Download 1 - San Diego Math Field Day

San Diego Junior High Math Field Day 2011
Mad Hatter Marathon – 8
1.
Write 2011 using Roman numerals.
2.
How much money would you make in 8 days if you made 8 dollars every
time the hands of a clock formed a 90 degree angle?
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 72011?
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.
Alice is 4 feet, 8 inches tall. She eats a cake that makes her 1/4 as tall, and
then she nibbles a mushroom that makes her shrink to 2/7 as tall as her
new height. Then, she drinks a potion that makes her grow 7/8 of a foot.
How many inches tall is she at the end of this eating adventure?
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?
San Diego Junior High Math Field Day 2011
Mad Hatter Marathon – 8
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 2011
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.
Alice was making a trip through Wonderland with a basket of flowers. On
her way, she came across the Duchess and gave her half the flowers plus
half a flower. Then she ran across the Mad Hatter, to whom she gave half
of her remaining flowers plus half a flower. Then she came upon the White
Rabbit, who also wanted half her flowers plus half a flower. Unfortunately,
this meant that, when Alice met the Queen of Hearts, she no longer had
any flowers left. How many flowers did Alice have at the beginning of her
journey?
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.
I am thinking of a special four-digit number that has the following traits:
 All the digits are different.
 The digit in the thousands place is 3 times the digit in the tens place.
 The number is odd.
 The sum of the digits is 27.
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
San Diego Junior High Math Field Day 2011
Mad Hatter Marathon – 8
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.
How many distinct isosceles triangles exist with a perimeter of 99 inches
and side lengths that are positive whole number inches?
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?
25.
Find the value of three cubed, to the one half power. Write your answer in
simplest radical form.
26.
Light travels 186,000 miles per second. How many minutes does it take the
Sun’s light to reach Earth, which is about 93,000,000 miles away?
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.
What fraction of 2 cubic yards is 4 cubic feet?
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?
San Diego Junior High Math Field Day 2011
Mad Hatter Marathon – 8
33.
How many positive integer factors of 22 x 32 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?
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 planted tomatoes on one-half of his garden. Then, he
planted broccoli on one-fourth of the remaining garden. Then, he planted
lettuce in one-half of the remaining garden. The rest of the garden was
planted with carrots. What percent of the garden is planted in carrots?
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
San Diego Junior High Math Field Day 2011
Mad Hatter Marathon – 8
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 2011
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.
The four horsemen of the Apocalypse are trying to unlock the end of the
world by determining the prime factorization of 5212011. Each horseman
represents one of the prime factors. You can prevent the end of the world
by finding the sum of the prime factors of 5212011. What is the sum of the
prime factors? (HINT: There are two single-digit and two three-digit
numbers in the prime factorization of 5212011).
San Diego Junior High Math Field Day 2011
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.
San Diego Junior High Math Field Day 2011
Mad Hatter Marathon – 8
KEY
1.
MMXI
21. 5 (years old)
41. 48 (degrees)
2.
$2816
22. 6/7
42. 800 (dollars)
3.
3/633
23. 72 (tarts)
4.
1011011
24. 5 (inches)
43. 60/13
44. 20 hours or
5.
301
25.
6.
9
26. 8 1 (minutes)
7.
3
8.
1536
28.

9.
14 1 or14.5 (in)
29. 13 (units)
2
3024 (ways)
31
10. 1358
30. 2/27
11.
22

31. 540 (feet)
12. 62 (cents)
32. 72 (scones)
13. 8 (feet)
33. 4
14. 6
34. 144:5 or
15. 7 (flowers)
35. 3 (grams)
16. 96 (dollars)
36. 50(degrees)
17. 247/210
37. 0
18. 5/9
38. 18 3 or 18.75 (%)
19.
39. 64.2 (cm2)
8 3 (inches)
20. 9837

45. 1170
3 3
3
 27.
144
5
4
40.
21

1200 minutes
San Diego Junior High Math Field Day 2011
Mad Hatter Marathon – 8