Download File - San Diego Math Field Day

San Diego Junior High Math Field Day 2009
Math Wits - 8
1.
Write MMIX in base 16.
2.
If the side lengths of a triangle are 6, 2x – 1, and x + 4, then what is the greatest
integral value that x can be?
3.
Juan's street has four-digit house numbers. He notices that the sum of the four
digits of his house total 30. What is the maximum number of houses that can have
this quality?
4.
A regular hexagon has an area of 24 3 inches. What is the length, in inches, of its
longest diagonal?
5.
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?
6.
What is the distance between (–3, 7) and (12, –5)? Express your answer in
simplest radical form.
7.
What is the measure, in degrees, of the smaller angle formed by the hands of a
clock at 9:22?
8.
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 number of feet in its perimeter?
9.
The sum of two numbers is 24. When each is squared, the difference is 144. What
is the positive difference of the two numbers?
10.
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.
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.
1 1 2
 
. If a  b and both a and b are positive whole numbers, find the
a b 15
smallest value of a + b.
San Diego Junior High Math Field Day 2009
Math Wits - 8
13.
How many ways can you rearrange the letters of the word TANGENT?
14.
What is the only three-digit positive integer that has exactly five distinct, positive
factors?
15.
In the trapezoid ABCD, AB is parallel to CD ,
1
AB = CD, and point P lies on AB . What is the
2
ratio of the areaof triangle DPC
to the area of
trapezoid ABCD? Express your answer as a

common fraction.

16.
The square of a number is also a factor of 6!. What is the greatest possible value
of the original number?
17.
In Exactburgh, 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
Exactburgh?
18.
Write an expression for the perimeter of a rectangle whose area is 6x2 +17x – 14.
19.
What is the 75th 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.
A square with side length s is inscribed as shown
in an equilateral triangle with side length t. What
is the ratio t:s? Express your answer in simplest
radical form.
22.
A square and a regular hexagon have the same perimeter. What is the ratio of the
area of the square to the area of the hexagon? Express your answer as a common
fraction in simplest terms.
San Diego Junior High Math Field Day 2009
Math Wits - 8
23.
What is the units digit of 72009 ?
24.
Elmo has seven white socks, six blue socks, and twelve black socks in his sock
drawer. How many socks would he have to pull out to guarantee that he had a
pair of the same color?
25.
A cube has the same number of square centimeters in its surface area as the
number of cubic centimeters in its volume. What is the length of one edge in
centimeters?
26.
The lengths of the legs of a right triangle are 5 cm and 12 cm. What is the length
of the altitude drawn to the hypotenuse? Express your answer as a common
fraction.
27.
What are the odds of drawing three straight cards of the same suit from a
standard deck of 52 cards?
28.
One Plorb is the same weight as five Glorbs. Three Glorbs are the same weight as
seven Blorbs. Five Blorbs are the same weight as four Slorbs. If you put six Plorbs
in a pile, how many Slorbs would you have to add in order to double the weight?
29.
For what value of k will the three lines y =
at a single point?
x
, x – 2y = 12, and y = kx + 84 intersect
3
30.
What is the sum of the first three positive integers that are both perfect squares

