Class 12 - Mathematics

Course Syllabus : for Class 12 - Mathematics

Part: I (Chapter 1 to 6)

• Chapter 1: Relations and Functions 8 Lectures 5 hrs 16 min
  • 01: Basic Concepts, Introduction Relations, Functions, Subsets, Empty Relation, Universal Relation, Types of Relations, SL Examples, NCERT Exercise 1.1 41 min
  • 02: Equivalence Relation, Reflexive, Symmetric, Transitive, Secret Hint, Functions, f-image, SL Examples, NCERT Exercise 1.1 37 min
  • 03: Domain, Range, Co-domain, Arrow Diagram, SL Examples, Types of Function, One-One function, Injective, Into Function, Onto function, Surjection, NCERT Exercise 1.2 39 min
  • 04: Natural numbers, Even numbers, Odd numbers, Prime numbers, Even prime numbers, Whole numbers, SL Examples, NCERT Exercise 1.2 32 min
  • 05: Quick Revision, Composite numbers, Integers, Rational numbers, Irrational numbers, Real numbers, Composition of function, SL Examples, NCERT Exercise 1.3 42 min
  • 06: Composition Function, Invertible Function, SL Examples, NCERT Exercise 1.3 46 min
  • 07: Quick Revision of Concepts, Binary Operations, Commutative, Associative, SL Examples, NCERT Exercise 1.4 37 min
  • 08: NCERT Exercise 1.4, NCERT Miscellaneous Exercise on Chapter 1 42 min
• Chapter 2: Inverse Trigonometric Function 4 Lectures 2 hrs 47 min
  • 01: Basic Concepts, Principal Value, Domain and Range (Principal value Branch), Open Interval, Close Interval, Trigonometric Identities Table, SL Examples, NCERT Exercise 2.1 45 min
  • 02: Sine function, Cosine function, tangent function, cotangent function, secant function, cosecant function, Some Important Formula on Trigonometry, NCERT Exercise 2.2 38 min
  • 03: Properties of Inverse Trigonometric Functions, Quick Revision of Concepts, SL Examples, NCERT Exercise 2.2 39 min
  • 04: SL Examples, NCERT Miscellaneous Exercise on Chapter 2 45 min
• Chapter 3: Matrices 8 Lectures 5 hrs 45 min
  • 01: Matrices, Order of Matrix, No. Of Elements, Types of Matrices, Column Matrix, Row Matrix, Square Matrix, Diagonal Matrix, SL Examples, NCERT Exercise 3.1 50 min
  • 02: Algebra (Operation) of Matrices, Addition of Matrices, Scalar multiplication, Multiplication of Matrices, Subtraction of Matrices, NCERT Exercise 3.2 42 min
  • 03: Equality of Matrices, Negative of Matrix, Difference of Matrices, Properties of Matrix Addition, SL Examples, NCERT Exercise 3.2 45 min
  • 04: Transpose of a Matrix, Properties of transpose of the matrices, SL Examples, NCERT Exercise 3.2 39 min
  • 05: Associate Law, Distribute Law, Symmetric and Skew Symmetric Matrices, Theorem 1, Theorem 2, SL Examples, NCERT Exercise 3.3 41 min
  • 06: Inverse of a matrix by elementary operations, Transformation of Matrix, Invertible Matrices, Theorem 3, Theorem 4, Secret Hint, NCERT Exercise 3.4 50 min
  • 07: Scalar Matrix, Identity or Unit Matrix, Zero Matrix, Null Matrix, Equality Matrix, SL Examples, NCERT Exercise 3.4 40 min
  • 08: Non-commutatively of multiplication of matrices, Principle of Mathematical Induction, Miscellaneous Exercise on Chapter 3, 38 min
• Chapter 4: Determinants 8 Lectures 5 hrs 52 min
  • 01: Determinant of a matrix of order one, Determinant of a matrix of order two, Determinant of a matrix of order three, SL Examples, NCERT Exercise 4.1 Preview49 min
  • 01: Determinant of a matrix of order one, Determinant of a matrix of order two, Determinant of a matrix of order three, SL Examples, NCERT Exercise 4.1 40 min
  • 03: Adjoint of a Matrix, Square Matrix, Area of Triangle, Golden Concepts for Area of Triangle, SL Examples, NCERT Exercise 4.3 43 min
  • 04: Minors, Cofactors, Minor of element, Cofactors of elements of second row, Cofactors of elements of third column, SL Examples, NCERT Exercise 4.4 48 min
