A Useful Method of Solving Problems in Senior High School Mathematics —— Eigenvalue Test
For a general mathematical problem, we can specialize the problem in the process of solving it, and use the principle that the problem does not hold in special circumstances and does not hold in general circumstances to achieve the purpose of removing the false and retaining the true.
Principle of extremism
Analyze the problem to be studied to the extreme state, so that the causal relationship becomes more obvious, thus achieving the purpose of solving the problem quickly. Extreme value is mainly used to find extreme value, range and analytic geometry. Many problems with complicated calculation steps and large amount of calculation can be solved instantly once extreme value analysis is adopted.
scalping method
Using the known conditions and the information provided by the selection branch, three wrong answers are eliminated from the four options, so as to achieve the purpose of correct selection. This is a common method, especially when the answer is a fixed value or has a numerical range, special points can be used instead of verification to exclude it.
A combination of numbers and shapes
According to the conditions of the topic, make a graph or image that conforms to the meaning of the topic, and get the answer through simple reasoning or calculation with the help of the intuition of the graph or image. The advantage of the combination of numbers and shapes is intuitive, and you can even measure the result directly with a square.
Recursive induction
Through the conditional reasoning of mathematical problems, we can find the law and summarize the method of correct answer.
Forward deduction method
Using mathematical theorems, formulas, rules, definitions and meanings, the method of obtaining results through direct calculus and reasoning.
Reverse verification (substitution of answers into stem verification)
Substitute the selected branch into the stem for verification, so as to deny the wrong selected branch and get the correct method of selecting branch.
If it is difficult, it is illegal.
When it is difficult to solve the problem from the front, we can find a qualified conclusion step by step from the choice of expenditure, or draw a conclusion from the opposite side.
Characteristic analysis method
This paper analyzes the characteristics of mathematical problem setting and branch selection, finds out the rules and summarizes the correct judgment methods.
Valuation selection method
Some problems cannot (or are not necessary) be accurately calculated and judged due to the limitation of subject conditions. At this time, we can only get the correct judgment method from the surface by means of estimation, observation, analysis, comparison and calculation.
Universal problem-solving skills in senior high school mathematics
Examine the problem carefully
Examine the questions carefully and don't ignore the key words. Don't you think so? Easy to ask questions? Just skim it, will you? Chen ti? There may be? New ideas? . And it doesn't look like it at first glance? New problem? Just give up because of difficulties, you know? Question? Maybe it's just a little difficult. New problem? Only one place is new.
Easy first, then difficult.
After you get the test paper, browse all the test questions quickly, which is in line with? Easy first, then difficult? Principles, determine the scientific order of answering questions, and try to reduce the number of theme changes in the process of answering questions. The principle of composing college entrance examination papers is to arrange similar topics from easy to difficult as far as possible. I suggest you answer from the front to the back, don't entangle the question.
Stability multiple choice questions
Be calm when doing multiple-choice questions, not too fast. There is only one option in biology and chemistry multiple-choice questions, so don't choose more. For uncertain questions, first determine the content of the question, and associate it with the knowledge and method choice of usual study; If you can't make the right choice, guess an answer and don't leave the question blank. The physics topic is indefinite item selection. If you are not sure, don't guess other answers after determining one answer, otherwise one is right and one is wrong, and the result is still zero. After the multiple-choice questions are finished, I suggest you get on the card immediately to avoid future trouble.