2010 Lee Webb Math Field DayMarch 13, 2010

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.

Junior Varsity Math Bowl

Round 1

Practice Problem – 20 seconds

Simplify

6 2 3 2x y x y x y

Problem 1.1 – 30 seconds

Find the point of intersection of the lines:

2 3 6 765 6 8 48x yx y

Problem 1.2 – 45 seconds

Shawn ran for 7 miles. Some of the time he was jogging at 4mph, and the rest of the time he was running at 6mph. In all he ran for 1.5 hours. How many miles did he jog?

Problem 1.3 – 15 seconds

Two positive integers have sum 11 and product 24. What is their difference (in absolute value)?

Problem 1.4 – 30 seconds

Suppose you have randomly drawn a 6, 7, 9, and 10 from a standard deck of cards. What is the probability that your next draw will be an 8? Answer as a fraction in lowest terms.

.

Problem 1.5 – 30 seconds

Solve

3 124 1/ 2x

Problem 1.6 – 45 seconds

Simplify

4 2 7 62( 2 ) 8x y xy x y

Problem 1.7 – 60 seconds

Allie bought 30 A tickets for the PiHedz concert at $17 each and 20 B tickets at $11 each. What are the other amounts of B tickets she could have bought and still spent the exact same amount of money on tickets?

Problem 1.8 – 30 seconds

A carbon atom weighs grams. How many atoms of carbon does it take to constitute one quarter of a gram? Answer in proper scientific notation.

232.00 10

Problem 1.9 – 30 seconds

17/25 is equal to x%. Find x.

Problem 1.10 – 60 seconds

What is the area of the largest triangle that can fit inside a unit circle?

Round 2

Problem 2.1 – 30 seconds

Find the ordered pair satisfying the system

3 2 165 2 64x yx y

Problem 2.2 – 30 seconds

The amount of agent X in a petri dish is growing exponentially. On the second day there was 6 gm. On the sixth day there was 18 gm. On which day will there be 162 gm?

Problem 2.3 – 30 seconds

A standard die is rolled 3 times. What is the probability that all the rolls show a number that is a power of 2?

Problem 2.4 – 30 seconds

What is the sum of all the positive odd integers less than 100 ?

Problem 2.5 – 30 seconds

How many positive integer divisors does 30 have?

Problem 2.6 – 15 seconds

Suppose G is the centroid of triangle ABC and that ray AG meets BC at D. What is the ratio of the lengths AG/GD?

Problem 2.7 – 30 seconds

A log is 4 feet long and 1 foot in diameter. After rolling it 2 revolutions, it left an impression in the ground. What is the area of the impression, in sq. feet?

Problem 2.8 – 60 seconds

Let E be inside square ABCD such that ABE is an equilateral triangle. What is the measure, in degrees, of ?CED

Problem 2.9 – 30 seconds

If ABCDE is a regular pentagon, Find the measure of

(in degrees) CAD

B

C A

D E

Problem 2.10 – 45 seconds

Moonbeam’s Health Food Store sells a raisin nut mixture. Raisins cost $3.50/kg and nuts cost $4.75/kg. How many kg of nuts should go into a 20kg sack, to make the whole thing worth $80?

Round 3

Practice Problem – 20 seconds

Solve for x.

x+20

x+10 x

Problem 3.1 – 45 seconds

Skier A finished the 3km race in 2.5 minutes. Skier B was .02 seconds slower. At these paces, if they had raced side by side, A would have finished how many meters ahead of B?

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 – 60 seconds

A rhombus has diagonals of lengths 10 and 20. Each vertex is extended outward 10 units. What is the ratio of the area of the outer figure to that of the rhombus?

Problem 3.4 – 30 seconds

Joey typed three letters and three envelopes. But then Mary put them in the envelopes randomly. What is probability that no letter is in the correct envelope?Answer in reduced fraction form.

Problem 3.5 – 30 seconds

If the given figure is folded up into a cube, what number will be opposite the 5?

6432

1

5

Problem 3.6 – 30 seconds

Simplify2 1xx i

Problem 3.7 – 30 seconds

Solve the following formula for C:

9 / 5 32F C

Problem 3.8 – 30 seconds

The graph of

goes through which quadrants?

| 1| | 1|y x x

Problem 3.9 – 45 seconds

A map is drawn with a 10000:1 scale. Two points that are 5 cm apart on the map are actually how many kilometers apart?

Problem 3.10 – 75 seconds

Each vertex of square ABCD is joined with the midpoint of an adjacent side, as in the diagram. In terms of area, the inner square is what percentage of the outer square? CD

A B

Round 4

Problem 4.1 – 45 seconds

Joey and Josh and three other boys line up randomly. What is the probability that the other three boys will be between Joey and Josh? Answer as a fraction in lowest terms.

Problem 4.2 – 45 secondsThe radius of the large circle is 6. What is the area of the lighter-shaded region.

Problem 4.3 – 45 seconds

On Pete’s farm, there are a number of rabbits and a number of chickens. If there are 32 heads and 100 feet, find the number of rabbits.

Problem 4.4 – 45 seconds

Marissa has been asked to design a parabolic mirror that focuses light at the point (0,10). The equation of the parabola is

Solve for a.

2y ax

Problem 4.5 – 30 seconds

The diagonal of a square is 48” What is the area of the square, in square feet?

Problem 4.6 – 30 seconds

A big wheel makes 16 revolutions in traveling 100m. A small wheel requires 20 revolutions to cover the same length. What is the ratio of the area of the big wheel to that of the small wheel?

Problem 4.7 – 45 seconds

Suppose AB=3, BC=4, and CA=5.D is a point on CA such that BD bisects . Find the length of AD.

ABC

Problem 4.8 – 45 seconds

All the diagonals are drawn in a regular pentagon, dividing it into a number of regions. How many of the regions are triangular?

Problem 4.9 – 45 seconds

If m<-3 and n>9, then which of the following must be true?

I. n/m>-3 II. mn<-27

III. m^2+n^2>90

Problem 4.10 – 45 seconds

Find the smallest positive value of Such that

Answer as a fraction in lowest terms.

x

35 20x x

That’s all (for now) folks