Here’s a concise list of essential math formulas across key topics:
Arithmetic
Sum of n natural numbers: S=n(n+1)2S = \frac{n(n+1)}{2}
Sum of squares: S=n(n+1)(2n+1)6S = \frac{n(n+1)(2n+1)}{6}
Sum of cubes: S=(n(n+1)2)2S = \left(\frac{n(n+1)}{2}\right)^2
Algebra
Quadratic formula: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
(a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2
(a−b)2=a2−2ab+b2(a-b)^2 = a^2 - 2ab + b^2
(a+b)(a−b)=a2−b2(a+b)(a-b) = a^2 - b^2
Geometry
Area of a rectangle: A=l×wA = l \times w
Area of a triangle: A=12×base×heightA = \frac{1}{2} \times base \times height
Area of a circle: A=πr2A = \pi r^2
Pythagoras theorem: a2+b2=c2a^2 + b^2 = c^2
Trigonometry
sin 2θ+cos 2θ=1\sin^2\theta + \cos^2\theta = 1
tan θ=sin θcos θ\tan\theta = \frac{\sin\theta}{\cos\theta}
Calculus
Derivative: ddx(xn)=n⋅xn−1\frac{d}{dx}(x^n) = n \cdot x^{n-1}
Integral: ∫xndx=xn+1n+1+C\int x^n dx = \frac{x^{n+1}}{n+1} + C
Let me know if you want specific formulas!
