2007 Alabama Mathematics Contest
12:02 AM
Muhammad Yusuf
, Posted in
1. Find the product
2. What is the value of
(A) 1/16
(B) 16777216
(C) 1/4
(D) 65536
(E) 4
3. Simplify
(A) x2 − y2
(B) xy/(x – y)
(C) (x + y)/xy
(D) x − y
(E) none of these
4. If g(x) = 1 − x2 and f(g(x)) = (1 − x2)/ x2 , find f(3/4)
(A) 1
(B) 2
(C) −1
(D) 3
(E) 0
5. What is the value of log27 3 ?
(A) 1/3
(B) 2
(C) −1/3
(D) 3
(E) none of these
6. Evaluate sin(arcsin 3/5 + arcsin 8/17)
(A) 4/5
(B) 77/85
(C) 84/85
(D) 91/85
(E) 15/17
7. If
then f(x) is
8. If 3a = 4b = 36, find 2/a + 1/b
(A) −1
(B) 0
(C) 1
(D) 2
(E) 3
9. Find the distance from the point
(3, 2) to the line y = 3x + 2 .
(A) 2/√3
(B) 3
(C) 3/√5
(D) 5
(E) 9/√10
10. If logx√8 = ½ , find x .
(A) 2
(B) 3
(C) 4
(D) 8
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