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 is 5 points awarded for a correct response, 1 point for no response, and 0 points for an incorrect response.

While supervising the set up of the chicken and rabbit barn for the County Fair, a 4-H leader (being a bit bored) started tracking heads and feet of the animals in the barn as time passed. 1. At one point there were 20 heads and 54 feet. How many rabbits were here?

A. 15 B. 8 C. 12 D. 5 2. Several hours later, after a steady flow of chickens and rabbits entering the barn, the 4-H leader noticed that

the number of heads after t hours was approximately 12.5t while the number of feet was approximately 42.5t. Of the chickens and rabbits, chickens were what percentage of those animals in the barn?

A. 10 B. 30 C. 50 D. 70 You are designing a target as shown. Each region on the target is to have the same area as each other region. The three circles have the same center. 3. What is the ratio of the area of the bulls-eye (small center circle) to the

area of the entire target? A. 1:12 B. 1:18 C. 1:19 D. 1:27

4. The radius of the medium size circle is what percentage of the radius of the largest circle?

A. 60% B. 70% C. 100% D. 85% 5. Which of the following is equal to the distance from A to B?

A. 0.5(AC) B. 0.6(AC) C. 0.7(AC) D. 0.8(AC) 6. Which of the following is equal to the distance from F to G?

A. 1.0(AC) B. 1.1(AC) C. 1.2(AC) D. 1.3(AC) 7. If the length of arc FDE is some constant times the distance from A to C, then what is the value of the

constant? A. 0.7 B. 0.6 C. 0.8 D. 1.9

WSMC High School Regional Competition

Topical Problems Part One

March 9, 2011

A B F D E C G

The three digits, 3, 5, and 8 are each used once and are arranged to make a three-digit number. Also, let digit reduction, be defined as adding each individual digit of a number and if the answer is not a single digit, add the digits of the sum until the sum is a single digit for example: digit reduction of 697 —› 6+9+7=22 —› 2+2=4 8. What is the largest difference between any two of the possible three-digit numbers?

A. 495 B. 505 C. 485 D. 450 9. What is the average of all possible three-digit numbers using 3, 5, and 8?

A. 495 B. 545 C. 595 D. 645 10. If the average in the question above is rounded to the nearest integer, what is the rounded average’s digit

reduction? A. 1 B. 0 C. 7 D. 9

11. What is the largest difference between the digit reduction of any three digit number AND the digit reduction of the average of the numbers created from all possible arrangements of the digits?

A. 0 B. 1 C. 2 D. 3 A treasure map describes the way to find the hiding place of a treasure by the following:

o Travel from the center of Dry Gulch two miles towards the setting sun (W) to a fork in the creek. o Heading toward Santa’s home (N), travel three miles to a fallen tree. o Find a hidden pass by scrambling ½ mile North by North East (halfway between NE and N). o Upon reaching the pass, follow the ridge South 600 paces (yards) to a boulder hiding the entrance to

a cave and your glorious future. (1 mile is 1760 yards.) 12. How many yards is the straight-line distance between Dry Gulch and the fallen tree?

A. 8800 B. 7040 C. 6030 D. 6350 13. How many yards is it from the fallen tree to the cave entrance?

A. 400 B. 600 C. 550 D. 500 14. If a person can walk for 15 minutes and cover 1000 paces and maintains this rate, how long in hours would

it take to get from Dry Gulch to the cave entrance by walking the described route? A. 2.6 B. 2.3 C. 2.9 D. 3.2

15. How many degrees clockwise from North is Dry Gulch from the cave entrance? A. 110 B. 60 C. 145 D. 150

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 is 5 points awarded for a correct response, 1 point for no response, and 0 points for an incorrect response. Uyen lives in a high-rise apartment building and to get her exercise, Uyen walks up the stairway to her apartment on the 32nd floor from the ground floor (floor 1). She usually reaches the 4th floor in 15 seconds. However, after each floor, her average speed drops 2% of the average for all of the average of all of the previous floors. 1. What was Uyen’s average speed in floors per minute for a trip from ground floor to the 4th floor?

A. 16.0 B. 12.0 C. 0.27 D. 0.20 2. How many seconds does it take Uyen to go from the 1st to the 5th floor?

A. 19.0 B. 19.5 C. 20.0 D. 20.5 3. How many minutes does it take Uyen to go from the ground floor to her 32nd floor?

A. 4.0 B. 5.5 C. 5.0 D. 4.5

The formula for converting Fahrenheit temperature to Centigrade is C(f)=5(f-32)/9 where f is the Fahrenheit temperature and C(f) is the corresponding Centigrade temperature. However, doubling the Centigrade temperature and adding 30 degrees is often use to estimate Fahrenheit temperature. 4. Which function represents the estimation method?

