1. Equation:
The solution of (1) unary quadratic equation: -b+√(b2-4ac)/2a -b-√(b2-4ac)/2a.
(2) Relationship between root and coefficient: x1+x2 =-b/ax1* x2 = c/a?
(3) discriminant:
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.
2. Triangle inequality:
| a+b |≤| a |+| b | | a-b |≤| a |+| b | | a |≤b & lt； = & gt-b≤a≤b
3. Multiplication and factorization:
a2-B2 =(a+b)(a-b)a3+B3 =(a+b)(a2-a b+B2)a3-B3 =(a-b(a2+a b+B2)
4. Trigonometric function:
(1) The formula of the sum of two angles:
sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-sinBcosA
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
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)
(2) Double angle formula:
tan2A = 2 tana/( 1-tan2A)ctg2A =(ctg2A- 1)/2c TGA
cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
(3) Half-angle formula:
sin(A/2)=√(( 1-cosA)/2)sin(A/2)=-√(( 1-cosA)/2)
cos(A/2)=√(( 1+cosA)/2)cos(A/2)=-√(( 1+cosA)/2)
tan(A/2)=√(( 1-cosA)/(( 1+cosA))
tan(A/2)=-√(( 1-cosA)/(( 1+cosA))
ctg(A/2)=√(( 1+cosA)/(( 1-cosA))ctg(A/2)=-√(( 1+cosA)/(( 1-cosA))
(4) Sum-difference product:
2sinAcosB=sin(A+B)+sin(A-B)
2cosAsinB=sin(A+B)-sin(A-B)
2cosAcosB=cos(A+B)-sin(A-B)
-2sinAsinB=cos(A+B)-cos(A-B)
sinA+sinB = 2 sin((A+B)/2)cos((A-B)/2 cosA+cosB = 2 cos((A+B)/2)sin((A-B)/2)
tanA+tanB=sin(A+B)/cosAcosB
tanA-tanB=sin(A-B)/cosAcosB
ctgA+ctgBsin(A+B)/Sina sinb-ctgA+ctgBsin(A+B)/Sina sinb
(5) Sine theorem: a/sinA=b/sinB=c/sinC=2R?
(6) Cosine theorem: b2=a2+c2-2accosB
5. Sum of the first n items in sequence (A~C):
a: 1+2+3+4+5+6+7+8+9+…+n = n(n+ 1)/2 1+3+5+7+9+ 1 1+ 13+ 15+…+(2n- 1)= N2
b:2+4+6+8+ 10+ 12+ 14+…+(2n)= n(n+ 1) 12+22+32+42+52+62+72+82+…+N2 = n(n+ 1)(2n+ 1)/6
c: 13+23+33+43+53+63+…n3 = N2(n+ 1)2/4 1 * 2+2 * 3+3 * 4+4 * 5+5 * 6+6 * 7+…+n(n+ 1)= n(n+ 1)(n+2)/3
6. The standard equation of the circle:
(x-a)2+(y-b)2=r2
7. General equation of circle:
x2+y2+Dx+Ey+F=0
8. Parabolic standard equation:
y2 = 2px y2 =-2px； x2=2py x2=-2py
9. Area formula:
(1) Side area of right-angle prism: s = c * h；; Side area of oblique prism: S = c'* h
(2) The side area of the right pyramid is S= 1/2c*h'
(3) the side area of the prism: S = 1/2(c+c')h'
(4) frustum side area: S = 1/2(c+c')l = pi(R+R)l?
(5) cylindrical lateral area: s = c * h = 2pi * h
(6) lateral area of the cone: s =1/2 * c * l = pi * r * l.
(7) Arc length formula: l = a * r；; Sector area formula s= 1/2*l*r
(8) Cone volume formula: V= 1/3*S*H (cone volume formula V= 1/3*pi*r2h).
(9) Oblique prism volume: V=S'L
(10) Cylinder volume formula: v = s * h；; Cylinder: V=pi*r2h.