Allocation method of mathematics examination time in college entrance examination
Make full use of 5 minutes before the exam.
Many students or parents don't know that according to the requirements of large-scale exams, five minutes before the exam is the time to distribute papers, and candidates fill in the admission ticket. You are not allowed to do the questions for five minutes, but you can look at the questions. I found that many candidates began to read the first question after they got the test paper. My advice to you is that if you get this set of papers, these five minutes will be the key moment to formulate the whole strategy. You didn't see the topic before, but you were dreaming. When you see the question, you should use these five minutes to quickly work out the strategy for the whole exam.
Examine the questions before the exam.
After the exam begins, many students like to write hard; But remember: the exam must be careful and slow. Math problems often hide the key to solving problems in a sentence and a data. You can't understand the word and the data, or you can't find the key to solving the problem, or you misread the topic. If you do it on the basis of misreading, you may feel relaxed, but you won't get any points on this question. Therefore, you must carefully examine the questions. Only when you understand the meaning of the question can you answer correctly. Problems that can be done don't waste time. What really wastes time is in the process of reviewing questions and finding ideas. As long as you find an idea, simply writing down those steps doesn't take time.
Choose the way to do the problem from simple to difficult
Candidates who want to get high marks in the college entrance examination should remember that they are unwilling to give up when they encounter problems, and they should know appropriate circuitous tactics. When they encounter problems, they should skip them first, and then use the remaining time to study them slowly after other problems are completed to avoid the loss outweighs the gain. It can also save time and allocate the time for answering math questions in the college entrance examination. Moreover, every step of writing a math problem may score higher than a math multiple-choice question or a fill-in-the-blank question. So we should distinguish the importance of doing the problem.
Get into the good habit of checking.
A large number of college entrance examination candidates will shout out their regrets after the answers are announced, because many points are not deserved and are caused by casual negligence. Therefore, when this habit is formed, even in the tense college entrance examination field, it is natural to check with a peaceful mind and reduce unnecessary math scores.
The key to saving time is to do it right once.
Some students, when they finally come across a simple topic, try to hurry up and try to gain time to do the problem they can't do. As we all know, there is a big gap between the difficulty of the multiple-choice questions in front and the big questions in the back, but the gold content of the scores is the same. Some students despise the small scores in front and think that the big scores in the back are "valuable", which is a serious misunderstanding.
I hope students must get into the habit of doing the exam right once, and don't expect to turn the tide through the final exam. The more important the exam is, the less time you have to come back to check it, because the more difficult the topic is, the more likely you are to get stuck in it and start rolling it up as soon as you look up.
Answering skills of multiple choice questions in college entrance examination mathematics
Exclusion option method
Because the answer to multiple-choice questions is one of the four options, there must be only one correct answer, so we can use the exclusion method to exclude the answer that is easy to judge as wrong from the four options, so the remaining one is naturally the correct answer.
Method of assigning special values
That is, according to the conditions in the topic, select special values that meet the conditions or make special graphics for calculation and reasoning. When solving problems with special value method, we should pay attention to selecting values that meet the conditions and are easy to calculate.
By guessing and measuring, we can directly observe or get the results.
This method is often used to explore regular problems in college entrance examination questions in recent years. The main solution of this kind of problem is to use incomplete induction to solve the problem through experiment, guess, trial and error verification and summary.
Principle of extremism
Analyze the problem to be studied to the extreme state, so that the causal relationship becomes more obvious, thus achieving the purpose of solving the problem quickly. Extreme value is often used to find extreme value, range, analytic geometry and solid geometry. Many problems with complicated calculation steps and large amount of calculation can be solved instantly through extreme value analysis. As follows, directly take the extreme case of ab⊥cd, take the midpoint E of ab and the midpoint F of cd, and connect ef, so that ef⊥ab and ef⊥cd, and the calculated value is the maximum value without too much explanation.
Forward deduction method
Using mathematical theorems, formulas, rules, definitions and meanings, the method of obtaining results through direct calculus and reasoning. The following questions can be substituted into the function and its inverse function in turn according to the meaning of the question.
