San Diego Junior High Math Field Day 2010

San Diego Junior High Math Field Day 2010 Mad Hatter Marathon – 8

1. Write the result of 2(103) + 10 using Roman numerals.

2. The White Rabbit went down the rabbit hole at 7:48. What was the degree measure of the smaller angle formed by the minute hand and the hour hand of the clock at 7:48?

3. What is the probability of drawing two aces in a row from a normal deck of 52 playing cards? Express your answer as a common fraction.

4. The Mad Hatter needs 91 croissants for his tea party. He wants to get the croissants from the Binary Bakery, where all orders are taken using base 2. Help the Mad Hatter by converting 91, base 10, into base 2.

5. Help Alice pass into Wonderland, by answering the following riddle: “What is the smallest number that leaves a remainder of 1 when it is divided by 2, 3, 4, 5, or 6 but leaves no remainder when it is divided by 7?”

6. Alice’s street has two-digit house numbers. She notices that the sum of the two digits of her house total 10. What is the maximum number of houses that can have this quality?

7. What is the units digit of 72010?

8. The March Hare has six bins containing jellybeans. These bins contain 1358, 1331, 1999, 2075, 1358, and 1095 blue jellybeans. What is the mean number of blue jellybeans per bin?

9. On a map, 1/4 inch represents 15 feet. If the rabbit hole is 255 feet deep, what is its depth, in inches, on the map?

10. What was the mode in question 8?

11. The average of five numbers is 66. If one of the five numbers is removed, the average of the four remaining numbers is 77. What is the value of the number that was removed?

12. Three crumpets and a jar of jam cost $2.54. Five crumpets and a jar of jam cost $3.82. No prices include tax. In cents, what is the cost of a jar of jam? San Diego Junior High Math Field Day 2010 Mad Hatter Marathon – 8

13. The Queen of Hearts’s garden is a regular hexagon with an area of 24 3 square feet. What is the length, in feet, of its longest diagonal?

14. How many distinct positive integer factors does the number 147 have?

15. The Mad Hatter’s house number is a four-digit number. The sum of the ones digit and the thousands digit equals the difference between the hundreds digit and the tens digit. The ones digit equals the tens digit. What is the smallest number that can be the Mad Hatter’s house number?

16. The White Rabbit agreed to work one year for the Queen of Hearts for $240 and a watch. At the end of seven months, he quit and received $100 and the watch. What was the value of the watch, in dollars?

17. What is the sum of the reciprocals of the first four positive prime integers? Express your answer as a common fraction.

18. The Cheshire Cat vanished at 11:23 AM and reappeared at 12:43 AM the same day. For what fraction of the day had he vanished?

19. If the Mad Hatter’s 3-inch tall hat box has a volume of 144π, how many inches long is the diameter of its base? Express your answer in simplest radical form.

20. The sum of two consecutive odd numbers is the square of the product of the first and fourth prime numbers. What is the sum of the two odd numbers?

21. The Caterpillar is five times as old as Alice, and the March Hare is five times as old as the Caterpillar. The Mad Hatter is twice as old as the March Hare and the Walrus, who is as old as all of them put together, is celebrating his 81st birthday. Who many years old is the Caterpillar?

22. What is the slope of a line passing through the points (4, 5) and (–3, –1)?

23. The Queen of Hearts baked tarts for six days. She averaged 24 tarts a day for the first 5 days. Her overall average for the six days was 32 tarts per day. How many tarts did she bake on the last day if the Jack of Clubs ate twelve of them? 24. The Mad Hatter is and 5-and-one-quarter feet tall, and the March Hare is 4-and- five-sixths feet tall. How many inches taller is the Mad Hatter than the March Hare? San Diego Junior High Math Field Day 2010 Mad Hatter Marathon – 8

25. Find the value of three cubed, to the one half power. Write your answer in simplest radical form.

26. Alice has 187 dimes and 312 quarters. The White Rabbit has 781 dimes and 213 quarters. How many dollars do Alice and the White Rabbit have when they combine their money?

27. The Mad Hatter, March Hare, Alice, and the White Rabbit are seated in a row of nine chairs. In how many ways can they be arranged?

28. The sum of four consecutive odd integers is 112. What is the greatest of the four integers?

29. What is the number of units in the length of segment AB with endpoints at A(–1, 3) and B(4, 15)?

30. The White Rabbit checked his watch, then hurried from the rabbit hole to make it to 4 o’clock tea. He spent three-fifths of the available time looking for the Caterpillar and eleven minutes waking him up, before checking his watch again. If it showed he had only three minutes left, at what time did he leave the rabbit hole?

