Transcript 2010 Lee Webb Math Field Day March 13, 2010 Junior Varsity Math Bowl.

2010 Lee Webb Math Field Day
March 13, 2010
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.
Junior Varsity Math Bowl
Round 1
Practice Problem – 20 seconds
Simplify
6  x  y   2  x  y   3  x  2 y 
Problem 1.1 – 30 seconds
Find the point of
intersection of the lines:
2 x  3 y  6  76
5 x  6 y  8  48
Problem 1.2 – 45 seconds
Shawn ran for 7 miles. Some
of the time he was jogging at
4mph, and the rest of the time
he was running at 6mph. In all
he ran for 1.5 hours. How
many miles did he jog?
Problem 1.3 – 15 seconds
Two positive integers have
sum 11 and product 24.
What is their difference (in
absolute value)?
Problem 1.4 – 30 seconds
Suppose you have randomly
drawn a 6, 7, 9, and 10 from a
standard deck of cards. What is
the probability that your next draw
will be an 8? Answer as a
fraction in lowest terms.
.
Problem 1.5 – 30 seconds
Solve
4
 3 x 1 


 2 
 1/ 2
Problem 1.6 – 45 seconds
Simplify
42x  7 y  6x
2(2 y  x)  8 y
Problem 1.7 – 60 seconds
Allie bought 30 A tickets for the
PiHedz concert at $17 each
and 20 B tickets at $11 each.
What are the other amounts of
B tickets she could have
bought and still spent the
exact same amount of money
on tickets?
Problem 1.8 – 30 seconds
 23
A carbon atom weighs 2.00  10 grams.
How many atoms of carbon does it
take to constitute one quarter of a
gram? Answer in proper scientific
notation.
Problem 1.9 – 30 seconds
17/25 is equal to x%. Find x.
Problem 1.10 – 60 seconds
What is the area of
the largest triangle
that can fit inside a
unit circle?
Round 2
Problem 2.1 – 30 seconds
Find the ordered pair
satisfying the system
3 x  2 y  16
5 x  2 y  64
Problem 2.2 – 30 seconds
The amount of agent X in a
petri dish is growing
exponentially. On the
second day there was 6 gm.
On the sixth day there was
18 gm. On which day will
there be 162 gm?
Problem 2.3 – 30 seconds
A standard die is rolled
3 times. What is the
probability that all the
rolls show a number
that is a power of 2?
Problem 2.4 – 30 seconds
What is the sum of
all the positive odd
integers less than
100 ?
Problem 2.5 – 30 seconds
How many positive
integer divisors
does 30 have?
Problem 2.6 – 15 seconds
Suppose G is the
centroid of triangle
ABC and that ray AG
meets BC at D. What
is the ratio of the
lengths AG/GD?
Problem 2.7 – 30 seconds
A log is 4 feet long and 1 foot in
diameter. After rolling it 2
revolutions, it left an impression
in the ground. What is the area
of the impression, in sq. feet?
Problem 2.8 – 60 seconds
Let E be inside square
ABCD such that ABE is an
equilateral triangle. What
is the measure, in degrees,
of  C E D ?
Problem 2.9 – 30 seconds
If ABCDE is a regular
pentagon, Find the
measure of
B
A
C
CAD
(in degrees)
D
E
Problem 2.10 – 45 seconds
Moonbeam’s Health Food
Store sells a raisin nut
mixture. Raisins cost
$3.50/kg and nuts cost
$4.75/kg. How many kg of
nuts should go into a 20kg
sack, to make the whole thing
worth $80?
Round 3
Practice Problem – 20 seconds
Solve for x.
x+20
x+10
x
Problem 3.1 – 45 seconds
Skier A finished the 3km race
in 2.5 minutes. Skier B was
.02 seconds slower. At these
paces, if they had raced side
by side, A would have finished
how many meters ahead of B?
Problem 3.2 – 45 seconds
What is the remainder
when
x  2 x  3x  4x  5
is divided by x  1 ?
4
3
2
Problem 3.3 – 60 seconds
A rhombus has
diagonals of
lengths 10 and
20. Each vertex
is extended
outward 10 units.
What is the ratio
of the area of the
outer figure to that
of the rhombus?
Problem 3.4 – 30 seconds
Joey typed three letters and three
envelopes. But then Mary put
them in the envelopes randomly.
What is probability that no letter is
in the correct envelope?
Answer in reduced fraction form.
Problem 3.5 – 30 seconds
If the given figure is folded up into a
cube, what number will be opposite the
5?
1
2 3 4
5 6
Problem 3.6 – 30 seconds
Simplify
x 1
2
xi
Problem 3.7 – 30 seconds
Solve the following
formula for C:
F  9C / 5  32
Problem 3.8 – 30 seconds
The graph of
y | x 1|  | x 1|
goes through
which quadrants?
Problem 3.9 – 45 seconds
A map is drawn with a
10000:1 scale. Two
points that are 5 cm apart
on the map are actually
how many kilometers
apart?
Problem 3.10 – 75 seconds
Each vertex of square ABCD is
joined with the midpoint of an
adjacent side, as in the diagram.
In terms of area, the inner square
is what percentage of the outer
D
C
square?
A
B
Round 4
Problem 4.1 – 45 seconds
Joey and Josh and three other
boys line up randomly. What
is the probability that the other
three boys will be between
Joey and Josh? Answer as a
fraction in lowest terms.
Problem 4.2 – 45 seconds
The radius of the large circle is 6. What is the
area of the lighter-shaded region.
Problem 4.3 – 45 seconds
On Pete’s farm, there are a
number of rabbits and a
number of chickens. If there
are 32 heads and 100 feet,
find the number of rabbits.
Problem 4.4 – 45 seconds
Marissa has been asked to
design a parabolic mirror that
focuses light at the point (0,10).
The equation of the parabola is
y  ax
2
Solve for a.
Problem 4.5 – 30 seconds
The diagonal of a square
is 48” What is the area
of the square, in square
feet?
Problem 4.6 – 30 seconds
A big wheel makes 16
revolutions in traveling 100m.
A small wheel requires 20
revolutions to cover the same
length. What is the ratio of
the area of the big wheel to
that of the small wheel?
Problem 4.7 – 45 seconds
Suppose AB=3, BC=4, and CA=5.
D is a point on CA such that BD
bisects  A B C . Find the length of
AD.
Problem 4.8 – 45 seconds
All the diagonals are drawn in
a regular pentagon, dividing it
into a number of regions. How
many of the regions are
triangular?
Problem 4.9 – 45 seconds
If m<-3 and n>9, then
which of the following
must be true?
I. n/m>-3
II. mn<-27
III. m^2+n^2>90
Problem 4.10 – 45 seconds
Find the smallest positive value of
Such that
5x 
3
x
20 x
Answer as a fraction in lowest terms.
That’s all (for now)
folks