School Name: | Himalaya Public School, Sector 13, Rohini, Delhi 110085 India |
Class: | 12th Standard (CBSE) |
Subject: | Mathematics |
Time Duration: | 03 Hours |
Maximum Marks: | 80 |
Date: | 28 / 06 / 2022 |
General Instructions: 12th Pre-Mid Term Mathematics Exam
- SECTION A: Q (1 to S) short answer type Questions of 1 marks each.
- SECTION B: Q (6 to 12) of 2 marks each.
- SECTION C: Q (13 to 24) long answer type Questions of 3 marks each.
- SECTION D: Q (25 to 29) long answer type Questions of 5 marks each.
Download PDF File:
87 KB – Download Now!Syllabus For 12th Pre-Mid Term Mathematics
Unit I: Relations and Functions
Chapter 1: Relations and Functions
- Types of relations:
- Reflexive
- Symmetric
- transitive and equivalence relations
- One to one and onto functions
- composite functions
- inverse of a function
- Binary operations
Chapter 2: Inverse Trigonometric Functions
- Definition, range, domain, principal value branch
- Graphs of inverse trigonometric functions
- Elementary properties of inverse trigonometric functions
Unit II: Algebra
Chapter 1: 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 2: Determinants
- Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle
- Ad joint 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