2009 Lee Webb Math Field Day

Junior Varsity Math Bowl

Before We Begin:

• 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 the students on stage once the round has begun.

• Answers that are turned in by the checkers are examined at the scorekeepers’ table. An answer that is incorrect or in unacceptable form will be subject to a penalty. Points will be deducted from the team score according to how many points would have been received if the answer were correct (5 points will be deducted for an incorrect first place answer, 3 for second, etc.).

• 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.

2009Math 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

27 6 1y y

210 4 7y y

Problem 1.2 – 30 seconds

Cookie’s Old Timey Key-Limey Pie Recipe calls for 3 egg yolks and 4 egg whites. This recipe makes 2 pies. Cookie needs to prepare 100 of these pies – how many dozen eggs are needed?

Problem 1.3 – 35 seconds

Zacky’s Pizzeria offers a choice of 3 different sizes, 2 different kinds of crusts, and 10 different kinds of toppings. How many different 1-topping pizzas can be ordered?

Problem 1.4 – 25 seconds

In the year 2000, the International Table Tennis Federation changed the diameter of the tournament table tennis ball from 38 millimeters to 40 millimeters.  What percentage of the new radius is the old radius?

.

Problem 1.5 – 20 seconds

Solve

2 63 81x

Problem 1.6 – 20 seconds

Simplify

7 2 4 1

5 3 (3 2)

x x

x x

Problem 1.7 – 30 seconds

How many solutions does the following equation have?

22 | 3 |

5 | 4 | 06

xx

Problem 1.8 – 20 seconds

Simplify

2

2

1

1

xyxy

Problem 1.9 – 15 seconds

Joe has lost his marbles! Mary has 42 marbles, which is three times as much as Joe. Before he lost his marbles, he had 10 more than Mary. How many marbles did Joe lose?

Problem 1.10 – 20 seconds

A circle has radius equal to . Find its area, in terms of .

Problem 1.11 – 35 seconds

Solve

2 4 1 9 5x x

Round 2

Practice Problem – 20 seconds

Solve for x.

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?

30

Problem 2.3 – 20 seconds

A standard die is rolled 3 times. What is the

probability that at least one of the rolls gives a number less than 3?

Problem 2.4 – 20 seconds

How many square meters are in 1 square kilometer?

Problem 2.5 – 25 seconds

Find all numbers that when added to their squares give 12.

Problem 2.6 – 25 seconds

Suppose each vertex of a triangle is joined to the midpoint of the opposite side. These segments intersect at a point. What is the name of this point?

Problem 2.7 – 25 seconds

If the height of a pyramid is stretched by a factor of 10, then the sides of the base must shrink by a factor of what, in order to keep the same volume?

Problem 2.8 – 20 seconds

A cylinder has circumference equal to and height equal to . What is its volume?

63

Problem 2.9 – 20 seconds

If ,Find the measure of .

ABC DEC

E

E

D

C

B

A

37

46

Problem 2.10 – 20 seconds

Evaluate the sum: a+b+c+d+e+f (in degrees)

105145

f

ed

c

ba

Problem 2.11 – 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

Cali needs 3 hours to weed the garden. Daly can do the same job in 2 hours. How many minutes will it take, if they work together?

Problem 3.2 – 45 seconds

What is the remainder when

is divided by ?

4 3 22 3 4 5x x x x 1x

Problem 3.3 – 20 seconds

The area of this parallelogram is 50. What is the length of the diagonal?

10

29

Problem 3.4 – 30 seconds

Five points are placed evenly around a circle. A line segment connects every pair of points. How many regions do these segments divide the circle into?

Problem 3.5 – 25 seconds

Between 3:14:19AM and 3:14:19PM, how many times will the minute and hour hands of a standard clock be exactly in line with each other?

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

Simplify:3 2

2 3

i

i

Problem 3.8 – 20 seconds

Simplify

||||1 2 | 3 | 4 | 5 |

Problem 3.9 – 35 seconds

At Zila’s Boutique, a dress has been discounted 20%, three times. All together this represents a discount of what percentage?

Problem 3.10 – 25 seconds

A pyramid with square base of length 10 and height 9, is cut parallel to the base, half-way between top and bottom. What is the volume of the larger piece?

Problem 3.11 – 30 seconds

Solve

2 2 36 12x x

Round 4

Problem 4.1 – 30 seconds

Five songs are to be played in random order. Two of the songs are by the same group. What is the probability that these two songs are not played consecutively? Answer as a fraction in lowest terms.

Problem 4.2 – 20 seconds

If is multiplied out, what will be the coefficient on the term?

3( )a b c

abc

Problem 4.3 – 20 seconds

Zacky’s Pizzeria offers a choice of 3 different sizes, 2 different kinds of crusts, and 10 different kinds of toppings. How many different 3-topping pizzas can be ordered?

Problem 4.4 – 30 seconds

Give the equation of the line perpendicular to 7x-11y=15 that goes through the point (2,3). Your equation should be in the same form as the given line, using only natural numbers.

Problem 4.5 – 15 seconds

A dart hits a circular board randomly. What is the probability that it hits

closer to the center than the edge?

Problem 4.6 – 15 seconds

What is the maximum value possible for y?

29 66 144y x x

Problem 4.7 – 40 seconds

A football field is 50 yards wide and 100 yards long. It has stripes every 10 yards of its length – including the ends. How many rectangles can be placed on the field, so that no two of them intersect the same number of stripes?

Problem 4.8 – 25 seconds

If a ring of radius 1 yard is placed randomly somewhere

on a standard football field (as in the previous problem), what is the probability that it will not

overlap any of the stripes?

Problem 4.9 – 45 seconds

A regular square pyramid has base length 12 and height 7. What is the distance from the apex to a corner of the base?

Problem 4.10 – 25 seconds

An octagon is formed from a square of area 1 by marking each side into thirds and then cutting off the corners along the lines formed by these marks. What is the area of the octagon?

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?

Extra

x7.5

8

6

y

An angle is calculated to be 25.9858333333 degrees. This measure is equivalent to 25 degrees and how many minutes and seconds?

FOA:

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?

• Ordero f flags questions