1. If there is a transcendental expression in an equation or inequality, the thinking method of combining numbers and shapes is preferred, bearing in mind various function models and the characteristics of each model;

2. The topics of functions, equations or inequalities should be directly considered before the relationship between them is established. Consider the domain first, and then use the "three-in-one theorem". The zero point of the function is the root of the equation.

3. In the face of elementary functions with parameters, we should grasp the invariance of the parameters when learning. Such as constant fixed point, symmetry axis of quadratic function, period of trigonometric function, etc.

4. The problem of constant establishment or its opposite can be transformed into a maximum problem. Pay attention to the application of quadratic function, flexibly use the maximum value on the closed interval, and the idea of classification discussion is not repeated or omitted;

5. To find the value range of parameters, we should establish an equation or inequality about parameters, complete or solve the inequality with the definition domain or value domain of the function, take the separation constant, and finally become a constant establishment problem to find the maximum value;

6. To solve the problem of curve equation, if you know the shape of the curve, you can choose the undetermined coefficient method. If you don't know the shape of the curve, the steps are to establish the system, set points, formulate and simplify (pay attention to remove the special points that don't meet the conditions);

7. The topic of conic curve should be clear first, and the intersection problem between straight line and conic curve should be solved. If it is related to the chord midpoint, we should choose the method of setting instead of finding the point difference, and if it is not related to the chord midpoint, we should choose the method of Vieta theorem formula. When using Vieta theorem, we should first consider whether it is the discriminant of quadratic sum root;