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Class: XII Subject: Mathematics NO. OF TOPIC SUB-TOPIC LEARNING OBJECTIVES / ASSESSMENT / LEARNING OUTCOMES PERIOD SKILLS TO BE DEVELOPED ACTIVITIES 15 Continuity and Continuity, Differentiability, Points of discontinuity of Practice sheet To identify points of discontinuity differentiability Exponential and logarithmic functions, identify points of of functions, To identify points of functions, Logarithmic non-differentiability of non-differentiability of functions, differentiation, Derivatives in functions, derivatives of To find derivatives of exponential parametric form, Second exponential and logarithmic and logarithmic functions, To find order derivatives, Mean functions, derivatives of derivatives of functions in value theorem functions in parametric form parametric form 15 Applications of Rate of change of Quantities, Rate of change of dependent Practice sheet To find Rate of change of Derivatives Increasing and decreasing variable due to change in dependent variable due to functions, Tangents and independent variable, change in independent variable, normal, Approximations, increasing and decreasing To identify increasing and Maxima and minima functions, equation of tangent decreasing functions, To find and normal at a point on the equation of tangent and normal given curve, error in a variable at a point on the given curve, To due to error in another find error in a variable due to variable, approximate values error in another variable, To find of quantities using derivatives, approximate values of quantities maxima and minima points of using derivatives, To find maxima a function and minima points of a function 12 Matrices Types of Matrices, Add 2 matrices, Expressing Practice sheet To add 2 matrices, Expressing Operations on matrices, matrix as sum of symmetric matrix as sum of symmetric and Transpose of a matrix, and skew symmetric matrices, skew symmetric matrices, To find Symmetric and skew inverse of a matrix by using inverse of a matrix by using symmetric matrices, elementary row elementary row transformations Elementary row transformations transformations of a matrix, Inverse of a matrix Taurian World School, Ranchi 1|Page Class: XII Subject: Mathematics NO. OF TOPIC SUB-TOPIC LEARNING OBJECTIVES / ASSESSMENT / LEARNINGOUTCOMES PERIOD SKILLS TO BE DEVELOPED ACTIVITIES 12 Determinants Properties of determinants, Area of triangle, To Practice sheet To find area of triangle, To Area of a triangle, Minors understand properties to understand properties to simplify and cofactors, Adjoint and simplify determinants, system determinants, To solve system of inverse of a matrix, of equations using matrices. equations using matrices. Applications of determinants and matrices 15 Relation and Types of relations, Types of Identify one to one, onto and Practice sheet To identify one to one, onto and functions functions, Composition of invertible functions., inverse of invertible functions., To find functions and invertible a function if it exists., whether inverse of a function if it exists., functions, Binary operations the binary operation is To identify whether the binary associative, commutative., find operation is associative, identity and inverse of binary commutative., To find identity operations and inverse of binary operations 15 Inverse Basic concepts and graph, Inverse values of trigonometric Practice sheet To find inverse values of trigonometric Properties of Inverse functions trigonometric functions functions trigonometric functions 20 Integrals Integration as an inverse Indefinite and definite Practice sheet To solve both indefinite and process of differentiation, integrals definite integrals Methods of Integration, Integration of special functions, Method of Partial fractions, By-Parts, Definite Integral, Definite integral using substitution and properties 10 Applications of Introduction, Area under Area using integration Practice sheet To find Area using integration Integrals simple curves, Area between 2 curves Taurian World School, Ranchi 2|Page Class: XII Subject: Mathematics NO. OF TOPIC SUB-TOPIC LEARNING OBJECTIVES / ASSESSMENT / LEARNING OUTCOMES PERIOD SKILLS TO BE DEVELOPED ACTIVITIES 15 Differential Introduction, Degree and Degree and order of a Practice sheet To identify degree and order of a Equations order, General and particular differential equation, form differential equation, To form solution, Formation of differential equation when differential equation when differential equation, solution is given, differential solution is given, To solve Solution to first order, first equations using variable differential equations using degree differential equations separable, homogeneous, variable separable, Linear DE method homogeneous, Linear DE method 15 Vector Algebra Introduction, Types of Dot product and cross product Practice sheet To find dot product and cross vectors, Addition of vectors, of 2 vectors, Scalar triple product of 2 vectors, To find Multiplication of vectors by product of 3 vectors, Scalar triple product of 3 vectors, scalar, Dot and cross product, projection of one vector on To find projection of one vector Scalar triple product another , To analyze vectors if on another , To analyze vectors if dot product or cross product is dot product or cross product is zero zero 15 Three Direction cosines and ratios Equation of line in space in Practice sheet To find equation of line in space Dimensional of a line, Equation of line in Cartesian and vector form, in Cartesian and vector form, To geometry space, Angle between 2 lines, equation of plane in Cartesian find equation of plane in Shortest distance between 2 and vector form , To find angle Cartesian and vector form , To lines , Equation of plane, between 2 lines using DCS, find angle between 2 lines using Coplanarity of 2 lines, Angle distance between 2 lines, DCS, To find distance between 2 between 2 planes, Distance angle between 2 planes using lines, To find angle between 2 of a point from a plane, Angle normal lines, distance planes using normal lines, To find between a line and a plane between a point from a plane distance between a point from a plane Taurian World School, Ranchi 3|Page Class: XII Subject: Mathematics NO. OF TOPIC SUB-TOPIC LEARNING OBJECTIVES / ASSESSMENT / LEARNING OUTCOMES PERIOD SKILLS TO BE DEVELOPED ACTIVITIES 13 Linear The problem and Solutions to problems Practice sheet To find solutions to problems programming mathematical formulation, Applications in daily life 20 Probability Conditional probability, Probability using conditional Practice sheet To find probability using Multiplication theorem , probability formula, solve conditional probability formula, Addition theorem, problem by Bayes’ theorem, To identify and solve problem by Independent events , Bayes’ probability distribution of Bayes’ theorem, To find theorem, Random variables different random variables, probability distribution of and its probability solve problem by using different random variables, To distribution, Bernoulli trials Bernoulli trials, identify and solve problem by and binomial distribution using Bernoulli trials, Taurian World School, Ranchi 4|Page
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