Download Practice Questions - Missouri State University

SW-ARML 1-22-12
1.
Given a finite set A of real numbers, let m(A) denote the mean of its elements. If S is a set
such that m(S ∪ {1}) = m(S) – 13 and m( S ∪ {2001}) = m(S) + 27. Find m(S).
2.
Find the sum of the all roots (including possibly complex roots) of the polynomial
x
2012
1

x 
2

2012
.
3.
A fair die is rolled four times. Find the probability that each number is no smaller than the
preceding number. (Note: There are 21 ways if only rolled twice, and 56 ways if rolled
three times.)
4.
The sequence x1, x2, x3, ... is defined by xk =
xm + xm+1 + ... + xn =
5.
1
and the sum of consecutive terms
k k
2
1
for some m and n. Find m and n.
29
The solutions to log 225 x + log 64 y = 4, logx225 – logy64 = 1 are (x, y) = (x1, y1) and (x2, y2).
Find log30( x1 y1 x2 y2 ).
6.
S is a set of positive integers containing 1 and 2002. No elements are larger than 2002. For
every n in S, the arithmetic mean of the other elements of S is an integer. What is the largest
possible number of elements of S?
7.
a, b, c are positive integers forming an increasing geometric sequence, b – a is a square, and
log6a + log6b + log6c = 6. Find a + b + c.
8.
9.
Find n such that log  sin x   log  cos x   1 , log  sin x cos x  
log n  1
.
2
Find the volume of the set of points that are inside or within one unit of a rectangular
3  4  5 box.
10. N is the largest multiple of 8 which has no two digits the same. What is N mod 1000?
1