Download Countdown round

Countdown round
1. If we set C = 19!, then express 21! –20! In terms of C.
2. Let C be the sum of the first 100 positive even numbers and let D be the sum of the first 100
positive odd numbers. Calculate (C + D)/(C – D).
3. What is the greatest possible number of points of intersection among four lines and a circle in the
plane?
4. Marija is really bored, so she writes all the integers from 1 to 1,000,000. How many times does
she write the digit 1?
5. Suppose that p and q are prime numbers such that p divides q + 1 and q divides p + 1. Determine
p + q.
6. How many times do the graphs of the line 5x + 8y = 10 and the circle x2 + y2 = 1 intersect?
7. Dave has a deck of cards consisting of the 2 through 5 of hearts and the 2 through 5 of spades.
He deals two cards at random to each of four players. What is the probability that no player
receives two of the same number?
8. Find the radius of the sphere which passes through points A, B, C, and D in space if mBAC =
mCAD = mBAD = 90o and AB = AC = AD = 6.
1. Two years ago, Eric was nine times as old as
Tessa. He is now seven times as old as she
is.
2. How many years from now will Eric be five
times as old as Tessa?
3. In the multiplication problem shown, each
letter stands for a distinct digit from 1 to 9.
What digit does E represent?
POLO
x3
HELP
4
4. During the first four days of Dave's new job,
he woke up at 5:30, 5:30, 7:10 and 7:30. On
average, at what time did he awake?
5. Kelly chooses 2 cards at random from a
standard deck of 52 playing cards. What is
the probability that she draws a pair?
6. Solve the equation 3-(4- (5 - (6 - (7 - x)))) =
8 for x
7. Bill sells corn at a roadside stand. He offers
individual ears of corn for $0.10 each, or
sells a box of fifteen ears for $1.00. Bill
sells a total of 148 ears of corn for $11.30.
How many boxes of corn did he sell?
8. A chocolate chip cookie recipe that produces
30 cookies calls for 2.25 cups of flour. If the
math club decides to make fifteen dozen
cookies for a bake sale, how many cups of
flour will they need?
9. One can obtain a total of 16 using each of
the numbers 10, 12, 14, and 17 exactly once,
combining them using any of the four
6:25
6
1/17
7
13.5
10 x 17 - 12 x 14
400C
201
14
600,001
5
0
4/7
3 3
common operations +, -,  and  along with
parentheses, by writing 10  (17 - 12) + 14.
Demonstrate how to obtain 2.
10. Which of the numbers 810, 99, or 108 is the
largest?
11. A triangle has sides of length 3 , 4 , and
7 . Is the triangle acute, right, or obtuse?
7 11 37
12. Which fraction is largest,
,
,
, or
11 18 54
91
?
136
13. What angle is formed by the hands of a
clock at 2:30 pm? Express your answer in
degrees between 0o and 180o.
14. Niki and Cassie are each reading the same
book. If Niki reads 2/3 as fast as Cassie,
what percentage more time will it take her to
finish?
15. For how many positive integers n is 9 < n
< 10?
16. If the five digit number 5DDDD is divisible
by 6, then find the digit D.
17. The speed of light is 3 x 108 m/sec. Written
in scientific notation, what is the velocity (in
m/sec) of an object moving at 12% the speed
of light?
810
Right
37/54
105o
50%
18
4
3.6 x 107