Are the most basic things. Students who study well can see what they have not mastered. Students with poor foundation can try to copy it down. It will definitely help you to take it out and look through it when you have time.
1, the applicable condition [straight line passing through the focus] must have ecosA=(x- 1)/(x+ 1), where a is the angle between the straight line and the focus axis, which is an acute angle.
X is the separation ratio and must be greater than 1. Note: The above formula is applicable to all conic curves. If the focus is internally divided (meaning that the focus is on the cutting line segment), use this formula; If it is divided (focusing on the extension line of the section), the right side is (x+ 1)/(x- 1), and the rest remains unchanged.
2, the periodicity of the function (memory 3):
(1) If f(x)=-f(x+k), then t = 2k(2) If f(x)=m/(x+k)(m is not 0), then t = 2k(3) If f (x) = f (x+k).
Note: A. Periodic function, the period must be infinite; B-periodic functions may have no minimum period, such as constant functions; C. periodic function plus periodic function is not necessarily a periodic function.
3. Symmetry problems (problems that countless people don't understand) can be summarized as follows:
(1) If r is satisfied (the same below): f(a+x)=f(b-x) is constant, and the symmetry axis is x = (a+b)/2; (2) the images of functions y=f(a+x) and y=f(b-x) are symmetrical about x=(b-a)/2; (3) If f(a+x)+f(a-x)=2b, the image of f(x) is symmetrical about the center of (a, b).
4. Functional parity:
(1) For odd function on R, there is f (0) = 0; (2) For parametric functions, odd function has no even power term, and even functions have no odd power term; (3) Parity has little effect and is generally used to fill in the blanks.
5, commonly used sequence bn=n×(2? N) sum Sn=(n- 1)×(2？ (n+ 1))+2 Subtract a 1 before the mnemonic method, then add one, and add a 2 as a whole.
6. Formula applicable to standard equation (focusing on X axis):
K ellipse =-{(b? )x？ }/{(a？ )y？ }; K double ={(b？ )x？ }/{(a？ )y？ }; K throw =p/y？ . Note: (x? ，y？ ) is the midpoint of the section where a straight line passes through a conic curve.
7. It is strongly recommended that two straight lines are perpendicular or parallel to each other.
Known straight line l? :a？ x+b？ y+c？ =0? ; Straight line l? :a？ x+b？ y+c？ =0
If they are vertical: (necessary and sufficient condition) A? Answer? +b？ b？ =0; If parallel: (necessary and sufficient condition) a? b？ =a？ b？ What about a? c？ ≠a？ c？ [This condition is to prevent two straight lines from overlapping]
8, products and differences:
sinαsinβ=[cos(α-β)-cos(α+β)]/2
cosαcosβ=[cos(α+β)+cos(α-β)]/2
sinαcosβ=[sin(α+β)+sin(α-β)]/2
cosαsinβ=[sin(α+β)-sin(α-β)]/2