# 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