1. Ultimate Math Championship 2007 Sixth Grade

2. E 2 E 3 E 4 E 5 E 8 A 1 A 2 A 3 A 4 A 5 D 1 D 2 D 3 E 1 Easy (E) (25 pts) Easy (E) (25 pts) Average (A) (50 pts) Difficult (D) (100 pts) F 2 F 3 F 1 D 4 E 6 E 7Final(Wager)

3. Return to Question Board See Answer 25 points Which list of numbers is ordered from least to greatest? A¼, 1 ¼, 0.4, 0.04 B0.04, 0.4, ¼, 1 ¼ C0.04, ¼, 0.4, 1 ¼ D0.4, ¼, 0.04, 1 ¼ E 1

4. A N S W E R: Return to Question Board 25 points C: 0.04, ¼, 0.4, 1 ¼ E 1

5. Return to Question Board 25 points See Answer E 2 What value of k makes the following equation true? k ÷ 4 = 36 A32 B144 C 9 D12

6. A N S W E R: Return to Question Board 25 points E 2 B: 144

7. I t takes a machine 16 minutes to fill 200 bottles of soda. At this rate, how many minutes will it take the machine to fill 500 bottles of soda? A40 minutes B30 minutes C28 minutes D25 minutes Return to Question Board 25 points See Answer E 3

8. A N S W E R: Return to Question Board 25 points E 3 A: 40 minutes

9. Which of the following fractions is closer to 0? A5/6 C-¾ B-2/3 D5/12 Return to Question Board 25 points See Answer E 4

10. A N S W E R: Return to Question Board 25 points E 4 D: 5/12

11. Return to Question Board 25 points See Answer E 5 A certain map uses a scale of 1 inch equals 30 miles. How many miles are represented by 5 inches on this map? A5 B120 C30 D150

12. A N S W E R: Return to Question Board 25 points E 5 D: 150

13. Return to Question Board 25 points See Answer E 6 What is the product of 3/8 and 1/8? A5/8 B3/64 C1/2 D1/4

14. A N S W E R: Return to Question Board 25 points E6 B: 3/64

15. What is the greatest common divisor of 48, 32, and 56? A6C8 B9D2 Return to Question Board 25 points See Answer E7

16. A N S W E R: Return to Question Board 25 points E 7 C: 8

17. Return to Question Board 25 points See Answer E 8 8 + 8 ÷ 4 + 3 = A10 B7 C15 D13

18. A N S W E R: Return to Question Board 25 points E 8 D: 13

19. Return to Question Board See Answer 50 points The vice president of sales took a client out to lunch. If the lunch was $ 64 and she gave a 20% tip, how much money did she spend on lunch? A$12.80 B$51.20 C$76.80 D$77.80 A 1

20. A N S W E R: Return to Question Board 50 points A 1 C: $76.80

21. Return to Question Board See Answer 50 points A group of hikers climbed from Salt Flats (elevation -55 feet) to Talon Peak (elevation 730 feet). What is the difference in elevation between Talon Peak and Salt Flats? A675 feet C775 feet B785 feet D685 feet A 2

22. A N S W E R: Return to Question Board 50 points A 2 B: 785 feet

23. A farmer harvested 18,000 pounds of almonds in a 8-acre orchard. Which proportion could be solved to find X, the expected harvest from a 30-acre orchard? A 8 = X 18,000 30 B 8 = 30 18,000 X C 30 = X 18,000 8D 30 = 8 18,000 X Return to Question Board See Answer 50 points A 3

24. A N S W E R: Return to Question Board 50 points A 3 B: 8 = 30 18,000 X

25. Return to Question Board See Answer 50 points The Ramirez family went on vacation. They started with $2,400. If they spent $200 each day, which expression represents how much money they had after x days? A2200xC2400 + 200x B200x D2400 - 200x A 4

26. A N S W E R: Return to Question Board 50 points D: 2400 - 200x A 4

27. Marisela had some change in her pocket. After her friend gave her $0.65, Marisela had $1.55 altogether. Which equation can she use to find the original amount of money, m, she had in her pocket? Am + 0.65 = 1.55 Cm = 1.55 X 0.65 B1.55 = m – 0.65Dm + 1.55 = 0.65 Return to Question Board See Answer 50 points A 5

28. A N S W E R: Return to Question Board 50 points A: m + 0.65 = 1.55 A 5

29. Return to Question Board See Answer 100 points D 1 A square with a side of x is inside a square with a side of 4, as pictured below. Which expression represents the area of the shaded region in terms of x? A16 - 2xC 16 - 4x B16 + x²D16 - x²

30. A N S W E R: Return to Question Board 100 points D: 16 - x² D 1

31. Return to Question Board See Answer 100 points D2 When wheel B turns 3 revolutions, wheel A turns 5 revolutions. When wheel A turns 40 revolutions, how many revolutions does wheel B turn? A4C24 B16D80

32. A N S W E R: Return to Question Board 100 points D 2 C : 24

33. Return to Question Board See Answer 100 points D3 If 50% of a number is 40, what is 75% of the number? A40 C80 B60 D120

34. A N S W E R: Return to Question Board 100 points D3 B: 60

35. Return to Question Board See Answer 100 points D4 If the rectangle below has length of 15 inches and perimeter p inches. Which equation could be used to find the width of the rectangle ? Aw = p/2 -15 Bw = 15 – p Cw = 2(p) -15 Dw = 15- p/2

36. A N S W E R: Return to Question Board 100 points D 4 A:w = p/2 -15

37. The three angles of a triangle are in the ratio 3:4:5. What is the measure of the middle angle? Return to Question Board See Answer WAGER T 1

38. A N S W E R: Return to Question Board WAGER T 1 60

39. The perimeter of a rectangular field is 3 times its length. If the perimeter is 240 m, find the width of the field. Return to Question Board See Answer WAGER T 2

40. A N S W E R: Return to Question Board WAGER T 2 40

41. What is the y-intercept of the graph of 4x + 2y = 12? Return to Question Board See Answer WAGER T 3

42. A N S W E R: Return to Question Board WAGER T 3 (0,6)