How do you think mathematically correctly so that you can solve a problem?

When this aspect is clear, you can slowly go deeper (in fact, this step can be difficult to do, because for mathematical problems, some known conditions are implicit, and some of the same sentence have several known conditions, which need to be solved slowly), after the first step is completed, it is to find the relationship between the known conditions and the quantity sought, which is nothing more than a column equation to see which quantities can be related to each other, after this step is completed, For example, look at the system of equations, how many unknowns, how many equations, n equations can only solve n unknowns, I believe you are also very clear (provided that the equations are valid), and it is important to clarify the relationship between the unknowns and the number of equations. The above is only for mathematical problems of general difficulty, if it is too difficult, it is difficult to have general rules to follow, which depends on accumulation, and the accumulation of some more skillful methods. By the way, there is another point, combined with my experience in math competitions, many times even the method has come up with it, but a large part of the reason why I haven't done it is not confident, I don't know if my method is counted out, this point is difficult to overcome, so far I can't overcome it, I may not be able to help you, I can only give advice, think of the method and calculate it, regardless of whether there is a result in the end.

If you feel that you are a little misguided, the above method will be selected according to your actual situation.

Some people say that math problems are very flexible and vary from one type to another, but this is not the case. From the perspective of the questioner, it is actually nothing more than the test points that have been studied. So if you want to solve the problem, the first thing to do is to master the knowledge you have learned, the so-called practice makes perfect, and then you should be more exposed to a variety of related question types, the question is done more, when you see a certain question, it will naturally exist out of ideas, I have seen too many people who are not geniuses, but they are talented people, the last thing to do is to calm down the mind, the more anxious the more they can't think of a way, and a little trick is that there are some difficult questions, don't break through head-on, try to solve with special value substitution method and hypothetical method.

Another thing I would like to say is that sometimes you will do better in exams by giving up a difficult question and checking a few easy questions.

Start with simple questions, but it's not a question that you will look at, it's a question that you can come up with with your brain, because when you come up with an answer through some thinking, you will have a sense of accomplishment, your self-confidence will be strengthened, and your interest will increase. And then go deeper and deeper. Cultivate competence with interest.

Use the idea of transformation in mathematics. In the process of solving the problem, you may wish to write on a blank piece of paper which knowledge points are tested in this question, which of these knowledge points are more important or which are more critical. In this way, when you do a problem, it is equivalent to solving the same type of problem, and over time, you will have a fundamental change.

Of course, if you are a senior in high school, don't always think about how many knowledge points you have taken the test, otherwise, you will not have time to do the questions.

It is more difficult for beginners to learn mathematics, it is easier to be numb after a long time, resulting in the limitations of thinking, to learn mathematics well, it is not possible to remember the formula, the most important thing is to live and learn, the conditions of the problem are only to provide us with the basis for solving the problem, as for how to use the conditions of the problem, it depends on the theme of the topic, to put it bluntly, it is to see the essence through the phenomenon, simplify the complex problem, and abstract the simple problem

Stop at the surface, it means that you don't understand, spend more effort on reading the topic, not only to help you think deeply, but also to correct your mistakes in inertial thinking, of course, very few topics in the words to make a fuss, but the old Chinese saying, read the book a hundred times, its meaning is self-seeing!

You can think forward and backward, proof questions can be pushed backwards, and after you get stuck in non-proof questions, you can assume some conditions that can be done, and then go down to see if there are any ideas.

Do more questions, do more can have a feeling.

Then, the question types are categorized to find out the common entry points of some questions.

There are many ways to think. Such as: limit thinking, classification discussion...

It's up to you whether you can use it or not.

Take a look.

As follows:

The problem of harmony and difference: the sum and the difference, the more and more it increases, the bigger it gets; Divide by 2 and it is great; and subtract the difference, the more you subtract the bump, the smaller the noise; Divide by 2 and it will be small.

Chickens and rabbits in the same cage: Suppose all chickens, suppose all rabbits. How many more feet, how many feet less? Divide by the difference in feet, and you will find the number of chickens and rabbits.

Add water to dilute: add water to seek sugar first, and then seek sugar water after sugar. Sugar water minus sugar water is the amount of sugar added.

