What are the skills and methods to do math problems?

There is a saying that people can do anything when they are in a hurry, but they can't do math problems, especially when they encounter problems. So how to make math problems easy? Let's share some skills and methods about doing math problems, hoping to help you.

1. Multiple choice answer strategy

1, exclusion method

Using the information provided by the known conditions and options, 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.

2, special value test method

For a general mathematical problem, in the process of solving it, the problem can be specialized, and the principle that the problem does not hold in special circumstances and does not hold in general circumstances can be used to achieve the purpose of removing the false and retaining the true.

3. Extreme principle

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 through extreme value analysis.

4. Push down-solution

Using mathematical theorems, formulas, rules, definitions and meanings, the method of obtaining results through direct calculus and reasoning.

5. Reverse verification method

The method of substituting the options into the stem of the question for verification, thus negating the wrong options and getting the correct answer.

6. It's illegal if it's difficult.

When it is difficult to solve the problem from the front, we can gradually find out the qualified conclusions from the options, or draw conclusions from the opposite side.

7. Number-shape combination method

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.

8. Recursive induction

Through the conditional reasoning of the topic, we can find the law and sum up the correct answer.

9. Characteristic analysis method

This paper analyzes the characteristics of questions and options, finds the rules and summarizes the correct judgment methods.

10, 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.

2. Fill in the blanks and answer the questions.

Math fill-in-the-blank questions are mostly computational (especially inferential calculation) and conceptual (qualitative) judgment questions, which can only be answered by actual calculation or logical deduction and judgment according to rules. The basic strategy to solve the fill-in-the-blank problem is to work hard accurately, skillfully and quickly. Commonly used methods include direct method, specialization method, multi-line combination method, equivalent transformation method and so on.

1, direct method

This is the basic method to solve the fill-in-the-blank problem, starting directly from the problem setting conditions, using the knowledge of definition, theorem, nature, formula, etc., and directly obtaining the result through the processes of deformation, reasoning and operation.

2. Specialized methods

When the conclusion of the fill-in-the-blank question is unique or its value is fixed, we only need to replace the parameter variables in the question with special values (or special functions, special angles, special series, special positions of graphs, special points, special equations, special models, etc.). ) come to a conclusion.

3. Number-shape combination method

With the help of the intuitive shape of graphics and the combination of numbers and shapes, the method of making quick judgments is called image method. Venn diagram, trigonometric function lines, images of functions and curves of equations are all commonly used graphics.

4. Equivalent transformation method

By "simplifying complexity and turning strangeness into familiarity", the problem is equivalently transformed into an easy-to-solve problem and the correct result is obtained.