Class 12 MathematicsChapter Summaries
13 chapters · Quick revision in under 3 minutes per chapter
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.
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Inverse Trigonometric Functions
Defines inverse trig functions, their domains and ranges, and principal values. Properties and identities of inverse trig functions are frequently asked.
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Matrices
Covers matrix types, operations (addition, multiplication, transpose), and properties. Symmetric and skew-symmetric matrices are important concepts.
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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.
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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.
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Application of Derivatives
Covers rate of change, increasing/decreasing functions, maxima and minima, tangents and normals. Optimization word problems are exam favourites.
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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.
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Application of Integrals
Covers finding areas under curves and between curves using definite integrals. Sketching the region before integrating is expected in board answers.
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Differential Equations
Covers order and degree of differential equations, formation, and solution methods — variable separable, homogeneous, and linear first-order DEs.
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Vector Algebra
Covers vectors and their types, dot product, cross product, and applications. Scalar and vector triple products are also included.
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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.
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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.
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Probability
Covers conditional probability, Bayes' theorem, random variables, and Binomial distribution. Bayes' theorem problems are very commonly asked in board exams.
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