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

Junior Varsity

Round 1

Practice Problem – 20 seconds

Simplify

6 2 3 2x y x y x y

Problem 1.1 – 20 seconds

Subtract

from

26 6 13y y

23 4 7y y

Problem 1.2 – 30 seconds

If a computer purchased for $11,200 depreciates at a

rate of $1600 per year, how many years will it take to depreciate completely?

Problem 1.3 – 35 seconds

If straight-line appreciation is assumed, an antique clock

is expected to be worth $350 after 2 years and $530 after 5 years. What will the clock

be worth after 7 years?

Problem 1.4 – 25 seconds

Find the equation of the line parallel to and passing through the midpoint of the

segment joining and .

3x

2, 4

8,12

.

Problem 1.5 – 20 seconds

Solve

4 22 64x

Problem 1.6 – 20 seconds

Simplify

3 2 3

2 4 5

x

x x

Problem 1.7 – 30 seconds

Write

as a sum or difference of fractions and simplify

completely.

2 2

2

x y x y

xy

Problem 1.8 – 20 seconds

Simplify

2

2

1

1

xyxy

Problem 1.9 – 15 seconds

Solve

2 3 24 0x

Problem 1.10 – 20 seconds

Simplify and factor

3 4 638x xy

Problem 1.11 – 25 seconds

Solve

21 5 2 3 7x x x

Problem 1.12 – 35 seconds

Solve

2 4 1 9 5x x

Round 2

Practice Problem – 20 seconds

Find the measure of each angle.

x+20

x+10 x

Problem 2.1 – 20 seconds

Find the ordered pair satisfying the system

4

2 13

x y

x y

Problem 2.2 – 20 seconds

The measure of an angle is more than its supplement. What is the measure of the

angle?

10

Problem 2.3 – 20 seconds

The area of a square is 169 in2.

What is the perimeter?

Problem 2.4 – 20 seconds

How many square millimeters are in 1

square meter?

Problem 2.5 – 35 seconds

For a particular word processor, the number of words w that can be typed

on a page is given by the formula

, where x is the font size. How many more words can be typed on a

page if font size 8 is used instead

of font size 16?

8000w

x

Problem 2.6 – 25 seconds

Find m ABD

4x+326x+8B

C

D

A

E

Problem 2.7 – 15 seconds

Write the standard

form of the equation of the circle with the graph:

Problem 2.8 – 20 seconds

If in isosceles trapezoid QRST,find .

65m T

m R

T S

RQ

Problem 2.9 – 20 seconds

If ,find .

ABC DEC

m E

E

D

C

B

A

37

46

Problem 2.10 – 15 seconds

What is the sum of the degree

measures of the exterior angles of a

heptagon?

Problem 2.11 – 25 seconds

Given that , determine the

measure of the two angles

that are labeled.

1 2||l l

l2

l1

2x+104x-10

Problem 2.12 – 45 seconds

A field bordering a straight stream is to be enclosed. The side

bordering the stream is not to be fenced. If 1000 yds of fencing is to be used, what are the dimensions of the largest rectangular field that

can be fenced?

Round 3

Problem 3.1 – 30 seconds

In a right triangle, one leg is 7 feet shorter than the other leg.

The hypotenuse is 2 feet longer than the longer leg.

Find the length of the hypotenuse.

Problem 3.2 – 45 seconds

What is the remainder when

is divided by

?

7 5 310 12x x x

2x

Problem 3.3 – 20 seconds

Solve for q:

2

7 1 3

2 1 2q q q q

Problem 3.4 – 30 seconds

The measure of each angle of a regular

polygon is . How many sides does it

have?

165

Problem 3.5 – 25 seconds

How much plastic

sheeting will be needed to

cover this swimming

pool?

Problem 3.6 – 25 seconds

Simplify

3

22

8 1 1

4 2 1 1

x x

x x x

Problem 3.7 – 25 seconds

Calculate7 4

2 5

i

i

Problem 3.8 – 20 seconds

Find all solutions of

29 25 0x

Problem 3.9 – 35 seconds

Solve for x and y.

x7.5

8

6

y

Problem 3.10 – 25 seconds

Find the volume of a cone with a height of 12 cm and a circular

base with diameter 10 cm.

Problem 3.11 – 30 seconds

Solve

2 2 36 12x x

Problem 3.12 – 20 seconds

What is the area of a circle with a

circumferenceof inches? 16

Round 4

Problem 4.1 – 30 seconds

A green (G), a blue (B), a red (R), and ayellow (Y) flag are hanging on a flagpole.

1. The blue flag is between the green andyellow flags.

2. The red flag is next to the yellow flag.3. The green flag is higher than the red

flag.What is the order of the flags from top tobottom?

Problem 4.2 – 20 seconds

Factor

completely.

ax ay az bx by bz cx cy cz

Problem 4.3 – 20 seconds

Find the domain of

3

1xy

x x

Problem 4.4 – 30 seconds

If one outlet pipe can drain a tank in 24 hours and another pipe can drain the tank in 36 hours, how long will it take to

drain the tank if both pipes are working together?

Problem 4.5 – 15 seconds

Simplify

99i

Problem 4.6 – 15 seconds

When the price is p dollars, an appliance dealer can sell refrigerators. What price will maximize

his revenue?

2200 p

Problem 4.7 – 40 seconds

A piece of tin 12 in on a side is to have 4 equal squares cut from its corners. If the edges are then to be folded up to make a box with a floor area of 64 sq in, what is the total area removed from the piece

of tin?

Problem 4.8 – 25 seconds

In 60 oz of alloy for watch cases, there are 20 oz of gold. How

much copper must be added to the alloy so that a watch case

weighing 4 oz, made of the new alloy, will contain 1 oz of gold?

Problem 4.9 – 15 seconds

How many real roots does

have?

2 2 1f x x x

Problem 4.10 – 25 seconds

Express as a fraction in lowest

terms.

.047

Problem 4.11 – 35 seconds

Simplify

2 2 2

1 2 1

3 2 4 3 5 6x x x x x x

Problem 4.12 – 35 seconds

A bowling ball is packaged within a

tightly fitting cubical box with 10

in sides. How much foam can fit around the bowling ball but still inside

of the box?