*8=64 kinds but there is still a one-bit password, you can reduce the attempt of one-bit password by half, so divide by 2, it is 32

This is the 2010 nuclear space model Annihilation of the Chinese Mathematical Olympiad problem, which is very difficult, and no one scored a full score at that time. This is the case of Da Dan Chong.

I have basically been in math competitions in my lower high school, and I have participated in two math competitions in my sophomore and junior years, and if you want to solve your problem better, I would like to reveal some basic information, such as whether your province and your high school are focused.

1. The "provincial mathematics competition" you mentioned is a bit problematic. The exams recognized by various colleges and universities are mainly the National High School Mathematics League, which is a national test with a unified national test paper, but the contestants generally call it a "provincial competition" or "semi-final" (to distinguish it from the national finals). The semi-finals are determined according to the preliminaries, which are provincial.

You may be clear about these things yourself, but the person you are asking may be misunderstood. The preliminaries are usually held on the first or second Sunday of September, and the semi-finals are usually held in mid-October.

2. Only those who have won the "first prize of a certain province" in the preliminaries can enter the semi-finals, and the semi-finals are commonly known as provinces.

1. Provinces. Second, province three, the award won by Shanxi upstairs is actually province two, because the certificate says "National Mathematics League Second Prize (Shanxi Division)". The first province in the semi-finals is eligible for escort, and 20 points will be added to the college entrance examination; Provincial two is conducive to independent enrollment; The third province is basically useless, and some of the lower universities may be useful.

3. The semi-final is divided into one test and two tests, with a total of 300 points. A full score of 120 exam time 80 minutes,,8 fill-in-the-blank + 3 big questions,8 points per fill-in-the-blank question is the key to grabbing points,Big question score 16 + 20 + 20,Question type function + analysis + number series,The difficulty of the question can refer to the college entrance examination problems in Jiangsu and Beijing,It is slightly more difficult than this,Of course, there will be two points for filling in the blanks。 But time is of the essence, and it must be done quickly and rightly.

The second test has a full score of 180 exam time of two and a half hours, 4 big questions, the score is 40 + 40 + 50 + 50, the question type is flat + number theory + algebra + combination, very difficult, of which the number theory is slightly easier, even if the competition has been studied for three years, it is normal to not be able to do a question.

4. The conditions for winning the award and whether training is required greatly depend on the province where it is located. The reason why friends in Shanxi can win the second province without studying is because the competition level in Shanxi Province is low. With the same test paper and the same provincial-to-provincial ratio, Shanxi can get a provincial one if it is more than 90, and Hunan can only get a provincial one if it is about 150.

If you are born in a strong province in the competition, to be honest, it is basically no fun to win the prize; If you were born in a weak province in a competition, then there are many people who have never studied mathematics and finally won the second province in the competition.

5. It is recommended to buy a trial textbook of Zhejiang University and a review of the classic questions of the Olympiad, and it is best to participate in a period of training.

The first one I don't know.

The second winning rate is 50 percent, you see the situation, the second volume of 4 questions (every 50) has to get 80 points, if you want to have good mathematical thinking, just practice.

The third is to find a teacher, do questions, this is generally more ruthless, and you will have a chance to be sent to the first prize, but this is generally a science student, if you work hard to get a 23rd prize, the help for your independent enrollment is only to pass the preliminary examination, see that your grades should be good, and this school recommendation should be able to get.

I'm from Shanxi. What is useful should be the National Mathematics League The third year of high school is about September and October, and it can be used to add points to the national first prize college entrance examination, and other awards are useful when they are self-recruited.

When I participated in it last year, I didn't watch any competitions, so I did what I learned, and if I didn't know how to do it, I wrote an idea or something, and won a national second prize.

To win a prize in a math competition, one relies on tutoring, and the other is to be talented. You can't force it.

Answer: 3=x(y-z) is obtained from xy=xz+3;

x, y, and z are all positive integers, so there must be x=1, y-z=3 or x=3, y-z=1;

When x=1, y-z=3, it is obtained by yz=xy+xz-7, z(z+3)=2z-4, that is, z 2+z+4=0, such a positive integer z does not exist; When x=3, y-z=1, it is obtained from yz=xy+xz-7, z(z+1)=6z-4, that is, z2-5z+4, and z1=1, z2=4;

When z=1, y=2;When z=4, y=5;So how much cardboard is needed for a carton is an area of 2x(xy+yz+xz)=22 or 94.

3 square meters are required. s=2(xy+xz+yz), bring xy and yz into the equation, only xz remains, you can find s=4xz-1, because xz, xy, yz are integers, and the minimum is 3 (otherwise the others are not positive), so we find s 11