Download 1 - San Diego Math Field Day

San Diego Junior High Math Field Day 2009
Mad Hatter Marathon – 8
1.
Write the result of 2(103) + 9 using Roman numerals.
2.
The White Rabbit went down the rabbit hole at 10:35. What was the degree
measure of the smaller angle formed by the minute hand and the hour
hand of the clock at 10:35?
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.
In a right triangle, if the hypotenuse measures 117 cm and one leg
measures 108 cm, what is the length of the other leg?
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 72009?
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
San Diego Junior High Math Field Day 2009
Mad Hatter Marathon – 8
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 2009
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 owns seven pairs of shoes. If he picks two shoes at
random, what are the odds that he has chosen a matching pair?
16.
Twelve caterpillars have yellow spots and blue spots, with each caterpillar
having at least one color of spots. Only six caterpillars have yellow spots
and exactly ten caterpillars have blue spots. How many caterpillars have
both yellow and blue spots?
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 2:18 PM 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.
In mathematics, a semi-prime number is a whole number that is the
product of exactly two prime numbers (they can be the same number).
What is the tenth semi-prime number?
21.
How many ounces are there in 3-and-one-fourth gallons?
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?
San Diego Junior High Math Field Day 2009
Mad Hatter Marathon – 8
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.
Alice has 87 dimes and 213 quarters. The White Rabbit has 213 dimes and
87 quarters. How many dollars do Alice and the White Rabbit have when
they combine their money?
27.
What is the sum of the series 50 – 49 + 48 – 47 + . . . + 4 – 3 + 2 – 1?
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 15 ft. If all of its side lengths are
whole numbers, then what is the least possible value of its perimeter?
32.
At the Mad Hatter’s tea party, the ratio of tea cakes to crumpets to scones
is 2:3:7, and the total number of tea cakes, crumpets, and scones is nine
dozen. How many scones are there?
33.
How many positive integer factors of 22 x 32 x 5 are multiples of 12?
34.
The caterpillar walked a mile in two hours. The Cheshire Cat ran four
miles in forty minutes. What is the ratio of speeds of the Cheshire Cat to
the Caterpillar?
San Diego Junior High Math Field Day 2009
Mad Hatter Marathon – 8
San Diego Junior High Math Field Day 2009
Mad Hatter Marathon – 8
35.
The sum of two numbers is 24. When each is squared, the difference is 144.
What is the positive difference of the two numbers?
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 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.
In Wonderland, they have only two denominations of money, $5 and $8
bills. Also, everyone always pays exactly the amount that something is
priced. What is the largest integer dollar amount that an item CANNOT be
priced in Wonderland?
43.
The lengths of the legs of a right triangle are 5 and 12. What is the length of
the altitude drawn to the hypotenuse? Express your answer as a common
fraction.
44.
How many different ways can the letters in HATTER be arranged?
San Diego Junior High Math Field Day 2009
Mad Hatter Marathon – 8
45.
Twelve people are invited to the Mad Hatter’s tea party, but only five of
them can sit at the table at one time. How many different combinations of party
guests can sit at the Mad Hatter’s table at one time?
San Diego Junior High Math Field Day 2009
Mad Hatter Marathon – 8
NAME
SCHOOL
1.
21.
41.
2.
22.
42.
3.
23.
43.
4.
24.
44.
5.
25.
45.
6.
26.
7.
27.
8.
28.
9.
29.
10.
30.
11.
31.
12.
32.
13.
33.
14.
34.
15.
35.
For grading room use only:
16.
36.
Scores:
17.
37.
18.
38.
19.
39.
20.
40.
San Diego Junior High Math Field Day 2009
Mad Hatter Marathon – 8
KEY
1.
MMIX
21. 416 (ounces)
41. 48 (degrees)
2.
107.5 or 107 1
22. 6/7
42. 27 (dollars)
3.
3/633
23. 72 (tarts)
43. 60/13
4.
1011011

24. 5 (inches)
44. 360 (ways)
5.
45 (cm)
25.
45. 792
6.
9
26. ($) 105
7.
7
8.
1536
28. 31
9.
4 1 or 4.25 (in)
29. 13 (units)
2
 27.
4
10. 1358
11.
22
25
30. 3:25
31. 36
12. 62 (cents)
32. 63
13. 8 (feet)
33. 4
14. 6
34. 12:1
15. 1:12
35. 6
16. 4 (caterpillars)
36. 50 (degrees)
17. 247/210
37. 0
18. 35/288
38. 13 (eggs)
19.
39. 64.2 (cm2)
8 3 (inches)
20. 26

3 3
40. 21
San Diego Junior High Math Field Day 2009
Mad Hatter Marathon – 8