|
Unit No. |
Unit Name |
Chapter Name |
Unit Period |
Unit Marks |
Chapter Period |
|
1 |
Relations and Functions |
Chapter-1: Relations and Functions |
30 |
10 |
15 |
|
Chapter-2: Inverse Trigonometric Functions |
15 |
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|
2 |
Algebra |
Chapter-3: Matrices |
50 |
13 |
25 |
|
Chapter-4: Determinants |
25 |
||||
|
3 |
Calculus |
Chapter-5: Continuity and Differentiability |
80 |
44 |
20 |
|
Chapter-6: Applications of Derivatives |
10 |
||||
|
Chapter-7: Integrals |
20 |
||||
|
Chapter-8: Applications of the Integrals |
15 |
||||
|
Chapter-9: Differential Equations |
15 |
||||
|
4 |
Vectors and Three-Dimensional Geometry |
Chapter-10: Vectors |
30 |
17 |
15 |
|
Chapter-11: Three - dimensional Geometry |
15 |
||||
|
5 |
Linear Programming |
Chapter-12: Linear Programming |
20 |
6 |
20 |
|
6 |
Probability |
Chapter-13: Probability |
30 |
10 |
30 |
|
|
|
|
240 |
100 |
240 |
Chapter-1: Relations and Functions
- Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one
Chapter-2: Inverse Trigonometric Functions
- Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.
Chapter-3: Matrices
- Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).
Chapter-4: Determinants
- Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.
Chapter-5: Continuity and Differentiability
- Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.
Chapter-6: Applications of Derivatives
- Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normal’s, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).
Chapter-7: Integrals
- Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation of definite integrals.
Chapter-8: Applications of the Integrals
- Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).
Chapter-9: Differential Equations
- Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:
Chapter-10: Vectors
- Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors.
Chapter-11: Three - dimensional Geometry
- Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines.Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.
Chapter-12: Linear Programming
- Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions(bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
Chapter-13: Probability
- Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.
|
QUESTION PAPER DESIGN - CLASS - XII (2017-18) |
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|
MATHEMATICS (CODE - 041) (Time 3 Hours, Max. Marks: 100) |
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|
S. No. |
Typology of Questions |
Very Short Answer (1 marks) |
Short Answer (2 marks) |
Long Answer I (4 marks) |
Long Answer II (6 marks) |
Marks |
% Weightage |
|
1 |
Remembering- (Knowledge based Simple recall questions, to know specific facts, terms, concepts, principles, or theories, Identify, define, or recite, information) |
2 |
2 |
2 |
1 |
20 |
20% |
|
2 |
Understanding- (Comprehension -to be familiar with meaning and to understand conceptually, interpret, compare, contrast, explain, paraphrase information) |
1 |
3 |
4 |
2 |
35 |
35% |
|
3 |
Application- (Use abstract information in concrete situation, to apply knowledge to new situations, Use given content to interpret a situation, provide an example, or solve a problem) |
1 |
|
3 |
2 |
25 |
25% |
|
4 |
High Order Thinking Skills- (Analysis & Synthesis- Classify, compare, contrast, or differentiate between different pieces of information, Organize and/or integrate unique pieces of information from a variety of sources) |
|
3 |
1 |
|
10 |
10% |
|
5 |
Evaluation- (Appraise, judge, and/ or justify the value or worth of a decision or outcome, or to predict outcomes based on values) |
|
|
1 |
1 |
10 |
10% |
|
|
TOTAL |
1x4=4 |
2x8=16 |
4x11=44 |
6x6=36 |
100 |
100% |
|
Module |
Duration |
Chapter Name |
NCERT Book |
Exemplar Book |
NCERT Solution |
Chapterwise Assignments |
|
Module 1 |
3 months |
Chapter-1: Relations and Functions |
Download | |||
|
Chapter-2: Inverse Trigonometric Functions |
Download | Download | ||||
|
Chapter-3: Matrices |
Download | Download | ||||
|
Chapter-4: Determinants |
Download | Download | ||||
|
Module 2 |
3 months |
Chapter-5: Continuity and Differentiability |
Download | Download | ||
|
Chapter-6: Applications of Derivatives |
Download | Download | ||||
|
Chapter-7: Integrals |
Download | Download | ||||
|
Chapter-8: Applications of the Integrals |
Download | Download | ||||
|
Chapter-9: Differential Equations |
Download | Download | ||||
|
Module 3 |
2 months |
Chapter-10: Vectors |
Download | |||
|
Chapter-11: Three - dimensional Geometry |
Download | Download | ||||
|
Chapter-12: Linear Programming |
Download | |||||
|
Chapter-13: Probability |
Download |
Download |
||||
|
Module 4 |
2 months |
Revision & Full Length Tests |
|
|
- Full Coverage of NCERT Text books and NCERT Exemplar Problems
- Chapter Revision Assignments (Based on Last 10 years question papers)
- Unit Revision Assignments (Based on Last 10 years question papers)
- Initial performance analysis based last class report card
- 13 Chapter tests to cover each chapters
- 5 Unit tests to cover 6 Units
- 3 cumulative tests
- 10 Full Length tests – 5 Model Test Papers, 5 Last Year papers
- Mathematics Part I - Textbook for Class XII, NCERT Publication
- Mathematics Part II - Textbook for Class XII, NCERT Publication
- Mathematics Exemplar Problem for Class XII, Published by NCERT