1 vector. When doing vector operations, we can use the orthogonal decomposition method of vectors in physics, which is beneficial to solve some vector problems.

2. Tetrahedron. In a tetrahedron whose three sides are perpendicular to each other, if the length of the three sides is h, there is,1/h ∧ 2 =1/a ∧ 2+1/c ∧.

3. Plane equation. For the plane equation in space rectangular coordinate system, first find a normal vector n=(a, b, c) of the plane, and then take any point A(e, f, g) in the plane, then the equation of the plane is a(x-e)+b(y-f)+c(z-g)=0, which becomes the general formula AX+.

4. Sum-difference product formula of sine and cosine

sinα+sinβ= 2 sin[(α+β)/2]cos[(α-β)/2]

sinα-sinβ= 2cos[(α+β)/2]sin[(α-β)/2]

cosα+cosβ= 2cos[(α+β)/2]cos[(α-β)/2]

cosα-cosβ=-2 sin[(α+β)/2]sin[(α-β)/2]

Note that the four groups of formulas above the minus sign before the formula on the right can all be derived from the product and difference formula.

5. The periodicity of the function (Note 3): 1) If f(x)=-f(x+k), then T = 2k2) If f(x)=m/(x+k)(m is not 0), then T = 2k3) If f (x) = f. Note: A. Periodic function, the period must be infinite B. Periodic function can have no minimum period, such as constant function. C. periodic function plus periodic function is not necessarily a periodic function, for example, y=sinxy=sin pie x is not a periodic function.

6, the ultimate weapon of the sequence, the characteristic root equation. Forget it if you don't understand. Firstly, the formula is introduced: for an+ 1=pan+q(n+ 1 is the lower corner, and n is the lower corner), if a 1 is known, then the characteristic root x=q/( 1-p), then the general term formula of the series is an = (A6550). (n- 1)+x, which is the application of the first-order eigenvalue equation. The second order is a bit troublesome and not commonly used. So I won't go into details. I hope the students will remember the above formula. Of course, this type of sequence can be constructed (both sides are added at the same time)

7. Supplement to the detailed explanation of the function: 1, parity of the compound function: inner parity, inner and outer strangeness 2, monotonicity of the compound function: same increase but different decrease 3, key knowledge about the cubic function: I am afraid that not many people know that the cubic function curve is actually a centrally symmetric figure. It has a symmetrical center. The solution is that the derivative after the second derivative is 0, the root X is the abscissa of the center, and the ordinate can be defined by bringing X into the original function. In addition, only one straight line must pass through the center tangent to both sides.

8. Commonly used sequence bn=n×(2? N) sum Sn=(n- 1)×(2？ (n+ 1))+2 mnemonic method: subtract a 1 from the front, add one after it, and add a 2 as a whole.

9, applicable to the standard equation (the focus is on the X axis). Explosion intensity formula: k ellipse =-{(b? )xo}/{(a？ )yo} k double ={(b？ )xo}/{(a？ ) yo} k throw =p/yo Note: (xo, yo) is the midpoint of the cross section of a straight line passing through a conic curve.