City Montessori School IYMC Relay Round Question Paper : cmseducation.org

Name of the Organisation : City Montessori School
Exam : International Young Mathematicians’ Convention
Subject : IYMC Relay Round
Year : 2012
Document Type : Model & Past Question Papers
Website : http://www.cmseducation.org/
Download Model/Sample Question Paper : https://www.pdfquestion.in/uploads/13363-relayquestions.docx

IYMC Relay Round Question Paper :

Relay Questions :
Lower Division Relay 1:
LR1Q1 : Two squares with equal sides have the same center, but no side in common. The union of their two areas forms an eight-pointed “star” figure. How many sides does this figure have?

Related : City Montessori School IYMC Senior Individual Sample Question Paper : www.pdfquestion.in/13356.html

LR1Q2: TNWYR is the number of sides in a certain regular polygon. If we connect every fourth vertex of this polygon (starting at one vertex, skipping a second and third, and going to the fourth around the figure), we get another regular polygon. How many degrees are in each angle of this new regular polygon? (Pass back your answer as a number WITHOUT degrees as units.)

LR1Q3: TNYWR is the length of one side of a triangle, and another side has length 10. What is the smallest possible length of the third side, if its length is a whole number?

Lower Division Relay 2 :
LR2Q1. One solution of the equation x2 + ax – 19 = a (where x is the unknown) is given by x = 3. Find the value of a.

LR2Q2. Let TNYWR = N. A certain candy recipe requires 1 ounce of oil, 3 ounces of sugar, and 7 ounces of flour (and nothing else). If you have N ounces of oil to use in the recipe, and lots of sugar and flour, how many ounces of the candy can you make?

LR2Q3. TNYWR can be factored as (A +3)(A-3), where A is a positive integer. Find the value of A.

Lower Division Relays : Solutions
LR1Q1: Two squares with equal sides have the same center, but no side in common. The union of their two areas forms an eight-pointed “star” figure. How many sides does this figure have?
Answer: 16 sides:
Note that the ‘star’ need not be regular: the figure shows only the simplest example. The star will always have 16 sides.
Pass back 16.

LR1Q2: TNWYR is the number of sides in a certain regular polygon. If we connect every fourth vertex of this polygon (starting at one vertex, skipping a second and third, and going to the fourth around the figure), we get another regular polygon. How many degrees are in each angle of this new regular polygon?
Solution: TNYWR = 16. The new polygon is a square, so the answer is 90 degrees.
Pass back 90.

LR1Q3: TNYWR is the length of one side of a triangle, and another side has length 10. What is the smallest possible length of the third side, if its length is a whole number?
Answer: TNYWR = 90. A side of a triangle cannot be greater than the sum of the other two sides. So 90 must be less than the sum of 10 and the length of the third side, and this third side must be greater than 80. Since it must be an integer, it is 81.
Answer to relay: 81.

LR2Q1. : One solution of the equation x2 + ax – 19 = a (where x is the unknown) is given by x = 3. Find the value of a.
Solution :
The equation must be true if we substitute 3 for x, so we have 9+ 3a – 19 = a, or 3a – 10 = a, or 2a = 10 and a = 5.
Pass back 5.

LR2Q2. : Let TNYWR = N. A certain candy recipe requires 1 ounce of oil, 3 ounces of sugar, and 7 ounces of flour (and nothing else). If you have N ounces of oil to use in the recipe, and lots of sugar and flour, how many ounces of the candy can you make?
Solution :
TNYWR = 5. One ounce of oil, together with the other ingredients, makes 11 ounces of candy. So 5 ounces of oil, together with the other ingredients, makes 55 ounces of candy.
While waiting, students can reason that the answer is 11 times TNYWR.
Pass back 55.

LR2Q3. : TNYWR can be factored as (A +3)(A-3), where A is a positive integer. Find the value of A.
Solution :
TNYWR = 55. We have (A+3)(A-3) = A2 – 9 = 55, so A2 = 64 and A = 8.
Answer to relay is 8.
Working this problem, the student can make ‘tables’ of (A+3)(A-3) and just find the appropriate value in the table when TNYWR is passed back.

Upper Division Relay 1 :
UR1Q1.: One-fifth of the students in a class are wearing red hats, and one-seventh of the students are wearing green shirts. If the number of students in the class is between 50 and 100, how many students are in the class?
UR1Q2.: Let TNYWR = N. There are N students in a class. One-fifth of them are boys. Of the boys, all but four are wearing red hats. How many boys are wearing red hats?
UR1Q3.: Let TNYWR = N. The number 30 can be represented as the sum of two primes in k ways. Compute the number k+N. (Remember that 1 is not a prime number!)

Upper Division Relay 2 :
UR2Q1. : The base of an isosceles triangle has length 2 units, and each leg has length 5 units. Find the tangent of a base angle of the triangle.
UR2Q2. : Let TNYWR = N, and let k = N2. The altitude to the base of an isosceles triangle is k, and the base itself is . Find the sine of the VERTEX angle of the triangle.
UR23Q3.: Let TNYWR = N. If N is the sine of an acute angle, find the sine of half that acute angle.