# Olympiads

## International Olympiad Programme in Astronomy, Biology, Chemistry, Junior Science and Physics

## International Science Olympiads

**International Science Olympiad Stages:**

**Stage I: National Standard Examinations (NSEs)**

Sl. |
National Standard Examination Name |
Eligibility |
Pattern |
Syllabus |

1 | National Standard Examination in Astronomy (NSEA) | Continuing 12th Std.
(& other age conditions) |
Questions: 80 multiple choice questions with negative marking.
Language: English & Hindi |
Is broadly equivalent to senior secondary level (up to and including Class XII) of CBSE. There will be greater emphasis on Physics, Mathematics and Elementary Astronomy. |

2 | National Standard Examination in Biology (NSEB) | Continuing 12th Std.
(& other age conditions) |
Questions: 80 multiple choice questions with negative marking.
Language: English & Hindi |
Is broadly equivalent to senior secondary level (up to and including Class XII) of CBSE |

3 | National Standard Examination in Chemistry (NSEC) | Continuing 12th Std.
(& other age conditions) |
Questions: 80 multiple choice questions with negative marking.
Language: English & Hindi |
Is broadly equivalent to senior secondary level (up to and including Class XII) of CBSE |

4 | National Standard Examination in Physics (NSEP) | Continuing 12th Std.
(& other age conditions) |
Questions:
1. 3-mark questions, each with only one of four options correct. 2. 6-mark questions, each with one or more than one option correct. To get credit, all the correct option(s) and no incorrect option(s) should be marked. Language: English, Hindi, Gujarati, Bangla (last three on request) |
Is broadly equivalent to senior secondary level (up to and including Class XII) of CBSE. |

5 | National Standard Examination in Junior Science (NSEJS) | Continuing 10th Std.
(& other age conditions) Must not be appearing in any of NSEA, NSEB, NSEC or NSEP for the same year |
Questions: 80 multiple choice questions with negative marking.
Language: English & Hindi |
broadly equivalent to secondary school level (up to and including Class X) of CBSE. All the basic subjects of science (Biology, Chemistry and Physics) and Mathematics may have roughly equal emphasis. |

**Stage II: Indian National Olympiad Examinations (INOs) **

## Mathematical Olympiad Programme by Homi Bhabha Centre for Science Education (HBCSE)

## Mathematical Olympiad Programmes:

Apart from the International Mathematical Olympiad (IMO), in which India is participating since 1989, since 2015 India have also started participating in two more international Olympiad events: the Europen Girls’ Mathematical Olympiad (EGMO) and Asia Pacific Mathematics Olympiad (APMO).

**Selection Process for all the three International Math Olympiad events:**

The process for selection of students for participation in the events have been merged, and the same test will qualify candidates for different International Math Olympiad events.

**Regional Divisions:**

For the purpose of training and selection of students for the International Math Olympiad contest, 25 regions all over the country have been designated and each assigned a Regional Coordinator. Additionally, three group of Institutions Central Board of Secondary Education (CBSE), Navodaya Vidyalaya Samiti (NVS) and Kendriya Vidyalaya Sangathana (KVS) have a ‘Regional Coordinator’ each.

**Step 1: Regional Mathematical Olympiad and Pre-RMO**

The Regional Mathematical Olympiad (RMO) is a three hour written test with six problems held at each region in order to select 30 candidates from each region for appearing Indian National Math Olympiad (INMO) the qualifying exam for selection to International Math Olympiad group representing India. INMO is the second stage in the process for appearing International Math Olympiads mentioned above.

**Features of Regional Math Olympiads:**

- The Regional Coordinators hold the charge of conducting the RMO in their respective regions.
- They have the option of preparing RMO question papers on their own or they may choose to use the central RMO question paper prepared by the Mathematical Olympiad Cell, HBCSE, TIFR.
- Some regions may hold a pre-RMO examination through which students will be selected to appear for RMO.
- All pre-RMOs will be conducted by the concerned regional coordinator in the respective regions
- The format of the Pre-RMO paper and the criteria for selecting students for RMO are at the sole discretion of the respective Regional Coordinators.
- In the context of participation in EGMO it is decided that up to five girls be additionally selected apart from the general quota of 30 students for each region. This provision is independent of the number of girls who may be part of the list of 30 students from the region.

**Timeline:**

- RMOs are conducted during 1st or 2nd week of October every year
- Results Declared by 6th December centrally by HBCSE

**Eligibility:**

All Indian students who are born on or after August 1 of the respective year and, in addition, are in Class IX, X, and XI are eligible to appear for the RMO. Class XII students will not be eligible to appear for RMO/pre-RMO. At the sole discretion of regional coordinator, highly motivated and well performing meritorious students from Class VIII may also be allowed to take the RMO.

