Transcript Junior/Senior Math Bowl (2011)

40th Annual
Lee Webb Math Field Day
March 12, 2011
Varsity Math Bowl
Before We Begin:
• Please turn all cell phones off, or set to
vibrate, while the Math Bowl is in progress.
• Students will use the TI-Inspire only to
electronically submit their answers. You will
not be able to use the calculator to perform
any computations.
• Turn on your calculator by pressing the ON
button in the lower left corner. The HOME
screen should appear, and A: Calculate
should be highlighted.
• For each question, a signal will be sent to your
calculator, and a screen will appear for your use in
submitting your answers.
• You will need to use the TAB button, located on the
upper left side of calculator, to the left of the large
round thumb cursor to submit your answers.
• We will first make sure that all calculators are
properly logged in before we start.
• We will do a sample question each
round, utilizing some keys that students
may need for their answers.
• There is to be no talking among the
students on stage once the round has
begun.
• Audience please do not shout out any
answers.
2011
Math Bowl
Varsity
Round 1
Sample - 45 seconds
Submit the following answer, being sure to place
parentheses properly to dictate the desired
order of operations. Remember to use the tab
key to exit an exponent.
x
2 3
 2  i 
  , cos 

 7y 
Problem 1.1 - 30 seconds
Find the image of the point P(a, b)
under the following transformation:
A reflection in the line y = x, followed
by a reflection across the x axis.
Write your answer as an ordered pair.
Problem 1.2 - 45 seconds
• The sum of three numbers is 48. The
first number is three times as big as
the last number, while the second
number is 8 more than the last
number. Find the value of the three
numbers, and write them in
increasing order.
Problem 1.3 - 60 seconds
Find all real values of x that satisfy the
equation.
 2x  4   2x  4 

  
  6
x3
x3
2
Problem 1.4 - 30 seconds
• Simplify as much as possible.
28!
26!(36)
Problem 1.5 - 30 seconds
• Simplify the complex fraction.
x  25
5
16x
x5
2x
2
Problem 1.6 - 45 seconds
Find the center point of this
circle. Write your answer as an
ordered pair.
2
x
– 10x +
2
y
+ 6y + 34 = 25
Problem 1.7 - 60 seconds
It takes Ramon 10 hours to paint
a garage. If his friend Mike
helps, they can get the job done
in six hours. How many hours
would it take Mike to paint the
garage by himself?
Problem 1.8 - 30 seconds
If f(x) = x  5
-1
then f (x) = ?
Problem 1.9 - 30 seconds
Assume that each branch point in the maze
below is equally likely to be chosen.
Determine the probability that a person
entering the maze will end up in room A.
A
B
Problem 1.10 - 45 seconds
If log2x + log2(x - 4) = 5,
then x = ?
Problem 1.11 - 45 seconds
If the fifth number in a
geometric sequence is 625,
and the sixth number is 3125,
what is the first number in
the sequence?
Problem 1.12 - 30 seconds
3x  11
Let f(x) =
3
and g(x) = x + 4.
Find f(g(2)).
2011
Math Bowl
Varsity
Round 2
• For each question, a signal will be sent to your
calculator, and a screen will appear for your use in
submitting your answers.
• You will need to use the TAB button, located on the
upper left side of calculator, to the left of the large
round thumb cursor to submit your answers.
• We will first make sure that all calculators are still
properly logged in before we start.
• Next we will review the keyboard again.
Sample - 45 seconds
Submit the following answer, being sure to place
parentheses properly to dictate the desired
order of operations. Remember to use the tab
key to exit an exponent.
x
2 3
 2  i 
  , cos 

 7y 
Problem 2.1 - 15 seconds
The heights of 100 girls at a local high
school were measured, and the mean
was found to be 64 inches, with a
standard deviation of 2 inches.
Assume the heights are normally
distributed. How many of the girls
are between 60” and 68” tall?
Problem 2.2 - 30 seconds
A basketball is thrown straight up into the air.
The equation giving the height h of the ball
above the ground as a function of the time t
in seconds after the ball was thrown is
h(t) = -16t2 + 48t + 5.
What is the maximum height in feet that the
ball reaches?
Problem 2.3 - 30 seconds
Find the limit.
(n  8)(2n  3)
lim
n (n  1)(n  4)
Problem 2.4 - 30 seconds
Assume that the cost of CSUB
tuition continues to increase
annually at a rate of 10% per
year. If tuition costs $5000 in
your first year, what will be the
cost in dollars of tuition in your
fourth year?
Problem 2.5 - 15 seconds
Simplify:
6
ln x ln6
Problem 2.6 - 45 seconds
Solve the inequality.
(2t +6)(t - 2) < 0
Give your answer in interval
notation.
Problem 2.7 - 45 seconds
Find the degree measure of angle x.
(Drawing not to scale.)
2x
80
x
110
30
Problem 2.8 - 30 seconds
The chess club has 10
members. In how many
different ways can they
select a President, VicePresident and Secretary?
Problem 2.9 - 30 seconds
Solve for x.
log2(log16(x)) = -2
Problem 2.10 - 15 seconds
If xi = 2i + 5, find:
4