  • 05: Inverse of a Matrix, Steps for Inverse of Matrix, Theorem 1, Theorem 2, Theorem 3, Theorem 4, SL Examples, NCERT Exercise 4.5 42 min
  • 06: Applications of Determinants, Consistent system, Inconsistent system, Homogeneous, Non-homogeneous, SL Examples, NCERT Exercise 4.6 45 min
  • 07: Solution of system of linear equations using inverse of a matrix, Applications of Matrices, Matrix Method, Secret Hint, NCERT Exercise 4.6 40 min
  • 08: Matrix method, Golden Hint to Solve the Questions, Miscellaneous Exercise on Chapter 4 45 min
• Chapter 5: Continuity and Differentiability 13 Lectures 9 hrs 11 min
  • 01: Continuity, Dependent Variable, Independent Variable, Important Formula, Simple Differentiation, SL Examples, NCERT Exercise 5.1 Preview50 min
  • 02: Theorem 1, Theorem 2, Product Rule, SL Examples, Quotient Rule, Chain Rule, NCERT Exercise 5.2 49 min
  • 03: Implicit Function, NCERT Exercise 5.2, Theorem 3, Theorem 4, Golden Concepts, SL Examples, NCERT Exercise 5.3 45 min
  • 04: NCERT Exercise 5.3, Derivatives of composite function, Derivatives of implicit functions, SL Examples, NCERT Exercise 5.4 38 min
  • 05: Derivatives of inverse trigonometric functions, Exponential Functions, Theorem 5, SL Examples, NCERT Exercise 5.5 44 min
  • 06: Logarithmic Differentiation, NCERT Exercise 5.5 Preview40 min
  • 07: Derivatives of Functions in Parametric Forms, By expanding, By Logarithmic Differentiation, SL Examples, NCERT Exercise 5.6, 35 min
  • 08: Second Order derivative, NCERT Exercise 5.6, 38 min
  • 09: SL Examples, Higher Order derivatives, First derivatives, Second derivatives, NCERT Exercise 5.7 42 min
  • 10: Mean value theorem, Rolle’s Theorem, Steps for Rolle’s theorem, SL Examples, NCERT Exercise 5.7 40 min
  • 11: LMV Theorem, Steps for LMV Theorem, SL Examples, Some Important Points Discuss, NCERT Exercise 5.8 50 min
  • 12: NCERT Exercise 5.8, Continuity, Continuity at a Point, Continuity in a Interval, Continuity of a function, Secret Hint, NCERT Exercise 5.1 45 min
  • 13: NCERT Exercise 5.1 35 min
• Chapter 6: Application of Derivatives 17 Lectures 12 hrs 8 min
  • 01: Rate of Change of Quantities, Approximation, Some Important Formula, Approximate change in y, SL Examples, NCERT Exercise 6.4 42 min
  • 02: Change in Surface area, Change in Volume, Steps for Question solve, Formula Discuss, NCERT Exercise 6.4 41 min
  • 03: Application of Derivatives, Rate of change of Quantities, SL Examples, NCERT Exercise 6.1 39 min
  • 04: Tangents, Normal, Slope of tangent, Equation of tangent, Equation of curve, Golden Concepts, NCERT Exercise 6.1 51 min
  • 05: Equation of line, Angle between two lines, Condition – parallelism, perpendicularity , Slope of normal, NCERT Exercise 6.3 47 min
  • 06: Increasing Function, Decreasing Function, Strictly Increasing Function, Strictly Decreasing Function, SL Examples, NCERT Exercise 6.3 42 min
  • 07: Tangents and Normal, Equation of normal, NCERT Exercise 6.3 41 min
  • 08: Neither increasing and nor decreasing function, Steps for strictly increasing and strictly decreasing function, NCERT Exercise 6.2 57 min
  • 09: Types of Questions, Slope, Point, Equation, Miscellaneous, Make table, SL Examples, NCERT Exercise 6.2 40 min
  • 10: Increasing and Decreasing Function, NCERT Exercise 6.2 35 min
  • 11: Maximum value of function, Minimum value of function, Test for Maxima and Minima, NCERT Exercise 6.2 39 min
  • 12: Maxima and Minima, Use of Maxima and Minima, Application of Maxima and Minima, Point of inflection, SL Examples 41 min
  • 13: Words Problem of Maxima and Minima, NCERT Exercise 6.5 42 min
  • 14: First Derivates Test, Second Derivates Test, Steps of Second Derivates Test, Tips for How to solve Questions, NCERT Exercise 6.5 40 min
