Math problem-solving skills in college entrance examination 12.
First, adjust the brain thinking and enter the mathematical situation in advance.
Before the exam, we should abandon distracting thoughts, eliminate distracting thoughts, make the brain in a "blank" state, create mathematical situations, then brew mathematical thinking, enter the "role" in advance, and comfort ourselves by counting utensils, prompting important knowledge and methods, and reminding common misunderstandings and mistakes in solving problems, so as to reduce stress, go into battle lightly, stabilize emotions, enhance confidence, and make thinking simple, mathematical, stable and confident.
Second, "tight inside and loose outside", concentrate on eliminating anxiety and stage fright.
Concentration is the guarantee of success in the exam. A certain degree of nervousness and nervousness can accelerate the nerve connection, which is conducive to positive thinking. It is called internal tension, but if you are too nervous, you will go to the opposite side, forming stage fright, causing anxiety and inhibiting thinking. So be sober, happy and open-minded, which is called external relaxation.
Third, calmly facing the battle and ensuring victory will help to cheer up the spirit.
A good beginning is half the battle. From the psychological point of view of examination, this is indeed very reasonable. After getting the test questions, don't rush for success, solve the problem immediately. Instead, we should browse the whole set of questions, find out the situation of the questions, and then firmly grasp one or two easy-to-learn questions, so that we can have a good start and quickly enter the best mental state.
Fourth, "six before six", because people are suitable for rolling.
After reviewing the whole volume and successfully completing the simple questions, the mood tends to be stable, the situation tends to be single, the brain tends to be excited, and the thinking tends to be positive. Then there is the golden season of exerting the ability to solve problems on the spot. At this point, candidates can choose to implement the tactical principle of "six first and six later" according to their own problem-solving habits and basic skills, combined with the structure of the whole set of questions.
1. Easy first, then difficult. Is to do simple questions first, and then do comprehensive questions, should be based on their own reality, decisively skip the topics that can't be chewed, from easy to difficult, but also pay attention to take every question seriously, strive for practical results, and can't just skim through it and retreat when it's difficult, which hurts the mood of solving problems.
2. Mature first and then grow. Looking at the whole volume, we can get many favorable positive factors and some unfavorable factors. For the latter, there is no need to panic. We should think that the test questions are difficult for all candidates. Through this hint, you can ensure emotional stability. After grasping the whole volume as a whole, you can practice the method of pre-cooking, that is, you can do those questions with familiar content, familiar question structure and clear thinking of solving problems. In this way, while winning familiar questions, you can make your thinking fluent and extraordinary, and achieve the goal of winning advanced questions.
3. Similarity before difference. Doing the same topic in the same subject first, thinking more deeply, exchanging knowledge and methods easier, is conducive to improving the efficiency of unit time. Generally speaking, the topic requires the transfer of the "exciting focus" to be fast, and "the same before the different" can avoid the "exciting focus" jumping too fast and too frequently, thus reducing the burden on the brain and maintaining effective energy. 4. Small problems are generally less informative and easy to master, so don't let them go easily. We should try to solve major problems as soon as possible before they appear, so as to gain time for solving major problems and create a relaxed psychological foundation. In recent years, most of the math problems in the college entrance examination are presented as "gradient problems", which need not be examined in one go, but should be solved step by step, and the solution of the previous problems has prepared the thinking foundation and problem-solving conditions for the later problems, so it is necessary to proceed step by step, from point to surface. 6. that is, the second half of the exam, we should pay attention to time efficiency. If it is estimated that you can do both questions, then do the high score questions first. It is not easy to estimate the two questions. First, the high-scoring questions should be graded by sections, and the score should be increased on the premise of insufficient time.
5. A "slow" and a "fast" complement each other.
Some candidates only know that the examination room should be fast, and as a result, the meaning of the question is unclear and the conditions are incomplete, so they are eager to answer. Don't you know that haste makes waste, and as a result, their thinking is blocked or they walk into a dead end, leading to failure. It should be said that the questions should be slow and the answers should be quick. Examination of questions is the "basic project" in the whole process of solving problems, and the questions themselves are the information sources of "how to solve problems". We must fully understand the meaning of the question, synthesize all the conditions, refine all the 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 completed as quickly as possible.
Six, to ensure accurate operation, based on a success.
The number of math college entrance examination questions is 120 minutes and 26 questions. The time is very tight, so it is not allowed to do a lot of detailed post-solution tests, so we should try our best to calculate accurately (key steps, strive for accuracy, rather slow than fast) and base ourselves on one success. The speed of solving problems is based on the accuracy of solving problems, not to mention the intermediate data of mathematical problems often affect the answers of subsequent steps not only in quantity, but also in quality. Therefore, under the premise of taking speed as the first priority, we should be steady and steady, well-founded at all levels and accurate step by step. We should not lose accuracy or even important scoring steps in pursuit of speed. If speed and accuracy cannot be achieved at the same time, we have to be quick and accurate, because the answer is wrong, and it is meaningless to be quick.
Seven, stress standardized writing, and strive to be both correct and complete.
