Here are some common math formulas that cover various mathematical concepts:
- Geometry Formulas:
- Area of a Rectangle: A = length × width
- Area of a Triangle: A = 1/2 × base × height
- Area of a Circle: A = πr² (where r is the radius)
- Circumference of a Circle: C = 2πr
- Volume of a Cube: V = side³
- Volume of a Cylinder: V = πr²h (where r is the base radius and h is the height)
- Algebra Formulas:
- Quadratic Formula: x = (-b ± √(b² - 4ac)) / (2a)
- Slope of a Line: m = (y₂ - y₁) / (x₂ - x₁)
- Distance Formula: d = √((x₂ - x₁)² + (y₂ - y₁)²)
- Binomial Theorem: (a + b)ⁿ = Σ [C(n, k) * a^(n-k) * b^k], where Σ is the sum from k = 0 to n, and C(n, k) is the binomial coefficient.
- Trigonometry Formulas:
- Sine Rule: a/sin(A) = b/sin(B) = c/sin(C)
- Cosine Rule: a² = b² + c² - 2bc * cos(A)
- Tangent Identity: tan(θ) = sin(θ) / cos(θ)
- Calculus Formulas:
- Derivative of a Function (f'(x)): It depends on the function and can involve rules like the power rule, product rule, and chain rule.
- Integral of a Function (∫f(x) dx): It also depends on the function and involves techniques like integration by parts, substitution, etc.
- Probability and Statistics Formulas:
- Mean (Average): μ = Σx / N (where Σx is the sum of all values and N is the number of values)
- Standard Deviation: σ = √[Σ(xi - μ)² / N] (where xi is each data point)
- Probability of an Event: P(A) = (Number of favorable outcomes) / (Total number of possible outcomes)
- Logarithmic and Exponential Formulas:
- Logarithm Rules: Log(a * b) = Log(a) + Log(b), Log(a / b) = Log(a) - Log(b), Log(a^n) = n * Log(a)
- Exponential Growth: A = P(1 + r/n)^(nt), where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
These are just a few examples of mathematical formulas. The specific formulas you need may vary depending on the math topic you're studying or the problem you're trying to solve. If you have a specific math concept or formula you'd like to know more about, please feel free to ask!
