For high school math, what methods can be used to solve problems quickly?

For high school math, what methods can be used to solve problems quickly?

Some candidates only know that they blindly want to be fast in the examination room, but the result is that the question is not clear and the conditions are not complete, so they are in a hurry to answer. It should be said that the examination of questions should be slow and the answers should be fast. The examination of the problem is the "basic engineering" of the whole problem-solving process, and the topic itself is the information source of "how to solve the problem", which must fully understand the meaning of the topic, integrate all conditions, refine all clues, form an overall understanding, and provide a comprehensive and reliable basis for the formation of problem-solving ideas.

Once an idea is formed, it can be done as quickly as possible.

As. 1. Image method.

An important way to discuss the properties of functions is the image method, which is to look at the image and get the properties.

Defines the part of the image that corresponds to the x-axis.

The value of the domain of the image corresponds to the part on the y-axis.

Monotonnia. From left to right, the interval corresponding to the continuous rise on the x-axis is the increasing range; From left to right, the interval corresponding to the continuous decline on the x-axis is the subtraction range.

Maximum: There is a maximum value at the highest point of the image, and a minimum value at the lowest point of the image.

Parity is an even function with respect to y-axis symmetry and odd function with respect to origin symmetry.

Second, solve the problem of absolute value.

It mainly includes simplification, evaluation, equations, inequalities, functions and other problems, and the basic idea is to transform a problem with an absolute value into a problem without an absolute value. The specific conversion methods are:

Classification Discussion Method: Remove the absolute value according to the positive, zero, and negative fractions of the number or formula in the absolute value symbol.

Zero-point segmentation method: This is useful for multiple absolute values with a single letter.

Two-sided flat method: Applies to equations or inequalities that are non-negative on both sides.

Geometric Meaning: Applicable to situations where there is obvious geometric significance.

Also note:

The capacity of mathematics college entrance examination questions is to complete 26 large and small questions in 120 minutes, the time is very tight, and it is not allowed to do a lot of detailed post-solution testing, so it is necessary to try to calculate accurately (key steps, strive to be accurate, rather slow than fast), based on a success. The speed of solving the problem is based on the accuracy of the solution, not to mention that the intermediate data of the math problem often affects the solution of each subsequent step not only in terms of "quantity" but also in terms of "nature".

Therefore, under the premise of being fast, we must be steady and steady, well-founded, and accurate step by step, and we cannot lose accuracy in pursuit of speed, or even lose important scoring steps.

Inverse method, hypothetical method. Some questions are very complex and error-prone because the ideas and steps of the direct solution are very complex, so the answer is solved indirectly. There has always been no idea of how to solve a difficult problem hypothetically.

High school math problems are actually to test students' ability to change their thinking, and many of the questions are based on learning a type of question, so the other questions will basically be done. If you really don't have a clue, you can watch more online classes, and your reasoning ability will gradually become stronger.

Brush up on questions appropriately, master the ideas and methods of problem solving, and organize notes on mistakes from time to time. Mastering problem-solving routines can improve the speed of problem solving; Doing a good job of summarizing mistakes can improve the accuracy rate and problem solving efficiency.

In high school, whether it is a liberal arts student or a science student, if you are good at math, you must have a very advantage. High school mathematics must understand the connotation of various problem-solving methods, not just learn the surface. If you have reached the third year of high school and still can't improve, students with a poor foundation can try to copy and analyze.

Some basic and common problems summarize some basic problem solving ideas and commonly used problem solving procedures, as long as you follow these problem solving ideas, you can easily find the answers to the exercises by accumulating them in peacetime.

Set of formulas, drawing, elimination, substitution, application, these are the methods of mathematics to solve problems quickly, especially the application of the problem drawing is the most suitable, a drawing relationship is a lot clearer.

Summarize and summarize the usual knowledge points, and familiarize yourself with some commonly used concepts, formulas, and theorems. You need to master the basic knowledge, you need to memorize these basic formulas, and you also need to learn to draw pictures, turn abstract thinking into visual thinking, which is more conducive to understanding, and computing The study of high school is very particular about problem-solving skills, and you usually need to read and write more to be able to use it flexibly.

High school math problem-solving skills are as follows:

1. Matching

The method of solving a mathematical problem by using the method of identity deformation of an analytic expression and matching some terms into a sum of the powers of a positive integer of one or several polynomials is called the matching method. It is an important method of identity deformation in mathematics, and its application is very, very wide, and it is often used in factorization, simplification of radicals, solving equations, proving equations and inequalities, finding the extreme value of functions and analytic formulas, etc.

2. Factorization

Factorization, which is to transform a polynomial into the form of several integer products, is the basis of identity deformation, and it plays an important role in solving problems in algebra, geometry, trigonometry, etc. as a powerful tool in mathematics and a mathematical method. There are many methods of factorization, in addition to the method of extracting common factors, formula method, group decomposition method, cross multiplication method, etc., which are introduced in middle school textbooks, there are also methods such as using split terms to add terms, finding root decomposition, commutation, pending coefficients, etc.

3. Substitution method

The commutation method is a very important and widely used method of solving problems in mathematics. Unknowns or variables are usually called elements, and the so-called commutation method is to replace a part of the original formula with a new variable or transform the original formula in a relatively complex mathematical formula, so that it is simplified and the problem is easy to solve.

4. Discriminant formula method and Vedic theorem

The discriminant discrimination of the roots of the unary quadratic equation ax2bxc=0 (a, b, c belong to r, a≠0), =b2-4ac, is not only used to determine the properties of the root, but also as a method of problem solving, it has a very wide range of applications in algebraic deformation, solving equations (groups), solving inequalities, studying functions, and even geometry and trigonometric operations.

Vedic theorem finds another root in addition to knowing one root of a quadratic equation; In addition to simple applications such as finding the sum and product of two numbers, you can also find the symmetry function of the root, calculate the symbol of the root of the quadratic equation, solve the symmetry equation, and solve some problems about the quadratic curve.

5. Pending coefficient method

When solving a mathematical problem, if the result is first judged to have a certain definite form, which contains some coefficients to be determined, and then the equation about the coefficients to be determined is listed according to the conditions of the problem, and finally the values of these coefficients are solved or a certain relationship between these coefficients is found, so as to solve the mathematical problem, this method of solving the problem is called the method of undetermined coefficients. It is one of the commonly used methods in middle school mathematics.

6. Structural method

When solving problems, we often use such a method, through the analysis of conditions and conclusions, to construct auxiliary elements, which can be a graph, an equation (group), an equation, a function, an equivalent proposition, etc., to build a bridge connecting conditions and conclusions, so that the problem can be solved, this mathematical method of problem solving, we call the construction method. The use of construction method to solve problems can make various mathematical knowledge such as algebra, trigonometry, and geometry penetrate into each other, which is conducive to problem solving.