  • 15: Local Maxima, Local minima, Point of inflection, NCERT Exercise 6.5 45 min
  • 16: Maximum and Minimum value of a function in a closed interval, Theorem 5, Theorem 6, NCERT Exercise 6.5 39 min
  • 17: Quick revision, SL Examples, NCERT Exercise 6.5 47 min

Part: II (Chapter 7 to 13)

• Chapter 7: Integrals 27 Lectures 18 hrs 52 min
  • 01: Integrals, Indefinite Integrals, definite Integrals, Derivative, Anti-derivative, Basic formula, Linear function, Integrals formula, NCERT Exercise 7.1 52 min
  • 02: Trigonometry formula, Properties of indefinite integral, Integration as an inverse process of Differentiation, NCERT Exercise 7.1 47 min
  • 03: Comparison between differentiation and integration, Integration by substitution, Secret Hint, Formula Discuss, NCERT Exercise 7.2 42 min
  • 04: Quick Revision, Integration using Partial Fractions, Some Golden Concepts, NCERT Exercise 7.2 39 min
  • 05: SL Examples, Integration by Parts, Integration of form, NCERT Exercise 7.3 40 min
  • 06: Integration using trigonometric identities, Integration by substitution, SL Examples, NCERT Exercise 7.3 39 min
  • 07: Some Special Integrals, Integrals of Some Particular Functions, Evaluation of the Integral, NCERT Exercise 7.4 41 min
  • 08: SL Examples, Integration of the type, NCERT Exercise 7.4 47 min
  • 09: Integration of different type, Some Important Integrals, Integrals of some more types, NCERT Exercise 7.4 46 min
  • 10: Some Special types of standard integrals, NCERT Exercise 7.7 42 min
  • 11: Integration by Partial Fractions, Rational Functions, Partial Functions, SL Examples, NCERT Exercise 7.5 37 min
  • 12: NCERT Exercise 7.5, Methods of Integration, Method 2 Integration by Parts, Golden Concepts, NCERT Exercise 7.6 40 min
  • 13: Inverse Trigonometric Function, Logarithmic Function, Algebraic Function, Exponential Function, NCERT Exercise 7.6 41 min
  • 14: Some other Important Formula, SL Examples, Integration of the form, NCERT Exercise 7.6 47 min
  • 15: Definite Integrals, Upper limit, Lower limit, Fundamental Theorem of Calculus, Area function, Secret Hint, NCERT Exercise 7.9 45 min
  • 16: First fundamental theorem of integral calculus, Second fundamental theorem of integral calculus, NCERT Exercise 7.9 43 min
  • 17: Evaluation of Definite Integrals by Substitution, NCERT Exercise 7.10 37 min
  • 18: Limit of Sums, Sum of G.P series, Definite Integral, Definite Integral as the limit of a sum, NCERT Exercise 7.8 40 min
  • 19: Trigonometric Function, SL Examples, NCERT Exercise 7.8 45 min
  • 20: Important Formula Discuss, Properties of Definite integrals, NCERT Exercise 7.11 37 min
  • 21: SL Examples, Proof of Po, Proof of P1, Proof of P2 to P7, NCERT Exercise 7.11 46 min
  • 22: Properties Discuss, Formula Discuss, SL Examples, NCERT Exercise 7.11 41 min
  • 23: Some Golden Concepts Discuss, Miscellaneous Exercise on Chapter 7 37 min
  • 24: Integrals of some more types, Miscellaneous Exercise on Chapter 7 40 min
  • 25: Some special types of integrals, Miscellaneous Exercise on Chapter 7 35 min
  • 26: Integrals of some special functions, SL Examples, Miscellaneous Exercise on Chapter 7 47 min
  • 27: Integration by partial functions, SL Examples, Miscellaneous Exercise on Chapter 7 39 min
• Chapter 8: Application of Integrals 6 Lectures 4 hrs 39 min
  • 01: Basic Concepts, Bounded Area, Parabola, Ellipse, Circle, Line, Golden Concepts, Vertex, Major Axis, Minor Axis, radius, centre, Standard equation of circle, SL Examples Preview48 min
  • 02: Area under simple curves, elementary area, Whole area enclosed by given circle, Required area, Intersection points, NCERT Exercise 8.1 Preview49 min
