City Montessori School IYMC Senior Team Sample Question Paper : cmseducation.org
Name of the Organisation : City Montessori School
Exam : International Young Mathematicians’ Convention
Subject : IYMC Senior Team
Year : 2012
Document Type : Model & Past Question Papers
Website : http://www.cmseducation.org/
Download Model/Sample Question Paper : https://www.pdfquestion.in/uploads/13359-IYMCSENIORTeam.docx
IYMC Senior Team Sample Question Paper :
Time:60 minutes
Instructions:
** Do not turn to the first page until you are told to do so.
** Remember to write down your team name in the space indicated on every page.
Related : City Montessori School IYMC Senior Individual Sample Question Paper : www.pdfquestion.in/13356.html
** There are 6 problems in the Team Contest, arranged in increasing order of difficulty.
** Each question is printed on a separate sheet of paper.
** Each problem is worth 40 points and complete solutions of all problems are required for full credits.
** Partial credits may be awarded. In case the spaces provided in each problem are not enough, you may continue your work at the back page of the paper.
** The three team members are allowed 10 minutes to discuss and distribute the problems among themselves.
** Each student must attempt at least one problem.
** Each will then have 50 minutes to write the solutions of their allotted problem independently with no further discussion or exchange of problems.
** No calculator or calculating device or electronic devices are allowed.
** Answer must be in pencil or in blue or black ball point pen.
1. In the figure, E is a point inside the square ABCD such that BE=CE and BEC = 150. Prove that ADE is an equilateral triangle.
2. The figure shows a polyhedron in which each vertex lies on one regular decagon, one regular hexagon and one square. If this polyhedron have V vertices, E edges, F faces, find the value of V+E+F.
3. Five boxes contain 120 coins in all. Some are golden coins, some are silver coins and the rest are copper coins. Any two boxes contain less than 30 golden coins. Any three boxes contain less than 20 silver coins. Prove that some four boxes contain at least 15 copper coins.
4. A man uses a gold chain consisted of 159 links to repay a debt. By agreement, he must hand in one link per week. He may hand in more links if he can get exact change. The debt is paid when all 159 links have been handed in. What is the minimum number of links that must be broken?
5. The sequence { f (1), f (2), f (3), …. } of increasing positive integers satisfies f(f(n))=3n . Find the value of f(2012).
6. In the figure, P and Q are two distinct points inside the acute triangle ABC . If APB = BPC = CPA = 120. Prove that PA+PB+PC<QA+QB+QC.
Road to Championship :
** The Prize Distribution will be the culminating event of the competition. The Primary, Middle School and Senior Level competitions are independent of each other.
** 5 points will be awarded for each first position, 3 points for each second position and 1 point for each third position.
** The Primary team that accumulates the most points will be declared the Primary Level Champions of IYMC Mathematica 2018.The first runner-up team for the Primary Level will also be declared.
** The Middle School team that accumulates the most points will be declared the Middle School Level Champions of IYMC Mathematical 2018. The first runner-up team for the junior level will also be declared.
** The Senior team that accumulates the most points will be declared the Senior Level Champions of IYMC Mathematical 2018. The first runner-up team for the Senior Level will also be declared.
** A team participating in the IYMC- Mathematical should consist of eight contestants – two from the Primary Level (10-13 years of age), three for the Middle School Level (14-15 years of age) and three for the Senior Level ( 16-18 years of age and not enrolled for an Undergraduate Programme at a College or University).
** A Teacher-Team Leader must accompany the team. The participation of the Mathematics Teacher as the Team Leader is desirable.
** Competition is open only for Registered schools. Coaching Centres/institutes or tutorials are not eligible for participation.
** As IYMC Mathematica is being organized from the 2nd to the 5th of December, 2018 teams are requested to arrive before 12 noon of 2nd December, 2018. Teams are, however, welcome a day earlier and may leave a day after. We will be happy to extend hospitality to all outstation teams during their entire stay in Lucknow.
** Participating teams with Team Leaders must be present at the venue at all times. The Leaders are responsible for good conduct of their team members.
** Only writing and drawing instruments are permitted at the contest venue. Books, papers, tables, calculators and computers will not be allowed in the examination rooms.
** The participants are required to carry their own stationary kit comprising- blue or black pens, pencil, eraser, sharpener, scale, and black or blue bold marker.
** The participants are expected to be formally dressed in their complete school uniform during the four days of IYMC- Mathematica 2018.