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What is the shaded area, if the rectangle is 2 by 4? (in terms of π )

What is the shaded area, if the rectangle is 2 by 4? (in terms of π ). What is the shaded area, if the rectangle is 2 by 4? (in terms of π ). =. -. Don’t worry about moving slowly, worry about standing still. -- Chinese Proverb.

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What is the shaded area, if the rectangle is 2 by 4? (in terms of π )

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  1. What is the shaded area, if the rectangle is 2 by 4? (in terms of π)

  2. What is the shaded area, if the rectangle is 2 by 4? (in terms of π) = -

  3. Don’t worry about moving slowly, worry about standing still.-- Chinese Proverb

  4. If 3 < x < 7, and 4 < y < 7, which of the following best describes x – y?A) -1 < x – y < 0 B) -4 < x – y < 1C) -7 < x – y < 7 D) -4 < x – y < 3E) 3 < x – y < 4

  5. If 3 < x < 7, and 4 < y < 7, which of the following best describes x – y?A) -1 < x – y < 0 B) -4 < x – y < 1C) -7 < x – y < 7 D) -4 < x – y < 3E) 3 < x – y < 4Smallest x – biggest y is 3 – 7 = -4Biggest x – smallest y is 7 – 4 = 3All others will be between -4 and 3

  6. The most difficult thing is to just start the ball rolling. Once it starts, it is actually more difficult to stop it!---Butch Lovelace

  7. For how many positive numbers b is it true that b x b x b = b + b + b ?A) 0 B) 1 C) 2 D) 3 E) more than 3

  8. For how many positive numbers b is it true that b x b x b = b + b + b ?A) 0 B) 1 C) 2 D) 3 E) more than 3b3 = 3b  b3 – 3b = 0 b(b2 – 3) = 0 This has one positive root (√3)

  9. If x and y are positive odd integers, which of the following MUST be even?I. (x + y) / 2 II. xy + 1 III. (xy + 1) / 2A) None B) I only C) II only D) I & II onlyE) I , II , and III

  10. If x and y are positive odd integers, which of the following MUST be even?I. (x + y) / 2 II. xy + 1 III. (xy + 1) / 2A) None B) I only C) II only D) I & II onlyE) I , II , and IIITry numbers:1 & 3  (1 + 3) / 2 , 1*3 + 1 , and (1*3 + 1) / 2 are all evenBUT… try 1 & 5  (1 + 5) / 2 is odd1*5 + 1 is even, but (1*5 +1)/ 2 is oddC) II only

  11. Your actions speak so loud, I can't hear what you say.

  12. If two sides of a triangle are 7 and 13, what could the length of the third side be?

  13. Opportunity is missed by most people because it is dressed in overalls and looks like work.-- Thomas Edison

  14. Which of the following could not be the sides of a triangle?A) 1 , 1 , 1 B) 1 , 1 , 17 C) 1 , 17 , 17D) 3 , 4 , 5 E) 5 , 6 , 10

  15. Which of the following could not be the sides of a triangle?A) 1 , 1 , 1 B) 1 , 1 , 17 C) 1 , 17 , 17D) 3 , 4 , 5 E) 5 , 6 , 10The sum of the smaller two sides must be greater than the largest side in a triangle1 + 1 is not > 17

  16. If 3 yaps equals 4 yips, and 5 yips equals 6 yups, then what is the ratio of yups to yaps?A) ½ B) 5/8 C) 2/3 D) 8/5 E) 2/1

  17. If 3 yaps equals 4 yips, and 5 yips equals 6 yups, then what is the ratio of yups to yaps?A) ½ B) 5/8 C) 2/3 D) 8/5 E) 2/1Need “common denominator” 3 yaps = 4 yips 15 yaps = 20 yips = 24 yups  24/15 = 8/5 5 yips = 6 yups

  18. If 3 yaps equals 4 yips, and 5 yips equals 6 yups, then what is the ratio of yups to yips?A) ½ B) 5/8 C) 2/3 D) 8/5 E) 2/1or, another way: (4yips/3yaps)(6yups/5yips)=24yups/15yaps(the yips / yips cancels)

  19. What do you throw away the outside and cook the inside, then eat the outside and throw away the inside?

  20. For all positive numbers a and b, let aΔb = √(ab). If n > 1, what does nΔ(1/n) equal?A) √n B) √n2 C) 1/√n D) 1/√n2 E) 1

  21. Neither you nor the world knows what you can do until you have tried.----Ralph Waldo Emerson

  22. If the 3rd Tuesday of the month is the 21st, what date is the second Friday?A) 10th B) 14th C) 17th D) 21st E) 24th

  23. If the 3rd Tuesday of the month is the 21st, what date is the second Friday?A) 10th B) 14th C) 17th D) 21st E) 24thSketch a calendar, and count backwards…Friday before is the 17thBefore that is the 10thBefore that is the 3rd2nd Friday must be the 10th…

  24. One number is four times another. If the sum of the two numbers is -1, what is the smaller of the two numbers?A) -.8 B) -.75 C) -.25 D) -.2 E) 4

  25. One number is four times another. If the sum of the two numbers is -1, what is the smaller of the two numbers?A) -.8 B) -.75 C) -.25 D) -.2 E) 4x + 4x = -15x = -1x = -1/5 = -.24x = -.8Trap: here, 4x is smaller than xthe smaller number is -.8“Killer Rabbit”

  26. Follow these steps and see if you can figure this out.1) Get a brown, cardboard box.2) Get purple, orange, and turquoise paints.3) Paint the box orange.4) Paint on purple spots.5) Paint on turquoise stripes.7) Turn it upside down.8) Lie on your side.What is missing from this sequence?