Another feature of the exam is that the paper is the only basis. This requires not only conformity, but also correctness, correctness, completeness, completeness and standardization. Unfortunately, it will be wrong; Yes, but incomplete, the score is not high; Non-standard expression and scrawled handwriting are another major aspect that causes non-intellectual factors to lose points in the college entrance examination mathematics paper. Because the handwriting is scrawled, it will make the marking teacher have a bad first impression, and then make the marking teacher think that the candidates are not serious in their studies, their basic skills are not too hard, and their "emotional score" is correspondingly low. This is the so-called psychological "halo effect". It is this truth that "the handwriting should be neat and the papers can be scored".
Eight, in the face of problems, pay attention to methods and strive for scores.
Of course, we should strive to do the right thing, complete it, and get full marks. More questions are how to score the incomplete questions. There are two common methods.
1. Missing step solution. When a problem is really difficult to solve, a wise solution is to divide it into a sub-problem or a series of steps. First, solve part of the problem, that is, to what extent it can be solved. After calculating several steps, write several steps, and each step will get a score. For example, from the beginning, translating written language into symbolic language, translating conditions and goals into mathematical expressions, setting the unknowns of application problems, setting the coordinates of moving points of trajectory problems, and drawing figures correctly according to the meaning of problems can all be scored. There are also simple situations such as completing the first step of mathematical induction, classified discussion, and reduction to absurdity, all of which can be scored. Moreover, it is expected that in the above treatment, from perceptual to rational, from special to general, from local to whole, we will have an epiphany, form ideas and successfully solve problems.
Step by step. When the problem-solving process is stuck in an intermediate link, you can admit the intermediate conclusion and push it down to see if you can get the correct conclusion. If you can't get it, it means this road is wrong. If you can't get it, it means this road is wrong. Change direction immediately and find another way out. If we can get the expected conclusion, we will go back and concentrate on overcoming this transitional link. If the intermediate conclusion is too late to be confirmed due to time constraints, we have to skip this step and write the subsequent steps to the end; In addition, if there are two problems, and the first problem can't be solved, you can call the first problem "known" and complete the second problem, which is called jumping problem solving. Maybe later, due to the positive transfer of solving problems, I remembered the intermediate steps, or if time permits, I tried to catch the intermediate difficulties and could make up for them at the end of the corresponding questions.
Nine, retreat for progress, based on special.
Divergence Generally speaking, for a relatively general problem, if you can't get a general idea at the moment, you can treat the general as special (for example, solving multiple-choice questions in a special way), treat the abstract as concrete, treat the whole as local, treat parameters as constants, treat weak conditions as strong conditions, and so on. In short, retreat to the extent that you can solve it, and solve the "special" by thinking and inspiring thinking, so as to achieve the purpose of solving the "general".
Ten, holding the fruits of the cause, thinking backwards, and turning back when it is difficult.
When thinking in a positive way is blocked, we can often use the method of reverse thinking to explore new ways to solve the problem, so as to make breakthrough progress. If it is difficult to push forward, push back. If it is difficult to prove directly, disprove it. For example, we can use analysis to find sufficient conditions from positive conclusions or intermediate steps. By reducing to absurdity, we can find the necessary conditions from negative conclusions.
XI. Avoid affirming and denying the conclusion and solve exploratory problems.
For exploratory questions, there is no need to pursue the "yes" and "no" or "yes" and "no" of the conclusion. We can synthesize all the initial conditions and conduct strict reasoning and discussion, then the steps will arrive and the conclusion will be self-evident.
Application of ideas: face-point-line.
To solve practical problems, we must first comprehensively examine the meaning of the problem and quickly accept the concept, which is called "face"; Through lengthy narration, grasping key words and putting forward key data, this is the "point"; Synthesize the connection, refine the relationship, and establish a mathematical model by mathematical method, which is called "line", thus transforming the application problem into a pure mathematical problem. Of course, the solution process and results are inseparable from the actual background.
Answering skills of mathematics big questions in college entrance examination
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.
Instructions for college entrance examination
1, pay attention to the step-by-step answer form. If every small question is dominated by the major premise, then it is likely that the above conclusion is the condition of the following question. Pay attention to this. At the same time, if the small question is restricted separately, its conclusion cannot be applied to the answer to the next small question, so we should examine it carefully and not neglect it.
2. In the process of operation, one-time operation is required accurately. Otherwise, if there is an operational error, candidates are often influenced by the mindset and it is difficult to find out. As long as you are careful, you should have confidence in yourself. Don't do a problem and then double-check whether it is accurate, which will waste a lot of precious time. On this issue, we should grasp "rather slow than rough".
3. For solving problems, we should pay attention to general methods, and don't pursue skills too much to mystify the college entrance examination. Because the college entrance examination pays more and more attention to the examination of basic and general methods. For example, in analytic geometry, it is difficult for most students to get full marks. Usually analytic geometry is placed in the last or penultimate question of the college entrance examination, which is regarded as the finale. The general method of this kind of analytic geometry problem is to combine linear equation with curve equation. Although it may be troublesome to calculate sometimes, it can still be done. If you pay too much attention to skills, it will not be applicable to some topics.
4. For most students, we should focus our energy and time on regular topics (generally referring to the pre 19 questions and the post 1 questions). Judging from the test paper of the college entrance examination, its basic score may account for 70% to 80%. The basic questions and routine questions are well done, and it is no problem to get a medium grade. On this basis, you can get an ideal score by taking some more difficult questions. On the other hand, if you are eager for quick success, it is easy to make avoidable mistakes on the previous basic questions, and the latter questions may not get points, so the gap with others will widen, which is also a loss.
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