There are many formulas in high school mathematics that we need to memorize. These formulas in mathematics can help us to answer the questions in college entrance examination mathematics more easily. Here I have sorted out some key mathematical formulas for you.
High school mathematics 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.