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Chapter - Relations and Functions
OFFICIAL SYLLABUS 2022
Subject - Mathematics
Subject Code - 15
There will be only one paper of 03:15 Hours of 80 marks.
Unit Name and Marks
1. RELATIONS AND FUNCTIONS - 7 Marks
2. ALGEBRA - 10 Marks
3. CALCULUS - 36 Marks
4. VECTORS AND THREE - DIMENSIONAL GEOMETRY - 16 Marks
5. LINEAR PROGRAMMING - 4 Marks
6. PROBABILITY - 7 Marks
DETAILED SYLLABUS
RELATIONS AND FUNCTIONS
Relations and Functions
Types of relations: reflexive, symmetric, transitive, and equivalence relations. One to one and onto functions Composition of Functions and Invertible Function. Binary operations.
Inverse Trigonometric Functions
Basic Concepts, Properties of Inverse Trigonometric Functions
ALGEBRA
Matrices
Matrices, Order of a matrix, Types of matrices: Column matrix, Row matrix,Square matrix, Diagonal matrix, Scalar matrix, Identity matrix,zero matrix, Operations on Matrices, Addition of matrices, Multiplication of a matrix by a scalar, Properties of matrix addition, Properties of scalar multiplication ofa matrix, Multiplication of matrices, Properties of multiplication of matrices, Transpose of a Matrix, Properties of transpose of matrices, Symmetric and Skew Symmetric, Elementary Operation, Invertible Matrices (Transformation) of a matrix.
Determinants
Determinant, Determinant of a matrix of order one, Determinant of a matrix of order two, Determinant of a matrix of order 3 × 3, properties of determinants, Area of a Triangle minors and cofactors Adjoint and inverse of a matrix. Applications of Determinants and matrices.
CALCULUS
Continuity and Differentiability
Continuity ,Algebra of continuous functions differentiability, Derivatives of composite functions, Derivatives of Implicit Functions, Derivatives of Inverse Trigonometric Functions , Exponential and Logarithmic Functions , Logarithmic Differentiation, Derivatives of Functions in Parametric Forms, Second Order Derivative, Mean Value Theorem.
Applications of Derivatives
Applications of derivatives: Rate of Change of Quantities, increasing and decreasing functions, Tangents and Normals, use of derivatives in approximation, maxima and minima, Maximum and Minimum Values of a Function in a Closed Interval , Working Rule.
Integrals
Integration as inverse process of differentiation: Geometrical interpretation of indefinite integral, Some properties of indefinite integrals, Comparision between differentiation and integration, Methods of Integration, Integration by substitution, Integrals of Some Particular Functions, Integration by Partial Fractions, Integration by Parts:(Integrals of some more types, Definite Integral, Definite integral as the limit of a sum, Fundamental Theorem of Calculus: Area function, First fundamental theorem of integral calculus, Second fundamental theorem of integral calculus, Evaluation of Definite Integrals by Substitution, Some Properties of Definite Integrals.
Applications of the Integrals
Area under simple curves: The area of the region boundedby a curve and a line,Area Between Two Curves,, areas of circles,parabolas/ellipses (in standard form only), area between the two above said curves(the region should be clearly identifiable).
Differential Equations
Basic Concepts: Order of a differential equation, Degree of a differential equation, General and Particular Solutions of a Differential Equation, Formation of a Differential Equation whose Solution is Given, Procedure to form a Differential Equation that will represent a given Family of curves, Differential equations with variables separable, Homogenous differential equations. Linear differential equations.
VECTORS AND THREE-DIMENSIONAL GEOMETRY
Vectors and three dimensional geometry
Basic Concepts. Types of Vectors. Addition of Vectors. Multiplication of a Vector by a Scalar. Components of a vector. Vector joining two points. Section Formula. Product of Two Vectors. Scalar (or dot) product of two vectors. Projection of a vector on a line. Vector (or cross) product of two vectors.
Three Dimensional Geometry
Direction Cosines and Direction Ratios of a Line. Relation between the direction cosines of a line. Direction cosines of a line passing through two points. Equation of a Line in Space. Equation of a line through a given point A and parallel to a given vector b. Equation of a line passing through two given points. Angle between two lines. Shortest Distance between two lines. Distance between two skew lines. Distance between parallel lines. Plane. Equation of a Plane in normal form. Equation of a plane perpendicular to a given vector and passing through a given point. Equation of a plane passing through three non-collinear points. Intercept form of the equation of a plane. Plane passing through the intersection of two given planes. Co planarity of two lines. Angle between two planes. Distance of a point from a plane. Vector Form and Cartesian form. Angle between a line and a plane.
LINEAR PROGRAMMING
Linear Programming
Introduction, definition of 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, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
PROBABILITY
Probability
Probability Conditional probability, Properties of conditional probability, Multiplication theorem on probability, independent events, total probability, Baye’s theorem, theorem of total probability , Random variable and its probability distribution, Probability distribution of a random, variable. mean and variance of random variable. Repeated
...There will be One Paper in this Subject.
Time Duration : 3:15 Hrs.
