Name of the Organisation : City Montessori School
Exam : International Young Mathematicians’ Convention
Subject : IYMC Senior Individual
Year : 2012
Document Type : Model & Past Question Papers
Website : http://www.cmseducation.org/
Download Model/Sample Question Paper : https://www.pdfquestion.in/uploads/13356-IYMCSENIORInd.docx
IYMC Senior Individual Sample Question Paper :
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 Junior Team Sample Question Paper : www.pdfquestion.in/13353.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.
** All papers shall be collected at the end of this test.
1. If 15xy2 and 21xy are perfect squares, where x and y are positive integers, what is the smallest value of x + y?
2. Determine y-x if x and y are real numbers that satisfy 2x-2y =1 and 4x-4y =5/3
3. A password consists of four distinct digits such that their sum is 19 and such that exactly two of these digits are primes. For example 0397 is a possible password. How many possible passwords are there?
4. For any positive integer n, we define n as the product of the integers from 1 to n, and call it the factorial of n. Also 0 is defined as 1. Some numbers are equal to the sum of the factorials of their digits. For example 40585=4 +0 +5 +8 +5 . Find such a number with three digits.
5. All six faces of a cube are completely painted. It is cut into 64 identical cubes. One of these cubes is chosen at random and rolled. Find the probability that none of the five faces showing is painted
6. Solve the equation , where all square roots are taken to be positive
7. In the figure, BC>AC, AE=EB, CH>AB, ACF=FCB and HCF=FCE. Find the measure of ACB, in degrees.
8. How many ordered triple (x, y, z) of integers satisfy xyz = 2012?
Rules & Regulations :
** A team participating in the IYMC- Mathematica 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.
** The i-cards provided at the time of Registration at the venue should be worn throughout the event on their school uniform.
** All participating schools must carry their school flag for representing their school in the procession at the Inaugural ceremony.
Meal Timings :
** Outstation participants are requested to abide by the following timings for the convenience of the catering staff:-
Breakfast : 07:00 to 07:45 am
Lunch : 01:00 to 02:00 pm
Dinner : 08:30 to 09:30 pm
** Friends, relatives and outsiders will not be allowed to meet the Participants or Team Leaders until the competition concludes on the 5th December, 2018.
** The participants are allowed to use a non-electronic translation dictionary during the competition. The officials of the event will be informed about it beforehand and they will have the authority to check anything they deem fit.
** Participating teams may prepare one three-to-five minutes cultural presentation for the cultural function to be organized at the venue. A dance or song sequence, a short skit in an ethnic dress, unique to their country or region, will ideally suit the cultural function. (Not to be included in the competition).