  • 03: Area of region bounded by a curve and a line, area of region bounded by ellipse, Area of shaded region, Area of required region, NCERT Exercise 8.1 50 min
  • 04: Intercept form, X-intercept, y-intercept, parabola standard form, Vertices of triangle, Equation of line, Area between the two arc, NCERT Exercise 8.2 52 min
  • 05: Area bounded by ellipse, Area between two curves, Interior region, exterior region, Area enclosed between parabola, Miscellaneous Exercise on Chapter 8 35 min
  • 06: Area bounded by two parabola, Area of region bounded by triangle, Area of the region enclosed between two circles, Area bounded by x-axis, Miscellaneous Exercise on Chapter 8 45 min
• Chapter 9: Differential Equations 9 Lectures 6 hrs 24 min
  • 01: Order of Differential Equation, Highest order derivatives, Degree of Differential Equation, Power, Golden Concepts, NCERT Exercise 9.1, NCERT Exercise 9.2 Preview37 min
  • 02: Dependent variable, Independent variable, Variable separable form, Linear Differential Equation, NCERT Exercise 9.4 40 min
  • 03: Differential equations with variables separable, Polynomial equation in derivatives, Ordinary differential Equation, NCERT Exercise 9.5 42 min
  • 04: Equation of circle, Homogeneous differential equations, Arbitrary constant, Golden Hint, NCERT Exercise 9.5 37 min
  • 05: Trigonometric Function of Derivatives, General solution of Differential Equation, Particular solution of Differential Equation, NCERT Exercise 9.5 48 min
  • 06: First degree of differential equation, Linear Differential Equation, Golden Hints, SL Examples, NCERT Exercise 9.5 43 min
  • 07: Integrating Factor, First order linear differential equation, Formulation of Differential Equation, NCERT Exercise 9.6, 51 min
  • 08: Formation of a Differential Equation whose General Solution is given, Procedure to form a differential equation, NCERT Exercise 9.3 47 min
  • 09: Standard Equation of parabola, Standard equation of hyperbola, Standard equation of ellipse, Standard equation of circle, NCERT Exercise 9.3 39 min
• Chapter 10: Vector Algebra 8 Lectures 5 hrs 33 min
  • 01: Initial point, Terminal point, Vector, Magnitude or length, Directed line segment, Position Vector, Direction cosines, Direction ratios, Positive direction, Direction angles, Section formula, Scalar, NCERT Exercise 10.1 38 min
  • 02: Sum of vector, Triangle law of addition, Parallelogram law of addition, Properties of vector addition, Properties of vector multiplication, Addition inverse of vector, Unit vector, Vector joining two points 39 min
  • 03: Addition of vectors, Parallelogram law of vector addition, Multiplication of a vector by a Scalar, Two vectors are collinear, Relationship between l, m, and n, NCERT Exercise 10.2 42 min
  • 04: Product of two vectors, Scalar product of two vectors, Angle between two non-zero vectors, Properties of scalar product, Projection of a vector on a line, NCERT Exercise 10.3 45 min
  • 05: Anticlockwise Direction, Vector (or cross) product of two vectors, Properties of vector product, NCERT Exercise 10.4 51 min
  • 06: Types of Vector, Zero ve0ctor, Null vector, Unit vector, Collinear vector, Co-initial vector, Equal vector, Negative vector, Free vectors, NCERT Exercise 10.4 37 min
  • 07: Components of a vector, Unit vectors along the axes, Scalar components, Vector components, Rectangular components, Miscellaneous Exercise on Chapter 10, 35 min
  • 08: Scalar Product, Projection, Cross Product, Adjacent side of parallelogram, Adjacent side of triangle, Miscellaneous Exercise on Chapter 10 46 min
• Chapter 11: Three Dimensional Geometry 8 Lectures 5 hrs 31 min
  • 01: Basic Concepts, Direction Cosines and Direction Ratios of a Line, Direction cosines of a line passing through two points, Golden Concepts , NCERT Exercise 11.1 49 min