### Step 2: Indian National Mathematical Olympiad (INMO)

- The INMO is being held on the third Sunday of January
- Only those students who are selected in RMO (Step 1) for the particular year and those who have received an INMO certificate of merit are eligible to appear for the INMO provided they are in class XI or below.
- This contest is a four hour written test.
- On the basis of the INMO, the top 30 students in merit from all over the country will be chosen as INMO awardees.
- In addition to INMO awardees, the next 45 students who are in class XI or lower and have performed well in INMO, but have not qualified as INMO awardee, are awarded INMO certificate of merit. These students will be eligible to appear for INMO next year directly without qualifying through RMO next year, provided they are not in class XII at the time of writing INMO.
- In addition to the 30 students in the list of INMO awardees as above, up to five girl students (outside the INMO awardees list) will be chosen based on the performance in INMO, for training and possible selection to EGMO team.
- The INMO results will be declared in the last week of February.
- All INMO awardees, the selected girl students as above and all the students designated as senior students of IMOTC previous year will be eligible to write APMO. The APMO tests will be held in the respective regions.

**Step 3: International Mathematical Olympiad Training Camp (IMOTC):**

- The INMO awardees and the girls selected from INMO for training are invited to a month long training camp in April-May each year at the Homi Bhabha Centre for Science Education (HBCSE), Mumbai.
- Besides, the INMO awardees from the previous years and the selected girl students of the previous years who are eligible for IMO-2017/EGMO-2018 and have gone through postal tuition throughout the year satisfactorily are invited to the training camp as senior students.
- An INMO awardee who has completed one year of 12th standard will not be eligible for the next year’s IMOTC.
- On the basis of a number of selection tests during the Camp, a team of the best six students is selected from the combined pool of junior and senior batch participants as the IMO 2017 Team.
- A team of upto four girl students will be selected for participation in EGMO 2018, based on the performance of girl students from the combined pool at IMOTC.

**Step 4: Pre-Departure Training Camps:**

- The selected team of six students goes through another round of training and orientation for about ten days prior to departure for IMO.
- A Pre-departure camp will also be arranged for girl students selected for participation in 2018, at a suitable time.

### More Details about International Math Olympiads:

**International Mathematical Olympiad (IMO)**

- The six member team selected at the end of IMOTC accompanied by a leader, a deputy leader and observers represent the country at the IMO, held in
**JULY**each year in a different member country of the IMO. - The IMO contest consists of two written tests held on two consecutive days. On each day of the contest the test consists of three problems and lasts for four and half hours.
- India has been participating in the IMO since 1989.
- The selected students need to have a valid Indian passport meeting the visa regulations of the host country apart from other requirements.
- Students aiming to go through the Mathematical Olympiad programme leading to international participation (IMO) should note that RMO is the first essential step for the programme.
- To appear for the RMO, the students should get in touch with the RMO coordinator of their region well in advance for enrollment and payment of stipulated (nominal) fees.

**European Girls Mathematical Olympiad (EGMO):**

- A team of at most
**four girl students**selected at the end of IMOTC accompanied by a leader, a deputy leader and an observer represent the country at the EGMO, held in**April each year**in a different European country. - The EGMO contest consists of two written tests held on two consecutive days. On each day of the contest the test consists of three problems and lasts for four and half hours.
- India has been participating in the EGMO since 2015. The selection of the members of the Indian team for EGMO will be subject to their fulfilling criteria and need to have a valid Indian passport meeting the visa regulations of the host country.
- Students aiming to go through the Mathematical Olympiad programme leading to participation in EGMO should note that RMO is the first essential step for the programme.

**Asia Pacific Mathematics Olympiad (APMO):**

- APMO is a contest specifically held for students in Asian countries and the countries in the rim of Pacific ocean.
- There is a senior coordinating country which coordinates this examination.
- The advantage of this contest is that one can participate in it being in her/his country. India has started participating in it from 2015.
- The contest consists of solving 5 problems in four and a half hours. The requirement for participation in APMO is like IMO: one should not have entered university and below the age of 20 years. Besides the contestants should have been selected through a national selection process.
- In view of this, all the INMO-2017 awardees and all the senior batch students for the year 2017 are eligible to write APMO-2017.
- Generally, it is on the second Monday of March and the following Tuesday in some countries. (For the exact date and timings of the contest, see HBCSE website.)
- The students can take their examination in their respective regions. The regional coordinator will conduct the test in his region.

## Syllabus for Mathematical Olympiad:

The syllabus for Mathematical Olympiad (regional, national and all international) is **pre-degree college mathematics**. The areas covered are:

- arithmetic of integers,
- geometry,
- quadratic equations and expressions,
- trigonometry,
- co-ordinate geometry,
- system of linear equations,
- permutations and combination,
- factorisation of polynomial,
- inequalities,
- elementary combinatorics,
- probability theory and number theory,
- finite series and complex numbers and elementary graph theory.

**Note:**

The syllabus does not include **calculus and statistics**. The major areas from which problems are given are algebra, combinatorics, geometry and number theory . The syllabus is in a sense spread over **Class XI to Class XII levels**, but the problems under each topic involve high level of difficulty and sophistication.

