Download File - San Diego Math Field Day

San Diego Junior High Math Field Day 2009
Math Bowl - 7
1.
Write MMIX in base 2.
2.
In the addition problem to the left, AB and BA
each represent a two-digit number, and A and
B stand for different digits. What is the value of
A?
BA
AB
+ AB
CAA
3.
The sum of the ages of Alice, Betty and Clara is 29 years. Betty is 4 years older
than Alice. Clara is 6 years older than Betty. What is Alice’s age?
4.
A rectangular tile is 2 inches by 3 inches. What is the least number of such tiles
that are needed to completely cover a square region that is 2 feet on each side?
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.
If angle A and angle B are supplementary, what is the measure, in degrees, of
angle A if angle B = 161 degrees?
7.
What is the measure, in degrees, of the smaller angle formed by the hands of a
clock at 10:20 am?
8.
The numbers 6, 14, and 15 are factors of the natural number N. What is the
smallest value that N can have?
9.
13 minutes and 20 seconds is equivalent to what fraction of an hour?
10.
In a group of 30 students, a total of 8 study French, a total of 12 study Spanish,
and a total of 3 study both languages. How many students of the group take
neither French nor Spanish?
11.
The average of five numbers is 7. If one of the five numbers is removed, the
average of the four remaining numbers is 6. What is the value of the number that
was removed?
12.
The front wheels of a truck have a circumference of 3 feet while the rear wheels
have a circumference of 4 feet. If the truck travels 1 mile in a straight line, how
many more complete turns will the front wheels make than the rear wheels?
b. +
c. CA
San Diego Junior High Math Field Day 2009
Math Bowl - 7
1 2 3 4 5
+ + + + ) = ?
6 6 6 6 6
13.
8x(
14.
The top, front, and one end of a rectangular block have areas of 2 cm2, 5 cm2, and
10 cm2, respectively. How many centimeters cubed is the volume of the block?
   

