Mathematical operation is a key question in the national civil service examination. In the process of reviewing mathematical operations, candidates should focus on mastering the common problem-solving methods of mathematical operations. These methods can not only help candidates find ideas quickly, simplify the problem-solving process and optimize the calculation steps, but also have several methods that are often used and suitable for most questions. Next, Chinese public education experts will introduce several common problem-solving methods for everyone.

First, the substitution exclusion method.

Alternative exclusion starts with options. After replacing an option, if it does not meet the known conditions or is contradictory, it can be excluded. Substitution exclusion method includes direct substitution exclusion method and selective substitution exclusion method. Among them, the direct substitution method is to substitute the options one by one for verification until the options that meet the meaning of the question are obtained; Selective substitution is a method of screening according to the characteristics of numbers (parity, divisibility, mantissa, remainder, etc.) and then replacing exclusion. ).

Substitution exclusion method is widely used in multi-digit problems, indefinite equation problems, residual problems, age problems, complex travel problems, and difference ratio problems.

Second, the special value method

The special value method is a method to take an appropriate special value within the given range of the topic and substitute it directly to simplify the complex problem. The special value method must choose a special number, a special point, a special function, a special series or a special graph to meet the main problem rather than the general situation, and calculate the results from it, so as to solve the problem quickly.

In the civil service examination, the special value method is often applied to the problems of comparison, travel, engineering, concentration, profit, geometry and so on. Among them, when the proportion problem is related to engineering problems and concentration problems, the special value is generally set to1; When multiple scales are involved, sometimes in order to integer values, special values can be set to the least common multiple of the total.

When using the special value method, Chinese public education experts remind candidates that determining this special value will not affect the desired results; The data should be convenient for fast and accurate calculation, and the calculation result should be an integer as far as possible; Flexible use in combination with other methods.

Third, the equation method

Equation method refers to the method of using variables (such as x, y) to represent the unknowns in the topic, listing the equations (groups) containing the unknowns according to the equivalence relationship contained in the topic, and solving the application problems by solving the values of the unknowns. Because of its positive thinking and simple thinking, it does not need a complicated analysis process.

Equation method is widely used, and most problems in the mathematical operation of civil service examination, such as travel problems, engineering problems, profit and loss problem, difference and multiple ratio problems, concentration problems, income problems and age problems, can be solved by equation method.

Main steps: setting unknown quantity-finding equivalence relation-listing equation (group)-solving equation (group).

Fourth, the graphic method

Graphic method is a method to solve mathematical operations by using graphics. The graphic method is simple and intuitive, and can clearly show the process change of the problem. Generally speaking, the graphic method is suitable for most questions, especially those that emphasize the analysis process, such as travel questions, age questions, tolerance questions and so on.

The graphics used in the graphic method include line graph, network graph/tree graph, venn diagram, table, etc.

A line graph is a method to express the relationship between numbers and quantities with line segments. In general, we will use line segments to represent the multiple relationship between quantities or the whole movement process. , solve the problem of sum-difference ratio and travel. Line drawing is very effective in travel problems, because it can help candidates quickly sort out the movement process of various objects, so as to find the relationship between the speed or distance of objects.

Network diagram or tree diagram is generally used to solve problems with complex process or quantitative relationship, such as permutation and combination problem, reasoning problem or game analysis problem of time arrangement.

Venn's diagram is a graph that uses circles to represent a kind of things. Generally speaking, Venn diagram is only used to include and eliminate problems.

This table can be used to show the complex process of multiple operation problems and reduction problems one by one. At the same time, tables can also be used to clarify the quantitative relationship, which is helpful to form equations.

Five, the division method

Division is a method to solve mathematical operations by dividing and combining two different ways of thinking. The so-called "dividing" means dividing a problem into several small problems, and then considering each small problem locally; The so-called "combination" means putting several problems together and thinking as a whole. In other words, "division" is local consideration and division; "Combination" means overall consideration and integration. Division is generally suitable for permutation and combination, probability problems, solving equations and so on.

Two common ideas of classification methods are classified discussion method and holistic method.

Classified discussion

Classification discussion refers to the method of classifying the research objects according to certain standards, studying them one by one, and finally summing up the conclusions to get the solutions when the given objects cannot be studied uniformly. When discussing classification, we should pay attention to the unification of classification standards, and the classification situation should not be omitted, repeated or discussed beyond the level. Classification discussion and addition principle are often used together. Generally, addition principle is used to find the total number of situations after classified discussion.

(2) Integral method

The holistic approach is just the opposite of the classified discussion, which emphasizes grasping the changes as a whole rather than sticking to local treatment.

The overall method has two forms:

1. treat a part as a whole, and always consider it together in the problem, not solve it separately;

2. Do not care about local relations, only care about the overall situation of the problem, and directly consider the relationship according to the overall situation. This form is often used in the average problem.

Six, cross method

Cross method is a simple method to find the average amount of two parts after mixing by using "cross". Cross method is generally only used for the average problem of two related parts, and the premise of application is to know the overall average R.

Seven. Extreme law

Extreme value method is a common method to explore the direction of problem solving or transformation by considering the extreme state of the problem. Extreme method is generally applicable to the problems of chicken and rabbit in the same cage and countermeasure analysis.

The application of extreme value method in civil service examination mainly includes analyzing extreme value state and considering extreme value graph and extreme value position.

(A) extreme state analysis

First, analyze and find out the limit state of the problem, then compare it with the stem condition, make corresponding adjustments, and get the solution of the problem. In the civil service examination, the problem of chickens and rabbits in the same cage, as well as the problems with words such as "most" and "at least", can be solved by analyzing the extreme state of the problem.

(2) consider the limit diagram and limit position

Extreme graphics: mainly using some geometric knowledge. For example, the space geometry, the same surface area, the closer to the sphere, the greater the volume; Similarly, when the volume is the same, the closer to the sphere, the smaller the surface area.

Limit position: first find the extreme position that meets the conditions in the graph, then judge the relationship between the extreme position and the question, and then find the answer to the question.

Come on, I wish the exam success!

If in doubt, please consult the public education enterprises in China.