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# Amity International Indian Mathematics Olympiad Sample Question Paper

** Name of the Organisation **: AMITY International

**: Amity International Indian Mathematics Olympiad**

__Name of the Exam__**Subject**: Mathematics

**: Sample Question Paper**

__Document Type__**: https://www.amity.edu/**

__Website__**: https://www.pdfquestion.in/uploads/22872-Maths.pdf**

__Download Question Paper__## Amity International Indian Mathematics Olympiad Paper

** Amity took an enormous stride by organizing International Olympiad for Physics, Chemistry, Mathematics and Biology in May 2012, which had brought students from across the globe on one platform to inculcate mathematic and scientific temperament among the students.

Related: Amity Global Talent Search Exam Question Paper Class XI – Model : www.pdfquestion.in/7483.html

## Highlights Of The Olympiad

** Subjects **: Physics, Chemistry, Mathematics and Biology

**:**

__Examination Pattern__**: Theory Exam – 1 paper in each subject**

__First Day__**: Experiment – in each subject**

__Second Day__**: Arbitration between the team leaders and examination committee**

__Third Day__**: Result declaration and the award ceremony**

__Fourth Day__## Olympiad Programme

**Features :**

** IX (2 years)/X Studying (1 year) – 610 hrs./300 hrs.

** Once a week, 6 hrs. a day

** One subject per class (Physics/Chemistry/Maths)

** Classes by renowned Olympiad experts

**Workshops Schedule :**

** Mathematics Olympiad Workshop: Held every year in the month of May for 8 days.

** Science and Mathematics Olympiad Workshop: Held every year in the month of October for 8 days.

## Sample Paper For Mathematics

** Please read this first **:

1. The time available for the Mathematical Competition is 3 hours. There are four questions.

2. Use only the pen provided.

3. Use of calculator, mobile or any electronic items is not allowed.

4. You are provided with Writing sheet and additional paper. You can use the additional paper for drafts of your solutions but these papers will not be checked. Your final solutions which will be evaluated should be on the Writing sheets. Please use as little text as possible. You should mostly use equations, numbers, figures and plots.

5. Use only the front side of Writing sheets. Write only inside the boxed area.

6. Begin each question on a separate sheet of paper.

7. Fill the boxes at the top of each sheet of paper with your country (Country), your student code (Student Code), the question number (Question Number), the progressive number of each sheet (Page Number), and the total number of Writing Sheets used (Total Number of Pages). If you use some blank Writing sheets for notes that you do not wish to be evaluated, put a large X across the entire sheet and do not include it in your numbering.

8. At the end of the exam, place the papers inside the envelope and leave everything on your desk. You are not allowed to take any paper out of the room.

** Problem 1 **: (7 points)

Let q (n) denote the number of positive integers less than or equal to n and relatively prime to n. Find the value of k such that ? (18522) = ? (1800) + k. Results required to be used while solving this problem should be proved.

** Problem 2 **: (7 points)

In a triangle ABC right angled at C, E is the mid-point of AC, BD bisects ?ABC and BE bisects ?ABD. Prove that 5/2 < (AB/BC) < 3.

** Problem 3 **: (7 points)

Let a and b be natural numbers such that 1 1 1 1 1 1 2 3 4 1570 1571 b a Prove that 2357 divides b.

** Problem 4 **: (7 points)

Let m and n be positive integers such that the equation x2 – mx + n = 0 has real roots a and ß. Prove that a and ß are integers if and only if [m a] + [m ß] is the square of an integer. (Here [x] denotes the largest integer not exceeding x).

## Indian Mathematics Olympiad

This programme consists of 4 stages and is similar to the Science Olympiads programme, except that it has no experimental component.

** Stage 1**: Regional Mathematical Olympiad (RMO) is held in each region normally between September and the first Sunday of December each year. All high school students up to class XII are eligible to appear for RMO. On the basis of the performance in RMO, a certain number of students from each region are selected to appear for the second stage.

** Stage 2**: Indian National Mathematical Olympiad (INMO)INMO is held on the first Sunday of February each year at various centres in different regions. Only students selected on the basis of RMO from different regions are eligible to appear for INMO.

** Stage 3**: International Mathematical Olympiad Training Camp (IMOTC). The INMO certificate awardees are invited to a month long training camp (junior batch) conducted in May-June, each year. In addition, INMO awardees of the previous year that have satisfactorily gone through postal tuition throughout the year are invited again for a second round of training (senior batch).

** Stage 4**: International Mathematical Olympiad (IMO). The team selected at the end of the camp, a “leader” and a “deputy leader,” represent India at the IMO that is normally held in July in a different member country of IMO each year