SYLLABUS - 2020- 2021 No. of MonthsWorking Topics Class - XII Sub - English Days July 25 FL - Indigo Books Prescribed : Poets & Pancakes 1. Flamingo (FL) Keeping Quiet (Poem) 2. Vistas (VS) AWS - Letter of Enquiry No. of - Invitation (Formal & Informal) MonthsWorking Topics Days - Poster - Speech Writing March 0 FL - My Mother at Sixty Six (Poem) The Last Lesson August 20 FL - Going Places AWS - Notice - A Thing of Beauty (Poem) Letter to the Editor A Roadside stand (Poem) Note - Making VS - Should Wizard Hit Mommy AWS - Debate April 21 FL - Lost Spring An Elementary School Sept25 Revision for 1st Term Classroom in a Slum (Poem) FL - The Interview VS - The Third Level Aunt Jennifer's Tiger (Poem) AWS - Letter to the School Authority The Tiger King AWS - Article Writing Oct 18 VS - On the Face of It (Play) Advertisements (Display & Classified) - Memories of Childhood May 12+5 FL - Deep Water Nov 10 FL - Revision VS - Journey to the end of the Earth VS - Evans Tries an O-Level The Enemy Dec21 Revision AWS - Letter for Placing Order & Cancellation Report Writing Job Application June 13 FL - The Rat Trap AWS - Letter of Complaint 1 2 Subject - Mathematics (Code - 041) No. of MonthsWorking Portion No. of Days MonthsWorking Portion Days matrices), properties of determinants, minors, co-factors and applications of de- March 07 Linear Programming terminants in finding the area of a triangle. Introduction, related terminology such as Adjoint and inverse of a square matrix. constraints, objective function, optimiza- Consistency, inconsistency and number of tion, different types of linear programming solutions of system of linear equations by (L.P.) problems, mathematical formulation examples, solving system of linear equa- of L.P. problems, graphical method of tions in two or three variables (having solution for problems in two variables, unique solution) using inverse of a matrix. feasible and infeasible regions (bounded Vectors or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to Vectors and scalars, magnitude and direc- three non-trivial constraints). tion of a vector. Direction consines and Mat rices direction ratios of a vector. Types of vectors. (equal, unit, zero,parallel and col- Concept, Notation, Order, Equality, Types linear vectors), Positon vector of a point, of Matrices, zero and identity matrix, trans- negative of a vector, components of a pose of a matrix, symmetric and skew sym- vector, addition of vectors, multiplication metric matrices. Operation on matrices : of a vector by a scalar, position vector of a Addition and multiplication and multiplica- point dividing a line segment in a given tion with a scalar. Simple properties of ratio. Definition, Geometrical Interpreta- addition, multiplication and scalar multipli- tion, properties and application of scalar cation. Non-commutativity of multiplication (dot) product of vectors, vector (Cross) of matrices and existence of non-zero product of vectors, scalar triple product of matrices whose product is the zero matrix vectors. (restrict to square matrices of order 2). Activity No. 13 Activity No. 5 April 21 Matrices Three - Dimensional Geometry Concept of elementary row and column Direction consines and direction ratios of operations. Invertible matrices and proof a line joining two points. Cartesian equa- of the uniqueness of inverse, if it exists; tion and vector equation of a line, copla- (Here all matrices will have real entries). nar and skew lines, shortest distance be- 2. Determinants tween tow lines. Cartesian and vector equation of a plane. Angle between (i) Two Determinant of a square matrix (up to 3x3 3 4 No. of No. of MonthsWorking Portion MonthsWorking Portion Days Days lines (ii) Two planes (iii) A line and a plane. Aug 21 1. Differentiation : Distance of a point from a plane. Derivative of composite functions, chain rule, derivative of inverse trigonometric May 12+06 Probability : functions, derivative of implicit functions. Conditional probability, multiplication theo- Concept of exponential and logarithmic rem on probability, independent events, functions. Derivatives of logarithmic and total probability, Bayes' theorem, Random exponential functions. Logarithmic variable and its probability distribution, differentiation, derivative of functions mean and variance of random variable. expressed in parametric forms. Second Repeated independent (Bernoulli) trials order deriatives. Rolle's and Lagrange's and Binomial distribution. Mean Value Theorems (without proof) and Activity No. 14 their geometric interpretation. June 12 QUALIFYING EXAMINATION Activity No. 6, 7 and 8 Relations 2. Applications of Derivatives Types of relations : reflexive, symmetric, transitive and equivalence relations. Applications of derivatives : rate of change Activity No. 1 of physical quantities, increasing / decreasing functions, tangents and normals, use of July 25 1. Functions derivatives in approximation, maxima and One to one and onto functions, composite minima (first derivative