## IMO class 12 **syllabus**

School Connect Online Olympiad is an integrated learning program for schools organised with a key goal of establishing a wide entrance for the learning process bringing together every aspiring student, teacher, school and parent under an umbrella of the disciplined domain of schools. School Connect Online guarantees to strengthen the academic excellence of young minds and to foster their aspirations by delivering them a unique learning platform to crack Olympiads, one of the most prestigious examinations.IMO for Class 12

With a perfect blend of video lessons, practice questions, mock tests and assessment, School Connect Online aims to furnish the young aspirants with the best learning materials to deal with Olympiads. This kernel provides a self-organised learning ambience to furnish the aspiring students with effective strategies and study plans to deal with Olympiad exams and to bring out the best in them.

School Connect Online is funded and incubated by Startup Oasis, Jaipur an initiative of CIIE –** Indian Institute of Management Ahmedabad (IIM-A)**.

Students aiming for Maths Olympiad, Science Olympiad, AI Olympiad, Coding Olympiad can get free access to the preparation materials supported by video lessons for each topic, practice questions, mock tests, sample papers and performance analysis.

School Connect Online promotes the best support to aspiring students meticulously planned study materials and till now we have successfully completed Online Maths Olympiad, Online Science Olympiad, Online Coding Olympiad and Online AI Olympiad.

## Benefits of School Connect Online Olympiad –

- The best disciplined e-learning portal with Read, Practice,Test and Analysis flow.
- Mock Tests to practice real exam like situation.
- 70,000+ non repeating Questions for students to prepare for Olympiad Exam with CBSE followed syllabus.
- Participating students will get exposure to analytical based questions.
- First time in any Olympiad,School Connect give students an opportunity to analyse the questions with solution post Olympiad exam.
- Reading notes to students with best learning linked videos.
- Teachers of School can see the learning flow of students and their performance.
- A single window view report of the entire school’s performance. With Lesson Plan/Class Plan driven learning progress.

**Register Now for IMO Olympiad 2021-22,and access to the best free learning materials and free adaptive videos.**

**Practice Unlimited with School Connect with –**

**Online Chapter-wise Practice and Tests:**The modus operandi to have a learning and practice concept by helping you brush up topics from every chapter. The chapter exercise questions cover all important topics and concepts through its progressive levels of test, designed in increasing order of difficulty level.**Daily Practice Problems (DPP):**As you learn more and more topics during your preparation, it is imperative not to compromise on your evaluation process. DPP provides practice tests covering all topics which help students memorise the important topics thoroughly.**Online Test Series (OTS):**Time Management, Preparation and Proper Exam Management with the error-free learning environment. It’s the fundamental tool for success in any exam. OTS will help you build confidence which is important for attaining success in any exams.

**Maths Olympiad Syllabus for Class 12**

Unit | Topic | Marks |

I. | Relations and Functions | 10 |

II. | Algebra | 13 |

III. | Calculus | 44 |

IV. | Vectors and 3D Geometry | 17 |

V. | Linear Programming | 6 |

VI. | Probability | 10 |

| Total | 100 |

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

Subject | Participating Classes | Exam Date | Mode of Exam | Offline/Online Exam Day | Time Duration |

International Science Olympiad (ISO) | Class 1 to 12 | 26th November 2021 | Online/Offline | Friday | 45 min (Attend anytime) |

International Science Olympiad (ISO) | Class 1 to 12 | 27th November 2021 | Online/Offline | Saturday | 45 min (Attend anytime) |

International Science Olympiad (ISO) | Class 1 to 12 | 29th November 2021 | Online/Offline | Monday | 45 min (Attend anytime) |

International Science Olympiad (ISO) | Class 1 to 12 | 30th November 2021 | Online/Offline | Tuesday | 45 min (Attend anytime) |

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

Subject | Participating Classes | Exam Date | Mode of Exam | Offline/Online Exam Day | Time Duration |

International Maths Olympiad (IMO) | Class 1 to 12 | 19th November 2021 | Online/Offline | Friday | 45 min (Attend anytime) |

International Maths Olympiad (IMO) | Class 1 to 12 | 20th November 2021 | Online/Offline | Saturday | 45 min (Attend anytime) |

International Maths Olympiad (IMO) | Class 1 to 12 | 4th December 2021 | Online/Offline | Saturday | 45 min (Attend anytime) |

International Maths Olympiad (IMO) | Class 1 to 12 | 11th December 2021 | Online/Offline | Saturday | 45 min (Attend anytime) |

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

Subject | Participating Classes | Exam Date | Mode of Exam | Offline/Online Exam Day | Time Duration |

International Artificial Intelligence Olympiad | Class 5 to 12 | 15th October 2021 | Online/Offline | Friday | 45 min (Attend anytime) |

International Artificial Intelligence Olympiad | Class 5 to 12 | 29th October 2021 | Online/Offline | Friday | 45 min (Attend anytime) |

International Artificial Intelligence Olympiad | Class 5 to 12 | 5th November 2021 | Online/Offline | Friday | 45 min (Attend anytime) |

