###### 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