Quiz Bowl

1. Quiz Bowl • 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.

2. 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.

3. 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.

4. Quiz BowlRound 1: All Groups Can Answer Round 1 will consist of 10 questions. All teams that provide the correct answer to a question posed by a moderator will earn 5 points.

5. Bear is not next to Rabbit Deer is not next to Owl Squirrel is next to Bear Owl is not next to Squirrel Starting with Bear, in what order do Bear, Rabbit, Deer, Owl, and Squirrel sit around the campfire?

7. Solution Rules Bear is not next to Rabbit Deer is not next to Owl Squirrel is next to Bear Owl is not next to Squirrel Start with Bear • Put Squirrel next to Bear • That leaves 3 open spots • Owl can’t go in the middle of those 3 spots because that would force Deer to sit next to Owl • Owl can’t go next to Squirrel either • So put Owl next to Bear • Then put Deer next to Squirrel (not next to Owl) • That leaves Rabbit between Deer and Owl • Final answer: Bear, Squirrel, Deer, Rabbit, Owl OR Bear, Owl, Rabbit, Deer, Squirrel

8. Find the area of isosceles triangle ABC

10. Solution To quickly find the area we need to find the height of the triangle. Because the triangle is isosceles I know the altitude bisects the base, creating a 3-4-5 right triangle. Therefore, the height is 4, and the Area is: 0.5 * 6 * 4 = 12 cm2

11. Solve for x: 5(x + 2) – 3(x + 2) + x = 2(x + 2) + 10

13. Solution • 5(x + 2) – 3(x + 2) + x = 2(x + 2) + 10 • Therefore, 2(x + 2) + x = 2(x + 2) + 10 • Therefore, x = 10 (by subtraction property of equality)

14. The diagonal of a square measures 10 miles. Find the area of the square.

16. Solution • Use the Pythagorean Theorem: • side2 + side2 = 102 • 2 * side2 = 100 • side2 = 50 • Do I have to keep solving? No! • Area = side2 = 50 • Area = 50 square miles

17. Seven small, congruent rectangles form a large rectangle as shown. The area of each of the 7 small rectangles is 48 u2. Find the indicated length.

19. Solution • I notice 4 of the widths = 3 of the lengths of the small rectangles • Length * width = 48 • 4W = 3L, LW = 48 • Guess W = 6, L = 8 • 4*6 = 3*8, 6 * 8 = 48 • ? = 6 + 6 + 6 + 6 = 24

20. Your “friend” offers to share some Bertie Bott’s Every Flavour Beans with you. He’s got a pile of 12 identical beans and explains that 2 are barf-flavored and 10 are peach- flavored. He offers to let you randomly take 5 beans. What is the probability that you will get 5 peach-flavored beans?

22. Solution • When you choose the first bean, you have a 10/12 chance of getting peach-not bad. • If you get the first bean right, you have a 9/11 of getting second bean right too. • You have an 8/10 chance of getting the 3rd right, a 7/9 chance of getting the 4th, and a 6/8 chance of getting the 5th • All together, you have a 10/12 * 9/11 * 8/10 * 7/9 * 6/8 = 42/132 or 7/22 chance of getting all good beans.

23. You are trying to bring your quiz average up to a 95%. So far, you’ve had 9 quizzes and averaged a 92%. Is it possible to bring your average up to a 95% by acing the 10th quiz? The maximum possible score is 100% -- no extra credit!

25. Solution • If you averaged 92% on 9 quizzes, you earned a total of 92 * 9 percentage points on those 9 quizzes. • 92 * 9 = 828 percentage points • To have a 95% average on 10 quizzes, you need to have 950 total percentage points • 950 – 828 = 122, more than is possible. • Alternatively, assume you get the top score, 100, on your last quiz. That brings you up to 938 points/10 quizzes, a 94%

26. Logan, Sam, and Pat share 3 large pizzas. Logan eats: • 1/3 of the pepperoni pizza, • ¼ of the cheese pizza, • 1/6 of the everything pizza. Sam eats • 1/6 of the pepperoni pizza, • 1/3 of the cheese pizza, • ½ of the everything pizza. Pat eats • ½ the pepperoni pizza, • 1/6 of the cheese pizza, • none of the everything pizza (Pat hates anchovies). Are the leftovers more than or less than one whole pizza?

28. Solution • Look pizza by pizza: • Amount of pepperoni eaten: 1/3 + 1/6 + ½ = 1 • Amount of cheese eaten: ¼ + 1/3 + 1/6 = 3/12 + 4/12 + 2/12 = 9/12 • Amount of everything pizza eaten: 1/6 + ½ = 2/12 + 6/12 = 8/12 • Total amount eaten: 12/12 + 9/12 + 8/12 = 29/12. 29/12 is more than 2 pizzas (24/12) so there is less than one whole pizza left over.

29. Points A, B, C, D, and E are marked between 1 and 1 billion on a number line. Which of A, B, C, D, and E is closest to where 1 million would be marked?

31. Solution • 1 million is 1,000,000 • 1 billion is 1,000,000,000 • 1 million is one one-thousandth of a billion • Therefore, 1 million is one one-thousandth of the way from one to 1 billion • 1 million is closest to point A

32. Find the value of x:

34. Solution

35. Quiz BowlRound 2: Multiple Answers–1 Minute 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.

36. Max’s special: scrambled-egg sandwiches. Toast options: white or wheat Cheese options: American or none Meat options: ham, bacon, or none. List all possible sandwich orders

38. Solution • White toast, American cheese, ham • White toast, American cheese, bacon • White toast, American cheese, no meat • White toast, no cheese, ham • White toast, no cheese, bacon • White toast, no cheese, no meat • Wheat toast, American cheese, ham • Wheat toast, American cheese, bacon • Wheat toast, American cheese, no meat • Wheat toast, no cheese, ham • Wheat toast, no cheese, bacon • Wheat toast, no cheese, no meat

39. The partitions of a number are the ways to write that number as a sum of positive integers. For example, the partitions of 3 are: • 3 • 1 + 2 • 1 + 1 + 1 List all the partitions of 6.

41. Solution • 1 + 1 + 1 + 1 + 1 + 1 • 2 + 1 + 1 + 1 + 1 • 2 + 2 + 1 + 1 • 3 + 1 + 1 + 1 • 2 + 2 + 2 • 3 + 2 + 1 • 4 + 1 + 1 • 3 + 3 • 4 + 2 • 5 + 1 • 6

42. A probability experiment consists of flippingthree quarters to see if they land HEADS or TAILS. List all the equally likely outcomes of the experiment.

44. Solution

45. Quiz BowlRound 3: Speed Round with Follow Up Questions 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.

46. Q: Let the operation be defined for all real numbers a and b as follows. a b = a + ab Find (3 17) + (1 -1)

48. Solution • (3 17) + (1 -1) = • (3 + 3*17) + (1 + 1*-1) = • 3 + 51 + 1 + -1 = 54

49. F: If x 7= 32, find x.