Summarize the key formula of high school mathematics compulsory examination and ellipse circumference's calculation formula.

Ellipse circumference formula: L=2πb+4(a-b)

Ellipse circumference's Theorem: The circumference of an ellipse is equal to the circumference (2πb) of an ellipse with the radius of the short semi-axis length plus four times the difference between the long semi-axis length (a) and the short semi-axis length (b) of an ellipse.

Elliptic area calculation formula

Elliptic area formula: S=πab

Ellipse area theorem: the area of an ellipse is equal to π times the product of the major semi-axis length (a) and the minor semi-axis length (b) of an ellipse.

Although there is no ellipse πT in the above formula of ellipse circumference sum area, these two formulas are all derived from ellipse πT .. Constant is the body, so it can be used.

Formula for calculating the volume of an elliptical object Long radius * Short radius * Height of the ellipse

Trigonometric function:

Two-angle sum formula

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)

cot(A+B)=(cotA cotB- 1)/(cot B+cotA)cot(A-B)=(cotA cotB+ 1)/(cot B-cotA)

Double angle formula

tan2A = 2 tana/( 1-tan2A)cot2A =(cot2A- 1)/2 cota

cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a

sinα+sin(α+2π/n)+sin(α+2π* 2/n)+sin(α+2π* 3/n)+……+sin[α+2π*(n- 1)/n]= 0

Cos α+cos (α+2π/n)+cos (α+2π * 2/n)+cos (α+2π * 3/n)+...+cos [α+2π * (n-1)/n] = 0 and

sin^2(α)+sin^2(α-2π/3)+sin^2(α+2π/3)=3/2

tanAtanBtan(A+B)+tanA+tan B- tan(A+B)= 0

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))

cot(A/2)=√(( 1+cosA)/(( 1-cosA))cot(A/2)=-√(( 1+cosA)/(( 1-cosA))

Sum difference product

2 Sina cosb = sin(A+B)+sin(A-B)2 cosa sinb = sin(A+B)-sin(A-B)

2 cosa cosb = cos(A+B)-sin(A-B)-2 sinasinb = 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)/cosa cosb tanA-tanB = sin(A-B)/cosa cosb

cotA+cot bsin(A+B)/Sina sinb-cotA+cot bsin(A+B)/Sina sinb

The sum of the first n terms of some series

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

2+4+6+8+ 10+ 12+ 14+…+(2n)= n(n+ 1) 1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+…+n^2=n(n+ 1)(2n+ 1)/6

1^3+2^3+3^3+4^3+5^3+6^3+…n^3=(n(n+ 1)/2)^2 1 * 2+2 * 3+3 * 4+4 * 5+5 * 6+6 * 7+…+n(n+ 1)= n(n+ 1)(n+2)/3

Sine theorem a/sinA=b/sinB=c/sinC=2R Note: where r represents the radius of the circumscribed circle of a triangle.

Cosine Theorem b2=a2+c2-2accosB Note: Angle B is the included angle between side A and side C..

Multiplication and factorization A2-B2 = (a+b) (a-b) A3+B3 = (a+b) (A2-AB+B2) A3-B3 = (A-B (A2+AB+B2))

Trigonometric inequality | A+B |≤| A |+B||||| A-B|≤| A |+B || A |≤ B < = > -b≤a≤b

|a-b|≥|a|-|b| -|a|≤a≤|a|

The solution of the unary quadratic equation -b+√(b2-4ac)/2a -b-√(b2-4ac)/2a

The relationship between root and coefficient x1+x2 =-b/ax1* x2 = c/a Note: Vieta theorem.

Discriminant b2-4a=0 Note: The equation has two equal real roots.

B2-4ac > Note: The equation has two unequal real roots.

B2-4ac & lt； 0 Note: The equation has multiple yokes.

20 19 Summary of Key Formulas Required for Mathematics in College Entrance Examination

The standard equation of a circle (x-a)2+(y-b)2=r2 Note: (A, B) is the center coordinate.

General equation of circle x2+y2+Dx+Ey+F=0 Note: D2+E2-4f > 0

Parabolic standard equation y2=2px y2=-2px x2=2py x2=-2py

Lateral area of a straight prism S=c*h lateral area of an oblique prism s = c' * h.

Lateral area of a regular pyramid S= 1/2c*h' lateral area of a regular prism S= 1/2(c+c')h'

The lateral area of the frustum of a cone S = 1/2(c+c')l = pi(R+R)l The surface area of the ball S=4pi*r2.

Lateral area of cylinder S=c*h=2pi*h lateral area of cone s =1/2 * c * l = pi * r * l.

The arc length formula l=a*r a is the radian number r > of the central angle; 0 sector area formula s= 1/2*l*r

Conical volume formula V= 1/3*S*H Conical volume formula V= 1/3*pi*r2h

Oblique prism volume V=S'L Note: where s' is the straight cross-sectional area and l is the side length.

Cylinder volume formula V=s*h cylinder V=pi*r2h

Graphic perimeter area volume formula

The circumference of a rectangle = (length+width) ×2

Circumference of a square = side length ×4

Area of rectangle = length × width

Area of a square = side length × side length

Area of triangle

Given that the base of a triangle is h, then S=ah/2.

Given three sides A, B, C and half circumference P of a triangle, then S= √[p(p-a)(p-b)(p-c)] (Helen's formula) (p=(a+b+c)/2).

And: (a+b+c)*(a+b-c)* 1/4.