Mathematics Syllabus XII

Grade – XII

Teaching hours 150                                        

Unit 1: Permutation and Combination (10 Hours)

  • Basic Principle of counting
  • Permutation of (a) set of objects all different
  • (b) Set of objects not all different
  • (c) circular arrangement
  • (d) repeated use of the same object
  • Combination of things all different
  • Properties of combination.

 

Unit 2: Binomial Theorem (10 Hours)

  • Binomial theorem for a positive integral index
  • General term
  • Binomial coefficients
  • Binomial theorem for any index (Without proof)
  • Application to approximation
  • Euler's number
  • Expansion of ex, ax and log(1+x) (without proof)

 

Unit 3: Elementary Group Theory (8 Hours)

  • Binary operation
  • Binary operation on sets of integers and their properties
  • Definition of a Group
  • Groups whose element are not numbers
  • Finite and infinite groups
  • Uniquences of identity
  • Uniquences of inverse
  • Cancellation law
  • Abelian Group

 

Unit 4: Conic Sections (12 Hours)

  • Standard equation of parabola, Ellipse and Hyperbola
  • Equations of tangent and normal to a parabola at a given point

 

Unit 5: Co - Ordinates in Space (12 Hours)

  • Co - ordinate axes
  • Co - ordinate planes
  • The octants
  • Distance between two points
  • External and internal point of division
  • Direction cosines and ratios
  • fundamental relation between direction cosines
  • Projections
  • Angle between two lines
  • General equation of a plane
  • Equation of a plane in intercept and normal form
  • Plane through three given points
  • Plane through the intersection of two given planes
  • Parallel and perpendicular planes
  • Angle between two planes
  • Distance of a point from a plane.

 

Unit 6: Vectors and Its Applications (14 Hours)

  • Cartesian representation of vectors
  • Collinear and non - collinear vectors
  • Coplanar and non-Coplanar vectors
  • Linear combination of vectors
  • Scalar product of two vectors
  • Angle between two vectors
  • Geometric interpretation of scalar product
  • Properties of Scalar Product
  • Condition of perpendicularity
  • Vector product of two vectors
  • Geometric interpretation of vector product
  • Properties of vector product
  • Application of product of vectors in plane trigonometry.

 

Unit 7: Derivative and Its Application (14 Hours)

  • Derivative of inverse trigonometric, exponential and logarithmic functions by definition
  • Relationship between continuity and differentiability
  • Rules for differentiating hyperbolic function and inverse hyperbolic function
  • Composite function and function of the type f(x)^g(x)
  • L'Hospital's rule (for 0/0, ¥/¥)
  • Differentials
  • Tangent and Normal
  • Geometric interpretation and application of Rolle's theorem and Mean value theorem.

 

Unit 8: Antiderivatives (7 Hours)

 

Unit 9: Differential Equations and their Applications (7 Hours)

 

Unit 10: Dispersion, Correlation and Regression (12 Hours)

 

Unit 11: Probability (8 Hours)

 

Unit 12: Statics (9 Hours)

 

Unit 13: Statics (Continued) (9 Hours)

 

Unit 14: Dynamics (9 Hours)

 

Unit 15: Dynamics (Continued) (9 hours)

 

Unit 16: Linear Programming (11 Hours)

 

Unit 17: Computational Method (9 Hours)

 

Unit 18: Computational Method (Continued) (8 Hours)

 

Unit 19: Numerical Integration (8 Hours)