Mathematical formula

Here are important mathematical formulas from various branches of mathematics, commonly used in school-level studies (especially class 6 to 12):



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🔢 Arithmetic / Number System


1. Even Number = 2n



2. Odd Number = 2n + 1



3. HCF × LCM = Product of two numbers



4. Average = Sum of observations ÷ Number of observations





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➕ Algebra


1. (a + b)² = a² + 2ab + b²



2. (a − b)² = a² − 2ab + b²



3. (a + b)(a − b) = a² − b²



4. a³ + b³ = (a + b)(a² − ab + b²)



5. a³ − b³ = (a − b)(a² + ab + b²)





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📐 Geometry


1. Area of Square = side²



2. Area of Rectangle = length × breadth



3. Area of Triangle = ½ × base × height



4. Area of Circle = πr²



5. Circumference of Circle = 2πr



6. Pythagoras Theorem = a² + b² = c² (right triangle)





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📊 Mensuration


1. Surface Area of Cube = 6a²



2. Surface Area of Cuboid = 2(lb + bh + hl)



3. Volume of Cube = a³



4. Volume of Cuboid = l × b × h



5. Volume of Cylinder = πr²h



6. Volume of Cone = (1/3)πr²h



7. Volume of Sphere = (4/3)πr³





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📈 Trigonometry (Class 10/11/12)


1. sin²θ + cos²θ = 1



2. tanθ = sinθ / cosθ



3. sec²θ − tan²θ = 1



4. cosec²θ − cot²θ = 1





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📉 Coordinate Geometry


1. Distance between (x₁, y₁) and (x₂, y₂) =

√[(x₂ − x₁)² + (y₂ − y₁)²]



2. Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)



3. Slope (m) = (y₂ − y₁) / (x₂ − x₁)





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🧮 Calculus (Class 11/12)


1. d/dx (xⁿ) = n·xⁿ⁻¹



2. ∫ xⁿ dx = xⁿ⁺¹ / (n + 1) + C



3. d/dx (sin x) = cos x



4. d/dx (cos x) = −sin x





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If you'd like formulas specific to a topic (e.g., class 10 algebra, trigonometry only, physics formulas, etc.), let me know!



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