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Algebra II Contest #5, April 1, 2006
CCML
In Progress
1.
An auditorium has 20 rows of seats. There are 20 seats in the first row. 22 seats in the second row, 24 seats in the third
row, and so on. How many seats are there in all 20 rows?
2.
Find the sum of the first 30 numbers in the second diagonal of Pascal’s Triangle.
3.
Write the equation of the circle that passes through the point (2, 1), and is tangent to the x-axis at (3, 0). Write your
answer in the form ( x  h)2  ( y  k )2  r 2 .
4.
How many seven-digit phone numbers can begin with the prefix 364?
5.
If sin  
2
5
and  terminates in the first quadrant, then the tan  = _____.
6.
Find the 43rd term in the arithmetic sequence –19, -15, -11,
7.
Find the sum of the first seven terms of the series
8.
From a list of 10 books, how many groups of 4 books can be selected?
9.
The weights in pounds of the members of the wrestling team at Allen East High School are 124, 155,172, 117, 146,
138, 151, 160, and 142. Find the difference between the median and the arithmetic mean of their weights.
1 1 1
  
2 4 8
.
. Write your answer as a common fraction.
10.
Find the value of x so that the data in the set {2, 4, 6, 8, x} has an arithmetic mean of 7.5.
11.
How many five-letter patterns can be formed from the letters of the word teeth?
12.
`
Find the fourth term of (2a  b)7 .
13.
Solve the equation (25 x)3/ 4  125 for x.
14.
Simplify
15.
Find the sum
x!
as far as possible. Assume x is a positive integer, and x > 2.
( x  2)!
6
 (3) j .
j3
17.
x
where x and y are integers in lowest terms.
y
Solve the equation log 3  log t  log(t  4)  log 63 for t.
18.
What is the smallest positive integer n such that
19.
1 3 5 7
Find the sum of    
i i3 i5 i 7
16.
20.
Write 0.434343
in the form

53
i53
16!
is a perfect square?
n
, where i  1 .
The midpoints of the sides of an equilateral triangle are connected to form a second
triangle. This procedure is repeated on each resulting triangle. Find the sum of the
perimeters of all triangles so formed, if one side of the first triangle measures 60
centimeters.
Algebra II Contest 5 April 1, 2006 In Progress
CCML
ANSWER SHEET (KEY)
1.
2.
780
465
3.
4.
( x  3)2  ( y  1)2  1
10,000
5.
6.
2
149
7.
8.
9.
10.
30
12.
13.
560a 4b3
x  25
14.
15.
17.
x( x  1) or x2  x
540
43
99
t 3
18.
19.
20.
1430
27i
360 centimeters
16.
127
128
210
1 pound
17.5
Tie Breaker Questions
11.
20, 19, 18, 14, 8, 3