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.

2011Math 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.

x2 3 +π ,cos −2 + i7−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 −4x+ 3

⎛⎝⎜

⎞⎠⎟2

+2x−4x+ 3

⎛⎝⎜

⎞⎠⎟=6

Problem 1.4 - 30 seconds

• Simplify as much as possible.

28!

26!(36)

Problem 1.5 - 30 seconds

• Simplify the complex fraction.

x2 −2516x5

x+ 52x

Problem 1.6 - 45 seconds

Find the center point of this circle. Write your answer as an ordered pair.

x2 – 10x + y2 + 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) = then f -1(x) = ?

x+5

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.

B

A

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

Let f(x) = 3x−11 ( ) = and g x x3 + 4.

( (2)).Find f g

2011

Math BowlVarsity

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.

x2 3 +π ,cos −2 + i7−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.limn→∞(n+8)(2n−3)(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) < 0Give your answer in interval

notation.

Problem 2.7 - 45 seconds

Find the degree measure of angle x. (Drawing not to scale.)

2x

x

30

110

80

Problem 2.8 - 30 seconds

The chess club has 10 members. In how many different ways can they select a President, Vice-President and Secretary?

Problem 2.9 - 30 seconds

Solve for x.

log2(log16(x)) = -2

Problem 2.10 - 15 seconds

If xi = 2i + 5, find:

x

i

i = 1

4

∑

Problem 2.11 - 30 seconds

Find the length of x in the drawing. (Not to scale.)

5 x

2 3

Problem 2.12 - 15 seconds

Find cos−7π

2⎛⎝⎜

⎞⎠⎟

2011Math 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.

x2 3 +π ,cos −2 + i7−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+π). Whatis the absolut e

minimum of f on the interval [0, 2π]?

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 secondsPoints 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

Let f(x) = x, g(x) = 3−x. Find the domain of

fgx(). Choos e the letter of t he corre ct answ .er . (3a , ) 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.

2ex + 3e -x = 5ex

Problem 3.8 - 15 seconds

If g(x) = x3,

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?A=2−45310⎡⎣⎢⎤⎦⎥ B=10−5431⎡⎣⎢⎢⎢⎤⎦⎥⎥⎥

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 BowlVarsity

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.

x2 3 +π ,cos −2 + i7−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 4

C

120º

Problem 4.4 - 30 seconds

Let f(x) = x2 - 3x. Find the slope of the tangent line to the graph of f at x = 5.

Problem 4.5 - 30 seconds

Let radians.

Find

θ=π3 sec2θ+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

Given f(x) =

Find the critical numbers of f .

x33−3x2+5x−4

Problem 4.8 - 30 seconds

Given f(x) = x2cos(x),

find . f '(π).

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:x2dx3−3∫

Problem 4.12 - 45 seconds

Perform the division:x3+2x2−9x−18x+2

THE END

THANK YOU FOR PARTICIPATING.