The key formula of senior high school mathematics: 1 complete works and the solution of quadratic equation in one variable.
-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.
2, three-dimensional graphics and plane graphics formula
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 = 2 pxy 2 =-2 pxy 2 = 2 pxy 2 =-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*ra 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
3, graphics 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.
Given the angle c between two sides a and b of a triangle, S=absinC/2.
Let the three sides of a triangle be A, B and C respectively, and the radius of the inscribed circle be R.
Then the triangle area =(a+b+c)r/2.
Let the three sides of a triangle be A, B and C respectively, and the radius of the circumscribed circle be R.
Triangle area =abc/4r.
Summary of common formulas in senior high school mathematics 1, 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)
2. 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
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))
cot(A/2)=√(( 1+cosA)/(( 1-cosA))cot(A/2)=-√(( 1+cosA)/(( 1-cosA))
4. 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
5. 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
6. Sine Theorem a/sinA=b/sinB=c/sinC=2R Note: where R represents the radius of the circumscribed circle of a triangle.
7. Cosine Theorem b2=a2+c2-2accosB Note: Angle B is the included angle between side A and side C..
8. Multiplication and factorization A2-B2 = (A+B) (A-B) A3+B3 = (A+B) (A2-AB+B2) A3-B3 = (A-B (A2+AB+B2))
9. Trigonometric inequality | A+B |≤| A |+B||||| A-B|≤| A |+B |||| A |≤ B-B≤ A ≤ B.
10 、|a-b|≥|a|-|b| -|a|≤a≤|a|
Solution of quadratic equation in one variable in all formulas of senior high school mathematics -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.
b2-4ac0
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