Class XII Mathematics
Mathematics Part I & II
Matrices, determinants, calculus, integrals, vectors, 3-D geometry, probability.
1
Chapter 1: Relations and Functions
Mathematics
types of relationsequivalence relationstypes of functionscomposition of functionsinvertible functionsbinary operations
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2
Chapter 2: Inverse Trigonometric Functions
Mathematics
principal value branchesgraphs of inverse trig functionsaddition formulasidentities of inverse trig functionsapplications
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3
Chapter 3: Matrices
Mathematics
matrix and typesoperations on matricestranspose and symmetric matriceselementary operationsinvertible matrices
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4
Chapter 4: Determinants
Mathematics
determinant of a matrixproperties of determinantsarea of a triangleminors and cofactorsadjoint and inverseapplications to linear systems
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5
Chapter 5: Continuity and Differentiability
Mathematics
continuitydifferentiabilitychain ruleimplicit differentiationlogarithmic differentiationparametric and second derivatives
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6
Chapter 6: Application of Derivatives
Mathematics
rate of changeincreasing and decreasing functionstangents and normalsapproximationsmaxima and minimaapplied optimisation
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7
Chapter 7: Integrals
Mathematics
indefinite integralstandard integralsintegration by substitutionintegration by partspartial fractionsdefinite integral
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8
Chapter 8: Application of Integrals
Mathematics
area under a curvearea between two curvesarea bounded by line and curvearea bounded by parabolaarea bounded by ellipse and circleapplications
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9
Chapter 9: Differential Equations
Mathematics
order and degreegeneral and particular solutionsvariable separable equationshomogeneous differential equationslinear differential equationsapplications
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10
Chapter 10: Vector Algebra
Mathematics
scalars and vectorsvector additionscalar (dot) productvector (cross) productscalar triple productapplications in geometry
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11
Chapter 11: Three-Dimensional Geometry
Mathematics
direction cosines and direction ratiosequation of a lineangle between two linesshortest distance between two linesequation of a planeangle between line and plane
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12
Chapter 12: Linear Programming
Mathematics
linear programming problemsgraphical methodfeasible regioncorner-point methodapplications: diet, manufacturing, transportation
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13
Chapter 13: Probability
Mathematics
conditional probabilitymultiplication ruleindependent eventstotal probabilityBayes' theoremrandom variables
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