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Math Formulas

๐Ÿ“˜ Math Formulas โ€“ Complete Reference Guide

Welcome to the MathCity Formula Hub.
This page contains the most important mathematics formulas for Class 8, Class 9, and Class 10 students. Use this page as a quick revision sheet and follow the links to learn detailed explanations with solved examples.

๐Ÿ“Š 1. Algebra Formulas

๐Ÿ”น Laws of Exponents

amร—an=am+na^m \times a^n = a^{m+n}

aman=amโˆ’n\frac{a^m}{a^n} = a^{m-n}

(am)n=amn(a^m)^n = a^{mn}

a0=1a^0 = 1

๐Ÿ”น Algebraic Identities

(a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2

(aโˆ’b)2=a2โˆ’2ab+b2(a-b)^2 = a^2 – 2ab + b^2

a2โˆ’b2=(aโˆ’b)(a+b)a^2 – b^2 = (a-b)(a+b)

(a+b)(aโˆ’b)=a2โˆ’b2(a+b)(a-b) = a^2 – b^2

๐Ÿ”น Linear Equation Form

y = mx + b

Where:

  • m = slope of line
  • b = y-intercept

๐Ÿ”ต 2. Circle Formulas

๐Ÿ”น Circumference of a Circle

C=2ฯ€rC = 2\pi r

๐Ÿ”น Area of a Circle

A=ฯ€r2A = \pi r^2

๐Ÿ”น Diameter of a Circle

d = 2r

๐Ÿ”น Radius of a Circle

r=d2r = \frac{d}{2}

๐Ÿ”น Area of Semi-Circle

A=ฯ€r22A = \frac{\pi r^2}{2}

๐Ÿ”น Area of Sector

A=ฮธ360ร—ฯ€r2A = \frac{\theta}{360} \times \pi r^2

Where:

  • ฮธ = central angle in degrees

๐Ÿ“ˆ 3. Coordinate Geometry Formulas

๐Ÿ”น Distance Formula

d=(x2โˆ’x1)2+(y2โˆ’y1)2d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}

๐Ÿ”น Midpoint Formula

M=(x1+x22,y1+y22)M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)

๐Ÿ”น Slope of a Line

m=y2โˆ’y1x2โˆ’x1m = \frac{y_2 – y_1}{x_2 – x_1}

๐Ÿ”น Equation of a Line (Slope Form)

yโˆ’y1=m(xโˆ’x1)y\;-\;y_1\;=\;m\left(x\;-\;x_1\right)

๐Ÿ”น Standard Line Form

Ax + By + C = 0

๐Ÿ”ข 4. Integers Rules

๐Ÿ”น Addition Rules

(+)(+) = +

(โˆ’)(โˆ’) = +

(+)(โˆ’) = โˆ’

(โˆ’)(+) = โˆ’

๐Ÿ”น Multiplication Rule

Same signs โ†’ positive


Different signs โ†’ negative

๐Ÿ”น Division Rule

Same signs โ†’ positive


Different signs โ†’ negative

๐Ÿ” 5. Sequence Formulas

๐Ÿ”น Arithmetic Sequence nth Term

an=a1+(nโˆ’1)da_n=a_1\;+\;\left(n\;-\;1\right)\;d

Where:

  • aโ‚™ = nth term
  • aโ‚ = first term
  • d = common difference

๐Ÿ”น Sum of Arithmetic Sequence

Sn=n2[2a1+(nโˆ’1)d]S_n = \frac{n}{2} \left[ 2a_1 + (n – 1)d \right]

๐Ÿ“ 6. Factors & HCF/LCM

๐Ÿ”น HCF (Greatest Common Factor)

HCF = product of common prime factors

๐Ÿ”น LCM Formula (using prime factors)

LCM = product of highest powers of all prime factors

๐Ÿ”น Relationship

HCFร—LCM=Product of two numbers\text{HCF} \times \text{LCM} = \text{Product of two numbers}

๐Ÿ“š 7. Quick Revision Tips

  • Learn formulas first
  • Then understand examples
  • Then practice problems
  • Revise regularly

๐Ÿ”— Related Pages

๐Ÿง  IMPORTANT NOTE

This page is a quick reference guide only.
For step-by-step explanations and solved examples, visit the topic pages inside MathCity.