Mathematics Cheat Sheets

Instant access to vital formulas from Class 8 to Class 12.

Algebraic Identities
  • Square of a Sum (a + b)² = a² + 2ab + b²
  • Square of a Difference (a - b)² = a² - 2ab + b²
  • Difference of Squares a² - b² = (a - b)(a + b)
  • Standard Expansion (x + a)(x + b) = x² + (a+b)x + ab
Mensuration & Geometry
  • Area of a Trapezium ½ × h × (a + b)
  • Area of a Rhombus ½ × d₁ × d₂
  • Euler's Formula (Polyhedrons) F + V - E = 2
Surface Areas and Volumes
  • Volume of a Cylinder πr²h
  • Volume of a Cone ⅓πr²h
  • Surface Area of a Sphere 4πr²
  • Volume of a Sphere ⁴⁄₃πr³
Quadratic Equations & Progressions
  • Quadratic Formula x = (-b ± √(b² - 4ac)) / 2a
  • Discriminant Δ = b² - 4ac
  • nth Term of an A.P. aₙ = a + (n-1)d
  • Sum of an A.P. Sₙ = ⁿ⁄₂[2a + (n-1)d]
Basic Trigonometry
  • Pythagorean Identity sin²θ + cos²θ = 1
  • Tangent Ratio tan θ = sin θ / cos θ
Differential Calculus
  • Power Rule d/dx(xⁿ) = nxⁿ⁻¹
  • Product Rule (uv)' = u'v + uv'
  • Quotient Rule (u/v)' = (u'v - uv') / v²
Integral Calculus
  • Power Rule (Integration) ∫xⁿ dx = (xⁿ⁺¹) / (n+1) + C
  • Exponential Function ∫eˣ dx = eˣ + C
  • Logarithmic Integration ∫(1/x) dx = ln|x| + C

The Ultimate CBSE Mathematics Formula Cheat Sheet

Mathematics is a subject built on logical progression. Unlike subjects that rely on pure rote memorization of historical dates or vocabulary words, math requires you to understand deeply interconnected systems. However, at the very foundation of these systems are the formulas—the immutable laws and identities that allow you to solve complex problems. Forgetting a single negative sign or confusing a square with a cube in an exam hall can derail an entire 5-mark question. The MathHub Pro Cheat Sheet archives provide an instant, accessible digital repository of every critical formula from Class 8 through Class 12.

Building Foundations: The Importance of Class 8 and 9

Building a strong mathematical foundation starts early. The leap into rigorous algebra and mensuration often begins in middle school. Whether you are a student sitting in an 8th-grade classroom at a rigorous institution like Carmel Convent High School or studying independently at home, having instant access to foundational algebraic identities is critical. Formulas such as (a + b)² = a² + 2ab + b² and Euler's formula for polyhedrons are not just passing topics; they are the bedrock upon which high school calculus and competitive physics are built. The Class 9 syllabus expands this heavily into the physical world, demanding precise memorization of the surface areas and volumes of complex 3D shapes like cylinders, cones, and spheres.

Board Exams and High-Stakes Mathematics (Class 10)

Class 10 represents a major milestone for every Indian student: the CBSE Board Examinations. In this critical year, the mathematics syllabus pivots toward heavier, formula-dependent subjects. Students must master the Quadratic Formula to find the roots of complex parabolas, calculate the sum of Arithmetic Progressions (A.P.), and navigate the entirely new world of Trigonometry. In trigonometry specifically, knowing the Pythagorean identity (sin²θ + cos²θ = 1) by heart is an absolute non-negotiable requirement. Our digital cheat sheet organizes these formulas into clean, visually distinct cards, allowing students to quickly revise right before a mock test or final exam without thumbing through hundreds of pages of a textbook.

Advanced Calculus for JEE and Class 12

As students transition into the senior secondary stage (Classes 11 and 12), mathematics shifts from arithmetic and basic algebra to the study of continuous change: Calculus. The volume of formulas a student must memorize triples. Differential calculus requires strict adherence to the Power Rule, the Product Rule, and the Quotient Rule. Integral calculus introduces an entirely different set of inverse rules, complete with the constant of integration. For students aiming to crack the JEE Main or JEE Advanced, these formulas must become second nature. The MathHub Pro platform ensures that whether you are practicing complex integration by parts or solving differential equations, you have a flawless, ad-free reference guide right in your pocket.