Cheat Sheets


This section contains high school math cheat sheets, covering algebra, trigonometry, coordinate geometry and calculus. Each cheat sheet covers the summary of concepts and the most important formulas related to the particular chapter in a single page.

Currently there are 29 cheat sheets in total, with more to be added soon. Download them all !

3D Geometry Cheat Sheet

3D Geometry Cheat Sheet

Distance Formula, Section Formula, Equation of a Line: Passing through a given point and having given direction ratios or direction cosines, Equation of a Line passing through two points, Angle between two lines, Distance of a point from a line, Distance between parallel lines, Shortest distance between skew lines, Equation of a Plane: At a given distance from origin with known direction cosines of normal, Passing through a given point and known direction cosines of normal, Making given intercepts on the axes, Passing through a point and parallel to two lines, Passing through two points and parallel to a line, Passing through three non-collinear points, Angle between two planes, Angle between a line and a plane, Distance of a point from a plane, Distance between parallel planes

Area Cheat Sheet

Area bounded by a curve with the X axis, Area bounded by a curve with the Y axis, Area bounded by two or more curves

Circle Cheat Sheet

Circle Cheat Sheet

Standard Equation, Equation with known center and radius, Equation with known end-points of diameter, General Equation, Position of a point w.r.t. a Circle, Equation of Tangents: Slope Form and Point Form, Length of the Tangent from an External Point, Equation of Normal: Slope Form and Point Form, Chord of Contact, Chord with known Mid-Point, Family of Circles, Angle of Intersection of Circles, Orthogonal Intersection, Radical Axis, Relative Position of Two Circles, Common Tangents to Two Circles

Trigonometry Cheat SheetConditional Trigonometric Identities

A few identities and inequalities related to trigonometric ratios of angles of a triangle.

Coordinate Geometry Basics Cheat Sheet

Cartesian Coordinate System, Distance Formula, Section Formula, Internal Division, External Division, Mid-Point, Area of a Triangle, Area of a Polygon, Collinearity of Points, Centers in a Triangle – Centroid, Incentre, Excentre
Definite Integrals Cheat SheetDefinite Integrals Cheat Sheet Definite Integration as a Limit of Sum, Properties of Definite Integrals, Inequalities involving Definite Integrals, Differentiation under the Integral Sign (Leibniz Rule)
Determinants Cheat Sheet

Determinants Cheat Sheet

Expansion of Determinants, Properties of Determinants, Product of two Determinants, Summation of Determinants, Differentiation of Determinants

Differential Equations Cheat Sheet

Differential Equations Cheat Sheet

Methods of solution of some first order ordinary differential equations: Variable separable, reducible to variable separable, homogeneous, reducible to homogeneous, linear and reducible to linear.

Differentiation Cheat Sheet

Differentiation Cheat Sheet

Differentiation using First Principle, Rules of Differentiation: Multiplication by a constant, Sum Rule, Difference Rule, Product Rule, Quotient Rule, Chain Rule, Differentiation of Parametric Functions, Logarithmic Differentiation, Higher Order Derivatives; Differentiation Formulas of elementary functions

Ellipse Cheat Sheet

Ellipse Cheat Sheet

Standard Equation of an Ellipse, General Equation of an Ellipse, Parametric Equation of an Ellipse, Position of a point with respect to an Ellipse, Equation of Tangents: Slope Form, Point Form and Parametric Form, Point of Intersection of Tangents, Pair of Tangents from an external point, Equation of a Normal: Slope Form, Point Form and Parametric Form, Equation of a Chord with known end points, Equations of a Chord with known mid point, Equation of Chord of Contact, Some properties of the Ellipse

Graph Cheat Sheet

Graph Transformations Cheat Sheet

f(x+a), f(x) + a, a.f(x), f(ax), |f(x)|, f(|x|), |f(|x|)|, |y|=f(x)

Graph Cheat Sheet

Graph Transformations (Advanced) Cheat Sheet

Greatest integer of f(x): [f(x)], Function of Greatest integer of x: f([x]), Greatest Integer of y = f(x): [y] = f(x), Fractional part of f(x): {f(x)}, Function of fractional part of x: f({x}), Fractional part of y = f(x): {y} = f(x)

Hyperbola Cheat SheetHyperbola Cheat Sheet

Standard Equation of a Hyperbola, General Equation a Hyperbola, Parametric Equation a Hyperbola, Position of a point with respect to a Hyperbola, Equation of Tangents to a Hyperbola: Slope Form, Point Form and Parametric Form, Point of Intersection of Tangents, Pair of Tangents from an external point, Equation of the Normal: Slope Form, Point Form and Parametric Form, Equation of a Chord with known end points, Equations of a Chord with known mid point, Equation of Chord of Contact, Equation of Asymptotes, Angle between the Asymptotes, Some properties of the Hyperbola

Indefinite Integrals Cheat Sheet

Indefinite Integrals Cheat Sheet

Basic Formulas of Integration, Integration by Substitution – Substitution Methods for various functions, Special Integrals, Integration of Rational Functions using Partial Fractions, Integration by Parts

Inverse Trigonometry Cheat Sheet

Inverse Trigonometric Functions Cheat Sheet (Identities)

