Let me give you a simple example, A, b>0, A+B = 2, the scope of AB. If you read the high school textbooks thoroughly, you will find that there are many ways to draw a conclusion on this issue:
(1) mean inequality: a+b >; =2(ab)^0.5
(2)a+b=2, a=b-2 ab=b(b-2) and f (b) = b (b-2) (b >; 0) Find the range of the quadratic equation of one variable (using the method of finding the vertex in junior high school, that is, the matching method).
(3) Let f'(b)=0, and find the extreme value by derivative method.
Although these methods are simple. But they are undoubtedly not the importance of building a complete knowledge system.
Ask yourself, if you close the math book, can you frame the theoretical knowledge in the book in your mind, and then, can you prove the theorem in your own language?
2. Once you have complete theoretical knowledge, you should begin to cultivate your sensitivity to numbers. For example, when you see 12 1, you should immediately think of 1 1 2. In other words, remember more typical conclusions. For example, if I tell you that f(x+a)=f(-x+b), you should immediately understand that this means that the symmetry axis of f(x) is X = (A+B)/2. F(x+a)=-F(x), which means that the period of f (x) is T=2a.
These are all based on practicing typical questions and then reciting typical conclusions (just like the theorem on endorsement).
3. Then, master high school mathematics ideas, such as the combination of numbers and types, functions, inequalities, classification and so on.
Example: combination of numbers and types:
F(x)=|x- 1|+|x-3|, and find the range of f (x).
You should know that |x- 1| is equivalent to the distance from the point on the number axis to 1, and |x-3| is the distance to 3, so it is easy to draw a conclusion by drawing the number axis.
Theory and thought of function
Verify | a+b |/(1+a+b |) < = | a |/(1+| a |)+| b |/(1+| b |)
Consider f (x) = x/( 1+x), x >；; =0, the function is incremental. | A+B |
therefore
| a+b |/( 1+| a+b |)& lt； =(| a |+| b |)/( 1+| a |+| b |)& lt； =(| a |+| b |+2 | a | | b |)/( 1+| a |+| b |+| a | | b |)= | a |/( 1+| a |)+| b |/( 1+| b |)
Certificate of completion
I won't give examples for the last few.
This article is mainly obtained through excellent reference books.
4. Do crazy questions (especially after the third year of high school, basically one test paper a day)