Math Equations

1) Coordinate Geometry

• Equation of a Line y = mx + b
• Slope m = (y₂ - y₁) / (x₂ - x₁)
• Perpendicular Slope -1 / m where m is the original slope.
• Reflection of a Line y = -mx - b where original equation is y = mx + b
• Midpoint ((x₂ + x₁) / 2, (y₂ + y₁) / 2)
• Distance d = ((y₂ - y₁)² + (x₂ - x₁)²)^(1/2)

2) Plane Geometry

• Area of a Triangle A = 1/2 * b * h
• Pythagorean Theorem c² = a² + b²
• 30-60-90 Relationship 1 : √3 : 2
• 45-45-90 Relationship 1 : 1 : √2
• Area of a Circle A = πr²
• Circumference of a Circle C = 2πr
• Sector proportion θ / 360 = Sector Area / Circle's Area =
  Arc Length / Circle's Circumference.
• Area of a Parallelogram A = b * h
• Number of degrees in a Polygon with n sides Degrees = (n - 2) * 180

3) Algebra

• PEMDAS Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
• Powers (MADS)
  • x² * x³ = x⁵
  • x⁵ / x² = x³
  • (x²)³ = x⁶

4) Arithmetic

• Average Average = Total / Number of elements.
• Rate Rate = Distance / Time.
• Average Speed Average speed = Total distance / Total Time.
• Percent Change Percent Change = Change / Starting value.

5) Probability

• General Probability Prob = Desired outcomes / Total Outcomes.
• Probability of one event OR another Probability of a or b = Prob of a + Prob of b.
• Probability of one event AND another Probability of a and b = Prob of a * Prob of b.
• Combination nCr = n! / (r!(n - r)!)
• Permutation nPr = n! / (n - r)!

6) Sequences

• Arithmetic Sequence t_n = t₁ + D(n - 1)
• Geometric Sequence t_n = t₁ * R^{(n - 1)}