Shortcut Formulas for Exams

Shortcut Formulas for Exams
Shortcut Formulas for Exams

📘 Mathematics Formulas

  • (a + b)² = a² + b² + 2ab
  • (a - b)² = a² + b² - 2ab
  • (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
  • (a + b)³ = a³ + b³ + 3ab(a + b)
  • a³ + b³ = (a + b)(a² - ab + b²)
  • a³ - b³ = (a - b)(a² + ab + b²)
  • (x + 1/x)² = x² + 2 + 1/x²
  • Average = (Sum of all terms) / (Number of terms)
  • Simple Interest = (P × R × T) / 100
  • Compound Interest = P(1 + R/100)ⁿ – P

📐 Geometry & Mensuration

  • Area of Rectangle = l × b
  • Area of Square = side²
  • Area of Circle = πr²
  • Circumference of Circle = 2πr
  • Area of Triangle = ½ × base × height
  • Volume of Cube = a³
  • Volume of Cuboid = l × b × h
  • Volume of Cylinder = πr²h
  • Volume of Cone = (1/3)πr²h
  • Volume of Sphere = (4/3)πr³

💹 Percentage, Profit & Loss

  • Percentage = (Value / Total) × 100
  • Profit = Selling Price – Cost Price
  • Loss = Cost Price – Selling Price
  • Profit % = (Profit / Cost Price) × 100
  • Loss % = (Loss / Cost Price) × 100
  • Discount % = (Marked – Selling) × 100 / Marked
  • Selling Price = (100 + Profit%) × Cost Price / 100
  • Cost Price = (100 × Selling Price) / (100 + Profit%)

🔢 Number Series & Simplification

  • Square of 1–30 (1²=1, 2²=4, 3²=9 ...)
  • Cube of 1–20 (1³=1, 2³=8, 3³=27 ...)
  • (a+b)(a−b)=a²−b²
  • (x+y+z)² = x²+y²+z²+2(xy+yz+zx)
  • Divisibility Rule of 2: Last digit even
  • Divisibility Rule of 3: Sum of digits divisible by 3
  • Divisibility Rule of 5: Last digit 0 or 5
  • LCM × HCF = Product of Numbers

🧠 Reasoning Shortcuts

  • Alphabet position: A=1, Z=26
  • Opposite letter: (27 – position)
  • Clock angle = (30×hour – 11/2×minutes)
  • Mirror Image → Left ↔ Right reversal
  • Blood Relation → Apply Generation Tree
  • Ranking → Use left/right total formula

💻 Computer Awareness

  • 1 Byte = 8 Bits
  • 1 KB = 1024 Bytes
  • 1 MB = 1024 KB
  • 1 GB = 1024 MB
  • Binary of 1 = 0001
  • Binary of 10 = 1010
  • MS Word shortcut: Ctrl + S = Save
  • MS Excel shortcut: Ctrl + Shift + L = Filter
  • CPU = Central Processing Unit
  • ROM = Read Only Memory

🌍 General Knowledge (Static)

  • National Animal: Tiger
  • National Bird: Peacock
  • National Flower: Lotus
  • National Anthem: Jana Gana Mana
  • Currency of Japan: Yen
  • Capital of France: Paris
  • World’s Longest River: Nile
  • Largest Ocean: Pacific Ocean
  • Smallest Continent: Australia