HomeFactopediaBrainoffsRankingsCommunityLog In
You know 0 facts


Mathematical Formulae

Your overall rating on Mathematical Formulae =
0%
Your best rally score on Mathematical Formulae = 0 facts

Play Fact Master on Mathematical Formulae    

Challenge Friends to a Brainoff on Mathematical Formulae    

Play a Rally Game on Mathematical Formulae    



98 facts:

A^2 – B^2
   has the mathematical formula   
(a + B)(a – B)
Formula for factoring the difference of two squares
A^3 - B^3
   has the mathematical formula   
(a - B)(a^2 + Ab + B^2)
Formula for factoring the difference of two cubes
A^3 + B^3
   has the mathematical formula   
(a + B)(a^2 – Ab + B^2)
Formula for factoring the sum of two cubes
Arc Length of a Circle
   has the mathematical formula   
N/360(2Ï€r)
Where n= the number of degrees cut off by the arc of the circle and r=radius
Area of an Annulus
   has the mathematical formula   
Ï€(r^2 - R^2)
Where R=outer radius and r=inner radius of the annulus (washer)
Area of Any Regular Polygon
   has the mathematical formula   
½ Ap
Where a=apothem (distance from center to the midpoint of any side) and p= perimeter
Area of a Circle
   has the mathematical formula   
Ï€r^2
Where r=radius and π≈3.1415926
Area of an Ellipse
   has the mathematical formula   
Ï€ab
Where a=radius along the major axis and b=radius along the minor axis of the ellipse
Area of an Equilateral Triangle
   has the mathematical formula   
(s^2√3)/4
Where s=side of the triangle
Area of a Kite or Rhombus
   has the mathematical formula   
½ D1d2
Half the product of the diagonals
Area of a Parallelogram
   has the mathematical formula   
Bh
Where b=base and h=height
Area of a Rectangle
   has the mathematical formula   
Bh
Where b=base and h=height
Area of a Regular Hexagon
   has the mathematical formula   
6(s^2√3)/4
Where s=side of the hexagon
Area of a Sector
   has the mathematical formula   
N/360 (Ï€r^2)
Where n= number of degrees the circle’s sector covers, and r= radius … a sector looks like a piece of pie or slice of pizza
Area of a Square
   has the mathematical formula   
(side)^2
Area of a Trapezoid
   has the mathematical formula   
½ (b1 + B2)h
The 2 parallel bases and the height
Area of a Triangle
   has the mathematical formula   
½ Bh
Where b=base and h=height
Area of a Triangle (given 2 Sides & the Included Angle)
   has the mathematical formula   
½ Absinc
Learned in trigonometry
Area of a Triangle (only the 3 Sides Given)
   has the mathematical formula   
√[s(s-a)(s-b)(s-c)]
– where the 3 sides are a, b, and c … and s=semiperimeter=(a+b+c)/2 … heron’s formula
Associative Property of Addition
   has the mathematical formula   
A + (b + C) = (a + B) + C
Notice the only change is the variable that “b” associates with
Associative Property of Multiplication
   has the mathematical formula   
A(bc) = (ab)c
Notice the only change is the variable that “b” associates with
Central Angle of Any Regular Polygon
   has the mathematical formula   
360/n
Where n=number of sides of the regular polygon
Circumference of a Circle
   has the mathematical formula   
2Ï€r
Or alternatively C=πd, where r=radius, d=diameter and π≈3.1415926
Commutative Property of Addition
   has the mathematical formula   
A + (b + C) = (b + C) + a
Think of “commuters” as the terms are actually moving about
Commutative Property of Multiplication
   has the mathematical formula   
A X B X C = a X C X B
Think of “commuters” as the terms are actually moving about
Cos2θ
   has the mathematical formula   
(cosθ)^2 - (sinθ)^2
Double angle formula for cosine
Cos(a + B)
   has the mathematical formula   
Cosacosb – Sinasinb
Formula for the cosine of a sum
Cos(a – B)
   has the mathematical formula   
Cosacosb + Sinasinb
Formula for the cosine of a difference
Cosecant Ratio (cscθ)
   has the mathematical formula   
Hypotenuse/opposite Side
Only applies to right triangles, and θ must be one of the 2 acute angles
Cosine Ratio (cosθ)
   has the mathematical formula   
Adjacent Side/hypotenuse
Only applies to right triangles, and θ must be one of the 2 acute angles
Cotangent Ratio (cotθ)
   has the mathematical formula   
Adjacent Side/opposite Side
Only applies to right triangles, and θ must be one of the 2 acute angles
Diagonal of a Rectangular Prism
   has the mathematical formula   
√(l^2 + W^2 + H^2)