15.
The sum of the first 50 natural numbers is 1,275. What is the sum of the next 50
natural numbers?
16.
The square of a number is also a factor of 6!. What is the greatest possible value
of the original number?
17.
The four-digit number 3AA1 is divisible by 9. What digit does A represent?
18.
17% is ? percent of 68%?
19.
What is the 30th positive composite number?
20.
Three years ago Frances was a third the age of his brother Bill. Four years from
now, he will be half of Bill's age. How many years old is Bill now?
21.
Find the value of x: 54321 = 4321 + 5x
22.
If 30! is factored into primes, how many 5s will the factorization contain?
23.
What is the units digit of 72009 ?
24.
Find the product of all prime numbers between 10 and 20.
25.
The two shorter sides of a right triangle have lengths 7 inches and 24 inches.
What is the length, in inches, of the longest side of this triangle?
26.
Planet P orbits star S. Star S has 1,000,000 times the volume of planet P. If the
radius of planet P is 5000 kilometers, how many kilometers long is the radius of
star S?
27.
A rectangular garden is enclosed by 24 meters of fencing. What is the largest area
(in square meters) that the garden can contain?
San Diego Junior High Math Field Day 2009
Math Bowl - 7
28.
Write an expression for the perimeter of a rectangle whose area is 6x2 +17x – 14.
29.
If 12% of x is 45, what is 20% of x?
30.
12 + 22 + 32 + … + 252 = 5525. What is the value of 22 + 42 + 62 + … + 502?
31.
D is the sum of the odd numbers from 1 through 99 inclusive (1 + 3 + 5 +…+ 99).
N is the sum of the even numbers from 2 through 98 inclusive (2 + 4 + 6 +…+ 98).
What is the positive difference of D and N?
32.
Albert must choose to take exactly 2 different classes from among the 8 different
classes offered by his school. How many different combinations of 2 classes are
possible for Albert?
33.
A motorist made a 60-mile trip averaging 20 miles per hour. On the return trip,
he averaged 30 miles per hour. What was the motorist’s average speed, in miles
per hour, for the entire trip?
34.
Points A, B, C, D lie on the same line, in that order. If AD:BC = 3:2 and
AC:BD = 7:8, compute the ratio of AB:CD.
35.
A rectangular block is 6 inches wide. It is twice as deep as it is wide, and it is 5
times as tall as it is deep. What is the volume of the block in cubic feet?
36.
N = ((33)4)5/927. Express N as an integer.
37.
I have an equal number of nickels and dimes with a total value of $6. How many
nickels do I have?
38.
A square whose side is 6 inches has the same area as a triangle whose base is 4
inches. How many inches high is the altitude of the triangle?
39.
A fictional island is inhabited by two types of people: Liars, who always lie when
asked a question, and Truth-tellers who always tell the truth. You are visiting
this island and encounter 3 inhabitants, A, B and C. You ask A, “Are you a truthteller?” You do not hear A’s response, but B then says “A said he is a Liar” and
thereafter, C says “Don’t believe B! She is lying.” Which one of the inhabitants
must be a truth-teller?
40.
You roll 3 standard 6-sided dice. What is the probability that you roll 3 fives?
San Diego Junior High Math Field Day 2009
Math Bowl - 7
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
41.
You roll 3 standard 6-sided dice. What is the probability that you roll 3 different
numbers?
42.
In a basket of 72 apples, 1/3 are golden delicious apples, 25% are Fuji apples, and
the rest are McIntosh apples. How many McIntosh apples are in the basket?
43.
Express the number 193 in octal (Base 8).
44.
Consider the octal (Base 8) number 7,063. Express this number in binary (Base 2).
45.
A bag contains one tile numbered “1”, two tiles numbered “2”, etc., up to 20 tiles
numbered “20”. If I pick tiles from the bag without looking, what is the fewest
number of tiles I must pick from the bag to be certain of picking at least 5 tiles
that have the same number on them?
46.
What is the sum of the positive integers from 1 to 1000?
47.
What is the sum of the prime factors of 444?
48.
You are planning a party for 10 people (including yourself). You are buying
candy for the party and want to buy an amount that can be divided evenly
among everyone at your party, regardless of how many people show up. What is
the smallest number of pieces of candy that you can buy to accomplish this?
49.
Numbers of the form 2N-1, where N is an integer, are disproportionately likely to
be prime numbers. Those that are prime numbers are known as Mersenne
primes. For N between 1 and 20, there are 7 Mersenne primes. The largest known
prime number is a Mersenne prime, 232,582,657-1, which was discovered in 2006;
this number has 9,808,358 digits. (Note that there is a $100,000 prize for the first
person to discover a prime number that has over 10,000,000 digits.) What are the
first two Mersenne primes?
50.
If a 3-inch tall right cylinder has a volume of 144π, how many inches long is the
diameter of its base? Express your answer in simplest radical form.
51.
9
52.
22  53  ?
3
4
 12  ?
7
5
San Diego Junior High Math Field Day 2009
Math Bowl - 7
53.
At the Turntable, the price of all CD-players was reduced 33%. Store employees
are given an additional 7% discount off the sale price. Sales tax is 7.75%, and is
applied after all discounts are taken. In dollars, what is the final employee cost
for a CD-player originally priced at $415? Express your answer to the nearest
cent.
54.
How much is fourteen minus one tenth plus the square root of the reciprocal of
sixty-four? Express your answer as a mixed number.
17 cm
55.
Two adjacent identical rectangles form an “L” as
shown. How many square centimeters are in the
area of each rectangle?
25 cm
56.
N = ((32)3)4/276. Express N as an integer
57.
The algebra scale shown below is balanced. Each shape has a value, and an
algebra scale is balanced when the sum of the values represented by the shapes
on the left is equal to the sum of the values on the right. According to this algebra
scale, the value represented by one triangle is equivalent to the value of how
many squares?
58.
The number n is a prime number between 20 and 30. If you divide n by 8, the
remainder is 5. What is the value of n?
59.
The surface area of a particular sphere is 324 cm2. What is the volume, in cubic
centimeters, of the sphere? Express your answer in terms of .
60.
Let f(x) = 2x2 + 3x – 5. What is the value of f(-3)?
San Diego Junior High Math Field Day 2009
Math Bowl - 7
NAME
SCHOOL
1.
21.
41.
2.
22.
42.
3.
23.
43.
4.
24.
44.
5.
25.
45.
6.
26.
46.
7.
27.
47.
8.
28.
48.
9.
29.
49.
10.
30.
50.
11.
31.
51.
12.
32.
52.
13.
33.
53.
14.
34.
54.
15.
35.
55.
16.
36.
56.
17.
37.
57.
18.
38.
58.
19.
39.
59.
20.
40.
60.
Score:
San Diego Junior High Math Field Day 2009
Math Bowl - 7
KEY
5
9
1.
11111011001
21. 10,000
41.
2.
4
22. 7
42. 30
3.
5
23. 7
4.
96 (tiles)
24. 46,189
44. 111000110011
5.
45 (cm)
25. 25 (inches)
45. 75 (tiles)
6.
19 (degrees)
26. 500,000 (km)
46. 500,500
7.
160 (degrees)
27. 36 (m2)
47. 44
8.
210
28. 10x + 10
48. 2520
9.
2/9
29. 75
49. 3, 7
10. 13
30. 22,100
50.
8 3 (inches)
11. 11
31. 50
51.
12. 440 (turns)
32. 28
 52.
165
224
125
1
or 31
4
4
13. 20
33. 24 (mph)
 53.
$278.63
14. 10 cm3
34. 1:2 or 1/2
 54.
14

15. 3775
35. 2.5 (ft3)
55. 84 (cm2)
16. 12
36. 729
56.
729

17. 7
37. 40
57. 3
18. 25 (%)
38. 18 (inches)
58. 29
19. 45
39. C
59. 972
20. 24 (years old)
40.

1
216
43.
301 (Base 8)
60. 4
1
40