5. Inverse verification method substitutes answers into the stem verification method: a method of substituting options into the stem for verification, thereby denying wrong options and getting correct answers. Often used with exclusion; The following questions are obviously satisfied by substituting x=0, and AD is excluded; Substituting x=- 1 is obviously inconsistent, excluding c and choosing B.
A combination of numbers and shapes
According to the conditions of the topic, make a graph or image that conforms to the meaning of the topic, and get the answer through simple reasoning or calculation with the help of the intuition of the graph or image. The advantage of the combination of numbers and shapes is intuitive, and you can even measure the result directly with a square. As follows, after drawing, it is directly concluded that option A meets the requirements.
Recursive induction
Reasoning through topic conditions, looking for laws, and thus inducing the correct answers, for example, recursive induction is often used when analyzing related problems such as periodic series. The following problems can be analyzed by finding the law.
Characteristic analysis method
This paper analyzes the characteristics of questions and options, finds the rules and summarizes the correct judgment methods. The following problems, if you don't analyze the characteristics of this geometry, you will have a headache if you directly use the general excavation and filling method. Careful analysis, in fact, geometry is half the volume of a square with a side length of 2, and so on, you can know to choose C without calculation.
Estimation algorithm
For some problems, due to the limitation of subject conditions, it is impossible or unnecessary to make accurate calculations and judgments. At this time, we can only get the correct judgment method from the surface by means of estimation, observation, analysis, comparison and calculation. As follows, this unsolvable equation can only be solved by estimation. Of course, if you can use a calculator, the estimation can be very accurate. Using tables or solving functions, it can be calculated to be about 0.42.
Pay attention to the use of various methods when doing multiple-choice questions. Simply do the questions you know normally. If you encounter more complicated questions, see if you can use the skills of making multiple-choice questions to solve them. Generally, various methods can be comprehensively used to achieve the effect of quick decision. The same is true of fill-in-the-blank questions. Simple questions can be done normally. If the answer to a complex question is a certain value, it depends on whether the special value substitution method and the special case solution method can be used. Choose your own time to answer the fill-in-the-blank questions. If not, put it down and answer later. Our goal is to answer all the questions on the test paper correctly, read the questions carefully word by word and calculate them accurately step by step. There must be no carelessness.
Problem-solving skills of big math problems in college entrance examination
First, the trigonometric function problem
Pay attention to the correctness of normalization formula and induction formula. When they are transformed into trigonometric functions with the same name and the same angle, the normalization formula and induction formula are applied strangely and evenly. 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 it is proved that a sequence is an arithmetic geometric progression, who is the first term and who is the arithmetic geometric progression of the tolerance ratio should be written in the final conclusion;
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, when mathematical induction is generally considered, when n=k+ 1, the assumption of 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 inequalities, it is sometimes easy to construct functions, so you should have the consciousness of constructing functions.
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 range of the angle formed by the vector and the cosine range of the angle, the sign problem, the obtuse angle and the 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, if there is any difficulty, take p 1+p2+ as the basis ...+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 infiltration of "scattered" knowledge points, frequency distribution histogram and stratified sampling;
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 the trajectory equation. From the three curves of ellipse, hyperbola and parabola, ellipse is the most frequently tested. The methods include direct method, definition method, intersection method, derivative method and undetermined coefficient method.
2, pay attention to the straight line method 1 points have slope, no slope; Method 2 When the slope of x=my+b is not zero and 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.
6. Derivative, extreme value, maximum value, inequality constant or inverse problem of finding parameters
1, first find the domain of the function, and correctly find the derivative, especially the derivative of the composite function. Generally, monotonous intervals cannot be combined. Separate functions with "and" or ","and find the monotonous interval without equal sign; Understanding monotonicity, seeking universe, 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. Inequality problem has the consciousness of constructor;
5. The method of separating constants, the method of distributing function images and roots, and the method of finding the maximum value of functions;
6. Keep 6 points in overall thinking, strive for 10, and think 14.