Mathematics Syllabus XII

Grade – XII

Teaching hours 150             

Group 'A'                          

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)

  • Antiderivatives
  • Standard Integrals
  • Integrals reducible to standard forms
  • Integrals of rational functions.

 

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

  • Differential equation and its order and degree
  • Differential equations of first order and first degree
  • Differential equations with separable variables
  • Homogeneous and exact differential equations.

 

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

  • Dispersion
  • Measures of dispersion (Range, Semi interquartile range, Mean deviation, Standard deviation)
  • Variance
  • Coefficient of variation
  • Skewness
  • Karl Pearson's and Bowley's Coefficient of Skewness
  • Bivariate distribution
  • Correlation
  • Nature of correlation
  • Correlation coefficient by Karl Pearson's method
  • Interpretation of correlation coefficient
  • Properties of correlation coefficient (Without proof)
  • Regression equation
  • Regression line of y on x and x on y.

 

Unit 11: Probability (8 Hours)

  • Random experiment
  • Sample space
  • Event
  • Equally likely cases
  • Mutually exclusive events
  • Exhaustive cases
  • Favourable cases
  • Independent and dependent cases
  • Mathematical and empirical definition of probability
  • Two basic laws of probability
  • Conditional probability (without proof)
  • Binomial distribution
  • Mean and Standard deviation of binomial distribution (without proof)

 

Group 'B'

 

Unit 12: Statics (9 Hours)

  • Force and Resultant forces
  • Parallelogram of forces
  • Composition and resolution of forces
  • Resultant of coplanar forces acting at a point
  • Triangle of forces and Lami's theorem

 

Unit 13: Statics (Continued) (9 Hours)

  • Resultant of like and unlike parallel forces
  • Moment of a force
  • Varignon's theorem
  • Couple and its properties (without proof).

 

Unit 14: Dynamics (9 Hours)

  • Motion of particle in a straight line
  • Motion with uniform acceleration
  • Motion under gravity
  • Motion down a smooth inclined plane
  • The concepts and theorems can be restated and formulated as application of calculus.

 

Unit 15: Dynamics (Continued) (9 hours)

  • Newton's laws of motion
  • Impulse
  • Work
  • Energy and Power
  • Projectiles.

 

Group 'C'

 

Unit 16: Linear Programming (11 Hours)

  • Introduction of a linear programming problem (LPP)
  • Graphical solution of LPP in two variables
  • Solution of LPP by simplex method (two variables)

 

Unit 17: Computational Method (9 Hours)

  • Introduction to Numerical computing (Characteristics of Numerical computing, Accuracy, Rate of Convergence, Numerical Stability, Efficiency)
  • Number systems (Decimal, Binary, Octal & Hexadecimal system conversion of one system into another)
  • Approximation and error in computing Roots of nonlinear equation
  • Algebric, Polynomial & Transcendental equations and their solution by bisection and Newton - Raphson Methods.

 

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

  • Solution of system of linear equations by Gauss elimination method
  • Gauss - Seidel method
  • Ill Conditioned systems
  • Matrix inversion method

 

Unit 19: Numerical Integration (8 Hours)

  • Trapezoidal and Simpson's rules
  • Estimation of errors

Evaluation Scheme:

No. of questions Marks Total Remarks
15 2 30 Covering all Units
10 4 40 With four OR - questions from the same.
5 6 30 With two OR - questions from the same.