Topical Problems, Part 1
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. Clean away any smudges on your answer form to prevent errors in scoring.
Jorge borrowed money to buy a nice new car. His loan was for $6000 and he paid a down payment of $2500 out of his savings and traded in his old car for $4000. He was able to get a fixed interest rate of 9% compounded monthly when each payment was due.
1. If the entire loan amount went towards the cost of the car, what percent of the new car price was the down payment?
A) 42 B) 20 C) 25 D) 6
2. If he made payments of $300 a month, how many months would it take him to pay off the loan?
A) 20 B) 21 C) 22 D) 23
3. If he pays off the loan by making 48 equal monthly payments, how much total interest would he pay over the life of the loan?
A) $600 B) $800 C) $1000 D) $1200
Six test scores have the following statistics:
Mode = 75, Median = 74.5, Mean = 71, Range = 28, High Score = 80.
4. How many scores are greater than the mean?
A) 2 B) 3 C) 4 D) Can not be determined
5. What was the next to lowest score?
A) 75 B) 70 C) 74 D) 68
Centripetal acceleration (c) is the acceleration an object experiences as it turns in a circular path. It is calculated by the formula at the right where v is the speed measured in meters per second and r is the radius of the turn measured in meters.
6. If c = 9.8 and v = 20 find r.
A) 0.25 B) 4 C) 40 D) 0.025
7. What are the units for c?
A) B) C) D)
8. If v is constant and r doubles, how does c change?
A) doubles B) halves C) quadruples D) squares
Above is a drawing of a porcelain bowl that has a uniform thickness of 4 mm.
9. What is the surface area in square centimeters of the outside sides of the bowl.
A) 460 B) 360 C) 510 D) 590
10. What is the capacity in cubic centimeters of the bowl?
A) 1760 B) 1690 C) 1490 D) 1670
11. If porcelain is 1900 grams per liter, what is the mass in grams of the bowl?
A) 220 B) 370 C) 500 D) 270
Four identical fair coins are tossed.
12. If the coins are tossed 64 times, how many tosses are expected to show three or more heads?
A) 4 B) 12 C) 16 D) 20
13. What is the probability that two or more heads will be the result on any particular toss?
A) 0.20 B) 0.50 C) 0.75 D) 0.60
14. What is the probability that on three consecutive tosses, each toss results in exactly three tails and one head?
A) 0.005 B) 0.01 C) 0.05 D) 0.1
15. Now assume the coins were identically unfair with a 65% chance of landing heads up. You will be paid the sum in dollars equal to the number of heads if the number of heads is even. You will pay the sum in dollars equal to the number of heads if the number of heads is odd. How much on average would you expect to make per toss?
A) –25¢ B) 0¢ C) 25¢ D) 50¢
State Contest Topical Problems, Part 2
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. Clean away any smudges on your answer form to prevent errors in scoring.
Imagine the English capitol letters being used instead of the digits 0 through 10 as a counting system where A=0, B=1, C=2, and so on to Z=25. Also imagine that this system uses a similar place value system where BA is 26 and BB is 27.
1. Sort these numbers from smallest to largest: DARN, ZAP, RUN.
A) DARN, RUN, ZAP B) RUN, DARN, ZAP
C) ZAP, RUN, DARN D) RUN, ZAP, DARN
2. What would be the normal (base ten) value of CBA?
A) 1378 B) 1275 C) 1926 D) 321
3. Solve for x in : (BA)x + FZ = ZZ.
A) T B) U C) FA D) BA
A 300 ft. by 400 ft. rectangular piece of land is divided into four pieces that are privately owned and a piece owned by the county. The piece owned by the county is the access road that end at the corner in a turn around circle. Therefore the county's piece is a quarter of a circle as shown with a 50 ft. radius centered at the corner of the rectangle. Extended radii of the circle form the property lines for each of the four private pieces. David's lot forms a 25º central angle. Beatrice's back line is 150 feet.
4. How long in feet is the common property line between Beatrice and Courtney?
A) 480 B) 500 C) 510 D) 450
5. How much frontage in feet does David have? (Frontage is the edge of the property that touches the access road.)
A) 22 B) 33 C) 44 D) 55
6. What is the square footage of David's property?
A) 34600 B) 36800 C) 37300 D) 74100
7. Arrange the owner's first initial from the one that owns the parcel with the most area to the one that owns the least area.
A) ADCB B) ADBC C) DABC D) DACB
` Buildings' are made by placing 5 cubes in a row on a table and then placing 5 additional cubes, one at a time, directly on top of any cube already a part of the building. A possible front view of the structure is shown.
8. How many blocks high is the tallest possible building?
A) 3 B) 5 C) 6 D) 10
9. What are the maximum exposed faces of the cubes possible for any of the possible buildings? Do not count the faces on the table.
A) 30 B) 32 C) 35 D) 37
10. When viewing the `building' front, how many possible different looks can there be? (3 stacked on the left end and 2 on the right end is different than 2 on the left end and 3 on the right end.)
A) 130 B) 90 C) 70 D) 110
The Acme Co. produces two products Eglaers and Fotts. It takes an employee 9 hours to make a Eglaer and 10 hours to make a Fott. It takes 14 units of plastic for each Eglear and 11 for each Fott. The company makes $6.25 on each eglear and $5.90 on each Fott. If the Acme Co. has only 150 employee hours per week and 215 units of plastic that can be prepared for use each week, answer the following:
11. If the company chose to make 9 Eglears in a week, what is the most Fotts that could be completely made in a week?
A) 6 B) 7 C) 8 D) 9
12. How many Eglears should the Acme Co. make a week to maximize their profit?
A) 0 B) 2 C) 12 D) 14
The adjacent function relates the price, P(q), in dollars to the quantity produced, q, in thousands of units. The domain of the function is 0<q<25. The revenues R are found by multiplying the price by the quantity produced.
13. What is the price in dollars when 15000 units are produced?
A) 1225 B) 1600 C) 400 D) 900 million
14. If P(q) were graphed, which of the following could represent R?
A) Area bounded by P(q), q=0, P=0.
B) Area of the rectangle with two sides on the axes and one vertex on P.
C) The distance from the origin to P.
D) The distance from the origin to the P intercept multiplied by the distance from the origin to the q intercept.
15. What is the maximum value in dollars of the R?
A) 10,000 B) 8000 C) 9000 D) 15000
Topical Problems Answer Keys
Part 1 1 B 2 C 3 D 4 C 5 B 6 C 7 D 8 B 9 A 10 D 11 C 12 D 13 C 14 B 15 D |
Part 2 1 D 2 A 3 B 4 D 5 A 6 B 7 D 8 C 9 D 10 A 11 A 12 C 13 C 14 B 15 C |
© 2000 WSMC, Jim Miller, and Richard Edgerton