40th Annual Lee Webb Math Field Day

MARCH 12, 2011

Junior 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

Junior 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 - 15 seconds

Which of the following decimals is the smallest? Enter the decimal, not the letter.

a) .031 b) .029 c) .03 d) .009

Problem 1.2 - 15 seconds

Find f(4) when f(x) = -2x - 7.

Problem 1.3 - 30 seconds

What is the y intercept of the line perpendicular to the line y = 3x + 5, and passing through the point (3, 5)?

Problem 1.4 - 30 seconds

The ratio of men to women in a certain Iowa farm town is 5 to 3. If there are 600 adults in the town, how many are men?

Problem 1.5 - 15 seconds

Simplify:

12 - 3(x - 2)

Problem 1.6 - 45 seconds

The length of a rectangle is 8 in. longer than its width.

If its perimeter is 32 in., what is its area, in sq. in.?

Problem 1.7 - 30 seconds

The cost of producing n suncatchers is given by C(n) = 150 + 3n; while the revenue from the sale of these suncatchers is given by R(n) = 8n. How many suncatchers must the manufacturer sell to break even?

Problem 1.8 - 15 seconds

Simplify as much as possible:

(751/2)(3001/2)

Problem 1.9 - 30 seconds

What is the volume, in square centimeters, of a 5 cm. tall right cylinder, if the base has a radius of 3 cm.?

3 cm.

5 cm.

Problem 1.10 - 30 seconds

A pair of shoes that originally sold for $100.00 was marked down 20%. Two weeks later it was marked down an additional 50%. What is the new price, in dollars?

Problem 1.11 - 30 seconds

What is the greatest common factor of 312 and 48?

Problem 1.11 - 45 seconds

State all values of x which satisfy the equation.

3x - 2(x2 - x + 1) = 0

Problem 1.13 - 30 seconds

A couple has $21.00 to spend on lunch, and want to leave a 20% tip.

What is the maximum amount of money, in dollars, they can spend on their food order?

Problem 1.14 - 15 seconds

A, B, C are points on the circle centered at O.

If , what is , in degrees? B

A

C

m∠AOB=110º m∠ACB O

2011Math Bowl

Junior 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.

x2 3 +π ,cos−2 + i7 −y

⎛⎝⎜

⎞⎠⎟

Problem 2.1 - 15 seconds

How many cubic feet are in 2 cubic yards?

Problem 2.2 - 30 seconds

Find the degree measure of angle x.

x + 30º

x x - 15º

Problem 2.3 - 45 seconds

Find the ordered pair that satisfies the linear system. 2x+y=83x−2y=5⎧⎨⎩

Problem 2.4 - 15 seconds

Rewrite as a fraction in lowest terms..03

Problem 2.5 - 30 seconds

The number of houses sold by Apple Realty decreased from 300 in the year 2009 to 180 in 2010.

What is the percentage decrease in the number of houses sold?

Problem 2.6 - 15 seconds

What is the maximum value in the range of the function

f(x) = -(x – 5)2 - 3 ?

Problem 2.7 - 30 seconds

Find the area of the parallelogram, in square centimeters.

6 cm.

12 cm.

10 cm.

Problem 2.8 - 15 seconds

What is the median of the following set of numbers?

{2, 5, 7, 5, 3}

Problem 2.9 - 30 seconds

Solve the absolute value equation. −32x−4=0

Problem 2.10 - 15 seconds

Find the distance between the points

(-2, 6) and (4, -2).

Problem 2.11 - 30 seconds

Suzanne volunteered to make 180 cookies for a bake sale. In 90 minutes, she has only made 30 cookies.

At that rate, how many hours will it take her to make the rest of the cookies?

Problem 2.12 - 45 seconds

Solve for x:35x−1+6=15

2011Math Bowl

Junior 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 - 45 seconds

Bill is making decorative plaques from scrap lumber to sell at the flea market. If each plaque measures 15” long by 5” wide, and he has four 8 foot long 10" wide boards available, how many plaques can he make?

Problem 3.2 - 15 seconds

Simplify:

log12 123

Problem 3.3 - 30 seconds

Let M = kN - 4.

When N = 9, M = 2.

Find the value of M when

N = 15.

Problem 3.4 - 30 seconds

Find n!n=1

4

∑

Problem 3.5 - 45 seconds

At a discount store, similar items are the same price.

One sweater and three shirts cost $42, while three sweaters and two shirts cost $56.

How much does one shirt cost, in dollars?

Problem 3.6 - 30 seconds

Find the value(s) of the x intercept(s) of the circle.

(x + 3)2 + (y - 5)2 = 25

Problem 3.7 - 15 seconds

Simplify:

i275

Problem 3.8 - 30 seconds

Find all values of x > 0 that satisfy the equation.

6

x=

x+ 73

Problem 3.9 - 30 seconds

In a university calculus class, 6% of the students received an A. If 12 students received an A, how many students were in the class?

Problem 3.10 - 60 seconds

A hexagon is enclosed in a circle of radius 6 cm., as shown. Find the area of the hexagon, in square centimeters. Leave your answer in radical form.

6

Problem 3.11 - 30 seconds

A family has six children. What is the probability that they have at least one girl?

Problem 3.12 - 30 seconds

A company bought a new truck for $45,000, and depreciated it over 5 years, using straight line depreciation. What was the dollar value of the truck four years after purchase?

2011Math Bowl

Junior 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.

x2 3 +π ,cos−2 + i7 −y

⎛⎝⎜

⎞⎠⎟

Problem 4.1 - 15 seconds

Two angles are supplementary. The second angle is 30º larger than the first. What is the degree measure of the first angle?

Problem 4.2 - 30 seconds

Find all values of x that satisfy the equation.

2x −5 =7 −4x

Problem 4.3 - 45 seconds

Assume x = 2, a = 3, b = 4, c = 5. Evaluate:

x−2a+6b−c

x3ax2b

⎛

⎝⎜⎞

⎠⎟x

(5a−4b+2c)

( )

Problem 4.4 - 15 seconds

Simplify:

log46 - log43 + log48

Problem 4.5 - 30 seconds

Assume l1 and l2 are parallel. Find the degree measure of x.

3x-20

2x+30

l1 l2

Problem 4.7 - 45 seconds

If f(x) = 5(x - 1)3;

find f -1(40).

Problem 4.8 - 15 seconds

Multiply the complex numbers. Give your answer in the form a + bi.

(3 + 4i)(-3 + 2i)

Problem 4.9 - 45 seconds

A small plane flying with a tail wind can travel 450 miles in three hours. Flying against the same wind, it would take five hours to travel 450 miles.

What is the average wind speed, in mph?

Problem 4.10 - 30 seconds

Find all values of x that satisfy the equation.

7

x2 −5x+ 6+

1x−2

=4

x−3

Problem 4.11 - 15 seconds

Find the next term in the geometric sequence that begins:

3, 15, 75, …

Problem 4.12 - 45 seconds

A right square pyramid has a square base with sides of length 12 cm., and a height of 8 cm. What is the surface area of the pyramid, in square centimeters?

Problem 4.13 - 30 seconds

Choosing a person at random from a certain group of college freshman, the probability the individual is a woman is .55, the probability the individual is married is .10, and the probability the individual is a married woman is .05.

What is the probability that the individual is married or a woman?

THE END

THANK YOU FOR PARTICIPATING.