General Math Formula Sheet Covering Key Topics

Algebra

• Quadratic Formula:x=−b±b2−4ac2ax=2a−b±b2−4ac​​
• Slope of a Line:m=y2−y1x2−x1m=x2​−x1​y2​−y1​​
• Point-Slope Form:y−y1=m(x−x1)y−y1​=m(x−x1​)
• Distance Formula:d=(x2−x1)2+(y2−y1)2d=(x2​−x1​)2+(y2​−y1​)2​

Geometry

• Area of a Circle:A=πr2A=πr2
• Circumference of a Circle:C=2πrC=2πr
• Pythagorean Theorem:a2+b2=c2a2+b2=c2
• Area of a Triangle:A=12bhA=21​bh
• Volume of a Sphere:V=43πr3V=34​πr3

Trigonometry

• Basic Trigonometric Ratios:sin⁡θ=oppositehypotenuse,cos⁡θ=adjacenthypotenuse,tan⁡θ=oppositeadjacentsinθ=hypotenuseopposite​,cosθ=hypotenuseadjacent​,tanθ=adjacentopposite​
• Pythagorean Identity:sin⁡2θ+cos⁡2θ=1sin2θ+cos2θ=1
• Law of Sines:asin⁡A=bsin⁡B=csin⁡CsinAa​=sinBb​=sinCc​
• Law of Cosines:c2=a2+b2−2abcos⁡Cc2=a2+b2−2abcosC

Calculus

• Derivative Rules:ddx[xn]=nxn−1,ddx[ex]=ex,ddx[ln⁡x]=1xdxd​[xn]=nxn−1,dxd​[ex]=ex,dxd​[lnx]=x1​
• Product Rule:ddx[uv]=u′v+uv′dxd​[uv]=u′v+uv′
• Quotient Rule:ddx[uv]=u′v−uv′v2dxd​[vu​]=v2u′v−uv′​
• Chain Rule:ddx[f(g(x))]=f′(g(x))⋅g′(x)dxd​[f(g(x))]=f′(g(x))⋅g′(x)
• Definite Integral:∫abf(x) dx=F(b)−F(a)∫ab​f(x)dx=F(b)−F(a)

Statistics

• Mean:Mean=∑xinMean=n∑xi​​
• Variance:σ2=∑(xi−μ)2nσ2=n∑(xi​−μ)2​
• Standard Deviation:σ=σ2σ=σ2​

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