12/14/2010. Directions

Transcription

1 Directions You will have 4 minutes to answer each question. The scoring will be 16 points for a correct response in the 1 st minute, 12 points for a correct response in the 2 nd minute, 8 points for a correct response in the 3 rd minute, 4 points for a correct response in the 4 th minute. A sliding scale will be used. Once your hand has been raised with the answer sheet, it must stay up. If you put your hand down, your answer will be disqualified for that question. Your answer must be submitted on the official answer sheet that has been correctly filled out. Otherwise your answer will be disqualified. Your answer must be in the specific form that the question asks for. 1

2 Directions If not otherwise noted, the answers should be in one of the following generally accepted forms: Denominators rationalized Simplest radical form Fractions, improper fractions, or mixed numbers in simplest form Equations should have integral coefficients in standard form No units are necessary Calculators are not allowed in any division except Statistics. Headphones, beepers, cell phones, or electronic devices are not permitted. Sunglasses and hats are not to be worn during the competition. 2

3 1. When five times a number is decreased by 1, it has the same value as four times the number increased by 10. What is the number? 2. A paycheck varies directly with the number of hours worked. Suppose the pay for 20 hours of work is $ What is the pay for 500 hours of work? 3

4 3. Find the slope of the graph of the linear function f with the following conditions; f( 3) = 6 & f(3) = Machine A, Machine B and Machine C are three different models of balloon stamping machines. In one week, Machine A stamps four times as many balloons as Machine B. Machine C stamps 400 more balloons than Machine A. All three machines working together stamp 20,200 balloons in one week. Find the number of balloons stamped by each machine in one week. 4

5 5. The total cost of an item including an 8.9% sales tax is $65. Find the tax paid for this purchase. 6. Find two numbers with sum 82 and difference 30. 5

6 7. Solve the system of equations. Write the solution as an ordered triple of the form (x, y, z). x + y + z = 25 y = 8z x = 12z 8. Your weight on Mars varies directly with your weight on Earth. A person weighing 125 lb on Earth weighs lb on Mars, since Mars has less gravity. If you weigh 155 lb on Earth, how much will you weigh on Mars? 6

7 9. Write a system of linear inequalities that defines a triangle with vertices at (0, 0), ( 5, 0) and ( 2, 5). 10. A mountain climber is 3600 meters from the peak. He climbs 50 meters per hour for 12 hours per day. How many days will it be before he reaches the peak? 7

8 11. Find the equation of the line which passes through the points ( 6, 3), (5, 2) in point slope form. 12. Solve, and write the solution(s) as integers. 4s 2 20 = 124 8

9 13. A contestant on a game show has to guess the price of a car correctly within $2500. If the value of the car is $30,000, write a compound inequality to represent the winning guesses. 14. An object is dropped from a height of 168 feet. Assuming that there is no air resistance, how long does it takes to reach the ground? 9

10 15. A student is assigned a 3000 word paper for a class. He types 120 words in 4 minutes. At this rate how long will it take him to complete the paper? 16. The width of a rectangle is 18 cm less than the length. The perimeter is 88 cm. Find the dimensions of the rectangle. 10

11 17. What is the degree of the following polynomial? 11