Sunday, May 8, 2011

High School Problem Set

Solve the following problems. Show complete solutions. Be prepared to discuss this tomorrow. To be collected at 9AM.

  1. 1. ABCDE is a regular pentagon. AC and BD intersect in F. What is the measure of angle AFB?

    2. Two tangents PA and PB to a circle O (A and B are points on the circle) are drawn from a point outside the circle. If the tangents form a 46 degree angle, what is the measure of angle AOB?

    3. A point is 12 cm from the center of a circle with radius of 15 cm. Find the lengths of the longest and shortest chords that can be drawn through this point.

    4. In a circle, a chord 12 cm long is parallel to a tangent and bisects the radius drawn to the point of tangency. How long is the radius?

    5. A chord, 18 cm long is perpendicular to a radius of a circle. The distance from the intersection of chord and radius to the outer end of the radius is 3 cm. Find the length of the radius.

    6. Triangle ABC has side lengths AB = 65, BC = 33, and AC = 56. Find the radius of the circle tangent to sides AC and BC and to the circumcircle of triangle ABC.

    7. Convex quadrilateral ABCD has sides AB = BC = 7, CD = 5, and AD = 3. Given additionally that ÐABC=60˚, find BD.

    8. Find the distance between the centers of the inscribed and circumscribed circles of a right triangle with sides of length 3, 4 and 5.

Complete List of IRML 2011 Participants

We are happy to announce the following list of people who will be representing our country in the IRML to be held in Las Vegas, Nevada, USA on June 3-4, 2011.
  1. Abdao, DeAnne Rochelle L. (Philippine Science High School - Main)
  2. Aguilar, Kyle Darryl (Philippine Cultural College)
  3. Belonio, Jeska (Xavier University - High School)
  4. Bisnar, Janine Caryl O. (Integrated Montessori Center - Taguig)
  5. Candido, Glicerio III (Philippine Science High School - Eastern Visayas Campus)
  6. Chan, Zernon Ezra (Philippine Tong Ho Institute)
  7. Cobol, Marx Vincent (Philippine Science High School - Southern Mindanao Campus)
  8. Concepcion, Georemie Arriane (Philippine Science High School - Main)
  9. Datuin, Jyronz Daniel T. (Baguio City National High School
  10. Dela Cruz, Claire Klemaine (Integrated Montessori Center - Taguig)
  11. Destura, Gail Denise (La Salle Academy)
  12. Deypalan, Mariefel Nicole (Mindanao State University - Iligan Institute of Technology - IDS)
  13. Fetalvero, King James (Philippine Science High School - Southern Mindanao Campus)
  14. Gepilango, Nicole Joyce (Iloilo Central Commercial High School)
  15. Go, Ransel Simon O. (Tarlac Living Faith Academy(
  16. Guerrero, Dann Erika (Integrated Montessori Center - Taguig)
  17. Juntilla, Dave Laurence A. (Philippine Science High School - Southern Mindanao Campus)
  18. Laza, Raina Carlin (Sta. Rosa National Science High School)
  19. Lee, Andrea Louise (Ateneo de Davao High School)
  20. Lofranco, Life Christian (Philippine Science High School - Eastern Visayas Campus)
  21. Mirabueno, Jose Alfonso Ignacio K. (Philippine Science High School - Southern Mindanao) Campus
  22. Ochiai, Mikael Adriane (Makati Science High School)
  23. Ong, Olsen John (Trinity Christian School)
  24. Palaganas, Jerome Jean (Angelicum College)
  25. Palaganas, Jerome Claude (Angelicum College)
  26. Rivera, Miguel Luis (Philippine Science High School - Main)
  27. Sawali, Akkiara Symonn May (St. Augustine's School)
  28. Soria, Gwendolen (Precious International School of Davao)
  29. Utanes, Kerwin (Philippine Science High School - Main)
  30. Utleg, Miguel (St. Paul University Philippines - Tuguegarao)
We shall have a continuous training until May 27, 2011, days before the team is scheduled to leave for the competition.

Elementary Problem Set

Solve the following completely. Show complete and neat solutions. This will be collected first period tomorrow morning. Be ready to explain your solutions in class.

1. Angge the ant walks through all vertices once along the edges of a cube using the shortest possible route. If the total distance she covered is 49 cm., what is the surface area and volume of the cube?

2. A tennis ball fits exactly inside a cube of side length 6 cm. What is the volume of the sphere?

3. A cone of height 7 cm. has a radius of 1.5 cm. If a semi-spherical ice cream scoop is placed on top of it, what is the total volume formed by the ice cream cone?

4. A uniform hexagonal prism has a side length of 8 cm. What is its volume?

5. If a rectangular prism block of wood has dimension 5 cm x 4 cm x 6 cm and cost $60 , what is the fair price in dollars of a 15 cm x 24 cm x 48 cm block of the same type if price is determined solely by volume?

6. What percent of the volume of a 10 '' x 10'' x 10'' box can be filled with 4'' x 4'' x 4'' wooden cubes? Express your answer as a decimal to the nearest tenth.

7. A hollow piece of cylindrical pipe has an outside radius of 2 inches and an inside radius of 1.9 inches. The pipe is 3 feet long. What is the surface area and volume of the pipe? Use Pi=3.14.

8. The slant height of a cone is 51 cm , and the height from the vertex to the center of the base is 45 cm . What is the number of cubic centimeters in the volume of the cone? The answer is x Pi . What is x?

9. A wooden model of a square pyramid has a base edge of 42 cm and an altitude of 21 cm. A cut is made parallel to the base of the pyramid that separates it into two pieces: a smaller pyramid and frustum. The height of the smaller pyramid is 9 cm. What is the volume of the frustrum?

10. A 15 cm x 11 cm x 7 cm box is to be filled with 3 cm x 3 cm x 3 cm cubes. The extra spaces would then be filled with 1 cm x 1 cm 1 cm cubes. If the box is to be filled with as many 3 cm cubes as possible before being filled by 1 cm cubes, and that there would be no extra space after, how many cubes will be needed in all?


Suspension of Classes

Due to the typhoon, classes today, May 9, 2011, in DEECO for MTG MOSTP 2011 is cancelled. Please visit this blog for your problem set, which will be posted today.

Classes will resume tomorrow, May 10, 2011, as the typhoon is expected to exit the Philippine Area of Responsibility by then.

Please be advised.

Regards,

MTG MOSTP 2011 Team