2008 Alabama Mathematics Contest
12:16 AM
Muhammad Yusuf
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8. The difference between the largest and smallest roots of 30x3 − 31x2 − 66x+ 72 = 0 is
(A) −3/2
(B) 6/5
(C) 4/3
(D) 17/6
(E) 27/10
9. If x + 2y + 3z = 6, 2x − 3y + 2z = 14 and 3x + y − z = −2, then x + y + z is
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
10. The number of common points shared by the graphs of |x| + |y| = 2 and x2 − y = 2 are
(A) 0
(B) 2
(C) 3
(D) 4
(E) 5
11. Jack had an average score of 85 on his first eight quizzes, and an average score of 81 on his first nine quizzes. What score did he receive on his ninth quiz ?
(A) 49
(B) 51
(C) 53
(D) 55
(E) 57
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