Download File - San Diego Math Field Day

San Diego Junior High Math Field Day 2011
Math Bowl - 7
1.
If 2011 is a base 3 number, what is its base 10 equivalent?
2.
Grace is decorating her store window for a
sale. She wants to design some art that looks
like the design on the right. If she plans to
paint the shaded area, how many square
meters will she need to paint? Round to the
nearest hundredth square meter.
3.
On a planet far, far away, 1/2 of 5 is 3. Assuming that the same proportion holds,
what would 1/3 of 10 be on this strange planet?
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 104 cm and one leg measures 40
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.
How many seconds are in 3% of a week?
8.
The width of the Circumference River is 3100 meters. The Square Root Bridge
spans the Circumference River. If 1/8 of the bridge stands on one side of the
river, and 1/10 of the bridge is on the other side, how many meters long is the
Square Root Bridge?
9.
13 minutes and 20 seconds is equivalent to what fraction of an hour?
San Diego Junior High Math Field Day 2011
Math Bowl - 7
10.
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?
11.
Find the sum of the least and greatest two-digit prime numbers whose digits are
also prime.
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?
1
4
1
13.
Find the value of the expression at the right.
Write your answer as a common fraction.
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.
Ms. Descartes’ mathematics class took the same test as Mr. Euclid’s students. Ms.
Descartes’ class has 20 students, and the mean test score was 90. The mean of Mr.
Euclid’s class was 80. If you combine both classes, the mean score on the test was
84. How many students does Mr. Euclid have in his mathematics class?
16.
17% is ? percent of 68%?
17.
On his last test, Jacob scored a 95, raising his average exactly 1 point, to 89. What
must he score on his next test to raise his average one more point, to a 90?
18.
Find the slope of a line perpendicular to the line that is represented by the
equation 4x – 5y = 15.
4
1
1
4
4
San Diego Junior High Math Field Day 2011
Math Bowl - 7
19.
Jesse is going to a sporting goods store to buy a pair of tennis shoes and a pair of
in-line skates. The original cost of the shoes was $150, but today that pair is 40%
off. The original price of the skates was $200, but today they are 20% off. What is
the percent discount on the total purchase (without taxes)? Round to the nearest
percent.
20.
There are eight different routes between cities A and B and seven different routes
between cities B and C. How many routes are there between cities A and C by
way of city B?
21.
Find the value of x: 54321 = 4321 + 5x
22.
If 3 hens lay 4 eggs in 5 days, how many days will it take a dozen hens to lay 8
dozen eggs?
23.
How many distinct isosceles triangles exist with a perimeter of 99 inches and side
lengths that are positive whole number inches?
24.
What is the units digit of 72011?
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?
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?
San Diego Junior High Math Field Day 2011
Math Bowl - 7
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 = ((23)4)5 – 820. 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?
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).
San Diego Junior High Math Field Day 2011
Math Bowl - 7
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.
The sum of four consecutive odd integers is 112. What is the greatest of the four
integers?
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  ?
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.
3
4
 12  ?
7
5


San Diego Junior High Math Field Day 2011
Math Bowl - 7
55.
Two adjacent identical rectangles form an “L” as
shown. How many square centimeters are in the
area of each rectangle?
17 cm
25 cm
56.
N = ((32)3)4/276. Express N as an integer
San Diego Junior High Math Field Day 2011
Math Bowl - 7
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 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 .
59.
Let f(x) = 2x2 + 3x – 5. What is the value of f(-3)?
60.
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).
THE END
San Diego Junior High Math Field Day 2011
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 2011
Math Bowl - 7
KEY
5
9
1.
58
21. 10,000
41.
2.
2.36 (m2)
22. 30 (days)
42. 30
3.
4
23. 25 (triangles)
4.
96 (tiles)
24. 3
44. 111000110011
5.
96 (cm)
25. 25 (inches)
45. 75 (tiles)
6.
19 (degrees)
26. 500,000 (km)
46. 500,500
7.
18,144 (secs)
27. 36 (m2)
47. 44
8.
4000 (meters)
28. 10x + 10
48. 2520
9.
2/9
29. 75
49. 31
10. 11
30. 22,100
50.
8 3 (inches)
11. 96
31. 50
51.
12. 440 (turns)
32. 28
 52.
165
224
125
1
or 31
4
4
33. 24 (mph)
 53.
$278.63
34. 1:2 or 1/2
 54.

14
13.
72
305
14. 10 cm3
 15.
301 (Base 8)
1
40
35. 2.5 (ft3)
55. 84 (cm2)
16. 25 (%)
36. 0
56.
729

17. 97
37. 40
57. 3
38. 18 (inches)
58. 972
39. C
59. 4
18.
30
43.

5
4
19. 29
 20.
40.
56 (ways)

1
216
60. 1170