A, geometry:

1- 1 analytic geometry:

Unified polar coordinate equation of conic curve: ρ = EP/(1-ecos θ);

The focal radius and chord length are expressed by inclination angle;

Angle formula;

1-2 plane geometry:

Several simple properties of "five hearts": the center of gravity is divided into the middle line 2: 1, and the straight line passing through the center of gravity intersects with both sides at two points. If two points are regarded as fixed score points on both sides of the original triangle, the reciprocal sum of the two ratios is 3 ... (I'm afraid there are many more, now let me think of a few);

Menelaus theorem and inverse theorem, Seva theorem and inverse theorem, Ptolemy theorem and inverse theorem. ...

1-3 solid geometry: I really didn't expect anything.

Second, the algebra part:

2- 1 inequality: Cauchy inequality, rank inequality ...

2-2 integration: It is best to know indefinite integration, that is, to find the original function of a function and add an integral constant C (this method is often used in physical problems, especially Faraday's law of electromagnetic induction, and I find that the teacher's final "equilibrium" state is mostly approximate).

2-3 Combinatorial Mathematics, Combinatorial Thought: This is too complicated. I suggest you read more books and feel the feelings.

E (≈ 2.718281828 ...): lim (n →∞) (1+1/n) n = e 2-4;

2-5 determinant: it can be used to solve linear equations and equations of circles passing through three points;

2-6 simple number theory: that is, when answering fill-in-the-blank questions, you won't answer ridiculous mistakes such as ten fifths and root number 256;

"Great Division" of 2-7 polynomials: Similar to integer division, when solving a polynomial equation, we use "Great Division" to decompose the factors and get the solution. For example, if X 3-3x+2 = 0 finds that a root is 1, then divide x- 1 by the factor X 3-3x+2 to get X 2+X-2 = 0, so X 3-3x+2 = 0 is equivalent to (x-65438+. This example is relatively simple.

2-8……

I feel that there will be many more, but I will show you these now, hoping to help you!