The difficulty level increases from RMO to INMO to IMO. A good idea of what is expected of students in mathematical Olympiad can be had from the question papers of earlier years (which are available at http://olympiads.hbcse.tifr.res.in/subjects/mathematics/previous-question-papersand-solutions) and the following books:

- Problem Primer for Olympiads C R Pranesachar, B J Venkatachala and C S Yogananda (Prism Books Pvt. Ltd., Bangalore).
- Challenge and Thrill of Pre-College Mathematics V Krishnamurthy, C R Pranesachar, K N Ranganathan and B J Venkatachala (New Age International Publishers, New Delhi).
- An Excursion in Mathematics Editors: M R Modak, S A Katre and V V Acharya and V M Sholapurkar (Bhaskaracharya Pratishthana, Pune).
- Problem Solving Strategies A Engel (Springer-Verlag, Germany).
- Functional Equations B J Venkatachala (Prism Books Pvt. Ltd., Bangalore).
- Inequalities an approach through problems (texts & readings in mathematics), B J Venkatachala ( Hindustan Book Agency)
- Mathematical Circles Fomin and others (University Press, Hyderabad).

Many other interesting references may also be found in the book **An Excursion in Mathematics** mentioned above.

### INMO Scholarship:

The INMO awardees successfully completing IMOTC, who pursue B.Sc., or other courses adjudged by the Board to be on the same footing, with mathematics as one of the principal subjects of study, are eligible to receive a scholarship of NBHM, which is at present Rs. 4,000 per month, through the period of their undergraduate studies (subject to satisfactory progress). An enhanced scholarship would be available for pursuing masters studies in mathematics.

**Previous Year Question Papers (Pre-RMO, RMO, INMO, RMO)**:

INMO

Year | INMO Question Papers with Solution | Download Links |

2016 | INMO 2016 Question Paper English
INMO 2016 Question Paper Hindi INMO 2016 Solution |
Link |

2015 | INMO 2015 Question Paper with Solution | Link |

2014 | INMO 2014 Question Paper with Solution | Link |

2013 | INMO 2013 Question Paper with Solution | Link |

2012 | INMO 2012 Question Paper with Solution | Link |

2011 | INMO 2011 Question Paper with Solution | Link |

2010 | INMO 2010 Question Paper with Solution | Link |

2009 | INMO 2009 Question Paper with Solution | Link |

2008 | INMO 2008 Question Paper with Solution | Link |

2007 | INMO 2007 Question Paper with Solution | Link |

2006 | INMO 2006 Question Paper with Solution | Link |

2005 | INMO 2005 Question Paper with Solution | Link |

2004 | INMO 2004 Question Paper with Solution | Link |

2003 | INMO 2003 Question Paper with Solution | Link |

2002 | INMO 2002 Question Paper with Solution | Link |

2001 | INMO 2001 Question Paper with Solution | Link |

2000 | INMO 2000 Question Paper with Solution | Link |

RMO

Year | RMO Question Paper with Solution | Download Links |

2016 | ||

2015 | CRMO Question Paper 1
CRMO Paper 1 Solution CRMO Question Paper 2 CRMO Paper 2 Solution CRMO Question Paper 3 CRMO Paper 3 Solution CRMO Question Paper 4 CRMO Paper 4 Solution RMO Mumbai Question Paper RMO Mumbai Solution |
Link |

2014 | CRMO Question Paper 1
CRMO Paper 1 Solution CRMO Question Paper 2 CRMO Paper 2 Solution CRMO Question Paper 3 CRMO Paper 3 Solution CRMO Question Paper 4 CRMO Paper 4 Solution RMO Mumbai Question Paper RMO Mumbai Solution |
Link |

2013 | CRMO Question Paper 1
CRMO Paper 1 Solution CRMO Question Paper 2 CRMO Paper 2 Solution CRMO Question Paper 3 CRMO Paper 3 Solution CRMO Question Paper 4 CRMO Paper 4 Solution RMO Mumbai Question Paper RMO Mumbai Solution |
Link |

2012 | CRMO Question Paper 1 with Solution
CRMO Question Paper 2 with Solution CRMO Question Paper 3 with Solution CRMO Question Paper 4 with Solution RMO Mumbai Solution |
Link |

2011 | CRMO 2011 Question Paper with Solution | Link |

2010 | CRMO 2010 Question Paper with Solution | Link |

2009 | CRMO 2009 Question Paper with Solution | Link |

2008 | CRMO 2008 Question Paper with Solution | Link |

2007 | CRMO 2007 Question Paper with Solution | Link |

2006 | CRMO 2006 Question Paper with Solution | Link |

2005 | CRMO 2005 Question Paper with Solution | Link |

2004 | CRMO 2004 Question Paper with Solution | Link |

2003 | CRMO 2003 Question Paper with Solution | Link |

2002 | CRMO 2002 Question Paper with Solution | Link |

2001 | ||

2000 | CRMO 2000 Question Paper with Solution | Link |

Pre-RMO

Year | Pre-RMO | Download Links |

2015 | Mumbai Pre-RMO 2015 Question Paper Set A
Mumbai Pre-RMO 2015 Question Paper Set B |
Link |

2014 | Mumbai Pre-RMO 2014 Question Paper Set A | Link |

2013 | Mumbai Pre-RMO 2013 Question Paper Set A | Link |

2012 | Mumbai Pre-RMO 2012 Question Paper Set A | Link |