Where l, w, and h are the length, width and height of the Prism respectively (this formula finds the longest item you can ship in any box)
Distance Formula Between 2 Points on a Plane
   has the mathematical formula   
√[(x2 – X1)^2 + (y2 – Y1)^2]
Where the 2 points are (x1, y1) and (x2, y2)
Distributive Property
   has the mathematical formula   
A(b + C) = Ab + Ac
Eccentricity of Any Conic Section
   has the mathematical formula   
E=c/a
Where c=focal radius and a= vertex radius
Equation of Any Horizontal Line
   has the mathematical formula   
Y = #
Equation of Any Vertical Line
   has the mathematical formula   
X = #
Equation of a Circle
   has the mathematical formula   
(x – H)^2 + (y – K)^2 = R^2
Where (h,k)=center of the circle, and r=radius
Equation of an Ellipse
   has the mathematical formula   
(x – H)^2/ A^2 + (y – K)^2/ B^2 = 1
Where (h,k)=center, a=semi-major axis length, and b=semi-minor axis length
Equation of a Hyperbola
   has the mathematical formula   
(x – H)^2/ A^2 - (y – K)^2/ B^2 = 1
Where (h,k)=center, a=semi-transverse axis length, and b=semi-conjugate axis length
Final Population (after a Decay Period)
   has the mathematical formula   
Po(1 - R)^t
Where Po = original population, r=growth rate and t=time
Final Population (after a Growth Period)
   has the mathematical formula   
Po(1 + R)^t
Where Po = original population, r=growth rate and t=time
Final Value With Interest Compounded Continuously
   has the mathematical formula   
Pe^(rt)
Where P=principle, r=rate, t=time, and e≈2.71828
Final Value With Interest Compounded Periodically
   has the mathematical formula   
P(1 + R/n)^(nt)
Where p=principle, r=rate, t=time, and n=the number of periods (times) compounded per year
Formula for Motion Word Problems
   has the mathematical formula   
R X T = D
Where R=rate, T=time and D=distance
Lateral Area of a Cone
   has the mathematical formula   
Ï€rl
Where r=radius and l=slant height of the cone
Lateral Area of a Cube
   has the mathematical formula   
4e^2
Where e=edge of the cube
Lateral Area of a Cylinder
   has the mathematical formula   
2Ï€rh
Where r=radius and h=height of the cylinder
Lateral Area of a Prism
   has the mathematical formula   
Ph
Where p=perimeter of the base, and h=height of the prism
Lateral Area of a Pyramid
   has the mathematical formula   
1/2pl
Where p=perimeter of the base and l=the slant height
Law of Cosines
   has the mathematical formula   
A^2 = B^2 + C^2 – 2bc(cosa)
Helpful in solving non-right triangles given SSS or SAS
Law of Sines
   has the mathematical formula   
Sina/a = Sinb/b = Sinc/c
Helpful in solving non-right triangles given ASA, SSA, or AAS
Measure of Each Exterior Angle of a Regular Polygon
   has the mathematical formula   
360/n
Where n=number of sides of the regular polygon
Measure of Each Interior Angle of a Regular Polygon
   has the mathematical formula   
(n – 2)180/n
Where n=number of sides of the regular polygon
Midpoint Formula
   has the mathematical formula   
[(x1 + X2)/2 , (y1 + Y2)/2]
Where the 2 endpoints are (x1, y1) and (x2, y2)
N!
   has the mathematical formula   
N (n-1) (n-2) (n-3) … 3 X 2 X 1
This computes “n factorial”
Number of Diagonals in Any Regular Polygon
   has the mathematical formula   
N(n-3)/2
Where n=number of sides of the regular polygon
Point-slope Form of a Line
   has the mathematical formula   
Y – Y1 = M(x - X2)
Pythagorean Theorem
   has the mathematical formula   
A^2 + B^2 = C^2
One of the cornerstone formulas of Geometry, where a & b are the legs of a right triangle and c= the hypotenuse of the right triangle
Pythagorean Trig Identity
   has the mathematical formula   
(cosθ)^2 + (sinθ)^2 = 1
A staple in the trig student's arsenal
Pythagorean Trig Identity (divided by Cos2θ)
   has the mathematical formula   
1 + (tanθ)^2 = (secθ)^2
Another key trig formula
Pythagorean Trig Identity (divided by Sin2θ)
   has the mathematical formula   
(cotθ)^2 + 1 = (cscθ)^2
Another key trig formula
Quadratic Formula
   has the mathematical formula   
[-b ± √( B^2 – 4ac)] / 2a
This cornerstone formula of algebra solves any quadratic equation of the form ax2 + bx + c
Raioactive Half-life Formula
   has the mathematical formula   
A=ao(1/2)^(t/h)
Where Ao = original amount, t=time, and H=half-life time period
Secant Ratio (secθ)
   has the mathematical formula   
Hypotenuse/adjacent Side
