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Quiz Bowl

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- All eight students will solve problems as part of a quiz bowl.
- Students will work together to answer questions and compete head to head against other teams.
- Teams will be seated at tables.
- A moderator will ask a question using a microphone.
- Each team will write an answer to each question on the paper provided.

- Team captains will hand one answer to the table runner.
- The team captain should be seated in middle of the team.
- Teams should write answers clearly and neatly so that judges can read answers. Teams with unclear answers will not receive points.
- Time will begin once the moderator finishes reading the question.
- Teams should NOT include computational or scratch work on the paper; only answers should be written on the paper.

- Once a team turns in their paper, the team may NOT change their answer.
- Teams will be provided with scratch paper and pencils as well as their answer sheets.
- NO books, notes, calculators, or electronic devices, such as cell phones, may be used.
- Cell phones must be turned off.

Round 1 will consist of 10 questions.

All teams will have 20 minutes to complete their packets. Each correct answer at the end of the 20 minutes earns 5 points.

Find a two-digit number such that if you reverse its digits to get another two-digit number, then add this to the original number, you get 143.

Step 1

Step 2

Step 3

There are 5 squares in Step One, 10 squares in Step Two, and 17 squares in Step Three.

How many squares will be in Step 25?

The hypotenuse of Triangle ABD is 1 inch longer than the hypotenuse of Triangle CBD. Find x.

Two linear functions are plotted above. Find all x and y intercepts of the graph of their product.

Tennis balls have a diameter of

2.7 inches. They are sold in a

cylindrical can whose height is

8.1 inches (the exact height of 3

tennis balls) and whose diameter

is 2.7 inches.

Which is bigger, the height of the can

or the circumference of the can?

The following five statements apply to a line in the coordinate plane:

The line is perpendicular to the line 5x + 6y = -18.

The line has a negative y-intercept.

The line passes through the point (6,8).

The line has a positive slope.

The line is parallel to the line 5x - 3y = -12.

Four of the statements are true and one is false.

Find an equation of the line.

If , find the

value of:

The peak of Goose Bay Mountain is 400 meters higher than the local GBT airstrip. The horizontal distance from the end of the runway to a point directly below the mountain peak is 2025 meters.

A plane takes off at the end of a runway in the direction of the mountain at an angle that is kept constant until the peak has been cleared. If the pilot wants to clear the mountain by 50 meters, what should she punch into her calculator to calculate the angle of takeoff?

Juanita has a great job working as a mail messenger in a skyscraper downtown.

When she is delivering packages to the 38th floor, she is required to take a freight elevator up, but she can return in an express passenger elevator. The freight elevator travels at a speed of one foot in three seconds; the express passenger elevator, at three feet per second.

Find the average speed for the entire trip in feet per second.

You are working on the election campaign of Governor Calliope “Cal” Culus. The Governor is known for her environmentally friendly philosophy, and she would like you to develop an environmentally friendly handbill encouraging voters to vote for her in the upcoming election.

The handbill is to contain 50 square inches of printed material, with 4-inch top and bottom margins and 2-inch margins on each side. What dimensions for the page would use the least paper and thus be the most environmentally friendly?

Round 2 will consist of 3 questions that each have multiple answers.

Each team will earn 1 point for each correct answer and 1 bonus point if the team provides all of the possible answers or the number of possible answers.

4 plastic beads

are arranged to

make a bracelet.

Here you see 3 different views of the same bracelet.

List all the different bracelets that could be made with these 4 beads (including the bracelet in the picture).

- RBYG or BRGY (this is the given bracelet)
- or BYGR or YBRG
- or YGRB or GYBR
- or GRBY or RGYB

- RYBG or YRGB
- or YBGR or BYRG
- or BGRY or GBYR
- or GRYB or RGBY

- RBGY or BRYG
- or BGYR or GBRY
- or GYRB or YGBR
- or YRBG or RYGB

The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 8 are 1, 2, 4, and 8.

List all the numbers, from 1 to 30 (including 1 and 30) that have an odd number of factors.

