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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. - PowerPoint PPT Presentation
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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
Varsity
Round 1
Practice Problem – 15 seconds
Let .
Find .
/ 24 xf x
1f
Problem 1.1 – 25 seconds
Find the ordered triple that satisfies
the system2 42 0
0
x y zx y zx y
Problem 1.2 – 25 seconds
Several logs are stored in a pile with 20 logs on the bottom
layer, 19 on the second layer, 18 on the third, and so on. If
the top layer has one log, how many logs are in the pile?
Problem 1.3 – 30 seconds
Let and .
Find the polynomial .
25 3f x x
3 1g x x
f g x
Problem 1.4 – 20 seconds
For the sets , and ,
find ..
1,3,5,6,8A
2,3,6,7B 6,8,9C
B C A
Problem 1.5 – 20 seconds
If the point is on the graph of
, find a.
1,2
2 4f x ax
Problem 1.6 – 15 seconds
Write as a
simple trigonometric function.
seccscxx
Problem 1.7 – 25 seconds
Determine the domain of the
function 1 1 1
1 2f x
x x x
Problem 1.8 – 15 seconds
Find the length of x.
x25
30
Problem 1.9 – 30 seconds
Find the area of the parallelogram in the plane
with vertices
1,0 , 0,1 ,
1,0 , and 0, 1 .
A B
C D
Problem 1.10 – 25 seconds
Solve for y:
5 5log log 4 1y y
Problem 1.11 – 30 seconds
Find the arc length corresponding to a
central angle of on a circle with radius 7 cm.
314
Problem 1.12 – 20 seconds
Calculate
sin 30 cos 60 sin 60 cos30
Round 2
Practice Problem – 25 seconds
Simplify
2 2 21log 16 log 4 log32
Problem 2.1 – 15 seconds
Simplify
3ln 2 1xe
Problem 2.2 – 20 seconds
Simplify
completely.
2 2 24
2
ln36
m mem
Problem 2.3 – 25 seconds
Let .
Find .
2 3g x x
g a b g ab
Problem 2.4 – 15 seconds
Find the exact value
of .3
log 9
Problem 2.5 – 15 seconds
What are the next two terms in the
sequenceA, c, E, g, …
Problem 2.6 – 35 seconds
Find the center of the ellipse
2 24 16 6 21 0x y x y
Problem 2.7 – 20 seconds
Find the roots of
3 24 9 36 0x x x
Problem 2.8 – 25 seconds
If , , and , find
.
log 4 .6021a log 7 .8451a log 9 .9542a
63log4a
Problem 2.9 – 20 seconds
Find the next term of the sequence 20, 17, 13, 8, …
Problem 2.10 – 15 seconds
According to the rational root theorem, what are the
possible rational roots of
6 5 4 24 3 4 3 0?x x x x x
Problem 2.11 – 25 seconds
If ,find .
4 3z i
z
Problem 2.12 – 35 seconds
For whatinterval(s) of x
does producereal y values?
2 2
116 9x y
Round 3
Problem 3.1 – 30 seconds
The area of an equilateral triangle varies directly with the square of the
length of a side. Find the constant of
proportionality.
Problem 3.2 – 30 seconds
Solve
in the interval .
2tan tan 2 0x x
,2 2
Problem 3.3 – 20 seconds
Calculate
2 3 6 2i i
Problem 3.4 – 25 seconds
Find thelength of
CD in terms of x.
A
C
B
x D30
4545
Problem 3.5 – 20 seconds
Evaluate100
1
6
Problem 3.6 – 30 seconds
Find the inverse of1 1
1 0
Problem 3.7 – 20 seconds
Find the polar equation for the
Cartesian equation 2 2 7x y
Problem 3.8 – 30 seconds
Evaluate on the interval .
1tan 3
,2 2
Problem 3.9 – 40 seconds
Let and .
Find .
1 21 1
A
5 13 0
B
det BA
Problem 3.10 – 30 seconds
Find the coefficient of
in the expansion of .
3 4x y
7x y
Problem 3.11 – 25 seconds
How many times can the face 5 be expected to occur in a sequence of 2016 throws of a fair
die?
Problem 3.12 – 25 seconds
If , and ,find .
3,2u
1, 3v
u v
Round 4
Problem 4.1 – 20 seconds
Find .22
2lim4x
xx
Problem 4.2 – 35 seconds
Expand
into partial fractions.
2
2 55 6x
x x
Problem 4.3 – 20 seconds
Let .Find , with only positive exponents
in the answer.
3 4
12 4 1r
'r
Problem 4.4 – 25 seconds
Find the sum of the first five multiples
of 4.
Problem 4.5 – 20 secondsA couple is planning their
wedding. They can select from 2 different chapels, 4 soloists, 3
organists, and 2 ministers. How many different wedding arrangements are possible?
Problem 4.6 – 25 seconds
Find the distance between the
points and .
2, 4,3P
4,7, 3Q
Problem 4.7 – 15 seconds
If and ,
find .
.3P A
.6P B A
P A B
Problem 4.8 – 35 seconds
Find
6
lim 1 cos cscx
x
Problem 4.9 – 35 seconds
Find c in the interval such that
if .
1 ,22
12
2' 122
f ff c
1f x xx
Problem 4.10 – 30 seconds
Evaluate
0
22 5x dx
Problem 4.11 – 20 seconds
Find the slope of the tangent line to the
graph of ,at the point .
2 2f x x
1,3
Problem 4.12 – 45 seconds
A gum manufacturer randomly puts a coupon in 1 of every 5 packages. What is the
probability of getting at least one coupon if 4 packages
are purchased?