In space geometry, we should pay attention to geometric theorems. There are many things that are applicable in plane, but not in three-dimensional space. At this time, some theorems are needed. It is very important to know the conditions of theorem proving in detail, which is also the basis of doing space geometry problems. Grasping these foundations, doing more questions and getting familiar with some questions are basically OK.
Solid geometry should focus on cultivating spatial ability, and the relationship between straight line and plane angle should be solved by the theorem of three perpendicular lines. The relationship between the circle and the line is easy to learn, do more types, read more questions, and don't waste time on the type questions you can do. Have a good spatial imagination, pay attention to thinking and imagination at ordinary times! Secondly, doing more corresponding questions is actually very simple! Space imagination is good, and space problems are transformed into plane problems as much as possible. Read textbooks, examples, imagination and pictures carefully. Actually, this part is not very difficult.
Find some topics
Then divide all the geometric contents into several modules .. and then work on the topic of one module for a while, and then move on to the next module when you think it's ok.
When you think you have digested everything, start doing some college entrance examination questions.
Analytic geometry generally has methods, such as correlation point method, polar coordinate method, curve system method, coordinate subtraction and so on. As long as you master these common methods, analytic geometry is actually very simple.
When analyzing geometry, we should remember the characteristics of common curves and related conclusions.
Solid geometry is relatively simple, so we should make good use of theorems to infer, but if we can't use vectors, we can definitely solve it.
But this kind of thing depends on yourself, guard against arrogance and rashness, and take it slowly.
The main contents are as follows: 1. 1 structural characteristics of column, cone, platform and ball.
1.2 Three Views and Straight Views of Space Geometry
1 three views:
Front view: from front to back
Side view: from left to right
Top view: from top to bottom
2 the principle of drawing three views:
Long alignment, high alignment and equal width
3 orthographic drawing: oblique drawing.
4. The steps of oblique two drawing method:
(1). Lines parallel to the coordinate axis are still parallel to the coordinate axis;
(2) The length of the line parallel to the Y axis becomes half, while the length of the line parallel to the X and Z axes remains unchanged;
(3) the painting method should be written well.
5. Step of drawing a cuboid obliquely: (1) Draw an axis (2) Draw a bottom (3) Draw a side (4) for drawing.
1.3 surface area and volume of space geometry
(A) the surface area of space geometry
1 Surface area of prism and pyramid: the sum of the areas of each face.
2 Surface area of cylinder
3 Surface area of cone
4 Surface area of frustum of a cone
5 Surface area of ball
(2) the volume of space geometry
1 volume of cylinder
2 the volume of the cone
3 Volume of platform body
4 the volume of the sphere
First, textbooks should be "previewed, done well and repeated". Before each new lesson, preview it first, especially highlight the difficulties or things that you don't understand with colored pens, so that you can concentrate more in class. You can do the exercises after each lesson first, so that you can understand 70% of the new content and do 80% of the exercises. After learning a new lesson, we should compare and review the learned knowledge step by step according to the contents of the textbook, from easy to difficult, from simple to complicated, and summarize the concepts, theorems and formulas to deepen our understanding of the knowledge. The examples in the textbook are best done by yourself. Reasoning the concepts, theorems and formulas in the textbook to form an overall understanding of knowledge.
Second, we should "listen, remember and practice" in class. Listen to the questions in the preview in class, take notes when necessary, and consolidate them through some exercises. Mathematics is different from other subjects. It is impossible to solve practical problems by memorizing concepts, theorems and formulas. Only through practice can we reduce operational mistakes.
Third, homework should be "thinking, asking and gathering". Homework must develop the habit of independent thinking, from different methods and angles, explore various problem-solving methods from typical topics, and get association and inspiration from them. At the same time, we should also establish more mathematical problem-solving ideas, such as: equation ideas, function ideas, combination of numbers and shapes and other common methods; For difficult questions, we should ask more reasons, such as changing conditions, adding conditions, and exchanging conditions for conclusions. Is the original conclusion still valid? In addition, for the mistakes in homework and test papers, it is best to prepare a set of wrong questions for future review. Don't make the same mistake twice. In short, learning mathematics must have methods, plans and reasonable arrangements. After the new lesson, some students feel headache, so they look around and don't know what they have learned in the end. Therefore, every student should work out reasonable learning methods and goals according to his own actual situation; If there is no way, it will become a headless fly; Without goals, there will be no motivation.