Aptitude

📘 Complete Maths Formula Notes

Simplification

BODMAS → Bracket → Of → Division → Multiplication → Addition → Subtraction

Number System

Even Numbers = 2n

Odd Numbers = 2n + 1

Sum of n Natural Numbers = n(n+1)/2

Sum of Squares = n(n+1)(2n+1)/6

Sum of Cubes = (n(n+1)/2)²

LCM × HCF = Product of Numbers

Percentages

Percentage = (Value / Total) × 100

Increase % = (Increase / Original) × 100

Decrease % = (Decrease / Original) × 100

New Value = Original × (1 + x/100)

Successive Change = a + b + (ab/100)

Average

Average = Sum of Observations / Number

Total = Average × Number

Combined Average = (n₁a₁ + n₂a₂)/(n₁ + n₂)

Profit & Loss

Profit = SP − CP

Loss = CP − SP

Profit % = (Profit / CP) × 100

Loss % = (Loss / CP) × 100

SP = CP (1 + Profit/100)

SP = CP (1 − Loss/100)

Discount = MP − SP

Interest

Simple Interest = (P × R × T) / 100

Amount = Principal + Interest

Compound Amount = P(1 + R/100)^T

Compound Interest = Amount − Principal

Speed Time Distance

Speed = Distance / Time

Distance = Speed × Time

Time = Distance / Speed

Relative Speed (same direction) = S₁ − S₂

Relative Speed (opposite direction) = S₁ + S₂

Algebraic Identities

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab + b²

(a + b)(a − b) = a² − b²

(a + b)³ = a³ + b³ + 3ab(a + b)

a³ + b³ = (a + b)(a² − ab + b²)

Coordinate Geometry

Distance = √((x₂ − x₁)² + (y₂ − y₁)²)

Midpoint = ((x₁+x₂)/2 , (y₁+y₂)/2)

Mensuration

Rectangle Area = l × b

Square Area = a²

Circle Area = πr²

Cylinder Volume = πr²h

Sphere Volume = 4/3 πr³

Cone Volume = 1/3 πr²h

Maths Quick Revision Notes