Big questions are an important part of college mathematics subjects and a very important part of scores. Candidates need to master problem-solving skills in order to answer questions correctly. Here I bring you the best problem-solving skills in college mathematics, hoping to help you.

The best problem-solving skills of college mathematics problems

First, the trigonometric function problem

Pay attention to the correctness of normalization formula and induction formula (when transforming into trigonometric function with the same name and the same angle, apply normalization formula and induction formula (singular change, even invariance; When symbols look at quadrants, it is easy to make mistakes because of carelessness! One careless move will lose the game! )。

Second, a series of questions

1. When proving that a series is arithmetic (proportional) series, write arithmetic (proportional) series at the end of the conclusion, who is the first item and who is the tolerance (common ratio);

2. When the last question proves the inequality, if one end is a constant and the other end is a formula containing n, the scaling method is generally considered; If both ends are formulas containing n, mathematical induction is generally considered (when using mathematical induction, when n=k+ 1, the assumption when n=k must be used, otherwise it is incorrect. After using the above assumptions, it is difficult to convert the current formula into the target formula, and generally it will be scaled appropriately. The concise method is to subtract the target formula from the current formula and look at the symbols to get the target formula. When drawing a conclusion, you must write a summary: it is proved by ① ②;

3. When proving inequality, it is sometimes very simple to construct a function and use the monotonicity of the function (so it is necessary to have the consciousness of constructing a function).

Third, solid geometry problems

1, it is relatively easy to prove the relationship between line and surface, and generally there is no need to establish a system;

2. It is best to establish a system when solving the problems such as the angle formed by straight lines on different planes, the included angle between lines and planes, the dihedral angle, the existence problem, the height, surface area and volume of geometry.

3. Pay attention to the relationship between the cosine value (range) of the angle formed by the vector and the cosine value (range) of the angle (symbol problem, obtuse angle problem, acute angle problem).

Fourth, the probability problem.

1, find out all the basic events included in the random test and the number of basic events included in the request event;

2. Find out what probability model it is and which formula to apply;

3. Remember the formulas of mean, variance and standard deviation;

4. When calculating the probability, the positive difficulty is opposite (according to p1+P2+...+PN =1);

5. Pay attention to basic methods such as enumeration and tree diagram when counting;

6, pay attention to put back the sampling, don't put back the sampling;

7. Pay attention to the penetration of "scattered" knowledge points (stem leaf diagram, frequency distribution histogram, stratified sampling, etc. ) in the big question;

8. Pay attention to the conditional probability formula;

9. Pay attention to the problem of average grouping and incomplete average grouping.

Verb (abbreviation of verb) conic problem

1, pay attention to solving the trajectory equation, and consider three kinds of curves (ellipse, hyperbola and parabola). Ellipse is the most frequently tested, and the methods include direct method, definition method, intersection method, parameter method and undetermined coefficient method.

2, pay attention to the straight line (method 1 points have slope, no slope; Method 2: let x=my+b (when the slope is not zero), and when the midpoint of the chord is known, the point difference method is often used); Pay attention to discriminant; Pay attention to Vieta theorem; Pay attention to the chord length formula; Pay attention to the range of independent variables and so on;

3. Tactically, the overall idea should be 7 points, 9 points, 12 points.

Six, derivative, extreme value, maximum value, inequality constant (or inverse parameter) problem

1, first find the domain of the function, and correctly find the derivative, especially the derivative of the composite function. Generally, monotonous intervals can't be combined, so use "and" or ","(know the function to find the monotonous interval without equal sign; Know monotonicity, find the parameter range, with equal sign);

2. Pay attention to the consciousness of applying the previous conclusions in the last question;

3. Pay attention to the discussion ideas;

4. The inequality problem has the consciousness of the constructor;

5. The problem of constant establishment (separation of constants, distribution of function image and root, solution of maximum value of function);

6. Keep 6 points in overall thinking, strive for 10, and think 14.

Reflections on solving problems in college mathematics

1, the idea of function and equation

Function thought refers to analyzing and studying the quantitative relationship in mathematics from the viewpoint of movement change, and analyzing, transforming and solving problems by establishing the functional relationship and using the image and nature of the function; The idea of equation is to solve the problem by transforming the problem into an equation or inequality model with mathematical language from the quantitative relationship of the problem. Students can use transformation ideas to transform functions and equations when solving problems.

2. The combination of numbers and shapes.

The object of middle school mathematics research can be divided into two parts, one is number, the other is shape, but there is a connection between number and shape, which is called combination of number and shape or combination of shape and number. It is not only a "magic weapon" to find the breakthrough point of solving problems, but also a "good prescription" to optimize the way of solving problems. Therefore, it is suggested that students draw as many pictures as possible when solving math problems, which will help to understand the meaning of the problems correctly and solve them quickly.

3, special and general ideas

This way of thinking is sometimes particularly effective in solving multiple-choice questions, because when a proposition is established in a general sense, it is bound to be established in its special circumstances. Accordingly, students can directly determine the correct choice in multiple-choice questions. Not only that, it is also useful to explore the problem-solving strategies of subjective questions with this way of thinking.

4, extreme thinking problem solving steps

The general steps to solve problems with extreme thinking are as follows: 1. Try to imagine a variable related to an unknown quantity; Second, confirm that the result of this variable through infinite process is an unknown quantity; Third, construct a function (sequence) and use the limit calculation rules to get the results or use the limit position of the graph to directly calculate the results.

Learning methods of college mathematics

1. Learning mentality.

Most middle school students are expected to improve their math scores. On the one hand, with a certain foundation and hard work, there is nothing wrong with students' attitude, but they lack direction and appropriate methods. On the other hand, there is still enough time to prepare for the exam and adjust and optimize. Therefore, give yourself more positive psychological hints on weekdays and stick to practicing the learning methods that suit you.

2. the direction of preparing for the exam.

What is the preparation direction? The so-called preparation direction is the examination direction. When doing the problem at ordinary times, we should find out what kind of knowledge framework and question type the problem in front of us is, what is the method of this question type, and what is this question type? Wait a minute.

Questions and knowledge points are limited. As long as we look for ways to solve problems and carry out reasonable training according to the questions we often take, it is easy to improve our math scores.

3. Training methods.

Everyone's actual situation is different, and the training methods are different. The good results obtained in the exam are the result of reasonable training before the exam. Many students complain that there is not enough time, and they are exhausted after finishing their homework every day. In the face of a bunch of problems, especially math problems, we can pay attention to the following angles:

(1) Know your own needs. For example, if you get the homework assigned by the teacher, whether it is a test paper or a textbook exercise, if you do it with emotion, the effect will definitely be bad. First of all, we must understand our own needs, such as which of these topics are of good quality? What don't you get? Which ones have appeared frequently before? Are you sure what you want to do? Wait, which problem do you want to solve most?

(2) Set goals. If dealing with teachers to do problems will undoubtedly lead to poor quality, then you should set certain goals before doing them. As mentioned above, what questions do you use to train the correct rate? What topics are used to practice speed? What topics are used to improve the steps and so on. With the goal, we can achieve it better. In this process, you will certainly gain a lot.