Team Brainstorm Instructions

1. A team consists of 4 students from a school. The team members will work together to solve several questions with topics from algebra, geometry, and trigonometry.

2. Calculators, except calculators with symbolic manipulation capacity, are allowed.

3. Students may not have any other assistance. No books or notes are allowed. No other person may assist the team members. Any violation of the rules will result in disqualification.

4. The room number assignment was sent to the teacher with registration confirmation. All team members should go to their assigned room in Maybank Building at the scheduled time. There may be more than one team assigned to the same room.

5. While the other team members wait in the room, only the Team Captain goes to Maybank Room 219 to get the problems and the form for submitting solutions.

6. The team works together for at most 30 minutes to solve the problems. Students will not be told when time is up. When the team completes the questions or when time is up, the Team Captain returns the form with the final answers only to the proctor in Room 219.

7. NO RUNNING. Teams will be disqualified for running.

8. The judges will consider the solutions in the order in which they are received. At the end of 30 minutes, the first team with the maximum number of correct answers will be selected as the winner. Decisions of the judges will be final.

Team Brainstorming 2005

  1. Degrees Celsius (C) and degrees Fahrenheit (F) are related by the formula C=5/9(F-32). What is the temperature range in the Fahrenheit scale corresponding to the temperature range in Celsius of -10
  2. A ball thrown upward (neglecting air resistance) from the top of a building 128 feet high with an initial velocity of 48 feet/second has a height in feet of h(t)=-16t2+48t+128 t seconds later. At what time interval will the ball be at least 64 feet above the ground?

  3. A rectangular box with a square base of length x and height h is to have a volume of 20 ft3. The cost of the top and the bottom of the box is 20 cents per square foot, and the cost of the sides is 8 cents per square foot. Find the dimensions of the box which will minimize the cost.

  4. Find a polynomial of degree 4 that has integer coefficients, zeros at "i√2" and "2i", and constant term 8.

  5. Write the equation of a line with x-intercept at a and y-intercept at b. (Both a and b are non-zero). Give your answer in slope-intercept form.

Answers

  1. 14
  2. t=0 to t=4

  3. x=2ft h=5ft

  4. y=x4+6x2+8

  5. y=-(b/a)x+b