For many students, the finale in college entrance examination mathematics is a big problem. The following is a compilation of some answering skills for the finale of the college entrance examination for reference. I hope this year's college entrance examination can inspire you and achieve satisfactory results!

Problem-solving skills of mathematical finale

1 Six problem-solving skills for the finale of college entrance examination mathematics

First, the trigonometric function problem

Pay attention to the correctness of the normalization formula and induction formula {when converting into trigonometric functions with the same name and the same angle, apply the 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 an arithmetic (proportional) series, the arithmetic (proportional) series with the first item and the tolerance (common ratio) should be written in the final conclusion; 2. When proving the inequality in the last question, 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 it is generally 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, sometimes it is very simple to construct a function and use the monotonicity of the function (so you should have the consciousness of constructing a function).

Third, solid geometry problems

1. It is easy to prove the relationship between line and surface, and it is generally unnecessary to establish a system; 2. It is best to establish a system when solving the problems such as the angle formed by lines on different planes, the included angle between lines and planes, the dihedral angle, the existence of geometry, the height, the surface area and the volume. 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 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 frontal 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 the sample back, not put it back; 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. Note that when solving the trajectory equation, three kinds of curves (ellipse, hyperbola and parabola) are considered. 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 has slope and 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/maximum/inequality constant problem

1. 1. Find the definition 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 establishing constants (separation of constants, distribution of function images and roots, and finding the maximum value of functions); 6. Keep 6 points in overall thinking, strive for 10, and think 14.

2 college entrance examination mathematics finale problem solving ideas

Thoughts on solving the finale problem of college entrance examination mathematics: function and equation thought

The idea of mathematical function in senior high school refers to analyzing and studying the quantitative relationship in mathematics from the viewpoint of movement change, and analyzing, transforming and solving problems by establishing functional relationship (or constructing function) and using the image and nature of function; The idea of equation is to transform the problem into an equation (equation group) or an inequality model (equation, inequality, etc.) to solve the problem. ) By using mathematical language. Using the idea of transformation, we can also transform functions and equations.

Reflections on the axis problem of mathematics decompression in college entrance examination (ⅱ): the idea of combining numbers with shapes

The object of high 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 way to optimize the way of solving problems. So when we solve math problems, we should draw pictures as much as possible to help us understand the meaning of the problems correctly and solve them quickly.

Reflections on the decompression axis of mathematics in college entrance examination (III): special and general thinking

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. According to this, we can directly determine the correct choice in multiple-choice questions. Not only that, it is also wonderful to explore the problem-solving strategies of subjective questions with this way of thinking.

Reflections on the decompression axis of mathematics in college entrance examination (IV): the steps of solving problems with extreme thoughts

The general steps of extreme thinking to solve problems are:

(1) For the unknown quantity, first try to conceive a variable related to it;

(2) Confirm that the result of the infinite process of this variable is an unknown quantity;

(3) Construct a function (sequence) and use the limit calculation rule to get the result or use the limit position of the graph to directly calculate the result.

Thinking about the decompression axis of mathematics in college entrance examination (5): classified discussion thinking

We often encounter such a situation, after solving a certain step, we can't continue with a unified method and formula. This is because the research object contains a variety of situations, which requires classifying all situations, solving them one by one, and then summarizing them to get a solution. This is a confidential discussion. There are many reasons for the discussion of classification, and there are many situations in the mathematical concept itself, such as the limitations of mathematical operation rules, some theorems and formulas, and the uncertainty and change of graphic position. When discussing and solving problems by classification, we should unify the standards, and we should not focus on them or leave them out.