Maximum Marks : 80 Marks
Units & their Weightage
| S.No | Topic | Marks |
| 1 | Relations and Functions | 07 |
| 2 | Algebra | 10 |
| 3 | Calculus | 36 |
| 4 | Vectors and Three Dimensional Geometry | 28 |
| 5 | Linear Programming | 15 |
| 6 | Probability | 07 |
| Total | 80 |
Conditions of eligibility for admission to class XII
1. Candidates who have been studying in a School recognised by or affiliated to this Board or any other recognised Board of Secondary Education in India.
2. Candidates can not take admission directly in class XII.
3. Candidates had completed a regular course of study for class XI and passed class XI examination from a school affilicated to this Board.
4. The candidates percentage for attendance should be 75% so that the Board to make him/her eligible for the Examinations.
5. Candidate can be admitted to a school only on the transfer of the parents(s) or shifting of their families from one place to another, after procuring from the student the marksheet and the Transfer Certificate duly countersigned by the Educational Authorities of the Board Concerned.
6. There is no age limit for candidates taking the Examination.
7. Candidate should have doucments in support of his having passed the qualifying or equivalent qualifying examination.
OFFICIAL TIME TABLE 2022
Maths Paper dated 13th April, 2022 (Wednesday) from 9:00 AM to 11:45 AM
| Date | Subject(s) | Timing |
| March 24, 2022 | Psychology | 9:00 Am to 11:45 Am |
| March 25, 2022 | Environmental Science | 9:00 Am to 11:45 Am |
| March 26, 2022 | Public administration | 9:00 Am to 11:45 Am |
| March 28, 2022 | Physical education | 9:00 Am to 11:45 Am |
| March 29, 2022 | Vocal Music/ Instrumental Music | 9:00 Am to 11:45 Am |
| March 30, 2022 | Sociology | 9:00 Am to 11:45 Am |
| April 1, 2022 | Sanskrit literature, Sanskrit language | 9:00 Am to 11:45 Am |
| April 4, 2022 | Geography, Accountancy, Physics | 9:00 Am to 11:45 Am |
| April 6, 2022 | English (Compulsory) | 9:00 Am to 11:45 Am |
| April 8, 2022 | Hindi (Compulsory) | 9:00 Am to 11:45 Am |
| April 11, 2022 | History, Chemistry, Agricultural Chemistry, Business Studies | 9:00 Am to 11:45 Am |
| April 12, 2022 | English Literature/ Tankan Lipi (Hindi) | 9:00 Am to 11:45 Am |
| April 13, 2022 | Mathematics | 9:00 Am to 11:45 Am |
| April 16, 2022 | Economics, Biology, English, Shorthand Hindi, Agricultural Biology | 9:00 Am to 11:45 Am |
| April 18, 2022 | Computer Science, Informatics Practices | 9:00 Am to 11:45 Am |
| April 19, 2022 | Home Science | 9:00 Am to 11:45 Am |
| April 20, 2022 | Philosophy, General Science | 9:00 Am to 11:45 Am |
| April 21, 2022 | Political Science, Geology, Agriculture | 9:00 Am to 11:45 Am |
| April 22, 2022 | Vocational subjects | 9:00 Am to 11:45 Am |
| April 23, 2022 | Hindi literature, Urdu literature, Sindhi literature, Gujarati literature, Punjabi literature, Rajasthani literature, Persian literature, Prakrit language, Typing lipi (English) | 9:00 Am to 11:45 Am |
| April 26, 2022 | Painting | 9:00 Am to 11:45 Am. |
ANALYSIS - (SR. SECONDARY 2020) CODE - SS-15
1. There are total 30 questions in this part.
2. This question paper is divided into four parts: Part A (One Word Question), Part B (Very Short Answer Question), Part C (Short Answer Question) and Part D (Long Answer Question)
3. All parts are compulsory. Solve all the parts of a question together.
4. There are total 10 questions in Part A. Question 1 to 10 carry 1 marks for each question.
5. There are total 5 questions in Part B. Question 11 to 15 carry 2 marks for each question.
6. There are total 10 questions in Part C. Question 16 to 25 carry 3 marks for each question.
7. There are total 5 questions in Part D. Question 26 to 30 carry 6 marks for each question.
8. Draw the graph of Q. No. 25 on the graph paper
9. Internal Choice is not given in this Paper.
Comment
1. The difficulty level of the Maths paper 2020: Moderate
2. All the questions in the paper were asked from the latest syllabus and based on NCERT textbooks.
4. The average range of expected marks was 65+ (out of 80).
1. There are total 30 questions in this part.
2. This question paper is divided into four parts: Part A (One Word Question), Part B (Very Short Answer Question), Part C (Short Answer Question) and Part D (Long Answer Question)
3. All parts are compulsory. Solve all the parts of a question together.
4. There are total 10 questions in Part A. Question 1 to 10 carry 1 marks for each question.
5. There are total 5 questions in Part B. Question 11 to 15 carry 2 marks for each question.
6. There are total 10 questions in Part C. Question 16 to 25 carry 3 marks for each question.
7. There are total 5 questions in Part D. Question 26 to 30 carry 6 marks for each question.
8. Draw the graph of Q. No. 25 on the graph paper
9. Internal Choice is not given in this Paper.
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