Rules of Engagement Please turn off all cell phones while Math Bowl is in progress. The students participating in Rounds 1 & 2 will act as checkers for one another, as will the students participating in Rounds 3 & 4. There is to be no talking among team members once the round has begun. Any pairs caught talking, even between questions, will be ejected from the competition.

Checkers are more than welcome to take a chance that the answer their teammate gave is also correct, though it doesn’t appear as a possible answer. However, keep in mind that if the answer is in an unacceptable form or otherwise incorrect, points will be deducted from the team score according to how many points would have been received if the answer was correct. (5 points will be deducted for an incorrect first place answer.)

Checkers, please remember that multiplication and addition are commutative. Correct solutions not placed in the given answer space are not correct answers! Rationalize all denominators. Reduce all fractions, unless the question says otherwise. Do not leave fractions as complex fractions. Use only log base 10 or natural log.

It is only necessary to write an equation when asked for an equation or a function. Answers of the form are acceptable, unless both answers are rational. Use interval notation for domains and/or ranges. When units are given in the problem, units are required in the answer. Good luck, and most importantly, have fun!

2005 Math Bowl Junior Varsity Round 1

Practice Problem – 20 seconds Simplify

Problem 1.1 – 20 seconds Subtract from

Problem 1.2 – 30 seconds If a computer purchased for $11,200 depreciates at a rate of $1600 per year, how many years will it take to depreciate completely?

Problem 1.3 – 35 seconds If straight-line appreciation is assumed, an antique clock is expected to be worth $350 after 2 years and $530 after 5 years. What will the clock be worth after 7 years?

Problem 1.4 – 25 seconds Find the equation of the line parallel to and passing through the midpoint of the segment joining and..

Problem 1.5 – 20 seconds Solve

Problem 1.6 – 20 seconds Simplify

Problem 1.7 – 30 seconds Write as a sum or difference of fractions and simplify completely.

Problem 1.8 – 20 seconds Simplify

Problem 1.9 – 15 seconds Solve

Problem 1.10 – 20 seconds Simplify and factor

Problem 1.11 – 25 seconds Solve

Problem 1.12 – 35 seconds Solve

Round 2

Practice Problem – 20 seconds Find the measure of each angle.

Problem 2.1 – 20 seconds Find the ordered pair satisfying the system

Problem 2.2 – 20 seconds The measure of an angle is more than its supplement. What is the measure of the angle?

Problem 2.3 – 20 seconds The area of a square is 169 in 2. What is the perimeter?

Problem 2.4 – 20 seconds How many square millimeters are in 1 square meter?

Problem 2.5 – 35 seconds For a particular word processor, the number of words w that can be typed on a page is given by the formula, where x is the font size. How many more words can be typed on a page if font size 8 is used instead of font size 16?

Problem 2.6 – 25 seconds Find

Problem 2.7 – 15 seconds Write the standard form of the equation of the circle with the graph:

Problem 2.8 – 20 seconds If in isosceles trapezoid QRST, find.

Problem 2.9 – 20 seconds If, find.

Problem 2.10 – 15 seconds What is the sum of the degree measures of the exterior angles of a heptagon?

Problem 2.11 – 25 seconds Given that, determine the measure of the two angles that are labeled.

Problem 2.12 – 45 seconds A field bordering a straight stream is to be enclosed. The side bordering the stream is not to be fenced. If 1000 yds of fencing is to be used, what are the dimensions of the largest rectangular field that can be fenced?

Round 3

Problem 3.1 – 30 seconds In a right triangle, one leg is 7 feet shorter than the other leg. The hypotenuse is 2 feet longer than the longer leg. Find the length of the hypotenuse.

Problem 3.2 – 45 seconds What is the remainder when is divided by ?

Problem 3.3 – 20 seconds Solve for q:

Problem 3.4 – 30 seconds The measure of each angle of a regular polygon is. How many sides does it have?

Problem 3.5 – 25 seconds How much plastic sheeting will be needed to cover this swimming pool?

Problem 3.6 – 25 seconds Simplify

Problem 3.7 – 25 seconds Calculate

Problem 3.8 – 20 seconds Find all solutions of

Problem 3.9 – 35 seconds Solve for x and y.

Problem 3.10 – 25 seconds Find the volume of a cone with a height of 12 cm and a circular base with diameter 10 cm.

Problem 3.11 – 30 seconds Solve

Problem 3.12 – 20 seconds What is the area of a circle with a circumference of inches?

Round 4

Problem 4.1 – 30 seconds A green (G), a blue (B), a red (R), and a yellow (Y) flag are hanging on a flagpole. 1.The blue flag is between the green and yellow flags. 2.The red flag is next to the yellow flag. 3.The green flag is higher than the red flag. What is the order of the flags from top to bottom?

Problem 4.2 – 20 seconds Factor completely.

Problem 4.3 – 20 seconds Find the domain of

Problem 4.4 – 30 seconds If one outlet pipe can drain a tank in 24 hours and another pipe can drain the tank in 36 hours, how long will it take to drain the tank if both pipes are working together?

Problem 4.5 – 15 seconds Simplify

Problem 4.6 – 15 seconds When the price is p dollars, an appliance dealer can sell refrigerators. What price will maximize his revenue?

Problem 4.7 – 40 seconds A piece of tin 12 in on a side is to have 4 equal squares cut from its corners. If the edges are then to be folded up to make a box with a floor area of 64 sq in, what is the total area removed from the piece of tin?

Problem 4.8 – 25 seconds In 60 oz of alloy for watch cases, there are 20 oz of gold. How much copper must be added to the alloy so that a watch case weighing 4 oz, made of the new alloy, will contain 1 oz of gold?

Problem 4.9 – 15 seconds How many real roots does have?

Problem 4.10 – 25 seconds Express as a fraction in lowest terms.

Problem 4.11 – 35 seconds Simplify

Problem 4.12 – 35 seconds A bowling ball is packaged within a tightly fitting cubical box with 10 in sides. How much foam can fit around the bowling ball but still inside of the box?