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31-Dec-2027
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Class 12th Mathematics Series, Term I, Part A
(Course ID : MAC-57)
School & Boards Exam - (स्कूल और बोर्ड परीक्षायें) » CBSE - Central Board of Secondary Education » Class XII » Mathematics
कक्षा १२ के छात्रों के लिए गणित की शिक्षा।
The course "Class 12th Mathematics Series, Term I, Part A" is designed especially for class XII, CBSE Board students but other board students may also join the course. The course series has four parts to cover full class XII, Mathematics syllabus and Part A ie. Class 12th Mathematics Series, Term I, Part A contains the following chapters as shown below.
1) Relations and Functions (संबंध एवं फलन).
2) Inverse Trigonometric Functions (प्रतिलोम त्रिकोणमिति फलन).
3) Matrices (आव्यूह).
4) Determinant (सारणिक).
The course is available for both, English and Hindi Medium. Teachers are requested to mention their course medium while creating the batch for students' convenience.
1) Relations and Functions (संबंध एवं फलन).
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto, functions, Composite functions, Inverse of a function.
2) Inverse Trigonometric Functions (प्रतिलोम त्रिकोणमिति फलन).
Definition, range, domain, principal value branch.
3) Matrices (आव्यूह).
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. Noncommutativity of multiplication of matrices, Invertible matrices; (Here all matrices will have real entries).
4) Determinant (सारणिक).
Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.
Note: Basic Book - R. D. Sharma, 2 Test, One Objective and One Subjective. Solve Past 10 Years Papers in the class. Teachers are requested to consider the note.
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Topics :
| Days | Lecture Title | Topics Covered |
|---|---|---|
| Day # 1 | Relations and Functions (संबंध एवं फलन) | Introduction, Types of relations: reflexive, symmetric, transitive and equivalence relations |
| Day # 2 | Relations and Functions (संबंध एवं फलन) | Relation Domain, Range, Codomain, Mapping, Solved Problems |
| Day # 3 | Relations and Functions (संबंध एवं फलन) | Function, Domain, Range & Standard functions |
| Day # 4 | Relations and Functions (संबंध एवं फलन) | Domain & Range of Functions |
| Day # 5 | Relations and Functions (संबंध एवं फलन) | Types of functions, One-One, Many - One, Onto, Into functions & Solved Examples |
| Day # 6 | Relations and Functions (संबंध एवं फलन) | Odd and Even functions, Periodic functions, Solved Problems |
| Day # 7 | Relations and Functions (संबंध एवं फलन) | Composite functions, Inverse of a function and Past 10 Years Paper solving |
| Day # 8 | Practice Session - I | Relations and Functions (संबंध एवं फलन), Past years Paper, Miscellaneous, doubt solving |
| Day # 9 | Inverse Trigonometric Functions (प्रतिलोम त्रिकोणमिति फलन) | Introduction, f(f^-1(x)) = I(x), f^-1(f(x)) = I(x), domain, Range & graph of f(x) & f^-1(x). |
| Day # 10 | Inverse Trigonometric Functions (प्रतिलोम त्रिकोणमिति फलन) | Standard Inverse Trigonometric functions, Domain, Range & Graphs, Basic questions |
| Day # 11 | Inverse Trigonometric Functions (प्रतिलोम त्रिकोणमिति फलन) | Properties of ITF, addition & subtraction formulae, Solved Problems. |
| Day # 12 | Inverse Trigonometric Functions (प्रतिलोम त्रिकोणमिति फलन) | Miscellaneous Problems and Summary, Past 10 Years Papers |
| Day # 13 | Matrices (आव्यूह) | Introduction, Types of matrices, Order of matrix, Matrix construction, Algebra of Matrix, Transpose of matrix |
| Day # 14 | Matrices (आव्यूह) | Symmetric and Skew-Symmetric Matrix, Matrix Multiplication, Associative & Commutative Properties. |
| Day # 15 | Matrices (आव्यूह) | Determinant Basic, Singular and Non-Singular Matrix, Orthogonal Matrix |
| Day # 16 | Matrices (आव्यूह) | Elementary operations and Inverse of a matrix using elementary row and column operations |
| Day # 17 | Matrices (आव्यूह) | Invertible matrices, Minor, Cofactor and Adjoint of a Matrix, Inverse of a Matrix using A^-1 = adj(A)/|A|. |
| Day # 18 | Determinant (सारणिक) | Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of determinants in finding the area of a triangle. |
| Day # 19 | Determinant (सारणिक) | Properties of Determinant, Solving determinant using properties |
| Day # 20 | Determinant (सारणिक) | adjoint and its Properties, Aadj(A) = IA| I = adj(A)A and related solved problems |
| Day # 21 | Determinant (सारणिक) | System of linear Equations and Solving using Matrix Method |
| Day # 22 | Determinant (सारणिक) | Cramers Rule, System of Homogeneous equations |
| Day # 23 | Practice Session - II | Inverse Trigonometric Functions (प्रतिलोम त्रिकोणमिती फलन), Matrices (आव्यूह) and previous years Papers |
| Day # 24 | Practice Session - III | Determinant (सारणिक), Last 10 years Papers & One Full Objective Classroom Test + 1 Subjective test for Home. |
| Day # 25 | PTM and Next Course registration | Students' performance discussion, Improvement parameters & Next Course Series Batch Registration. |
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