A radar tower picks up a UFO (Unidentified Flying Object) at compass bearing of 178°

WSMC High School State Competition

Topical Problems Part 1

April 21, 2001

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.

Two metal pipes with a ten-inch inside diameter are being cut at 45° angles as near to the end as possible. The pipes are then fitted together to form a right angle and then welded together. The walls of the pipe are 3/8 of an inch thick.

What is the length in inches of the cut form A to B where A and B are on the outside surface of the pipe?
A) 14.7 B) 14.1 C) 10.5 D) 15.2
Imagine the origin of the coordinate plane being placed at the center of the cut and the x-axis is on the widest part of the cut. If the units of the coordinate plan are in inches, what is the equation of the inside edge of the cut?
A) x²+y²=100 B) x²/5 + y²/7 =1 C) x²/25 + y²/49 =1 D) 58x² + 29y² =1770
If the cut off piece was split open at its point of least amount of pipe and flattened out, its shape would most resemble which of the following?
A) B) C) D)
What is the approximate area in square inches of the actual cut surface on one of the pipes?
A) 12.5 B) 14.0 C) 15.5 D) 17.0
Kim has a GPA of 3.32 for the first five semesters of his high school career and has 3 semesters remaining. (Assume that he is on a 4 point system where the highest point is 4.00.)
What is the GPA he needs for his last three semesters if he wants to end with a GPA of 3.50? (Assume each semester he takes the same number of credits.)
A) 3.7 B) 3.8 C) 3.9 D) 4.0
If he were to take only two thirds of a normal load his last semester because he wants to work, what would his maximum GPA be?
A) 3.5 B) 3.6 C) 3.7 D) 3.8

A pie chart is made for the following data concerning the number of students in each class at a high school: 221 seniors, 243 juniors, 297 sophomores and 278 freshmen.
What is the central angle in degrees for the junior section of the pie chart?
A) 0.23 B) 23 C) 84 D) 1.45
If the answer is converted to degree-minute-second format, how many minutes would there be?
A) 11 B) 20 C) 12 D) 45
There is a three-digit number that is a multiple of four and the sum of the digits is 25.
What is the number?
A) 800 B) 900 C) 888 D) 996

Paper cups are stacked one inside the other and each cup is congruent to the others. When three cups are in the stack, the stack is 8.2 cm. When 7 cups are in the stack, the total height of the stack is 9.8 cm. The stack is 11 cm. when there are ten cups in the stack.
How tall in centimeters is a single cup?
A) 7.0 B) 7.5 C) 6.5 D) 10.0
How much taller in centimeters is the total stack when ten cups are added?
A) 4 B) 11 C) 3 D) 7

How many cups would fit in a box that holds a single stack and the box is 50 cm. tall?

A) 10 B) 95 C) 105 D) 125

There is a rural mail route between the towns: A, B, C, D, and E. Rosa delivers mail on the routes between the cities according to the matrix to the right where a one indicates a route where she delivers mail. Unfortunately the main post office is in town B. Rosa finds her route to be not to her liking. She would prefer to start delivering on one of her routes as soon as she left the post office and not have to deliver mail on her return.

If she were able to relocate the main post office to satisfy her liking, where should it be?
A) B or C B) C or D C) D or E D) E or A
Without knowing the location of the towns and where the roads are located, what is the minimum number of times that her routes cross if the main post office was relocated?
A) 0 B) 1 C) 2 D) 3
Rosa decided that it was unlikely that they would relocate the main post office to accommodate her and that they might remove a leg of her route and gut her pay. However she figured that if they added one route, she could deliver mail during her entire route and end up at the post She also thought that this solution would earn her a raise. Between which two towns is the route she is thinking of adding?

A) B or C B) C or D C) D or E D) E or A

Topical Problems Part 2

In the sketch to the right, A is the center and AB=10 cm. The segments from B to C and D to C are tangent to the circle.

If AC=20 cm. find DC in centimeters.
A) 15 B) 20 C) 22 D) 17
If AC=20 cm. find the length in centimeters of minor arc BD.
A) 10 B) 15 C) 20 D) 25
Find AC in centimeters if the area of triangle ABC is equal to the area of sector defined by major arc BED.
A) 35 B) 40 C) 25 D) 30
On a clock with an hour hand and a minute hand, the tip of the hour hand is 5 inches from the center of the dial and the minute hand is 8 inches. The following questions are related to the distance from the tip of the hour hand to the tip on the minute hand.
What is the distance in inches when the hands make a 135° angle?
A) 5.6 B) 32.4 C) 12.1 D) 9.4
What is the period in minutes of the function that describes the distance as time passes?
A) 60 B) 62 C) 64 D) 66
What is the shape of the periodic function that describes the distance as time passes?
A) B) C) D)

A car has tires with a twelve-inch radius. The car is traveling down a level road at 60 miles per hour.
How many revolutions per minute is the tire making?
A) 100 B) 200 C) 400 D) 800
What is the difference in speed in mile per hour between the road and a point on the top of the tire?
A) 30 B) 60 C) 90 D) 120
What is the vertical component of the speed of a point on the circumference of the tire relative to the road when that point is six inches from the road in inches per second?
A) 300 B) 1000 C) 900 D) 100

In a five-story building with an additional floor for the parking garage under the building, people enter the elevator to reach one of the five floors. Assume that the probability of any particular person getting off at any floor is equal.
If three people get on the elevator, what is the probability that they all get off on the same floor?
A) 0.60 B) 0.07 C) 0.06 D) 0.01
What is the probability that they all get off on different floors?
A) 0.5 B) 0.4 C) 0.3 D) 0.2
Carbon 14 dating is based on the decay of radioactive carbon 14 which exists in living creatures at a known level while the creature is alive. When the creature dies, it no longer maintains that level because it ceases to eat and breathe. The amount of carbon 14 left ( A(t)) of the original amount (A(0)) is found by the following equation where t is in thousands of years: A(t) = A(0)•(0.883)t
What percent of A(0) is left in the remains of creatures that died in the times of Jesus Christ?
A) 0 B) 40 C) 70 D) 90
If the percentage left is 10%, how many years old are the remains?
A) 200 B) 2000 C) 20,000 D) 200,000
Twenty-five students took a test and after the scores were recorded, the students were given their scores and the following statistics: the arithmetic mean is 26 and the standard deviation is 5.3.
If a student has a score of 30, how many students are expected to score higher?
A) 18 B) 5 C) 3 D) 9
Starting with a full glass of water, pour out half of the water into another container. Return half of that water. Now pour out a third of the water in the glass. Finish up by adding one third of a glass of water to the glass.
What fraction of the glass of water would then be filled with water?

A) 1/2 B) 5/6 C) 3/4 D) 2/3

Answers to the Topical Problems, State April 21, 2001

Part One

1 D

2 C

3 C

4 D

5 B

6 B

7 C

8 A

9 D

10 B

11 A

12 C

13 D

14 A

15 D

Part Two

1 D

2 C

3 B

4 C

5 D

6 A

7 D

8 D

9 C

10 C

11 A

12 C

13 C

14 B

15 B