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! )。
Sequence problem
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 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, 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).
Solid geometry problem
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).
Probabilistic 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.
Conic curve 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 points have 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.
The continuous establishment of derivatives, values and inequalities
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.