High school mathematical formula daquan 1, monotonicity of function
(1) Let x 1, x2[a, b], x 1x2.
F(x 1)f(x2)0f(x) is the increasing function on [a, b];
F(x 1)f(x2)0f(x) is a decreasing function on [a, b].
(2) Let the function yf(x) be derivable in a certain interval. If f(x) is 0, then f (x) is increasing function; If f(x)0, then f(x) is a decreasing function.
2. The parity of the function
F(-x)=f(x) For any x in the domain, then f(x) is an even function; F(x)F(x) exists for any X in the domain, then f(x) is a odd function. The images of odd functions are symmetrical about the origin, and the images of even functions are symmetrical about the Y axis.
3. Discrimination
B2-4ac=0 Note: This equation has two equal real roots.
B2-4ac >0 Note: The equation has two unequal real roots.
B2-4ac & lt； Note: The equation has no real root, but a complex number of the yoke.
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4. Two angles and formulas
sin(A+B)= Sina cosb+cosa sinb sin(A-B)= Sina cosb-sinb cosa
cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb
tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)ctg(A-B)=(ctgActgB+ 1)/(ctg B-ctgA)
5. Double angle formula
tan2A = 2 tana/( 1-tan2A)ctg2A =(ctg2A- 1)/2c TGA
cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
6.parabola
1, parabola: y=ax*+bx+c is the square of y = ax plus bx plus c.
A>0, parabolic opening upward; At a & lt0°, the parabolic opening is downward; When c=0, the parabola passes through the origin; When b=0, the axis of symmetry of parabola is the Y axis.
2. Vertex y=a(x+h)*+k means that y is equal to a times the square of (x+h) +k, -h is the x of vertex coordinates, and k is the y of vertex coordinates, which is generally used to find the maximum and minimum values.
3. Parabolic standard equation: y 2 = 2px, which means that the focus of parabola is on the positive semi-axis of X, and the focal coordinate is (p/2,0).
4. The directrix equation is x=-p/2. Because the focus of parabola can be on any half axis, there is a standard equation for * * *: y 2 = 2pxy 2 =-2pxy 2 =-2pxy.
Learning mathematics should pay attention to the acceptance of reviewing new knowledge in class and after class, and the cultivation of mathematical ability is mainly carried out in class, so we should pay attention to the learning efficiency in class and seek correct learning methods. In class, you should keep up with the teacher's ideas, actively explore thinking, predict the next steps, and compare your own problem-solving ideas with what the teacher said. In particular, we should do a good job in learning basic knowledge and skills, and review them in time after class, leaving no doubt. First of all, we should recall the knowledge points the teacher said before doing various exercises, and correctly master the reasoning process of various formulas. If we are not clear, we should try our best to recall them instead of turning to the book immediately. In a sense, you should not create a learning way of asking questions if you don't understand. For some problems, because of their unclear thinking, it is difficult to solve them at the moment. Let yourself calm down and analyze the problems carefully and try to solve them by yourself.