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 angle, apply the normalization formula and induction formula (singular change, even constant; 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 tolerance (common 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, 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 you draw 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).
Three, solid geometry problems:
1, it is easier to prove the relationship between line and surface, and generally it is not necessary 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 p 1+p2+...+pn= 1).
5. Pay attention to basic methods such as enumeration and tree diagram when counting.
6, pay attention to put back the sample, don't put back the sample.
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.