and perfect cubes?
31.
What is the measure, in degrees, of any interior angle of a regular decagon?
32.
A quadratic expression can be expressed as ax2 + bx + c. For one particular
quadratic, Optimus Prime substituted the set {1, 2, 3, 4, 5} for x and got
{0, 3, 10, 21, 36} as resulting values for the expression. What is the value of
a• b• c?
33.
Myrtle took a two-digit number and squared it. Then she took her original
number, reversed the digits, and squared it. She was amazed to find that the two
results had reversed digits as well. How many numbers fit this description that
do not have the same number for their units and tens digits?
San Diego Junior High Math Field Day 2009
Math Wits - 8
34.
The three sides of a triangle are 13, 20, and 21. What is the area of the triangle
in square units?
35.
A right triangle has side lengths of 6, 8, and 10 inches. How many inches long is
the radius of the biggest circle that can fit completely inside it?
36.
Superman can save 17 people in 4 minutes, Batman can save 5 people in 2
minutes, and Spider-Man can save 12 people in 5 minutes. If they all work
together, how many people can they save in 13 minutes? Round your answer
down to the nearest whole number.
37.
What is the area, in square centimeters, of a regular octagon that has a perimeter
of 32 cm? Round your answer to the nearest tenth of a square centimeter.
38.
Twelve players are on a basketball team, but only five of them start the game.
How many different sets of players can be chosen to start a game?
39.
80 barrels of applesauce was mixed together from two batches. The first batch
was made up of 32 barrels that contained applesauce that was 80% real apples.
The second batch contained applesauce that was 65% real apples. To the nearest
whole percent, what part of the final mix was real apples?
40.
A set of data has a range of 15 a mode of 15, and a median of 15. All of the data
are whole numbers, and the smallest number is 5. What is the least possible
value for the mean if there are 10 numbers in the set? Round your answer to the
nearest tenth.
41.
What is the distance between the point (6, 1) and the line represented by the
equation y = 2x – 3? Express your answer in simplest radical form.
42.
The four interior angles of a quadrilateral are in the ratio 2:4:4:5. In degrees, what
is the measure of the smallest interior angle of the quadrilateral?
43.
Line m contains the points (–1, 3) and (1, –1). Line n is perpendicular to line m
and contains the points (2, 2) and (–2, y). What is the value of y?
44.
Two lines y = 2x –13 and 3x + y = 92 intersect. What is the value of x at the point
of intersection?
45.
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 2009
Math Wits - 8
46.
Thomas walked a mile in two hours. Michela ran four miles in forty minutes.
What is the ratio of speeds of the Michela to Thomas?
47.
How many positive integer factors of 22 x 32 x 5 are multiples of 12?
48.
The sum of four consecutive odd integers is 112. What is the greatest of the four
integers?
49.
Find the value of three cubed, to the one half power. Write your answer in
simplest radical form.
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.
A square is inscribed in a circle. If the area of the
square is 196 cm2, what is the exact area of the
circle?
52.
Solve for x: 25x2 + 49 = 70x.
53.
The points A(0, 0), B(10, 0), C(10 + 5 2 , –10 – 5 2 ) and D(0, –10) form
quadrilateral ABCD. What is the number of square units in the area of the
quadrilateral? Express your answer in simplest radical form.
54.


What is the area, in square centimeters, of a rhombus that has diagonals measure
19 cm and 22 cm?
55.
For what value of n is 5 x 8 x 2 x n = 7! ?
56.
The diameter of circle B is 16 cm. Angle ABC
measures 55 degrees. What is the area of the sector
ABC, to the nearest centimeter?
San Diego Junior High Math Field Day 2009
Math Wits - 8
L
is used to find the time, T, in seconds for a pendulum
32
of length L feet to complete one period (back and forth). How many feet long
must the pendulum be to have a period of 3.5 seconds? Round your answer to
the nearest whole number.

57.
The formula T  2
58.
Evaluate
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.
How many distinct solutions are there to the equation 37x 2 – 7x  22  –1?
(x  y) 2 – (x – y) 2
for x = 6, y  0.
y

San Diego Junior High Math Field Day 2009
Math Wits - 8
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 Wits - 8
KEY

4 3
3
8 5
5
1.
7D9
21.
2.
10
22.
3.
84
 23.
4.
8 (inches)
24. 4
44. 21
5.
26
25. 6 (cm)
45. 50 (degrees)
6.
3 41
26. 60/13 (cm)
46. 12:1 or 12/1
7.
98.5 (degrees)
27. 22:403
47. 4
8.
36 (feet)
28. 56 (Slorbs)
48. 31
9.
6
29. –2
49.
3 3
10. 114.2 (cm2)
30. 794
50.
8 3 (inches)
11. 22
31. 144
 51.
98
12. 32
32. –6
 52.
7
or
5
13. 2520
33. 4
14. 625
34. 126 (units2)
15. 2/3
35. 2 (inches)
16. 12
36. 118 (people)
55. 63

56. 31 (cm)
17. 27
37. 77.3 (cm2)
57. 10 (feet)
18. 10x + 10
38. 797
58. 24
19. 102
39. 71
59. 972
20. 24
40. 11.5
60. 0
3
2
7
41.
42. 48 (degrees)
 43.
0
1 2 or 1.4
5
53. 100 + 50 2
 54. 209
(cm2)