Sets, Relations and Functions
Sets and their representations, Power set
medium • 1 min read
Operations on sets: Union, Intersection, Difference
medium • 2 min read
Types of relations: Reflexive, Symmetric, Transitive
medium • 3 min read
Functions: Domain, Codomain, Range
medium • 4 min read
Types of functions: One-to-one, Onto, Into
medium • 5 min read
Complex numbers in the form a+ib, Argand plane
medium • 1 min read
Modulus and Argument of complex numbers
medium • 2 min read
Square root of a complex number, Triangle inequality
medium • 3 min read
Quadratic equations and their roots, discriminant
medium • 4 min read
Relation between roots and coefficients
medium • 5 min read
Matrices and Determinants
Algebra of matrices: Addition, scalar multiplication
medium • 1 min read
Multiplication of matrices and their properties
medium • 2 min read
Determinants of order up to 3, Cramer's rule
medium • 3 min read
Adjoint and Inverse of a square matrix
medium • 4 min read
Solving linear equations using matrix inversion
medium • 5 min read
Permutations and Combinations
Mathematical Induction
Binomial Theorem
Sequences and Series
Arithmetic Progression (AP): General term and sum
medium • 1 min read
Geometric Progression (GP): General term and sum
medium • 2 min read
Arithmetic and Geometric Means (AM, GM)
medium • 3 min read
Relation between AM and GM, Arithmetic-Geometric series
medium • 4 min read
Sum to n terms of special series (n, n^2, n^3)
medium • 5 min read
Limits: Standard limits and L'Hopital's rule
medium • 1 min read
Continuity of a function at a point and in interval
medium • 2 min read
Differentiability and its connection to continuity
medium • 3 min read
Differentiation of algebraic and transcendental functions
medium • 4 min read
Successive differentiation and Rolle's Theorem
medium • 5 min read
Integral Calculus
Indefinite integrals: Integration by substitution/parts
medium • 1 min read
Integration of rational and irrational functions
medium • 2 min read
Definite integrals as limit of a sum
medium • 3 min read
Fundamental Theorem of Calculus and properties
medium • 4 min read
Applications of definite integrals for finding area
medium • 5 min read
Differential Equations
Order and degree of a differential equation
medium • 1 min read
Solution of differential equations by variable separable
medium • 2 min read
Homogeneous differential equations
medium • 3 min read
Linear differential equations of first order
medium • 4 min read
General and particular solutions of an equation
medium • 5 min read
Co-ordinate Geometry
Straight lines: Slopes, intercepts, normal form
medium • 1 min read
Distance between two parallel lines, Angle between lines
medium • 2 min read
Circles: Standard and general equation, tangent/normal
medium • 3 min read
Parabola, Ellipse and Hyperbola: Equations and properties
medium • 4 min read
Conic sections and their eccentricity
medium • 5 min read
Three Dimensional Geometry
Coordinates of a point in 3D space
medium • 1 min read
Direction cosines and direction ratios
medium • 2 min read
Equation of a line in space (Vector and Cartesian)
medium • 3 min read
Shortest distance between two lines
medium • 4 min read
Plane: Equation of a plane and angle between two planes
medium • 5 min read
Vector Algebra
Statistics and Probability
Measures of dispersion: Mean deviation and variance
medium • 1 min read
Standard deviation of discrete and continuous data
medium • 2 min read
Probability: Basic concepts and Addition/Multiplication laws
medium • 3 min read
Conditional probability and Bayes Theorem
medium • 4 min read
Bernoulli trials and Binomial distribution
medium • 5 min read
Trigonometry
Trigonometric functions and their periodicity/range
medium • 1 min read
Sum and difference formulas for trig functions
medium • 2 min read
Multiple and sub-multiple angles formulas
medium • 3 min read
Trigonometric equations and their general solutions
medium • 4 min read
Inverse trigonometric functions and their properties
medium • 5 min read