  27. What happens once a minute, twice in a moment, but never in a thousand years?

  28. Let . If 2 1 = 1 x, then what is the value of x?A) 2 B) 1 C) ½ D) - ½ E) -1

  29. Let . If 2 1 = 1 x, then what is the value of x?A) 2 B) 1 C) ½ D) - ½ E) -12 1 = (2 – 1) / (2 + 1) = 1/31 x = (1 – x) / (1 + x) = 1/33(1 – x) = 1 + x3 – 3x = 1 + x2 = 4xx = ½

  30. What is the next letter in this sequence?OTTFFSS

  31. What is the next letter in this sequence?OTTFFSSHint: Spelling class?

  32. If m § n = mn + n, and 5 § 7 = x § 3, what is the value of x?A) 5 B) 7 C) 9 D) 11 E) 13

  33. If m § n = mn + n, and 5 § 7 = x § 3, what is the value of x?A) 5 B) 7 C) 9 D) 11 E) 135 § 7 = 5(7) + 7 = 42 (5 = m and 7 = n)x § 3 = 3x + 3 (x = m and 3 = n)If 3x + 3 = 42, then x = 13

  34. How can you make 7 even?

  35. If j@k=jk-1, what is the value of 3@(2@1)?A) 6 B) 5 C) 4 D) 3 E) 2

  36. If j@k=jk-1, what is the value of 3@(2@1)?A) 6 B) 5 C) 4 D) 3 E) 22@1 = (2)(1) – 1 – 13@(2@1) = 3@1 = (3)(1) – 1 = 2

  37. In Pet-town, the 46 residents all own a dog, a cat, or both. If there are 36 dog owners, and 26 cat owners, then how many dog owners have no cat?A) 5 B) 8 C) 10 D) 16 E) 20

  38. In Pet-town, the 46 residents all own a dog, a cat, or both. If there are 36 dog owners, and 26 cat owners, then how many dog owners have no cat?A) 5 B) 8 C) 10 D) 16E) 20 Dog Cat 36 - x 26 - x x (36 – x) + x + (26 – x) = 46  62 – x = 46  x = 16 BUT… answer the question: 36 – 16 = 20

  39. A book collector has a collection of 1200 books, of which 900 are hardcover and the rest are paperback. If 1000 of the books are nonfiction and 50 of the paperbacks are fiction, how many of the books are hardcover and non-fiction?

  40. A book collector has a collection of 1200 books, or which 900 are hardcover and the rest are paperback. If 1000 of the books are nonfiction and 50 of the paperbacks are fiction, how many of the books are hardcover and non-fiction?

  41. A book collector has a collection of 1200 books, or which 900 are hardcover and the rest are paperback. If 1000 of the books are nonfiction and 50 of the paperbacks are fiction, how many of the books are hardcover and non-fiction? 7 5 0

  42. When r is divided by 5, the remainder is 3. What is the remainder when 3r is divided by 5?A) 4 B) 3 C) 2 D) 1 E) 0

  43. When r is divided by 5, the remainder is 3. What is the remainder when 3r is divided by 5?A) 4 B) 3 C) 2 D) 1 E) 0Strategy: plug in a number for rLet’s try 8 (8 / 5 has a remainder of 3)3r/5 = 24/5  remainder of 4another? r = 133r/5 = 39/5  remainder of 4

  44. If 3x + 2y = 10, and x + 4y = 2, then what is the value of 2x – 2y?A) -8 B) -6 C) 6 D) 8 E) cannot be determined

  45. If 3x + 2y = 10, and x + 4y = 2, then what is the value of 2x – 2y?A) -8 B) -6 C) 6 D) 8 E) cannot be determinedYou virtually never have to solve for x and y separately in these types of problems. Combine the information you’re given to find what you’re looking for. In this case, subtract…3x + 2y = 10x + 4y = 22x – 2y = 8 (D)

  46. If 10x – y = 37, and 10y – x = 8, what is the value of x + y?A) 3 B) 5 C) 7 D) 9 E) cannot be determined

  47. If 10x – y = 37, and 10y – x = 8, what is the value of x + y?A) 3 B) 5 C) 7 D) 9 E) cannot be determinedLet’s add the equations (don’t need to find x and y separately)10x – y = 37-x + 10y = 89x + 9y = 45x +y = 5Note: the answer will virtually never be E)

  48. On my bike, I ride up a steep 2 mile hill at 6 miles per hour. How fast must I ride down the hill to average 12 miles an hour for the entire trip? A) 12 B) 18 C) 24 D) 36 E) Call Einstein

  49. On my bike, I ride up a steep 2 mile hill at 6 miles per hour. How fast must I ride down the hill to average 12 miles an hour for the entire trip? A) 12 B) 18 C) 24 D) 36 E) Call Einstein6 mph  10 min / mile  20 min for 2 miles12 mph  5 min / mile  20 min for 4 milesIt is impossible to average 12 mph for the trip…

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