Olympiad problems, how to analyze, Olympiad problems, specific analysis

There is no such fixed routine, it is necessary to have and far-fetched, write the data that can be obtained according to the topic, look at the data, and transform it into other data, according to the problem, the main thing is the sea of questions.

Generally, there are classifications, such as tree planting problems, travel problems, chickens and rabbits in the same cage, and profit and loss problems. The most important thing is to figure out the example questions! And then draw inferences.

Each problem has its own kind, and you have to learn how to solve each type of problem first. In this way, the soldiers can come to the earth weir with enemy water. You can take a look at "Olympiad Mathematics Course", which I use to teach students.

The actual value of the Olympiad is not large, the spiritual value is still relatively large, I know many people who have won many awards in the Olympiad, they say that the Olympiad in addition to applying the routine of the example questions in the book is to use the method of making up the answer to do the problem. Personally, I don't think the Olympiad is worth learning.

It is recommended to take a look at G. Polya's How to Solve the Problem Sheet, to put it bluntly, it is to find ways to transform unknown problems into known or familiar problems to solve.

Olympiad mathematics is basically useless, if you are determined to study mathematics Olympiad is not very useful, at most it is useful for further education, this kind of question is best to ask the teacher!

Learn by type and master through practice.

If you do more, you will naturally form a mindset, and that's what I am.

It's OK to keep a fresh mind.

（3+3）÷120%=5

Since 20% of them coincide, 3+3 equals the length of the entire length.

*2008*〔1/(2006*2007)+1/(2007*2008)〕

4. If a=2005 2006, b=2006 2007, c=2007 2008, then the largest in a, b, c is c, and the smallest is a

5. If the price of a commodity is increased by 25%, if the sales amount after the price increase is the same as the sales amount before the price increase, the sales volume will be reduced by 25%.

6. Xiao Ming and Xiao Gang each have a number of glass pinballs. Xiao Ming said to Xiao Gang: "If I give you 2, we will have as many glass pinballs."

Xiao Gang said: "If I give you 2, my number of pinballs will be one-third of your number of pinballs." "Xiao Ming and Xiao Gang have a total of 10 +6 = 16 glass pinballs.

7. In a test, Xiao Ming answered 10 questions incorrectly, Xiao Gang answered 8 questions incorrectly, the number of questions answered correctly by Xiao Qiang was equal to the sum of the number of questions answered correctly by Xiao Ming and Xiao Gang, and Xiao Qiang answered 3 questions incorrectly. How many questions are there in this quiz?

Solution: There are a total of x questions in this quiz, then:

2x-(10+8)=x-3

x=15, i.e. there are 15 questions in this quiz.

Choir: 24 1 2 5 Penitentia 6 7) 45 people.

Dancing God Stool Team: 45-25 21 people.

Problem: Two brothers ride bicycles from home to point A at the same time. The elder brother travels 12 kilometers per hour, the younger brother travels 7 kilometers per hour, and the elder brother goes home half an hour after departure to pick up the items he forgot to bring, and there is a delay of 15 minutes after arriving home, and then he sets off to chase the younger brother, when the elder brother catches up with the younger brother, how many kilometers away from home?

Assuming that the elder brother catches up with the younger brother, they have not yet reached point A} He Zhilu.

Solution: According to the title, when the elder brother is at a speed of 12 kilometers, and the younger brother is at a speed of 7 kilometers, the elder brother finds that he has forgotten something to bring half an hour after he sets off, so it should take half an hour to return home, and when the elder brother returns home and delays for another 15 minutes, the younger brother has walked smoothly for 5 4 hours, which is equivalent to the elder brother letting the younger brother go 5 or 4 hours earlier, and then chase the younger brother, so it will come down to the tracking problem in our itinerary.

Equation: 7 5 4 (12-7) 12=21 (km) When the older brother catches up with the younger brother, it is 21 km away from home.

Set the only one to catch up when he is x kilometers away from home.

But the elder brother is busy and the total time is hours, that is, all the time the younger brother is in a hurry.

Multiply it by the younger brother's speed, which is equal to the younger brother's road distance, that is, the distance from home x x = 21 kilometers.

When the elder brother set off to chase his younger brother again, it was already half an hour + half an hour + 15 minutes = hours.

At this time, the younger brother walked 7* kilometers.

The elder brother caught up with the younger brother again, and it took him an hour.

It is 12*km away from home when it catches up.

Suppose the elder brother shares x hours from the time he turns around to catch up with the younger brother 15 minutes = 1 4 hours i.e. the elder brother actually walks x - 1 4 hours.

then 7x+7*

Solution x=Xiao Xiang burns the time.