A. C(f)=2(f-30) B. C(f)=2f+30 C. C(f)= (f-30)/2 D. C(f)=f/2-30 5. What Centigrade temperature is correctly predicted by the estimation method?

A. -2 B. 36 C. -40 D. 10 6. If a function, E(f), gives the percentage error in the Centigrade temperature predicted by the estimation

formula, then which best represents E(f)?

A.

€

f − 5010 f − 320

B.

€

10 f − 5003200 −100 f

C.

€

10 f − 500f − 32

D.

€

500 −10 ff − 32

Consider a convex equilateral polygon where the interior angle measures alternate between two values. 7. If the difference between the adjacent angles is 25°, what is the smallest angle (in degrees) possible?

A. 75 B. 72 C. 73 D. 74 8. If a side in the polygon above is 4 centimeters what is the area in square centimeters?

A. 16 B. 10 C. 14 D. 12

WSMC High School Regional Competition

Topical Problems Part Two

March 9, 2011

Chelsea had a cumulative grade point average (Cum GPA) of 3.167 where letter grades are converted to a numeric scale using the table shown. Assume that Chelsea takes six classes each term and each class is one half credit per term. She just completed a new term. Chelsea earned a GPA of 3.550 for this new term. 9. What could have been her lowest grade this term?

A. C- B. C+ C. D+ D. C 10. What could be her best lowest grade in this new term?

A. B B. B+ C. B- D. A- 11. If the new semester GPA of 3.55 raised her Cum GPA of 3.167 by 3.03%,

how many credits has Chelsea completed? A. 6 B. 12 C. 18 D. 9

12. If it takes 24 credits to graduate, what is the best possible Cum GPA Chelsea could have?

A. 3.7 B. 3.6 C. 3.8 D. 3.5

The Kentucky Derby in 2010 had its 136th running of the race. The race was changed to 10 furlongs in its 22nd running. Secretariat has the best winning time set in the 99th running of the race with a time of 1 minute 59 2/5 seconds. (A furlong is 220 yards and a mile is 5280 feet.) 13. What was the average

speed in miles per hour of Secretariat in his record time?

A. 42 B. 45 C. 27 D. 38

14. Among other things track conditions play a big part in the average speeds of the winning horses. But assuming that the slowest winning horse and Secretariat ran on the same day with their same winning average speeds, how many feet ahead would Secretariat have been when he crossed the finish line?

A. 50 B. 600 C. 300 D. 100 15. If the data were modeled by a quadratic function of the form W(r)=0.001r2+Br+C where r is the running and

W(r) is the winning time in seconds for running r, which best describes W? (Let ≈ mean “is approximately equal to”)

A. B≈ -50, C≈220 B. B≈ -0.2, C=130 C. B≈ -50, C≈130 D. B≈ -0.2, C≈220

A = 4.0 C+ = 2.3 A- = 3.7 C = 2.0 B+ = 3.3 C- = 1.7 B = 3.0 D+ = 1.3 B- = 2.7 D = 1.0

F = 0.0

Part One Part Two 1. B 7 1. B 12 2. B 30 2. D 20.4 3. C 1:19 3. D 4.64 4. A 60.7% 4. C 5. A 0.5(AC) 5. D 10 6. C 1.165(AC) 6. D 7. C 0.863 7. A 77.5 8. A 495 8. A 15.6 9. C 592 9. C 10. C 7 10. B 11. A 0 11. B 12. D 6346 12. B 3.62 13. A 398 13. D 37.69 14. A 2.57 14. B 771 15. D 149.91 15. B

Part One Part Two 1. B 7 1. B 12 2. B 30 2. D 20.4 3. C 1:19 3. D 4.64 4. A 60.7% 4. C 5. A 0.5(AC) 5. D 10 6. C 1.165(AC) 6. D 7. C 0.863 7. A 77.5 8. A 495 8. A 15.6 9. C 592 9. C 10. C 7 10. B 11. A 0 11. B 12. D 6346 12. B 3.62 13. A 398 13. D 37.69 14. A 2.57 14. B 771 15. D 149.91 15. B

WSMC High School Regional Competition

Topical Problems Key

March 9, 2011

WSMC High School Regional Competition

Topical Problems Key

March 9, 2011

WSMC High School Math Contest

Answer Form for Part One

WSMC High School Math Contest

Answer Form for Part One School School

Team Number Team Number

Name(s)

Name(s)

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

6. 6.

7. 7.

8. 8.

9. 9.

10. 10.

11. 11.

12. 12.

13. 13.

14. 14.

15. 15.

WSMC High School Math Contest

Answer Form for Part Two

WSMC High School Math Contest

Answer Form for Part Two School School

Team Number Team Number

Name(s)

Name(s)

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

6. 6.

7. 7.

8. 8.

9. 9.

10. 10.

11. 11.

12. 12.

13. 13.

14. 14.

15. 15.