Mathematics - XII Syllabus

Mathematics – XII Syllabus

Group A

UNIT 1: PERMUTATION AND COMBINATION (10 TEACHING 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 TEACHING 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 TEACHING 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
  • Uniqueness of identity
  • Uniqueness of inverse
  • Cancellation law
  • Abelian group

UNIT 4: CONIC SECTIONS (12 TEACHING HOURS)

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

UNIT 5: CO – ORDINATES IN SPACE (12 TEACHING 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 TEACHING HOURS)

  • Cartesian representation of vectors
  • Colinear and non-colinear vectors
  • Coplanar and non-Coplanar vectors
  • Linear combination of 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 TEACHING 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 TEACHING HOURS)

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

UNIT 9: DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS (7 TEACHING HOURS)

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

UNIT 10: DISPERSION, CORRELATION AND REGRESSION (12 TEACHING 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 TEACHING 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 TEACHING HOURS)

  • Forces 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 TEACHING 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 TEACHING 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 be restated and formulated as application of calculus

UNIT 15: DYNAMICS (CONTINUED) (9 TEACHING HOURS)

  • Newton’s laws of motion
  • Impulse
  • Work, energy and power
  • Projectiles

Group C

UNIT 16: LINEAR PROGRAMMING (11 TEACHING 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 TEACHING 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)
  • Approximations and error in computing Roots of nonlinear equation
  • Algebraic, polynomial & transcendental equations and their solution by bisection and Newton – Raphson Methods

UNIT 18: COMPUTATIONAL METHOD (CONTINUED) (8 TEACHING HOURS)

  • Solution of system of linear equations by Gauss elimination method
  • Gauss – Seidel method
  • Ill conditioned system
  • Matrix inversion method

UNIT 19: NUMERICAL INTEGRATION (8 TEACHING HOURS)

  • Trapezoidal and Simpson’s rules
  • Estimation of errors