Substitution exclusion method

Starting from the option, after substituting an option, if the known conditions are not met or there are contradictions, you can exclude this option.

① Direct substitution: substitute the options one by one for verification until you get an option that meets the meaning of the question.

(2) Selective substitution: a method of screening offspring for inclusion and exclusion according to the characteristics of numbers (parity, divisibility, mantissa, remainder, etc.). ).

graphical method

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

① Line graph: a method of expressing the relationship between numbers and quantities with line segments. Generally, line segments are used to represent the multiple relationship between quantities or the whole movement process. , solve the problem of sum-difference ratio and travel.

② Network diagram or tree diagram

A. network diagram

Generally, it consists of three groups of diagonal lines, and each group represents one thing. From top to bottom, the distribution rate decreases from 100%. In other words, the triangular grid represents the distribution of an object in three aspects.

B. Tree diagram

List all possible results of an event through a column chart and find out its probability.

③ venn diagram.

The closed curve is used to visually represent the graph of sets and their relationships, which can intuitively show the relationships between sets. One circle represents a class, two circles intersect, and the intersection part is the same part of the two classes. The two circles don't intersect, which means that the two classes don't have the same elements.

④ Form

The complex processes of multiple operation problems and reduction problems are presented one by one, and tables can also be used to clarify quantitative relations and help column equations.

division

Two different ways of thinking are used to solve mathematical operations: division and combination.

① classified discussion

It refers to the method that when the given object of the problem cannot be studied uniformly, it is necessary to classify the research objects according to certain standards, study them one by one, and finally summarize the conclusions to get the solution.

Attention should be paid to the unification of classification standards, and the classification situation should not be omitted, repeated or beyond the hierarchical discussion. Generally, after a variety of situations are classified and discussed, addition principle is used to find the total number of situations.

② Integral method

A. treat a part as a whole and always consider it together in the problem, rather than solving it separately;

B. 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.

Separation method

It solves the problem of different stacking of the same element. If n identical elements are assigned to m different objects, how many different division methods are there? You can use the Partition Method.

Applying the partition method requires the following three conditions:

① The elements to be divided must be exactly the same;

(2) The elements to be divided must be divided;

③ Each object is assigned at least one.

ratio method

There are usually multiple scales in a topic. It is a way to unify multiple scales through their relationship and then find the answer.

Steps of proportion method: write out the proportion, find the invariants and unify the number of copies.

(1) Writing proportion refers to the form of writing proportion according to the known conditions in the topic;

(2) Finding invariants means finding invariants in multiple proportions;

(3) Uniform number of copies refers to the number of copies in which invariants are unified into the same number of copies.