Then, when the elder brother catches up with the younger brother Duan and tells the younger brother, it is 7* kilometers away from home.

15 minutes = Slippery time.

When the older brother sets off again, the distance between the younger brother and the older brother is: 7 (km.)

When the elder brother catches up with the younger brother, he is in a state of vertical wax: hour.

At this time, the distance from home: kilometers.

15 minutes of stupid clock = 1 4 hours.

7 * 1 hour and hail 1 4 hours = 8 km and 3 4 km.

Cave 12-7) = hours).

12*km).

21 km from home.

When Ge Qing accompanied his brother to catch up with his younger brother, he was x kilometers away from home.

x 7=(12 2 x 12+15 60 multiplied by Min then 84 to get 12x=7(12+x)+21x=21 When the elder brother catches up with the younger brother, it is 21 kilometers away from home.

15 minutes to block the clock slag = hours.

12x[7x(1+

12x (21 (km) Jane beam destroyed.

The quotient of the number of peaches divided by 7 is equal to the remainder, i.e. the number of peaches is a multiple of 8, because the remainder divided by 7 is a maximum of 6, and this basket of peaches has a maximum of 6 8 = 48.

The meaning of this question is that there is a number divided by 7 and the remainder is equal to the number obtained. And the remainder must be less than the divisor, so the maximum remainder is 6, and the total number of peaches is 6 times 7 + 6 = 48

The goddess has 1 7 fewer than the boy, which is exactly 4, so the male Pei Sakura has 4 (1 7) = 28 people, and the female partner has 24-4 = 24 people.

1. Eat 20% of a cup of fresh juice, fill it with water and stir well, then eat 60%, then the fresh juice in the cup accounts for (20)% of the cup's capacity

Drink 20% and you're left with 80%, and then eat 60% and you'll have 20% left.

2. If there are three pieces of goods A, B and C, if you buy 3 pieces of A, 7 pieces of B and 1 piece of C, a total of 3,150 yuan, if you buy 4 pieces of A, 10 pieces of B and 1 piece of C need a total of 4,200 yuan, then you need (1,050) yuan to buy one piece of A, B and C.

Solution: From the problem: A * 3 + B * 7 + C * 1 = 3150, A * 4 + B * 10 + C * 1 = 4200, multiply by 3 to get: A * 9 + B * 21 + C * 3 = 9450, multiply by 2 to get: A * 8 + B * 20 + C * 2 = 8400, - get: A + B + C = 1050 yuan, A: 1050 yuan to buy A, B, and C

3. The ball falls into a cylindrical bucket filled with water, the bottom diameter of the bucket is 60 cm, the ball enters the cylindrical barrel, the diameter of the ball is 60 cm, and the water level in the bucket rises (80 3 cm. (v-ball = 4 3 r to the third power).

h=2v ball 3s bucket bottom area = 2*4 30 3*3* *30 =80 3 cm.

4. A fruit store stipulates that if the purchase of lychee does not exceed 10 kilograms, the price per kilogram is 3 yuan; If it exceeds 10 kilograms, the price of the excess is reduced by 10% per kilogram. Someone buys fruit (21) kilograms, and he should pay the money in dollars.

Solution: 10+(

10+ (, 10+, 10+, 11, 21 (kg).

A: This person buys a total of 21 kilograms of fruit.

5. As shown in the figure, it is known that cd=5, de=7, ef=15, fg=6, and the straight line ab divides the figure into two parts, the area of the left part is 38, and the area of the right part is 65. Then, the area of the triangle ADG is ().

Solution: From the meaning of the question, S aeg=3s ade, s bfe=5 4 bec, let s ade=x, then s aeg=3x, s bfe=5 4(38-x), the equation can be listed:

5/4（38-x）+3x=65，95/2-5x/4+3x=65

7x/4=35/2

x=10, so s adg=10 (1+3)=40

6. There are 45 students in the first (1) class of junior high school in physical education class, they line up in a row on the playground to face the teacher, and after reporting the number from 1 to 45, the teacher asks the person who reports the even number to turn back, and then calls the person who reports the multiple of 3 to turn back, then the student facing the teacher has ().

Solution: The number of people who report an even number is: 45 2 = 22....1 person;

The number of people who report multiples of 3 is: 45 3 = 15;

Numbers that are divisible by both 2 and 3 are:

45 6,7 people ....3 people

45-30, 15 (people).

A: At this time, there were 15 students facing teachers.

23000 (500-5) 46 days, will fall around the 45th day.