  • 02: Lines, Equation of line, Vector form, Cartesian form, Angle between two lines, Shortest Distance, Distance between two skew lines, Distance between two parallel lines, SL Examples 42 min
  • 03: Derivation of Cartesian form from vector form, Equation of a line passing through two given points, Distance from the origin, Vector Equation, Cartesian Equation, NCERT Exercise 11.2 37 min
  • 04: Plane, Equation of Plane, Normal form, Intercept form, Equation of plane where three points, Equation of plane through intersection of the planes, SL Examples 41 min
  • 05: Equation of a plane perpendicular to a given vector, Cartesian equation of plane, Plane passing through the intersection of two given planes, NCERT Exercise 11.3 47 min
  • 06: Co-planarity of Two Lines, Angle between Two Planes, Distance of a Point from a Plane, Angle between a Line and a Plane, NCERT Exercise 11.3 35 min
  • 07: Relationship between (l, m, n), Two lines are perpendicular to each other, Two lines are parallel to each other, Miscellaneous Exercise on Chapter 11 39 min
  • 08: Angle between two plane vector form, Distance of a point from the plane, Distance between two planes, Miscellaneous Exercise on Chapter 11 41 min
• Chapter 12: Linear Programming 5 Lectures 3 hrs 44 min
  • 01: Mathematical formulation of the problem, objective function, set of linear inequalities with variables, optimal value, linear constraints, decision variables, Golden Concept, SL Examples Preview52 min
  • 02: Optimisation problem, Subject to constraints, Feasible region, Unbounded feasible region, Types of LPP, At least, At most, NCERT Exercise 12.1 46 min
  • 03: Graphical method of solving linear programming problems, Feasible solution, Feasible choice, Corner Point Method, NCERT Exercise 12.2 47 min
  • 04: Allocation Problem, Manufacturing problem, Transportation problem, Diet Problem, Investment Problem, NCERT Miscellaneous exercise on chapter 12 39 min
  • 05: Important Questions for CBSE board exam, SL Examples, NCERT Miscellaneous exercise on chapter 12 40 min
• Chapter 13: Probability 14 Lectures 9 hrs 53 min
  • 01: Random Experiments, Outcome, Possible Result, Sample Space, sample point, Simple event, Important Formula, NCERT Exercise 13.1 Preview50 min
  • 02: Mutually Exclusive Events, Exhaustive Events, Conditional Probability, Compound event, SL Examples, NCERT Exercise 13.1 40 min
  • 03: Random Variables and its Probability Distribution, SL Examples, NCERT Exercise 13.1 37 min
  • 04: Multiplication Theorem on Probability, Independent Events, SL Examples, NCERT Exercise 13.2 42 min
  • 05: Independent events and mutually exclusive events, Attention Please, Some important concepts, NCERT Exercise 13.2 45 min
  • 06: Quick Revision, Discussion about cards, SL Examples, NCERT Exercise 13.2 39 min
  • 07: Baye’s Theorem, Golden Hint for Baye’s Theorem, SL Examples, NCERT Exercise 13.3 47 min
  • 08: Probability Distribution of a random variable, NCERT Examples, NCERT Exercise 13.3 40 min
  • 09: Probability Distribution, SL Examples, If a coin is tossed three times, If a coin is tossed four times, NCERT Exercise 13.4, 38 min
  • 10: Attention Please, Mean of a random variable, Variance of a random variable, SL Examples NCERT Exercise 13.4 46 min
  • 11: Mean, Variance, Standard Deviation, NCERT Exercise 13.4, Probability Distribution, Binomial Distribution, NCERT Exercise 13.5, 39 min
  • 12: Quick Revision of Binomial Distribution, Bernoulli Trials, SL Examples, NCERT Exercise 13.5 45 min
  • 13: Mean, Variance, Standard Deviation, NCERT Miscellaneous Exercise on Chapter 13 48 min
  • 14: Attention Please, NCERT Miscellaneous Exercise on Chapter 13 37 min