31. A right triangle has one of its sides be 225 ft. If all of its side lengths are whole numbers, then what is the least possible value of its perimeter, in feet?

32. At the Mad Hatter’s tea party, the ratio of tea cakes to crumpets to scones is 3:5:16, and the total number of tea cakes, crumpets, and scones is nine dozen. How many scones are there?

2 2 33. How many positive integer factors of 2 x 3 x 5 are multiples of 12?

34. The caterpillar walked a mile in three hours. The Cheshire Cat ran eight miles in fifty minutes. What is the ratio of speeds of the Cheshire Cat to the Caterpillar? 35. A sugar jar with 40 of the Mad Hatter’s special sugar cubes in it weighed 135 grams. The same jar, with 20 sugar cubes, weighed 75 grams. What is the mass, in grams, of each sugar cube?

36. Two of the four interior angles of a particular parallelogram are 130 degrees each. What is the number of degrees in each of the other two interior angles? San Diego Junior High Math Field Day 2010 Mad Hatter Marathon – 8

37. If a Cartesian grid were placed on top of the map of Wonderland, Chess Lane would go through the points (–1, 3) and (1, –1). Croquet Boulevard runs perpendicular to Chess Lane and passes through the points (2, 2) and (–2, y). What is the value of y?

38. The caterpillar can lay eggs that double in number every half-hour. If he has 3328 eggs at noon. How many eggs did he lay at 8 a.m. earlier that same day?

39. A square is inscribed in a circle of radius 10 cm. What is the positive difference between the area of the circle and the square? Round your answer to the nearest tenth of a square centimeter.

40. Two lines y = 2x –13 and 3x + y = 92 intersect. What is the value of x at the point of intersection?

41. The four interior angles of the quadrilateral croquet field at the Palace of Hearts are in the ratio 2:4:4:5. In degrees, what is the measure of the smallest interior angle of the quadrilateral?

42. At the Mad Hatter’s tea party, he invites the March Hare to play a game in which a box is filled with $100, $50, $20, and $5 bills. March Hare will be blindfolded and allowed to draw bills, one at a time, until he has drawn five bills of the same denomination. What is the largest possible amount, in dollars, that March Hare can win?

43. The lengths of the legs of a right triangle are 5 and 12. What is the length of the altitude drawn to the hypotenuse? Express your answer as a common fraction. San Diego Junior High Math Field Day 2010 Mad Hatter Marathon – 8

44. The White Rabbit started two pocket watches at the same time. One is slow and loses 2 minutes every hour. The other one is fast and gains one minute every hour. How long will it take for the faster watch to be one hour ahead of the slower watch?

45. At the end of the Mad Hatter’s party, a total of 28 handshakes is exchanged. Assuming that each person is equally polite to everyone else who is present, how many people were at the party? San Diego Junior High Math Field Day 2010 Mad Hatter Marathon – 8

NAME SCHOOL

1. 21. 41. 2. 22. 42. 3. 23. 43. 4. 24. 44. 5. 25. 45. 6. 26. 7. 27. 8. 28. 9. 29. 10. 30. 11. 31. 12. 32. 13. 33. 14. 34. 15. 35. For grading room use only: 16. 36. Scores: 17. 37. 18. 38. 19. 39. 20. 40.

KEY San Diego Junior High Math Field Day 2010 Mad Hatter Marathon – 8

1. MMX 21. 5 (years old) 41. 48 (degrees) 2. 54 (degrees) 22. 6/7 42. 800 (dollars) 3. 3/633 23. 72 (tarts) 43. 60/13 44. 20 hours or 4. 1011011 24. 5 (inches) 1200 minutes 5. 301 25. 3 3 45. 8 (people) 6. 9 26. ($) 228.05

7. 9 27. 3024 (ways) 8. 1536 28. 31 1 9. 4 or 4.25 (in) 29. 13 (units) 4 10. 1358 30. 3:25

11. 22 31. 540 (feet) 12. 62 (cents) 32. 72 (scones) 13. 8 (feet) 33. 4 144 14. 6 34. 144:5 or 5 15. 1100 35. 3 (grams)

16. 96 (dollars) 36. 50 (degrees) 17. 247/210 37. 0 18. 5/9 38. 13 (eggs)

19. 8 3 (inches) 39. 64.2 (cm2) 20. 196 40. 21