International Artificial Intelligence Olympiad | Class 5 to 12 | 12th November 2021 | Online/Offline | Friday | 45 min (Attend anytime) |

**International Coding and Learning Olympiad Dates and Time for Stage 1**

Subject | Participating Classes | Exam Date | Mode of Exam | Offline/Online Exam Day | Time Duration |

International Coding and Learning Olympiad | Class 1 to 12 | 16th October 2021 | Online/Offline | Saturday | 45 min (Attend anytime) |

International Coding and Learning Olympiad | Class 1 to 12 | 30th October 2021 | Online/Offline | Saturday | 45 min (Attend anytime) |

International Coding and Learning Olympiad | Class 1 to 12 | 6th Novemebr 2021 | Online/Offline | Saturday | 45 min (Attend anytime) |

International Coding and Learning Olympiad | Class 1 to 12 | 13th December 2021 | Online/Offline | Saturday | 45 min (Attend anytime) |

**International Maths Olympiad (IMO) Exam Pattern**

| ||||

Grade | Section | No. of Questions | Marks per Question | Total Marks |

1 to 4 | Logical Reasoning | 10 | 3 | 30 |

| Mathematical Reasoning | 8 | 3 | 30 |

| Everyday Mathematics | 12 | 3 | 30 |

| Achievers Section | 5 | 5 | 25 |

| Grand Total | 35 | 115 | |

5 to 12 | Logical Reasoning | 10 | 3 | 30 |

| Mathematical Reasoning | 20 | 3 | 30 |

| Everyday Mathematics | 10 | 3 | 30 |

| Achievers Section | 10 | 5 | 50 |

| Grand Total | 50 | 140 |

**Learning support from School Connect Online for Olympiad Studies**

1 | Practice Questions | Study Materials |

2 | Chapter wise | Reading Notes |

3 | Mock Tests | Free Videos |

4 | Maths Reasoning | Learning Platform |

5 | Achievers Practice questions | Performance Update |

6 | Sample Papers | Competition Update |

**Eligibility Criteria for School Connect Online Olympiad**

**Age: **Students of classes 1 to 12th are eligible to appear for the 1st level Olympiads. Students who qualify for the 2nd level exam include.

(a) Top 5% of students’ class wise, who appear for the 1st level exam,

(b) State wise top 25 rank holders class wise, and

(c) Class toppers from each participating school where at least 10 students from a class appear in the exam & scores 50% qualifying marks.

Note – **Students from classes 1 and 2 are not required to appear for the 2nd level exam and are ranked based on their performance in the first level exam.**

**Awards and Certificates Details**

Awards and Medals | Eligibility |

Certificate of Participation | All students participated in Olympiads |

Certificate of Merit | Rank holder of Class (Minimum 10 students participating each class) |

Qualifier of Gold Medal | Top Rank Stage 2 Selected Students |

Qualifier of Silver Medal | Second Top Rank Stage 2 Selected Students |

Certificate of Excellence/Appreciation | Outstanding Performance Certificate to all Stage 2 Participants |

Hall of Fame | Best Performing Students in Stage 2/Final Olympiad Exam |

Achievers Gold Medal | Rank holder in International Olympiad Ranking |

Cash Rewards | Top 10 Students |

**Olympiad Registration**

**Class:**You need to be a student in Classes 1 to 12 to be eligible for this exam.**Boards:**You must be a student of SSC, ICSE or CBSE boards.**Qualifying for second level examination:**

The top 5% of students (class-wise) also benchmark percentile score who appear for the first level exam.

Class toppers from each participating school; where at least 10 students participate and score a minimum of 50%.

**Year of attempt:**As long as you’re a student enrolled in any of Classes 1 to 12, you can apply for**International Science Olympiad and IMO or International Maths Olympiad)****Number of attempts:**You can attempt only once in a year for any olympiad with 2 qualifying stages.**Year of attempt:**As long as you’re a student enrolled in any of Classes 1 to 12, you can apply for**International Science Olympiad and IMO or International Maths Olympiad****once in every academic year**.

**Maths Olympiad **** **

Class | Syllabus | Class | Syllabus |

Class 1 | Maths Olympiad Class 1 | Class 4 | Maths Olympiad Class 4 |

Class 2 | Maths Olympiad Class 2 | Class 5 | Maths Olympiad Class 5 |

Class 3 | Maths Olympiad Class 3 | Class 6 | Maths Olympiad Class 6 |

Class 7 | Maths Olympiad Class 7 | Class 10 | Maths Olympiad Class 10 |

Class 8 | Maths Olympiad Class 8 | Class 11 | Maths Olympiad Class 11 |

Class 9 | Maths Olympiad Class 9 | Class 12 | Maths Olympiad Class 12 |

**Other National and International Level Olympiads**

AI Olympiad | International Artificial Intelligence Olympiad |

Coding Olympiad | International Coding Olympiad |

Maths Olympiad (IMO) | International Maths Olympiad |

Science Olympiad (ISO) | International Science Olympiad |

KVPY | Kishore Vaigyanik Protsahan Yojana |