Chapter SummariesClass 12 Mathematics
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Class 12 MathematicsChapter Summaries

13 chapters · Quick revision in under 3 minutes per chapter

Ch 1

Relations and Functions

Covers types of relations (reflexive, symmetric, transitive, equivalence) and types of functions (one-one, onto, bijective). Composition of functions and invertible functions are key topics.

Topics covered

Types of relationsOne-one and onto functionsComposition of functionsInvertible functions
Ch 2

Inverse Trigonometric Functions

Defines inverse trig functions, their domains and ranges, and principal values. Properties and identities of inverse trig functions are frequently asked.

Topics covered

Domain and range of inverse trig functionsPrincipal value branchProperties and identities
Ch 3

Matrices

Covers matrix types, operations (addition, multiplication, transpose), and properties. Symmetric and skew-symmetric matrices are important concepts.

Topics covered

Matrix typesMatrix operationsTranspose and its propertiesSymmetric and skew-symmetric matrices
Ch 4

Determinants

Covers evaluation of determinants, properties, Cramer's rule, and area of triangles. Adjoint and inverse of a matrix using determinants is a key exam topic.

Topics covered

Properties of determinantsCofactors and adjointInverse of a matrixSolution of linear equations using Cramer's rule
Ch 5

Continuity and Differentiability

Covers continuity, differentiability, and differentiation of composite, implicit, and parametric functions. Chain rule, logarithmic differentiation, and Rolle's/Mean Value theorems are included.

Topics covered

Continuity and differentiabilityChain ruleImplicit differentiationLogarithmic differentiationRolle's theorem and MVT
Ch 6

Application of Derivatives

Covers rate of change, increasing/decreasing functions, maxima and minima, tangents and normals. Optimization word problems are exam favourites.

Topics covered

Rate of change of quantitiesIncreasing and decreasing functionsTangents and normalsMaxima and minima (first and second derivative test)Optimization problems
Ch 7

Integrals

Covers integration as anti-differentiation and definite integrals. Methods: substitution, partial fractions, integration by parts. Properties of definite integrals are frequently used in board exams.

Topics covered

Integration by substitutionIntegration by partial fractionsIntegration by partsDefinite integrals and properties
Ch 8

Application of Integrals

Covers finding areas under curves and between curves using definite integrals. Sketching the region before integrating is expected in board answers.

Topics covered

Area under a curveArea between two curvesArea of standard figures using integration
Ch 9

Differential Equations

Covers order and degree of differential equations, formation, and solution methods — variable separable, homogeneous, and linear first-order DEs.

Topics covered

Order and degreeVariable separable methodHomogeneous differential equationsLinear differential equations
Ch 10

Vector Algebra

Covers vectors and their types, dot product, cross product, and applications. Scalar and vector triple products are also included.

Topics covered

Types of vectorsDot product and its applicationsCross product and its applicationsScalar and vector triple product
Ch 11

Three Dimensional Geometry

Covers direction cosines and ratios, equations of lines and planes in 3D, and angle between lines/planes. Distance of a point from a plane is a common numerical.

Topics covered

Direction cosines and ratiosEquation of a line in 3D (vector and Cartesian forms)Equation of a planeAngle between lines/planesDistance of a point from a plane
Ch 12

Linear Programming

Covers formulation of LPP, graphical method of solution, feasible region, and corner point theorem. Word problems on manufacturing, diet, and transportation are common.

Topics covered

Formulation of LPPFeasible region (bounded and unbounded)Corner point theoremOptimal solution
Ch 13

Probability

Covers conditional probability, Bayes' theorem, random variables, and Binomial distribution. Bayes' theorem problems are very commonly asked in board exams.

Topics covered

Conditional probabilityMultiplication theoremIndependent eventsBayes' theoremRandom variables and probability distributionBinomial distribution