Friday , August 19 2022

12th Pre-Mid Term Mathematics Examination 2022-23

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 Maths 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.

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Syllabus For 12th Pre-Mid Term Maths

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

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