Curriculum And Syllabus For Classes XI & XII

One Paper

3 Hours

100 Marks

Algebra

30 Marks

 63 Periods

1.

 Complex Numbers

2.

 Sequences 

3.

 Series

Direct variation, Inverse variation, Theorem on Joint variation.

Conditions for resolvability of an algebraic rational fraction, Exceptional cases (including repeated linear factors and irreducible quadratic factors in the denominator).

Binomial theorem for a positive integral index ,General term, Greatest term (a + x )ⁿ, Binomial theorem for any index (without proof), Application of Binomial theorem for approximate values, Logarithm, Exponential and Binomial Series.

Solution of simultaneous equations - One linear and the other quadratic, Solution of exponential equations and solution of exponential equations with the help of the logarithmic table.

(i) Definition of the root of an equation, Factor theorem, Proof of ,a quadratic equation cannot have more than two roots", Nature of roots (discriminate of a quadratic equation) Relation between the roots and coefficient of a quadratic equation. Formation of quadratic equations with given roots, Condition for common roots of two quadratic equations.

(ii) Quadratic expressions :

Sign of a quadratic expression, Maximum and Minimum value of a quadratic expression.

1. Measures of Dispersion ; Skewness and Kurtosis, Moments up to the 3rd order.

2. Probability-definition (Mathematical definition of probability), Terms related to probability, Simple and compound events, Conditional probability, Mathematical expectation, Sum and product theorems.

3. Three standard distributions (Binomial, Poisson and Normal) with special reference to mean and standard deviation.

Rectangular Cartesian co-ordinates , Oblique axes ,Polar co-ordinates, Advantages of the Rectangular Cartesian system , Relation between Cartesian and polar co-ordinates. Transformation of co-ordinates (change of origin only).

 

Distance between two points, section formulae, Area of a triangle and condition of collinearity of 3 points
 

Various forms of the equation of straight line :
Gradient form, Intercept form, Normal form through a given point ; General equation  with a given gradient, as joint of two given points ; General equation of 1st degree in two variables represents a straight line (proof); Transformation of the equation of straight line from one form to another ; Distance of a point from the straight line ; Angle between two straight lines ; Condition of perpendicularity and parallelism ; System of straight lines passing through the point of intersection of two lines ; Equation of the bisectors of the angles between two straight lines,
 

Definition ; Equation of a circle having origin as centre ; General equation of a circle ; Equation of a circle with the join of two points as diameter ; Interior and exterior of a circle Tangents and normals to a circle and their equations Condition of a straight line to be a tangent to a circle.
 

Definitions ( old and new ); Standard equation of a parabola, ellipse and hyperbola; Tangents and normals to them ; Condition of tangency.
 

Historical background of linear programming; Practical necessity ; Formation of inequations ;Objective functions ; Constraints ; Optimization ; Feasible reason; Unbounded region ;Infeasible solution; Basic feasible solution ; Basic variables, Degeneracy ; inadequacy of graphic methods in solving problems involving 3 or more variables ;Mathematical formulation of a linear programming - problem and its solution by graphic method.

Books Recommended

A Textbook of Mathematics (for class XI) by B.K. Dev Sharma and D. Nath published by Wiley Eastern Ltd., New Delhi.

Class XII

Inadequacy of the old concept of function; Concept of function as a mapping; Range and Domain of a function;

Graphs of functions including |x |, [x], log_e x and e^x ;

Idea of limits ;

Condition for the existence of limits;

Standard limits e. g.,

(1) lim  (x ⁿ- aⁿ)/(x- a)( with proof.) ,
     x→a

(2) lim     sin x (without proof),
     x→0   x

(3) lim      (1+1/x) x , x Є R ( without proof);
     x→∞       

Continuity :

Condition for continuity of a function at a point;

Derivatives ;

Differential coefficients of Trigonometric, Inverse Trigonometric, Algebraic, Transcendental , Implicit and parametric functions; Fundamental rules of differentiation; Derivative of function of a function; Derivative as rate measurer; Geometrical interpretation of dy/dx Equation of tangent and normal to a curve; Increasing and decreasing functions; Signs of derivatives; and Maxima and Minima,

Integration as anti - derivative ; Integration by parts; Integration by substitution and by partial fractions; Integration as the limit of a sum ; Fundamental theorem of Integral Calculus (without proof) ; Some properties of definite integrals ; Standard integrals ; Integration as area.

Differential equations ; order and degree ; formation of a differential equation ; general and particular solution of a differential equation; solution of a differential equation by the method of variable separable’; homogeneous equations and their solutions ; the linear equation of first order of the type dy / dx +p (x) y =Q (x) and their solutions.

Definition of a scalar and a vector ; Addition and subtraction of vectors ; Multiplication of vector by a scalar; Application to Geometry.

Decomposition of vectors; three fundamental unit vector product of two vectors ; Derivation of sine and cosine rules ; Physical interpretation of product of two vectors.
 

Kinematics : Rectilinear motion ; Analytical derivation of velocity , acceleration ; motion under more than one velocity ; Resolution and composition of velocities; Uniformly accelerated motion ; motion under gravity including projectiles in vacuum.

Kinetics : Newton’s laws of motion ; impulse ; Principle of conservation of energy ; Work – Energy relations.

Composition and resolution of forces (Concurrent and parallel); Moment of a force, Varignon’s theorem ;couples ; General condition of equilibrium of three coplanar forces (without proof).

Origin of determinants ; Definition of a determinant ; Minor co- factors; opening of determinants By Laplace's method ; Simple properties of determinants, viz,

(1) Invariance of the absolute value of determinant under different operations,

(ii) Vanishing of determinant.

(iii) Multiplication of a determinant by a constant ; Solution of linear equations by Cramer's rule.

Definition of m x n matrix ;Different types of matrices (Row, Column, Unit, Null, Scalar, Diagonal, Symmetric, Skew-symmetric, Square, Hermitian and Skew-Hermitian Matrices)

Multiplication of a matrix by a scalar ;

Conformability of addition (subtraction) of two matrices-Associative property ;

Conformability of multiplication of two matrices;

 Non-commutativity and distributive properties of the product of matrices ;

Adjoint of matrix, singular matrix, Inverse of a matrix (up to 3x3) ;Solution of linear simultaneous equations by matrix method ; Consistency of linear equations.

Different systems of co-ordinates-Rectangular Cartesian system, Cylindrical system, Spherical polar system (the latter two definitions only ) ; Octants; Distance between two points ; section formula ; Direction cosines and direction ratios Angle between two straight lines with given d.e’s/d.r’s ;conditions of perpendicularity and parallelism of two straight lines; Equation of planes in various forms; 1st degree equation in three variables represents a plane ; Angle between two planes; Distance of a point from a plane. Straight line ; Symmetrical form from non-symmetrical form ; General equation of a sphere; Equation of a sphere with the join of two points as diameter Interior and exterior of a sphere.

Books Recommended

1. Senior School Mathematics (for class XII) by Dr. J.N. Kapoor & Others, published by Frank Bros. & Co.

2. A Textbook of Mathematics ( for Class XII) by P.L. Singh, published by S.I. & Co., Paona Bazar, Imphal.