Formula

📘 Complete Math Formula Book

Select Topic Arithmetic Algebra Geometry Mensuration Trigonometry Probability Permutation & Combination Statistics Logarithm Coordinate Geometry

Arithmetic

Percentage \( = \frac{Part}{Whole}×100 \)

Profit \( = SP - CP \)

Simple Interest \( = \frac{P×R×T}{100} \)

Average \( = \frac{\sum x}{n} \)

Algebra

\( (a+b)^2 = a^2+2ab+b^2 \)

\( (a-b)^2 = a^2-2ab+b^2 \)

Quadratic \( ax^2+bx+c=0 \)

Roots \( = \frac{-b\pm\sqrt{b^2-4ac}}{2a} \)

Geometry

Triangle Area \( = \frac{1}{2}bh \)

Pythagoras \( a^2+b^2=c^2 \)

Circle Area \( = \pi r^2 \)

Mensuration

Cube Volume \( = a^3 \)

Cuboid Volume \( = lbh \)

Sphere Volume \( = \frac{4}{3}\pi r^3 \)

Cylinder Volume \( = \pi r^2 h \)

Trigonometry

\( \sin^2\theta + \cos^2\theta = 1 \)

\( \tan\theta = \frac{\sin\theta}{\cos\theta} \)

\( 1+\tan^2\theta=\sec^2\theta \)

Probability

\( P(A)=\frac{Favourable}{Total} \)

\( P(A')=1-P(A) \)

\( P(A\cup B)=P(A)+P(B)-P(A\cap B) \)

Permutation & Combination

\( ^nP_r=\frac{n!}{(n-r)!} \)

\( ^nC_r=\frac{n!}{r!(n-r)!} \)

Circular \( (n-1)! \)

Statistics

Mean \( = \frac{\sum x}{n} \)

Variance \( = \frac{\sum (x-\bar{x})^2}{n} \)

SD \( = \sqrt{Variance} \)

Logarithm

\( \log(ab)=\log a+\log b \)

\( \log(a^n)=n\log a \)

Change Base \( \frac{\log b}{\log a} \)

Coordinate Geometry

Distance \( = \sqrt{(x2-x1)^2+(y2-y1)^2} \)

Slope \( = \frac{y2-y1}{x2-x1} \)

Line \( y=mx+c \)