Essential Business Math Formulas & Concepts

Posted on Jun 28, 2025 in Mathematics

Applied Business Mathematics Formulas

1. Polynomials, Exponents, and Roots

Exponent Rules:

  • am ⋅ an = am+n
  • (am)n = am⋅n
  • a-n = 1/an
  • am/an = am-n

Factoring Techniques:

  • Common Factor: ab + ac = a(b + c)
  • Difference of Squares: a2 – b2 = (a – b)(a + b)
  • Quadratic Factorization: ax2 + bx + c = (px + q)(rx + s)

Quadratic Formula:

x = (-b ± √(b2 – 4ac)) / 2a

Example: Solving Quadratic Equations

  • Solve x2 – 5x + 6 = 0
  • Using the quadratic formula:
    • x = (-(-5) ± √((-5)2 – 4(1)(6))) / 2(1)
    • x = (5 ± 1) / 2
    • Solutions: x = 3, x = 2

2. Set Theory Fundamentals

Set Notation:

  • Union: A ∪ B (Elements in A or B)
  • Intersection: A ∩ B (Elements in both A and B)
  • Complement: Ac (Elements not in A)
  • Cartesian Product: A × B (Pairs (a,b) with a ∈ A, b ∈ B)

Example: Set Operations

If A = {1,2,3}, B = {3,4,5}, then:

  • A ∪ B = {1,2,3,4,5}
  • A ∩ B = {3}

3. Sequences and Series

Arithmetic Sequences:

an = a1 + (n-1)d

  • Sum: Sn = n/2 (a1 + an)

Example: Sum of Arithmetic Series

  • Find sum of first 5 terms of 2, 4, 6, 8, 10
  • S5 = 5/2 (2 + 10) = 30

Geometric Sequences:

an = a1 ⋅ r(n-1)

  • Sum: Sn = a1(1 – rn) / (1 – r), |r| < 1

4. Interest and Amortization

Simple Interest:

A = P(1 + rt)

Compound Interest:

A = P(1 + r/n)nt

Amortization Formula:

A = Pr(1+r)n / ((1+r)n – 1)

Example: Future Value Calculation

Find the future value of 100€ at 4% interest over 3 years.

  • A = 100(1 + 0.04/2)6
  • Approximately 112.61€

5. Limits and Functions

Limit Laws:

  • limx→a [f(x) + g(x)] = limx→a f(x) + limx→a g(x)
  • limx→a [f(x)g(x)] = limx→a f(x) ⋅ limx→a g(x)

Example: Evaluating Limits

  • Find limx→3 (x2 – 9) / (x – 3)
  • Factor: (x – 3)(x + 3) / (x – 3)
  • Cancel: Result: 6

6. Differentiation Principles

Differentiation Rules:

  • Power Rule: d/dx xn = nxn-1
  • Product Rule: (uv)’ = u’v + uv’
  • Quotient Rule: (u/v)’ = (u’v – uv’) / v2
  • Chain Rule: (f(g(x)))’ = f'(g(x))g'(x)

Example: Applying Power Rule

  • Find d/dx (x3 + 2x)
  • 3x2 + 2

7. Optimization and Extreme Values

Critical Points:

  • f'(x) = 0

Optimization Tests:

  • First Derivative Test: If f'(x) changes sign → max/min
  • Second Derivative Test: f”(x) > 0 (min), f”(x) < 0 (max)

Example: Finding Maximum Value

  • Find the maximum of f(x) = -x2 + 4x – 3
  • f'(x) = -2x + 4, solve -2x + 4 = 0, x = 2
  • f”(x) = -2 (negative, so maximum at x = 2)
  • f(2) = -22 + 4(2) – 3 = 1, maximum is 1