Algebra - I (Complex & Quadratic)
Complex numbers: Algebra, modulus, argument, and conjugate
medium • 1 min read
Triangle inequality and De Moivre's theorem (Conceptual)
medium • 2 min read
Roots of unity and their properties
medium • 3 min read
Quadratic equations: Real and complex roots, discriminant
medium • 4 min read
The relationship between roots and coefficients
medium • 5 min read
Algebra - II (Series & Binomial)
Arithmetic and Geometric Progressions (AP, GP)
medium • 1 min read
Harmonic Progression (HP) and AM, GM, HM relations
medium • 2 min read
Sum to n terms of special series (n, n^2, n^3)
medium • 3 min read
Binomial theorem for a positive integral index
medium • 4 min read
General and middle terms, binomial coefficients properties
medium • 5 min read
Algebra - III (Matrices & Det)
Types of matrices and elementary transformations
medium • 1 min read
Determinants of order 2 and 3, properties of determinants
medium • 2 min read
Adjoint and Inverse of a square matrix
medium • 3 min read
Consistency of linear equations using rank and determinants
medium • 4 min read
Cramer's rule and Matrix inversion method
medium • 5 min read
Probability
Addition and multiplication laws of probability
medium • 1 min read
Conditional probability and Bayes' Theorem
medium • 2 min read
Independent events and Bernoulli trials
medium • 3 min read
Probability distribution of random variables
medium • 4 min read
Binomial and Poisson distributions (Introductory)
medium • 5 min read
Trigonometry
Trigonometric functions and their periodicity
medium • 1 min read
Compound and multiple angles formulas
medium • 2 min read
Trigonometric equations and general solutions
medium • 3 min read
Inverse trigonometric functions and their properties
medium • 4 min read
Properties and solutions of triangles
medium • 5 min read
Straight lines: Slopes, intercepts, and normal form
medium • 1 min read
Distance between lines, family of lines passing through point
medium • 2 min read
Circles: Standard and general equation, parametric form
medium • 3 min read
Tangent and Normal to a circle from a point
medium • 4 min read
Orthogonality and radical axis of circles
medium • 5 min read
Analytical Geometry - II (Conics)
Parabola: Standard equation and focal properties
medium • 1 min read
Ellipse: Eccentricity, latus rectum, and major/minor axes
medium • 2 min read
Hyperbola: Rectangular hyperbola and asymptotes
medium • 3 min read
Tangents and Normals to conic sections
medium • 4 min read
Common tangents to two conics
medium • 5 min read
Limits of algebraic and trigonometric functions
medium • 1 min read
Indeterminate forms and L'Hopital's rule
medium • 2 min read
Continuity of a function at a point and in interval
medium • 3 min read
Differentiability and its connection to continuity
medium • 4 min read
First principles of differentiation
medium • 5 min read
Differentiation of composite, inverse, and implicit functions
medium • 1 min read
Logarithmic differentiation and successive differentiation
medium • 2 min read
Application of derivatives: Tangents and Normals
medium • 3 min read
Monotonicity: Increasing and decreasing functions
medium • 4 min read
Maxima and Minima of functions of one variable
medium • 5 min read
Integral Calculus - I (Indefinite)
Integration by parts and substitution methods
medium • 1 min read
Integration of rational and irrational functions
medium • 2 min read
Partial fractions in integration
medium • 3 min read
Standard integrals involving special functions
medium • 4 min read
Integration as reverse process of differentiation
medium • 5 min read
Integral Calculus - II (Definite)
Fundamental theorem of calculus and its applications
medium • 1 min read
Properties of definite integrals and periodic functions
medium • 2 min read
Definite integral as a limit of a sum
medium • 3 min read
Area bounded by curves using integration
medium • 4 min read
Estimation of definite integrals
medium • 5 min read
Differential Equations
Formation of differential equations (Order, Degree)
medium • 1 min read
Variables separable and homogeneous equations
medium • 2 min read
Linear differential equations of first order
medium • 3 min read
Orthogonal trajectories and Bernoulli's equation
medium • 4 min read
Applications to growth, decay, and geometry
medium • 5 min read
Vector Algebra
Addition of vectors and scalar multiplication
medium • 1 min read
Dot and Cross product of two vectors
medium • 2 min read
Scalar triple product and its geometrical meaning
medium • 3 min read
Vector triple product and its properties
medium • 4 min read
Applications of vectors in geometry
medium • 5 min read
Three Dimensional Geometry
Direction cosines and direction ratios of a line
medium • 1 min read
Vector and Cartesian equations of a line in space
medium • 2 min read
Shortest distance between two skew lines
medium • 3 min read
Equation of a plane in different forms
medium • 4 min read
Angle between line and plane, and between two planes
medium • 5 min read