- 1: 1
- 4: 1, 2, 4
- 9: 1, 3, 9
- 16: 1, 2, 4, 8, 16
- 25: 1, 5, 25

Maurice has a bag of marbles.

- When he counts them by 2s he has 1 left over.
- When he counts them by 3s he has 2 left over.
- When he counts them by 4s he has 3 left over.
- He has fewer than 60 marbles.
How many marbles could he have. List all the possibilities.

- If he had one more marble, his number of marbles would be a multiple of 2, 3, and 4
- Multiples of 2, 3, and 4 under 60:
- 12, 24, 36, 48

- One less than each:
- 11
- 23
- 35
- 47

Round 3 will consist of 5 questions.

The first team to give a correct answer to the runner will get 3 points.

The first team with the correct answer will then receive a follow-up question for 2 bonus points.

Q: Find the product:

-9 * -8 * -7 * -6 * -5 * -4 * -3 * -2 * -1 * 0 * 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9

- Anything multiplied by 0 is 0, so the answer is 0.

F: Find the sum:

-9 + -8 + -7 + -6 + -5 + -4 + -3 + -2 + -1 + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9

- Still zero… just make pairs of the positive and negative numbers.

Q: Solve for x

3(x + 10) = 5(x + 10)

- 3 (___) = 5 (___) can only be true when both sides equal 0
- Therefore, x + 10 must equal 0
- So x = -10

F: Solve for x

3(x + 10) + 2 = 5(x + 10)

- 3 somethings is 2 less than 5 somethings
- 3 ones is 2 less than 5 ones
- The statement will be true if (x + 10) = 1
- x = -9

Q: One fourth of the vehicles at Danielle’s Cycle Shop are tricycles. The rest are bicycles. Danielle counted a total of 45 wheels in her shop.

How many bicycles does she have?

- Every 4 vehicles has 9 wheels: 6 bike wheels and 3 trike wheels
- There are 5 sets of 9 wheels in 45 wheels
- She has 4 * 5 = 20 vehicles all together, 15 of which are bikes (3/4 of 20 is 15).

F: An outbreak of hoof-and-mouth disease is spreading through the land of Narnia. A vet examines each creature’s mouth and examines each hoof (4 per centaur and 2 per faun). At the end of the day the assistant says, “I need to record how many fauns and how many centaurs we checked.”

Faun

The vet replies, “I didn’t write that down, but I do know I checked 47 mouths and 122 hooves.”

How many centaurs were checked?

Centaur

- If she checked all fauns (2 legs each) she would have checked 47 * 2 = 94 hooves
- She checked 122 – 94 = 28 extra hooves
- That’s 14 extra pairs of hooves
- Therefore she checked 14 animals with 4 hooves (centaurs).
- 14 centaurs were checked.

Q: Find the product of

0.5 * 0.25 * 0.125

Your answer can be given as a fraction or decimal

- 0.5 * 0.25 * 0.125 = ½ * ¼ * 1/8
- ½ * ¼ * 1/8 = 1/(2*4*8)
- 1/(2*4*8) = 1/(8*8) = 1/64
- 1/64 = 0.15625

F: Evaluate

0.1 + + 0.25 +

0.1 + + 0.25 + =

0.1 + 0.5 + 0.25 + 0.05 =

0.9

Q: A jacket is on sale for 25% off. The sale price is $150.00.

How much money do you save by buying the jacket on sale?

- $150 is 75% of the jacket’s original price
- $50 is 25% of the jacket’s original price
- Therefore, you save $50.

F: Monica contributes 1/3 of the total cost of a mother’s day present. Nahim contributes ½ of the total cost. Their dad pitches in $9 so they have exactly enough money. How much was Monica’s contribution?

- Total – ½(Total) – 1/3(Total) = 1/6(Total)
- $9 was 1/6 of the price.
- The total price was $54
- 1/3 of $54 = $18
- Or, $9 was 1/6 of the price, so 1/3 of the price is 2 * $9 = $18