Only applies to right triangles, and θ must be one of the 2 acute angles
Simple Interest
   has the mathematical formula   
P X R X T
Computes interest given P=principle, r=rate and t=time(in years)
Sin2θ
   has the mathematical formula   
2sinθcosθ
Double angle formula for sine
Sin(a + B)
   has the mathematical formula   
Sinacosb + Cosasinb
Formula for the sine of a sum
Sin(a – B)
   has the mathematical formula   
Sinacosb – Cosasinb
Formula for the sine of a difference
Sine Ratio (sinθ)
   has the mathematical formula   
Opposite Side/hypotenuse
Only applies to right triangles, and θ must be one of the 2 acute angles
Slope-intercept Form of a Line
   has the mathematical formula   
Y = Mx + B
Where m=slope and b= the y-intercept of the line
Slope of a Line
   has the mathematical formula   
(y2 – Y1) / (x2 – X1)
Where the 2 points are (x1, y1) and (x2, y2)
Specific Term of Any Arithmetic Sequence
   has the mathematical formula   
A1 + (n-1)d
Where a1=first term, n=number of terms and d=common difference between terms
Specific Term of Any Geometric Sequence
   has the mathematical formula   
A1(r)^(n – 1)
Where a1=first term, r=common ratio between terms and n=number of terms
Standard Form of a Line
   has the mathematical formula   
Ax + by = C
Sum of the Angles in a Triangle
   has the mathematical formula   
180
It’s curious to note that in non-Euclidean Geometry, the same sum will be either < 180 or > 180, but never = 180
Sum of Any Arithmetic Series
   has the mathematical formula   
N/2 (a1 + An)
Where n=number of terms, a1=first term, and an=nth (or last) term
Sum of Any Geometric Series
   has the mathematical formula   
A1(1 – R^n)/(1 – R)
Where a1=first term, r=common ratio between terms and n=number of terms
Sum of the Exterior Angles of Any Polygon
   has the mathematical formula   
360
An interesting constant
Sum of an Infinite Geometric Series
   has the mathematical formula   
A1/(1-r)
Where a1 =first term and r=common ratio between terms
Sum of the Interior Angles of Any Polygon
   has the mathematical formula   
(n – 2)180
Where n=number of sides of the polygon
Surface Area of a Cone
   has the mathematical formula   
πr^2 + πrl
Where r=radius, and l=slant height
Surface Area of a Cube
   has the mathematical formula   
6e^2
Where e=edge of the cube
Surface Area of a Cylinder
   has the mathematical formula   
2Ï€rh + 2Ï€r^2
Where r=radius, and h=height
Surface Area of a Prism
   has the mathematical formula   
Ph + 2b
Where p=perimeter, h=height and B=Base Area
Surface Area of a Pyramid
   has the mathematical formula   
B + 1/2pl
Where B=base area, p=perimeter of the base, and l=slant height
Surface Area of a Sphere
   has the mathematical formula   
4Ï€r^2
Where r=radius of the sphere
Tan2θ
   has the mathematical formula   
Tan2θ/(1 – Tan2θ)
Double angle formula for tangent
Tangent Ratio (tanθ)
   has the mathematical formula   
Opposite Side/adjacent Side
Only applies to right triangles, and θ must be one of the 2 acute angles
Vertex of a Parabola
   has the mathematical formula   
(-b/2a , F(-b/2a))
Where the parabola is of the form y=ax^2 + bx + c
Volume of a Cone
   has the mathematical formula   
1/3(Ï€r^2h)
Where r=radius of the cone’s base and h=height of the cone … notice that solids that come to a pointed top have one-third the volume of their 2-based counterparts (cylinders)
Volume of a Cube
   has the mathematical formula   
E^3
Where e=edge of the cube
Volume of a Cylinder
   has the mathematical formula   
Ï€r^2h
Where r=radius of the cylinder’s base circle and h=height of the cylinder
Volume of a Hemisphere
   has the mathematical formula   
2/3(Ï€r^3)
Where r=radius of the hemisphere
Volume of a Prism
   has the mathematical formula   
Bh
Where B=area of the base of the prism, and h=height of the prism
Volume of a Pyramid
   has the mathematical formula   
1/3(bh)
Where B=area of the base of the pyramid, and h=height of the pyramid … notice that solids that come to a pointed top have one-third the volume of their 2-based counterparts (prisms)
Volume of a Rectangular Prism
   has the mathematical formula   
Lwh
Where l=length, w=width and h=height … Rectangular Prism is “math” for box
Volume of a Sphere
   has the mathematical formula   
4/3(Ï€r^3)
Where r = radius of the sphere


Facts contributed by:


mathdrew








   About - Terms - Privacy Log In