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!
a b
2005Math Bowl
Junior Varsity
Round 1
Practice Problem – 20 seconds
Simplify
6 2 3 2x y x y x y
Problem 1.1 – 20 seconds
Subtract
from
26 6 13y y
23 4 7y y
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 .
3x
2, 4
8,12
.
Problem 1.5 – 20 seconds
Solve
4 22 64x
Problem 1.6 – 20 seconds
Simplify
3 2 3
2 4 5
x
x x
Problem 1.7 – 30 seconds
Write
as a sum or difference of fractions and simplify
completely.
2 2
2
x y x y
xy
Problem 1.8 – 20 seconds
Simplify
2
2
1
1
xyxy
Problem 1.9 – 15 seconds
Solve
2 3 24 0x
Problem 1.10 – 20 seconds
Simplify and factor
3 4 638x xy
Problem 1.11 – 25 seconds
Solve
21 5 2 3 7x x x
Problem 1.12 – 35 seconds
Solve
2 4 1 9 5x x
Round 2
Practice Problem – 20 seconds
Find the measure of each angle.
x+20
x+10 x
Problem 2.1 – 20 seconds
Find the ordered pair satisfying the system
4
2 13
x y
x y
Problem 2.2 – 20 seconds
The measure of an angle is more than its supplement. What is the measure of the
angle?
10
Problem 2.3 – 20 seconds
The area of a square is 169 in2.
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?
8000w
x
Problem 2.6 – 25 seconds
Find m ABD
4x+326x+8B
C
D
A
E
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 .
65m T
m R
T S
RQ
Problem 2.9 – 20 seconds
If ,find .
ABC DEC
m E
E
D
C
B
A
37
46
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.
1 2||l l
l2
l1
2x+104x-10
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
?
7 5 310 12x x x
2x
Problem 3.3 – 20 seconds
Solve for q:
2
7 1 3
2 1 2q q q q
Problem 3.4 – 30 seconds
The measure of each angle of a regular
polygon is . How many sides does it
have?
165
Problem 3.5 – 25 seconds
How much plastic
sheeting will be needed to
cover this swimming
pool?
Problem 3.6 – 25 seconds
Simplify
3
22
8 1 1
4 2 1 1
x x
x x x
Problem 3.7 – 25 seconds
Calculate7 4
2 5
i
i
Problem 3.8 – 20 seconds
Find all solutions of
29 25 0x
Problem 3.9 – 35 seconds
Solve for x and y.
x7.5
8
6
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
2 2 36 12x x
Problem 3.12 – 20 seconds
What is the area of a circle with a
circumferenceof inches? 16
Round 4
Problem 4.1 – 30 seconds
A green (G), a blue (B), a red (R), and ayellow (Y) flag are hanging on a flagpole.
1. The blue flag is between the green andyellow 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 tobottom?
Problem 4.2 – 20 seconds
Factor
completely.
ax ay az bx by bz cx cy cz
Problem 4.3 – 20 seconds
Find the domain of
3
1xy
x x
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
99i
Problem 4.6 – 15 seconds
When the price is p dollars, an appliance dealer can sell refrigerators. What price will maximize
his revenue?
2200 p
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?
2 2 1f x x x
Problem 4.10 – 25 seconds
Express as a fraction in lowest
terms.
.047
Problem 4.11 – 35 seconds
Simplify
2 2 2
1 2 1
3 2 4 3 5 6x x x x x x
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?
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