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# Mathematical Formulae

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 A^2 â€“ B^2 has the mathematical formula (a + B)(a â€“ 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 â€“ 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 Â½ 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 Ï€â‰ˆ3.1415926
 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^2âˆš3)/4
Where s=side of the triangle
 Area of a Kite or Rhombus has the mathematical formula Â½ 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^2âˆš3)/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 circleâ€™s sector covers, and r= radius â€¦ 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 Â½ (b1 + B2)h
The 2 parallel bases and the height
 Area of a Triangle has the mathematical formula Â½ Bh
Where b=base and h=height
 Area of a Triangle (given 2 Sides & the Included Angle) has the mathematical formula Â½ Absinc
Learned in trigonometry
 Area of a Triangle (only the 3 Sides Given) has the mathematical formula âˆš[s(s-a)(s-b)(s-c)]
â€“ where the 3 sides are a, b, and c â€¦ and s=semiperimeter=(a+b+c)/2 â€¦ heronâ€™s formula
 Associative Property of Addition has the mathematical formula A + (b + C) = (a + B) + C
Notice the only change is the variable that â€œbâ€ associates with
 Associative Property of Multiplication has the mathematical formula A(bc) = (ab)c
Notice the only change is the variable that â€œbâ€ 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=Ï€d, where r=radius, d=diameter and Ï€â‰ˆ3.1415926
 Commutative Property of Addition has the mathematical formula A + (b + C) = (b + C) + a
Think of â€œcommutersâ€ 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 â€œcommutersâ€ as the terms are actually moving about
 Cos2Î¸ has the mathematical formula (cosÎ¸)^2 - (sinÎ¸)^2
Double angle formula for cosine
 Cos(a + B) has the mathematical formula Cosacosb â€“ Sinasinb
Formula for the cosine of a sum
 Cos(a â€“ B) has the mathematical formula Cosacosb + Sinasinb
Formula for the cosine of a difference
 Cosecant Ratio (cscÎ¸) has the mathematical formula Hypotenuse/opposite Side
Only applies to right triangles, and Î¸ must be one of the 2 acute angles
 Cosine Ratio (cosÎ¸) has the mathematical formula Adjacent Side/hypotenuse
Only applies to right triangles, and Î¸ must be one of the 2 acute angles
 Cotangent Ratio (cotÎ¸) has the mathematical formula Adjacent Side/opposite Side
Only applies to right triangles, and Î¸ must be one of the 2 acute angles
 Diagonal of a Rectangular Prism has the mathematical formula âˆš(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 âˆš[(x2 â€“ X1)^2 + (y2 â€“ 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 â€“ H)^2 + (y â€“ K)^2 = R^2
Where (h,k)=center of the circle, and r=radius
 Equation of an Ellipse has the mathematical formula (x â€“ H)^2/ A^2 + (y â€“ 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 â€“ H)^2/ A^2 - (y â€“ 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 eâ‰ˆ2.71828
 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 â€“ 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 â€“ 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) â€¦ 3 X 2 X 1
This computes â€œn factorialâ€
 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 â€“ 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 (cosÎ¸)^2 + (sinÎ¸)^2 = 1
A staple in the trig student's arsenal
 Pythagorean Trig Identity (divided by Cos2Î¸) has the mathematical formula 1 + (tanÎ¸)^2 = (secÎ¸)^2
Another key trig formula
 Pythagorean Trig Identity (divided by Sin2Î¸) has the mathematical formula (cotÎ¸)^2 + 1 = (cscÎ¸)^2
Another key trig formula
 Quadratic Formula has the mathematical formula [-b Â± âˆš( B^2 â€“ 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 (secÎ¸) has the mathematical formula Hypotenuse/adjacent Side
Only applies to right triangles, and Î¸ 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)
 Sin2Î¸ has the mathematical formula 2sinÎ¸cosÎ¸
Double angle formula for sine
 Sin(a + B) has the mathematical formula Sinacosb + Cosasinb
Formula for the sine of a sum
 Sin(a â€“ B) has the mathematical formula Sinacosb â€“ Cosasinb
Formula for the sine of a difference
 Sine Ratio (sinÎ¸) has the mathematical formula Opposite Side/hypotenuse
Only applies to right triangles, and Î¸ 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 â€“ Y1) / (x2 â€“ 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 â€“ 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
Itâ€™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 â€“ R^n)/(1 â€“ 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 â€“ 2)180
Where n=number of sides of the polygon
 Surface Area of a Cone has the mathematical formula Ï€r^2 + Ï€rl
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
 Tan2Î¸ has the mathematical formula Tan2Î¸/(1 â€“ Tan2Î¸)
Double angle formula for tangent
 Tangent Ratio (tanÎ¸) has the mathematical formula Opposite Side/adjacent Side
Only applies to right triangles, and Î¸ 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 coneâ€™s base and h=height of the cone â€¦ 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 cylinderâ€™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 â€¦ 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 â€¦ Rectangular Prism is â€œmathâ€ for box
 Volume of a Sphere has the mathematical formula 4/3(Ï€r^3)
Where r = radius of the sphere

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Facts contributed by:

 mathdrew

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