12th Pre-Mid Term Mathematics Examination 2022

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.

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