Maths Olympiad Syllabus class 12

Maths Olympiad Syllabus class 12

Maths Olympiad Syllabus class 12

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School Connect Online Olympiad, is a program to encourage students for the learning and knowledge of Science and Maths from Class 1st  to 12th.

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Science and Mathematics is one of the vital subjects in Science and Maths stream and it is also of very much importance while preparing for various competitive exams and hence it is essential to prepare it from the very beginning.

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Maths Olympiad of School Connect Online gives one of best learning and life time achievement for the students of class 1 to 12.

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Maths Olympiad Syllabus class 12

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Syllabus for Class 12 Maths Olympiad

Unit I: Relations and Functions

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.

2. Inverse Trigonometric Functions

  • Definition, range, domain, principal value branch.
  • Graphs of inverse trigonometric functions.
  • Elementary properties of inverse trigonometric functions.

 

Unit-II: Algebra

 

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.
  • Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse.

2. Determinants

  • Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint 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 using inverse of a matrix.
  •  

Unit III: Calculus 

1. Continuity and Differentiability

  • Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions.
  • Concept of exponential and logarithmic functions.
  • Derivatives of logarithmic and exponential functions.
  • Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives.
  • Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation.

 2. Applications of Derivatives

  • Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals.
  • Use of derivatives in approximation, maxima and minima.

 3. Integrals

  • Integration as inverse process of differentiation.
  • Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.
  • Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof).
  • Basic properties of definite integrals and evaluation of definite integrals.

 4. Applications of the Integrals

 Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses Area between any of the two above said curves (the region should be clearly identifiable).

 5. Differential Equations 

  • Definition, order and degree, general and particular solutions of a differential equation.
  • Formation of differential equation whose general solution is given.
  • Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree.
  • Solutions of linear differential equation of the type.
  •  

Unit IV: Vectors and Three-Dimensional Geometry

 1.Vectors

  • Vectors and scalars, magnitude and direction of a vector, direction cosines and direction ratios of a vector.
  • Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio.
  • Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors.
  •  

2. Three – dimensional Geometry

 Direction cosines and direction ratios of a line joining two points.

Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines, Cartesian and vector equation of a plane.

Angle between (i) two lines, (ii) two planes, (iii) a line and a plane, distance of a point from a plane.

Unit V: Linear Programming

 Linear Programming

  • Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming problems.
  • Mathematical formulation of L.P. Problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

 Unit VI: Probability

 Probability

  • Conditional probability, multiplication theorem on probability
  • Independent events, total probability, Baye’s theorem, Random variable and its probability distribution, mean and variance of random variable.
  • Repeated independent (Bernoulli) trials and Binomial distribution.

International Science Olympiad (ISO) Dates and Time  Class 1 to 12

International Science Olympiad (ISO) Dates and Time for Stage 1
SubjectParticipating Classes Exam DateMode of ExamOffline/Online Exam DayTime Duration
International Science Olympiad (ISO)Class 1 to 1226th November 2021Online/OfflineFriday45 min (Attend anytime)
International Science Olympiad (ISO)Class 1 to 1227th November 2021Online/OfflineSaturday45 min (Attend anytime)
International Science Olympiad (ISO)Class 1 to 1229th November 2021Online/OfflineMonday45 min (Attend anytime)
International Science Olympiad (ISO)Class 1 to 1230th November 2021Online/OfflineTuesday45 min (Attend anytime)

International Maths Olympiad (IMO) Dates and Time for Class 1 to 12

International Maths Olympiad (IMO) Dates and Time for Stage 1
SubjectParticipating Classes Exam DateMode of ExamOffline/Online Exam DayTime Duration
International Maths Olympiad (IMO)Class 1 to 1219th November 2021Online/OfflineFriday45 min (Attend anytime)
International Maths Olympiad (IMO)Class 1 to 1220th November 2021Online/OfflineSaturday45 min (Attend anytime)
International Maths Olympiad (IMO)Class 1 to 124th December 2021Online/OfflineSaturday45 min (Attend anytime)
International Maths Olympiad (IMO)Class 1 to 1211th December 2021Online/OfflineSaturday45 min (Attend anytime)

International Artificial Intelligence (AI) Olympiad Dates and Time for Stage 1

International Artificial Intelligence(AI) Olympiad Dates and Time for Stage 1
SubjectParticipating Classes Exam DateMode of ExamOffline/Online Exam DayTime Duration
International Artificial Intelligence OlympiadClass 5 to 1222nd October 2021Online/OfflineFriday45 min (Attend anytime)
International Artificial Intelligence OlympiadClass 5 to 125th November 2021Online/OfflineFriday45 min (Attend anytime)
International Artificial Intelligence OlympiadClass 5 to 1212th November 2021Online/OfflineFriday45 min (Attend anytime)
International Artificial Intelligence OlympiadClass 5 to 1226th November 2021Online/OfflineFriday45 min (Attend anytime)

International Coding and Learning Olympiad Dates and Time for Stage 1

International Coding and Learning Olympiad Dates and Time for Stage 1
SubjectParticipating Classes Exam DateMode of ExamOffline/Online Exam DayTime Duration
International Coding and Learning OlympiadClass 1 to 1216th October 2021Online/OfflineSaturday45 min (Attend anytime)
International Coding and Learning OlympiadClass 1 to 1230th October 2021Online/OfflineSaturday45 min (Attend anytime)
International Coding and Learning OlympiadClass 1 to 126th Novemebr 2021Online/OfflineSaturday45 min (Attend anytime)
International Coding and Learning OlympiadClass 1 to 1213th December 2021Online/OfflineSaturday45 min (Attend anytime)

Learning support from School Connect Online for Olympiad Studies

International Mathematics Olympiad (IMO)  on School Connect Online
1Practice QuestionsStudy Materials
2Chapter wiseReading Notes
3Mock TestsFree Videos
4Maths ReasoningLearning Platform
5Achievers Practice questionsPerformance Update
6Sample PapersCompetition Update

Important Links

Mathematics Olympiad Questions For Class 12 Pdf

Maths Olympiad Class 12 Exam Date

Maths Olympiad for Class 12 Registration

Maths Olympiad Class 12 Sample Papers

Maths Olympiad Sample Paper Class 12 2021

Olympiad Books for Class 12

Science Olympiad Class 12 Syllabus

Grade 12 Maths Olympiad Past Papers

Science Olympiad

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Class 12Science Olympiad Syllabus for Class 12

Important Links for reference

CBSE Syllabus For Class 9 Artificial Intelligence  Class 6 Geography (Social Science) Syllabus  
JEE Main Chemistry Syllabus – Check detailed Syllabus here  CBSE Class 12 Chemistry Deleted Syllabus Portion For 2020-21
Light, Shadows and Reflection Class 6 Notes Science Chapter 11CBSE Class 10 Social Science Syllabus For Academic Year 2020-2021  
NEET Syllabus 2020 – Complete Physics, Chemistry & Biology  JEE Main Syllabus 2021 – Physics, Chemistry, Mathematics  
JEE Advanced Syllabus For Physics, Chemistry, Maths In Detail  CBSE Class 12 Syllabus 2020-21 Pdf Download  
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