Sugar thickening: Seek water first after adding sugar, and seek sugar water after water. Sugar water minus sugar water, find out the solution.

Encounter problem: At the moment of meeting, the journey has been all traveled. Divide by the speed and get the time.

Profit and loss issues. Formula: All profit and all loss, the big one minus the small laughing line; One profit and one loss, the profit and loss add up. Divide by the difference in distribution, and the result is the thing or person that is distributed.

For example, children share peaches, each person has 9 peaches for 10 peaches; 8 more than 7 per person. How many children and how many peaches?

Solution: One profit and one loss, then the formula is: (nuclear reed 9 + 7) (10-8) = 8 (people), and the corresponding peach is 8x10-9 = 71 (pcs).

Let Xiaogang's speed be V1, the speed of the car is V2, and the departure interval is T: a*(V1+V2)=V2T....1] Catch up from behind: b*(v2-v1)=v2t

Therefore, a(v1+v2)=b(v2-v1).

a+b)v1=(b-a)v2

i.e.: v1=(b-a)v2(a+b).

Substituting the above equation into [1] gives :t

a[(b-a)v2/(a+b)+v2]=v2tt=a[(b-a)/(a+b)+1]=2ab/(a+b)

Set up apprentices for x days.

5 (1 6-1 x) + 3 (1 x) = 7 10x = 15 Answer: --

If you can't solve the fractional equation, you can set the efficiency, which is troublesome and difficult to list.

Set the distance to x, and the planned number of days is x 720

Now the road is 720 + 80 = 800 meters per day.

The actual number of days is the original planned number of days - 3 = x - 1200 800, so x 720 - 3 = x - 1200 800

x=10800

Let this section of the road be x meters.

x÷720=(x+1200）÷（720+80）+3x÷720=x÷800+1200÷800+3x÷720-x÷800=

x=x=32400 (m).

A: The road is 32,400 meters long.

Total length l, originally planned to be 720 meters per day, number of days needed, l 720;

The actual daily repair is 720+80=800m

The difference of 1200 meters can be caused three days in advance, and when it is completed three days in advance, the actual construction length: L-1200

Equations can be established:

l 720=(((l-1200) 800)+3 substantiation number theory. <>

If in doubt, you can continue to communicate!

1. Carefully review the topic. It is necessary to analyze the various keys in the question, write down all the conclusions obtained from each condition, and synthesize them.

2. Grasp the key to solving the problem. If you can't grasp the key to solving the problem, you will only do a lot of useless work, and you should pay attention to the characteristics of the land raid observation problem, the structure of the data, and the formulas and methods that may be used in association. To cultivate your own observation, in addition to contacting more, you should also know the common types of questions well.

3. Actively explore. This kind of problem needs to be constantly explored, and if one method does not work, then another method will always be suitable.

4. Master the problem-solving skills of this type of problem, and naturally deal with it calmly.

In fact, it is very simple, you have to study every condition given by the land boat. It's going to have to be used, and as long as you miss one of the tantarias in the solution, then it's basically a problem. In addition, you must be very familiar with mathematical formulas and their application, basically mathematical problems are the amount that can be solved by turning a few times between several formulas.

2.Let the equation of 1 yuan and 1 order.

10 minutes = 600 seconds, if Wang Qiang runs x seconds at a speed of 6 meters, then the time he runs at a speed of 4 meters is (600-x) seconds.

6x+4*(600-x)=3000, the solution is x=300, note that what you get here is the number of seconds, which should be converted into meters, so 6*300=1800 meters, get Wang Qiang ran 1800 meters at a speed of 6 meters and seconds.

Set up the purchase of type A TV x units, B type TV 50-x units, 1500 * x + 2100 * (50-x) = 90000

x=25，50-x=50-25=25

Set up the purchase of a type of TV Y station, C type TV 50-Y station, 1500 * Y + 2500 * (50-y) = 90000

y=35，50-y=50-35=15

Set up the purchase of B TV Z station, C TV 50-z station, 2100 * Z + 2500 * (50-Z) = 90000

z=greater than 50, this option is rounded.

Therefore, there are two schemes: 25 units each for A and B; or 35 units of A and 15 units of C.

Therefore, in order to make the most profits, you should not buy B TV, so you should choose 35 units of A and 15 units of C.