2009 Lee Webb Math Field Day
Junior Varsity Math Bowl
Before We Begin:
• 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 the
students on stage once the round has
begun.
• Answers that are turned in by the checkers
are examined at the scorekeepers’ table.
An answer that is incorrect or in
unacceptable form will be subject to a
penalty. Points will be deducted from the
team score according to how many points
would have been received if the answer
were correct (5 points will be deducted for
an incorrect first place answer, 3 for
second, etc.).
• 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.
2009
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
7 y  6 y 1
2
from
10 y  4 y  7
2
Problem 1.2 – 30 seconds
Cookie’s Old Timey Key-Limey
Pie Recipe calls for 3 egg
yolks and 4 egg whites. This
recipe makes 2 pies. Cookie
needs to prepare 100 of these
pies – how many dozen eggs
are needed?
Problem 1.3 – 35 seconds
Zacky’s Pizzeria offers a
choice of 3 different sizes,
2 different kinds of crusts,
and 10 different kinds of
toppings. How many
different 1-topping pizzas
can be ordered?
Problem 1.4 – 25 seconds
In the year 2000, the International Table
Tennis Federation changed the diameter
of the tournament table tennis ball from 38
millimeters to 40 millimeters. What
percentage of the new radius is the old
radius?
.
Problem 1.5 – 20 seconds
Solve
2 x 6
3
 81
Problem 1.6 – 20 seconds
Simplify
7  x  2  4 x  1
5x  3  (3x  2)
Problem 1.7 – 30 seconds
How many solutions does the
following equation have?
| x 3|
5| x 4| 
0
6
2
2
Problem 1.8 – 20 seconds
Simplify
x
1
y
2
x
1
2
y
Problem 1.9 – 15 seconds
Joe has lost his marbles!
Mary has 42 marbles, which
is three times as much as
Joe. Before he lost his
marbles, he had 10 more
than Mary. How many
marbles did Joe lose?
Problem 1.10 – 20 seconds
A circle has radius
equal to  . Find its
area, in terms of  .
Problem 1.11 – 35 seconds
Solve
2 4x 1  9  x  5
Round 2
Practice Problem – 20 seconds
Solve for x.
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 30 more
than its supplement.
What is the measure
of the angle?
Problem 2.3 – 20 seconds
A standard die is rolled
3 times. What is the
probability that at least
one of the rolls gives a
number less than 3?
Problem 2.4 – 20 seconds
How many square
meters are in 1
square kilometer?
Problem 2.5 – 25 seconds
Find all numbers
that when added
to their squares
give 12.
Problem 2.6 – 25 seconds
Suppose each vertex of a
triangle is joined to the
midpoint of the opposite
side. These segments
intersect at a point. What
is the name of this point?
Problem 2.7 – 25 seconds
If the height of a
pyramid is
stretched by a
factor of 10, then
the sides of the
base must shrink
by a factor of
what, in order to
keep the same
volume?
Problem 2.8 – 20 seconds
A cylinder has
circumference equal to 6
and height equal to 3 .
What is its volume?
Problem 2.9 – 20 seconds
If ABC  DEC ,
Find the measure
of E .
D
A
37
B
C
46
E
Problem 2.10 – 20 seconds
Evaluate
the sum:
a+b+c+d
+e+f (in
degrees)
d
e
c
f
a 145
105 b
Problem 2.11 – 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
Cali needs 3 hours to weed the
garden. Daly can do the same
job in 2 hours. How many
minutes will it take, if they work
together?
Problem 3.2 – 45 seconds
What is the remainder
when
x  2 x  3x  4 x  5
4
3
is divided by
2
x 1 ?
Problem 3.3 – 20 seconds
The area of
this
parallelogram
is 50. What
is the length
of the
diagonal?
29
10
Problem 3.4 – 30 seconds
Five points are placed evenly
around a circle. A line
segment connects every
pair of points. How many
regions do these segments
divide the circle into?
Problem 3.5 – 25 seconds
Between 3:14:19AM and
3:14:19PM, how many
times will the minute and
hour hands of a standard
clock be exactly in line with
each other?
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
Simplify:
3  2i
2  3i
Problem 3.8 – 20 seconds
Simplify
||||1  2 | 3 | 4 | 5 |
Problem 3.9 – 35 seconds
At Zila’s Boutique, a dress
has been discounted
20%, three times. All
together this represents a
discount of what
percentage?
Problem 3.10 – 25 seconds
A pyramid with square base of
length 10 and height 9, is cut
parallel to the base, half-way
between top and bottom. What is
the volume of the larger piece?
Problem 3.11 – 30 seconds
Solve
x  2 x  36  12
2
Round 4
Problem 4.1 – 30 seconds
Five songs are to be played in
random order. Two of the
songs are by the same group.
What is the probability that
these two songs are not
played consecutively? Answer
as a fraction in lowest terms.
Problem 4.2 – 20 seconds
If (a  b  c) is multiplied
out, what will be the
coefficient on the abc
term?
3
Problem 4.3 – 20 seconds
Zacky’s Pizzeria offers a choice
of 3 different sizes, 2 different
kinds of crusts, and 10
different kinds of toppings.
How many different 3-topping
pizzas can be ordered?
Problem 4.4 – 30 seconds
Give the equation of the line
perpendicular to 7x-11y=15
that goes through the point
(2,3). Your equation should be
in the same form as the given
line, using only natural
numbers.
Problem 4.5 – 15 seconds
A dart hits a circular board
randomly. What is the
probability that it hits
closer to the center than
the edge?
Problem 4.6 – 15 seconds
What is the maximum value
possible for y?
y  9 x  66 x  144
2
Problem 4.7 – 40 seconds
A football field is 50 yards wide and
100 yards long. It has stripes
every 10 yards of its length –
including the ends. How many
rectangles can be placed on the
field, so that no two of them
intersect the same number of
stripes?
Problem 4.8 – 25 seconds
If a ring of radius 1 yard is
placed randomly somewhere
on a standard football field (as
in the previous problem), what
is the probability that it will not
overlap any of the stripes?
Problem 4.9 – 45 seconds
A regular square pyramid has
base length 12 and height 7.
What is the distance from the
apex to a corner of the base?
Problem 4.10 – 25 seconds
An octagon is formed from a square of area
1 by marking each side into thirds and
then cutting off the corners along the lines
formed by these marks. What is the area
of the octagon?
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?
Extra
7.5
6
x
8
y
An angle is calculated to be
25.9858333333 degrees.
This measure is equivalent
to 25 degrees and how
many minutes and seconds?
FOA:
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?
• Ordero f flags questions