Kenyan High School Math Formula Generator
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Pythagoras' Theorem: a² + b² = c²
Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a
Area of Circle: A = πr²
Circumference of Circle: C = 2πr
Area of Triangle: A = ½bh
Volume of Cylinder: V = πr²h
Slope of a Line: m = (y₂ - y₁) / (x₂ - x₁)
Distance Formula: d = √((x₂ - x₁)² + (y₂ - y₁)²)
Perimeter of Rectangle: P = 2(l + w)
Area of Rectangle: A = l × w
Surface Area of Sphere: A = 4πr²
Volume of Sphere: V = (4/3)πr³
Compound Interest: A = P(1 + r/n)^(nt)
Simple Interest: I = Prt
Area of Parallelogram: A = b × h
Area of Trapezium: A = ½(a + b)h
Law of Sines: (sinA/a) = (sinB/b) = (sinC/c)
Law of Cosines: c² = a² + b² - 2ab cos(C)
Midpoint Formula: M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Arithmetic Sequence: aₙ = a₁ + (n-1)d
Geometric Sequence: aₙ = a₁ × r^(n-1)
Area of Sector: A = ½r²θ
Perimeter of Circle: P = 2πr
Volume of Cone: V = (1/3)πr²h
Volume of Pyramid: V = (1/3)Bh
Surface Area of Cone: A = πr(r + √(r² + h²))
Surface Area of Cylinder: A = 2πr² + 2πrh
Derivative of Power Function: d/dx (xⁿ) = n * x^(n-1)
Integral of Power Function: ∫xⁿ dx = (x^(n+1))/(n+1) + C
Logarithmic Properties: logₐ(xy) = logₐ(x) + logₐ(y)
Law of Exponents: a^m × a^n = a^(m+n)
Sine Rule for Area of Triangle: A = ½ab sin(C)
Cosine Rule for Area of Triangle: A = √(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2
Sum of a Polynomial: Σ aₙxⁿ = a₀ + a₁x + a₂x² + ... + aₙxⁿ
Area of Ellipse: A = πab
Surface Area of Ellipsoid: A = 4π[(a²b + ab² + b²a)/3]^(1/2)
Factorial: n! = n × (n-1) × (n-2) × ... × 1
Binomial Theorem: (a+b)ⁿ = Σ (nCk) a^(n-k) b^k
Perimeter of Polygon: P = n × s
Expansion of Binomials: (a+b)² = a² + 2ab + b²
Area of Rhombus: A = (d₁d₂)/2
Area of Kite: A = (d₁d₂)/2
Circumference of Ellipse: C ≈ π[3(a + b) - √((3a + b)(a + 3b))]
Arc Length: L = rθ
Surface Area of Ellipsoid: A = 4π[(a²b + ab² + b²a)/3]^(1/2)
Volume of Ellipsoid: V = (4/3)πabc
Definite Integral: ∫ₐᵇ f(x)dx = F(b) - F(a)
Logarithmic Equations: logₐ(x) = logₐ(y) implies x = y
Matrix Multiplication: AB = C
Determinant of a Matrix: |A| = ad - bc
Sum of Angles in Polygon: (n-2) × 180°
Angle Between Two Lines: θ = tan⁻¹(|(m₁ - m₂)/(1 + m₁m₂)|)
Distance Between Point and Line: d = |Ax + By + C|/√(A² + B²)
Area of Circle Sector: A = (θ/360) × πr²
Volume of Frustum: V = (1/3)πh(r₁² + r₁r₂ + r₂²)
Surface Area of Frustum: A = π(r₁ + r₂) √(h² + (r₁ - r₂)²) + π(r₁² + r₂²)
Polar Coordinates: r = √(x² + y²), θ = tan⁻¹(y/x)
Complex Numbers: z = a + bi
Addition of Complex Numbers: (a + bi) + (c + di) = (a+c) + (b+d)i
General Law of Sines: (sinA/a) = (sinB/b) = (sinC/c)
Euler's Formula: e^(ix) = cos(x) + i sin(x)