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 a  b 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
6  x  y   2  x  y   3  x  2 y 
Problem 1.1 – 20 seconds
Subtract
6 y  6 y  13
2
from
3y  4 y  7
2
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 x  3 and passing
through the midpoint of the
segment joining  2, 4
and 8,12 .
.
Problem 1.5 – 20 seconds
Solve
2
4 x 2
 64
Problem 1.6 – 20 seconds
Simplify
3 x  2  3
2 x  4   x  5
Problem 1.7 – 30 seconds
Write
 x  y   x  y
2
2
2 xy
as a sum or difference of
fractions and simplify
completely.
Problem 1.8 – 20 seconds
Simplify
x
1
y
2
x
1
2
y
Problem 1.9 – 15 seconds
Solve
2 3x  24  0
Problem 1.10 – 20 seconds
Simplify and factor
3
8x  xy
4
3
6
Problem 1.11 – 25 seconds
Solve
 x  1
2
 5  x  2   3x  7
Problem 1.12 – 35 seconds
Solve
2 4x 1  9  x  5
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
 x y 4

2
x

y


13

Problem 2.2 – 20 seconds
The measure of an
angle is 10 more
than its supplement.
What is the measure
of the angle?
Problem 2.3 – 20 seconds
The area of a
2
square is 169 in .
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
8000
w
,
where
x
is
the
font
size.
How
x
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
A
Find
m  ABD 
6x+8
D
C
B
4x+32
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 m  T   65 in isosceles
trapezoid QRST,
find m  R  .
Q
T
R
S
Problem 2.9 – 20 seconds
If ABC  DEC ,
find m  E  .
D
A
37
B
C
46
E
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 l1 || l2,
determine the
measure of
the two
angles that
are labeled.
l1
l2
4x-10
2x+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
x  x  10 x  12
7
5
3
is divided by
x  2?
Problem 3.3 – 20 seconds
Solve for q:
7
1
3


2
q  q  2 q 1 q  2
Problem 3.4 – 30 seconds
The measure of each
angle of a regular
polygon is 165 . 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
8x  1
x 1

2
2
4 x  2 x  1  x  1
3
Problem 3.7 – 25 seconds
Calculate
7  4i
2  5i
Problem 3.8 – 20 seconds
Find all solutions of
9 x  25  0
2
Problem 3.9 – 35 seconds
Solve for
x and y.
7.5
6
x
8
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
x  2 x  36  12
2
Problem 3.12 – 20 seconds
What is the area of a
circle with a
circumference
of 16 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
ax  ay  az  bx  by  bz  cx  cy  cz
completely.
Problem 4.3 – 20 seconds
Find the domain of
x 1
y 3
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
i
99
Problem 4.6 – 15 seconds
When the price is p dollars,
an appliance dealer can
sell  2200  p  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
f  x    x  2x 1
2
have?
Problem 4.10 – 25 seconds
Express .047 as a
fraction in lowest
terms.
Problem 4.11 – 35 seconds
Simplify
1
2
1
 2
 2
2
x  3x  2 x  4 x  3 x  5 x  6
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?