test motivated functions, inverse of a function. Binary geometrically and second derivative test operations. given as a provable tool). Simple problems Activity No. 3 and 4 (that illustrate basic principles and under- standing of the subject as well as real-life 2. Inverse Trigonometric Functions situations). Definition, range, domain, principal value Activity No. 9, 10, 11 and 15 branch. Graphs of inverse trigonometric functions. Elementary properties of inverse 3. Integrals trigonometric functions. Integration as inverse process of differen- Activity No. 2 tiation. Integration of a variety of functions by substitution, Evaluation of simple inte- 3. Continuity and Differentiability grals of the special types and problems Continuity and differentiability based on them by partial fractions. 5 6 No. of Lab Activity in Mathematics MonthsWorking Portion Days (Ten marks is allotted for Activity in Mathematics) Sept. 25 HALF YEARLY EXAM Integrals (Continued) : 1. To make a partition of a set of students of standard XII on the basis of a relation defined as R = {( a, b): a and Integration by parts, special integrals like b have same birth year .} and confirm it as an Equiva- 2 2 2 2 a - x , µ x +- a lence relation. -1 Oct 20 1. Integrals (Continued) : 2. To draw the graph of sin x using the graph of sin c Definite integrals as a limit of a sum, and demonstrate the concept of mirror reflection about Fundamental Theorem of Calculus (with- the line y = x. out proof). Basic properties of definite in- c tegrals and evaluation of definite integrals. 3. To sketch the graph of a and log a x, a > O, a 1 and 2. Applications of the Integrals to examine that they are mirror images of each other. Applications in finding the area under (Use a = 2 or 3) simple curves, especially lines, circles / parabolas / ellipses (in standard form only), 4. To establish a relationship between common logarithm Area between any of the two above said (to the base 10) and natural logarithm (to the base e) curves (the region should be clearly of number x. identifiable). Activity No. 12 5. Formation of code through matrix multiplication. Nov 19 Differential Equations : 6. To verify that for a function to be continuous at given Definition, order and degree, general and point x , Dy = | ( x + Dx) - (x )| is arbitrary small particular solutions of a differential o o o equation. Formation of differential provided , Dx is sufficiently small. equation whose general solution is given. 7. To verify Rolle's theorem by taking a suitable case. Solution of diffential equations by method of separation of variables, solutions of 8. To verify Langrange's Mean Value theorem. homogeneous differential equations. Solutions of linear differential equation of 9. To understand the concept of decreasing and increasing first order and first degree. functions. Pre Board - I 10. To understand the concepts of local maxima, local Dec 21 PRE - BOARD - II minima and point of inflection. 7 8 11. To understand the concept of Absolute maxima and Sub - Physics absolute minima of a function in a given closed No. of Month Working Topics to be covered interval through its graph. Days b March 13 Unit I : Electrostatics 12. To evaluate the definite integral 1 - 2 as the limit a x dx Ch. 1 : Electric Charges and Fields of the sum and verify it by actual integration. Electric charges; Conservation of charge, ç ç ç ç ç ç ç Coulomb's law-force between two point 13. To verify geometrically that c x ( a+ b) = ( c x a) + (c x b). charges, forces between multiple charges; superposition principle and continuous 14. To explain the computation of conditional probability of charge distribution. a given event A, when event B has already occurred Electric field, electric field due to a point through an example of throwing a pair of dice. charge, electric field lines, electric dipole, electric field due to a dipole, torque on a 15. To find the time when the area of a rectangle of given dipole in uniform electric field. dimension become maximum, of the length is decreasing April 21 Electric flux, statement of Gauss's theorem and breadth is increasing at a given rate. and its applications to find field due to infi- nitely long straight wire, uniformly charged Description of marks infinite plane sheet and uniformly charged Theory - 80 Marks thin spherical shell (field inside and outside). Periodic Test - 10 Marks Ch. 2: Electrostatic Potential and Lab Activity - 10 Marks Capacitance Total - 100 Marks Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipoten- tial surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field. Conductors and insulators, free charges and bound charges inside a conductor. Dielec- trics and electric polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without di- electric medium between the plates, energy stored in a capacitor. 9 10 No. of No. of Month Working Topics to be covered Month Working Topics to be covered Days Days Unit II : Current Electricity conductors-definition of ampere, torque Ch.