Regional Topical

March 21st

Directions: Mark on the answer form the letter that is closest to the correct answer. Make sure that your name(s) are on the answer form. If you are on a team put your team number and school name on the answer form. Remember that there are 5 points awarded for a correct response, 1 point for no response, and 0 points for an incorrect response.

A water tank is cylindrical, 20 feet high and 30 feet in diameter. It has steel sides and top. Its base is concrete 8 inches thick and 1 foot larger than the tank all around the tank.

  1. What is the tank's volume in cubic feet?

    a. 56000 b. 14000 c. 19000 d. 18000

  2. How many cubic yards of concrete are there in the base?

    a. 180 b. 60 c. 6400 d. 20

  3. What radius would give the maximum volume if the same total area of steel is used?

    a. 15.0 feet b. 16.5 feet c. 18.3 feet d. 20.1 feet

    If the following containers are being filled at a constant rate, match the time versus height graph to the container with the appropriate shape.

     

a. b. c. d.

 

4.

5.

 

    Pictured first is the front view and next the right side view of a 'building' made of blocks. 

 

  1. What is the minimum number of blocks in the building?

    a. 12 b. 15 c. 18 d. 21

  2. 7. What is the maximum number of blocks in the building?

    a. 25 b. 30 c. 35 d. 40

    Mario and Juanita have a 12 acre farm that they have decided to plant with strawberries and raspberries for supplemental income. It takes two days per acre to prepare the ground for strawberries and only one day per acre to prepare the ground for the raspberries. They have two weeks to prepare the ground. They believe that they can make a profit of $500 per acre from the strawberries and $300 per acre from the raspberries. The strawberry plants are planted an average of one plant per square foot and the raspberries are planted one every three square feet.

  3. How many raspberry plants are required for an acre? (640 acres in a square mile.)

    a. 1800 b. 200 c. 2000 d. 15000

  4. How many acres of strawberries should be planted to maximize their profit?

    a. 8 b. 5 c. 2 d. 0

    The patient is supposed to take 300 milligrams of medication every eight hours. 60% of the medication remains in the body after 8 hours.

  5. How many milligrams of medication are in the body after the fourth dose is taken?

    a. 400 b. 550 c. 700 d. 650

  6. How much difference is there in the number of milligrams of medication in the body after the 10th dose compared to after the 11th dose?

    a. 1.2 b. 1.5 c. 1.8 d. 2.1

  7. If the patient is not very consistent in taking the doses but does take three a day, no two doses less than 4 hours apart, what is the minimum milligrams of medication in the patient after the 5th day?

    a. 450 b. 350 c. 550 d. 250

    A toy car manufacturer has three models it produces. Each model is made from plastic, metal and rubber. Below are tables that show: the number of units of material needed to make each model, the manufacturer's price for each of the materials, the price each model sells for and the number ordered by two retailers.

    Plastic

    Metal

    Rubber

    Cost in $ per unit

    Selling Price

    Retailer #1

    Retailer #2

    Model A

    5

    4

    6

    Plastic

    0.29

    Model A

    3.57

    Model A

    50

    40

    Model B

    3

    1

    3

    Metal

    0.17

    Model B

    4.98

    Model B

    50

    40

    Model C

    4

    2

    1

    Rubber

    0.21

    Model C

    4.67

    Model C

    30

    50

  8. How much does it cost for the materials to make Model B?

    a. 1.67 b. 0.87 c. 0.17 d. 2.03

  9. What is the total bill for Retailer #2?

    a. 12 b. 5600 c. 570 d. 600

  10. What is the total cost of all the materials needed to fill the two retailers' orders?

a. 58 b. 592 c. 10907 d. 2540

Part 2

 

So far this semester Tammy has earned 100, 76, 86 and 100 points. Every one of her math tests has 100 points possible and all scores are integers. She wants to have an average of 92.

  1. If there are three more tests to go, what would have to be the mean of those three tests?

    a. 94.5 b. 94.0 c. 93.5 d. 95.0

  2. If there are three more tests to go, what is her lowest possible mode?

    a. 92 b. 91 c. 100 d. 86

  3. If there are three more tests to go, what is her lowest possible median?

    a. 92 b. 86 c. 94 d. 91

  4. What is the fewest number of additional tests needed if she were to end with a mean of 98?

    a. 5 b. 10 c. 15 d. 20

     

    The space shuttle leaves the earth and reaches orbit height in 8 minutes. It travels at 28000 km/hr in orbit and takes 90 minutes to orbit the earth. When it approaches the space station for docking, it initially approaches at a relative speed of 500 m/s and its thrusters can change its speed at a rate of 10 m/s/s. The radius of the earth is 6670 km.

  5. How many degrees of the earth's central angle does the shuttle cover in ten minutes?

    a. 5 b. 10 c. 15 d. 20

  6. How many minutes would it take the shuttle to slow to a stop relative to the space station?

    a. 1 b. 5 c. 80 d. 50

  7. What is the minimum distance the shuttle can be from the space station before firing its thrusters if the shuttle commander did not want to over shoot the space station?

    a. 500 b. 25,000 c. 2,500 d. 12,000

  8. How high above the earth is the shuttle when it is in orbit?

    a. 1,500,000 m. b. 14,500 km. c. 6,600 km. d. 14 km.

    An equilateral triangle is being packaged in a box. Each edge of the triangle is 2 meters and the thickness is 5 mm.

  9. If the bottom of the box is one meter by two meters, how tall in meters would the box have to be?

    a. 2.1 b. 1.2 c. 1.5 d. 1.8

  10. What is the minimum volume in cubic meters of a cubical box that would just hold the triangle?

    a. 8.0 b. 5.2 c. 2.8 d. 2.5

     

     

    A dot.com company sells one item and claims to bill on the following basis: "Regardless of the number ordered, each item cost the same. We add 7% sales tax on the price of the items and on any order we add the same fixed shipping charge."

              A customer thinks something is wrong with one of their bills. Here are the charges for the customers four separate orders:

    Number of items

    Price charged

    3

    46.20

    5

    74.00

    7

    111.80

    9

    129.59

  11. What should the bill be for eight items?

    a. 125.70 b. 130.20 c. 115.78 d. 120.70

  12. What is the shipping charge?

    a. 4.50 b. 4.00 c. 4.25 d. 4.75

  13. What should have been the price charged on the incorrect items?

    a. 76.50 b. 101.80 c. 45.20 d. 145.60

  14. How many different license plate "numbers" are there that begin with one letter and finish with 5 digits?

    a. 1300 b. 2,600,000 c. 76 d. 786,240

     

  15. I place four upside-down opaque cups on a table and hide a gold nugget under one of them. You select one of the cups. Instead of showing you what is under the cup you picked, I remove two of the cups that do not have the nugget under them. What is the probability that the nugget is under the cup that you did not pick?

a. 2/3 b. 1/4 c. 3/4 d. 1/2

 

2001 REGIONAL TOPICAL ANSWERS:

PART 1

  1. B
  2. D
  3. B
  4. C
  5. B
  6. A
  7. C
  8. D
  9. C
  10. D
  11. C
  12. D
  13. A
  14. C
  15. B

PART 2

  1. B
  2. D
  3. D
  4. C
  5. D
  6. A
  7. D
  8. D
  9. C
  10. C
  11. C
  12. A
  13. B
  14. B
  15. C