2009 Alabama Mathematics Contest
12:34 AM
Muhammad Yusuf
, Posted in
1. Which
of the following is equal to ∛108?
(A) 2∛9
(B) 3∛4
(C) 4∛3
(D) 6∛2
(E) 2∛6
2. The
average of two numbers is x. If you multiply one of the two
numbers by 18, the average of the two new numbers (one of which is unchanged)
is 2x. What is the ratio of the
smaller original number to the larger original number?
(A) 1/2
(B) 1/4
(C) 1/6
(D) 1/8
(E) 1/16
3. A line
of slope 2/3 passes through the point (-1, 2). What is its y-intercept?
(A) (0, 3)
(B) (0, 11/4)
(C) (0, 15/6)
(D) (0, 14/5)
(E) (0, 8/3)
4. What
is the value of (1000012 - 999992) : 100000?
(A) 4
(B) 5
(C) 8
(D) 10
(E) 20
5. If logx 81 = 4 then what is log3 x3?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 9
6. If it
is true that x3 < x < x2 then which of the following must also be true?
(A) 0 < x < 1
(B) 1 < x < 2
(C) -1 < x < 0
(D) x < -1
(E) x > 2
7. Let µ be an angle in the third
quadrant. If tan µ = 1/2, what is sec2 µ - 1?
(A) 1/4
(B) 1/2
(C) 3/4
(D) 1
(E) 3
8. How
many four digit PIN numbers can I make using only the digits 2, 3, and 4, and
using each of these digits at least once in each PIN number?
(A) 24
(B) 36
(C) 48
(D) 60
(E) 72
9. Let S be the set of all multiples of 6.
Which of the following are subsets of S?
I. The set of all multiples of 3.
II. The set of all multiples of 9.
III. The set of all multiples of 12.
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) II and III only
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