Mathematics Formula Sheet

Area and Circumference

• Trapezoid Area:

  • Formula:
    [ A = \frac{(b1 + b2) h}{2} ]
  • A = area
  • b₁, b₂ = lengths of the two bases
  • h = height

• Circle:

  • Circumference:
    [ C = 2\pi r ]
  • C = circumference
  • r = radius
  • Area:
    [ A = \pi r^2 ]

Volume

• Pyramid/Cone:

  • Formula:
    [ V = \frac{1}{3} Bh ]
  • V = volume
  • B = area of the base
  • h = height

• Sphere:

  • Volume:
    [ V = \frac{4}{3} \pi r^3 ]
  • r = radius of the sphere

Pythagorean Theorem and Trigonometric Ratios

• Pythagorean Theorem:

  • Formula:
    [ a^2 + b^2 = c^2 ]
  • c = hypotenuse (longest side of a right triangle)
  • a and b = lengths of the other two sides

• Trigonometric Ratios:

  • Sine:
    [ \sin B = \frac{b}{c} ]
  • Cosine:
    [ \cos B = \frac{a}{c} ]
  • Tangent:
    [ \tan B = \frac{a}{b} ]

Points in the Plane

• Points
  • Given two points ((x1, y1)) and ((x2, y2)) in the plane:
  • Distance:
    [ D = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} ]
  • Midpoint:
    [ M = \left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right) ]

Quadratic Equations

• Standard Form:
  • Form:
    [ ax^2 + bx + c = 0 ]
  • Quadratic Formula:
    [ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

Combinations and Permutations

• Combinations

  • Notation: ( C(k, m) ):
  • Formula:
    [ C(k, m) = \frac{k!}{m!(k - m)!} ]
  • k = number of objects in the set
  • m = number of objects selected

• Permutations

  • Notation: ( P(k, m) ):
  • Formula:
    [ P(k, m) = \frac{k!}{(k - m)!} ]
  • k = number of objects in the set
  • m = number of objects arranged