Domain and Range of Inverse Trigonometric Functions, Identities related to Inverse Trigonometric Functions
Inverse Trigonometry Cheat SheetInverse Trigonometric Functions Cheat Sheet (Graphs) Arc Sin x Graph, Arc Cos x Graph, Arc Tan x Graph, Arc Cot x Graph, Arc Sec x Graph, Arc Cosec x Graph, Arc Sin (Sin x) Graph, Arc Cos (Cos x) Graph, Arc Tan (Tan x) Graph, Arc Cot (Cot x) Graph, Arc Sec (Sec x) Graph, Arc Cosec (Cosec x) Graph
Limits Cheat SheetLimits Cheat Sheet Indeterminate Forms, Properties of Limits, Sandwich Theorem, L’Hôpital’s Rule, List of Common Limits / Formulas  
Logarithm Cheat SheetLogarithm Cheat Sheet Definition, Properties of Logarithm, Inequalities of Logarithm, Graph of Log(x)
Mathematical Logic Cheat Sheet

Mathematical Logic Cheat Sheet

Truth Tables: Logical Conjunction, Logical Disjunction, Logical Negation, Logical Implication, Logical Equivalence, Exclusive Disjunction. Laws of Logic: Double Negation Law, Identity Laws, Idempotent Laws, Annihilation Laws, Commutative Laws, Associative Laws, Distributive Laws, Absorption Laws, De Morgan’s Laws
Matrix Cheat Sheet

Matrix Cheat Sheet

Addition of Matrices, Properties of Addition, Product of Matrices, Transpose of a Matrix, Properties of Transpose, Adjoint of a Matrix, Properties of Adjoint, Inverse of a Matrix, Properties of Inverse, Types of Matrices Coming Soon
Modulus Function

Modulus Function Cheat Sheet

Definition of Modulus Function, Examples, Properties Modulus function, Derivative of Modulus Function, Integral of Modulus Function, Equations and Inequations involving Modulus Function, Graph of Modulus Function
Parabola Cheat SheetParabola Cheat Sheet Standard Equation, Equations with axes parallel to the coordinate axes, Equations with known focus and directrix, Parametric Equation, Position of a point with respect to a Parabola, Equation of Tangents: Slope Form, Point Form and Parametric Form, Point of Intersection of Tangents, Pair of Tangents from an external point, Equation of a Normal: Slope Form, Point Form and Parametric Form, Point of Intersection of Normals, Three Normals from a Point, Equation of a Chord with known end points, Equations of a Chord with known mid point, Equation of Chord of Contact, Some relations related to parametric equations, Some properties of the Parabola  
Triangles Cheat SheetProperties of Triangles Cheat Sheet Sine Rule, Cosine Rule, Tangent Rule, Projection Formula, Area of a Triangle, Half Angle Formula, In Radius, Ex Radius, Distance between Circumcenter and Incentre, Distance between Circumcenter and Excentres, Distance between Circumcenter and Orthocenter, Distance between Orthocenter and Incenter,Distance between Incenter and Exccenters, Distance between Excenters, Inequalities in a Triangle  
Quadratic Equations Cheat SheetQuadratic Equations Cheat Sheet  Roots, Nature of roots: Real and Distinct, Real & Equal, Imaginary, Rational Roots, Integral Roots, Relation between roots and coefficients, Common Roots, Range of a quadratic function, Sign of a quadratic function, Graph of a quadratic function, Location of the roots of a quadratic equation  
Sets Cheat Sheet

Sets Cheat Sheet

Set Notation, Subsets, Power Sets, Union of Sets, Intersection of Sets, Difference of Sets, Complement of Sets, Cartesian Product of Sets, Venn Diagrams, Laws of Union, Intersection, Difference and Complement
Straight Line Cheat SheetStraight Line Cheat Sheet Equations of a Straight Line – Parallel to Axes, Slope-Intercept Form, Intercept Form, Point-Slope Form, Two-Point Form, Parametric Form, General Form, Equations representing the same line, Angle between Lines, Point of Intersection, Concurrency of Lines, Distance of a Point from a Line, Distance between Parallel Lines, Position of point w.r.t. a Line, Angle Bisectors, Family of Lines, Pair of Straight Lines through Origin
Triangles Cheat SheetSolution of Triangles Cheat Sheet Finding angles and lengths of sides of a triangle, when some of them are known: Three sides, Three angles, Two sides and included angle, one side and two adjacent angles, one side one adjacent angle and one opposite angle, Two sides and an angle not included between them (Ambiguous Case),  
Trigonometry Cheat SheetTrigonometry Cheat Sheet Basic Identities, Compound Angle Formulas, Multiple Angle Formulas, Sub-multiple Angle Formulas, Sum to Product Formulas, Product to Sum Formulas, Miscellaneous Formulas
Trigonometric EquationsTrigonometric Equations Cheat Sheet Basic Trigonometric Equations: sinx = sinα, cosx = cosα, tanx = tanα, sin2x = sin2α, cos2x = cos2α, tan2x = tan2α

Special Cases: sinx = 0, sinx = 1, sinx = -1, cosx = 0, cosx = 1, cosx = -1, tanx = 0, cotx = 0

Vectors Cheat SheetVector Algebra Cheat Sheet Scalar Multiplication, Vector Addition, Linear Combination, Dot Product, Cross Product, Scalar Triple Product, Vector Triple Product, Vector Quadruple Product, Geometrical Interpretations

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