i 1
xi
Problem 2.11 - 30 seconds
Find the length of x in the drawing.
(Not to scale.)
5
2
x
3
Problem 2.12 - 15 seconds
Find
 7 
cos  2 
2011
Math Bowl
Varsity
Round 3
• For each question, a signal will be sent to your
calculator, and a screen will appear for your use in
submitting your answers.
• You will need to use the TAB button, located on the
upper left side of calculator, to the left of the large
round thumb cursor to submit your answers.
• We will first make sure that all students have the
correct calculator and that the calculators are
properly logged in before we start.
• Next we will review the keyboard again.
Sample - 45 seconds
Submit the following answer, being sure to place
parentheses properly to dictate the desired
order of operations. Remember to use the tab
key to exit an exponent.
x
2 3
 2  i 
  , cos 

 7y 
Problem 3.1 - 30 seconds
Let f(x) = 7x + 2. Find:
f (x  h)  f (x)
h
Problem 3.2 - 15 seconds
Let f (x)  2sin(x   ).
What is the absolute
minimum of f on the
interval [0, 2 ]?
Problem 3.3 - 30 seconds
Calculate the sum of the base four numerals.
Write your answer in base four.
321
+ 123
Problem 3.4 - 45 seconds
Points A and C are on the circle centered at O, and AB is
tangent to the circle. Given that OA and AC both have
length 5, find the length of AB in the figure below.
Express your answer in radical form.
Problem 3.5 - 30 seconds
x , g(x) = 3  x .
f
Find the domain of x .
g
Let f(x) =
Choose the letter of the correct answer.
a. (3, ) b. (0, 3) c. (-3, 0] d. [0, 3)
Problem 3.6 -30 seconds
Given log2x + log2y = log2z.
Solve for y in terms of x and z.
Problem 3.7 - 45 seconds
Solve for x.
x
2e
+
-x
3e
=
5
x
e
Problem 3.8 - 15 seconds
3
x,
If g(x) =
and h(g(x)) = x9 + 3,
give the expression for h(x).
Problem 3.9 - 30 seconds
Let C equal the matrix product AB, where
A & B are given below. What is the value
of C12?
 2 4 5 
A

3
1
0


 1 0
B   5 4 


 3 1 
Problem 3.10 - 15 seconds
If the radius of a sphere is
doubled, the surface area of
the same sphere will
increase by what factor?
Problem 3.11 - 60 seconds
Of the ten teachers who have
volunteered for a school committee,
3 are men and seven are women.
If three of these people are chosen
randomly, what is the probability
that at least one of them will be
male? Give your answer in lowest
terms.
Problem 3.12 - 30 seconds
A six foot tall man standing
near a streetlight casts a six
foot long shadow. What is
the angle of elevation, in
degrees, from the tip of his
shadow to the streetlight?
2011
Math Bowl
Varsity
Round 4
• For each question, a signal will be sent to your
calculator, and a screen will appear for your use in
submitting your answers.
• You will need to use the TAB button, located on the
upper left side of calculator, to the left of the large
round thumb cursor to submit your answers.
• We will first make sure that all calculators are still
properly logged in before we start.
• Next we will review the keyboard again.
Sample - 45 seconds
Submit the following answer, being sure to place
parentheses properly to dictate the desired
order of operations. Remember to use the tab
key to exit an exponent.
x
2 3
 2  i 
  , cos 

 7y 
Problem 4.1 - 30 seconds
Find the derivative of :
y = sin(3x + 2)
Problem 4.2 - 15 seconds
Find the magnitude of the vector:
2, 3, 5
Problem 4.3 - 45 seconds
Given AC = 3 and BC = 4, find the
length of AB in the figure below.
A
B
3
120º
C
4
Problem 4.4 - 30 seconds
2
x
Let f(x) = - 3x. Find the
slope of the tangent line to
the graph of f at x = 5.
Problem 4.5 - 30 seconds

3
Let   radians.
Find sec
2
 1
Problem 4.6 - 30 seconds
The half-life of a certain
radioactive substance is 100
days. How many grams of a
6 gram sample remains after
300 days?
Problem 4.7 - 45 seconds
3
x
Given f(x) = 3  3x  5x  4
2
Find the critical numbers of f .
Problem 4.8 - 30 seconds
Given f(x) = x2cos(x),
find f '(. ).
Problem 4.9 - 45 seconds
Find the fourth derivative of
y = 2x5 + 3x4 + 4x3 + 5x2 + 6x + 7
Problem 4.10 - 45 seconds
What is the next number in
the sequence:
5, 6, 9, 14, 21,…?
Problem 4.11 - 30 seconds
Evaluate:

3
3
2
x dx
Problem 4.12 - 45 seconds
Perform the division:
x  2x  9x 18
x2
3
2
THE END
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