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목록AMC12 (16)
수악중독
A function \(f\) has domain \([0, \; 2]\) and range \([0, \; 1]\). (The notation \([a, \; b]\) denotes \( \{ x\; : \; a \le x \le b \}\).) What are the domain and range, respectively, of the function \(g\) defined by \(g(x)=1-f(1+x)\) ? (A) \([-1, \; 1 ], \; [-1, \; 0]\)(B) \([-1, \; 1 ], \; [0, \; 1]\)(C) \([0, \; 2 ], \; [-1, \; 0]\)(D) \([1, \; 3 ], \; [-1, \; 0]\)(E) \([1, \; 3], \; [0, \; 1..
Points \(\rm A\) and \( \rm B\) lie on a circle centered at \( \rm O\), and \( \rm \angle AOB= 60 ^{\rm o} \). A ssecond circle is internally tangent to the first and tangent to both \( \overline{\rm OA}\) and \( \overline{\rm OB}\). What is the ratio of the area of the smaller circle to that of the larger circle? (A) \(\dfrac{1}{16}\) (B) \(\dfrac{1}{9}\) (C) \(\dfrac{1}{8}\) (D) \(\dfrac{1}{6}..
What is the area of the region defined by the inequality \(|3x-18| + |2y+7| \le 3 \) ? (A) \(3\) (B) \(\dfrac{7}{2}\) (C) \(4\) (D) \(\dfrac{9}{2}\) (E) \(5\) 정답 (A)
Let \(k=2008^2 + 2^{2008}\). What is the units digit of \(k^2 + 2^k\) ? (A) \(0\) (B) \(2\) (C) \(4\) (D) \(6\) (E) \(8\) 정답 (D)
The numbers \(\log \left ( a^3 b^7 \right ) , \log \left ( a^5 b^{12} \right ) \), and \(\log \left ( a^8 b^{15} \right )\) are the first three terms of an arithmetic sequence, and the \(12^{th}\) term of the sequence is \( \log \left ( b^n \right ) \). What is \(n\) ? (A) \(40\) (B) \(56\) (C) \(76\) (D) \(112\) (E) \(143\) 정답 (D)
Let \(a_1 , \; a_2 , \; \cdots\) be a sequence of integers determined by the rule \(a_n = \dfrac{a_{n-1}}{2}\) if \(a_{n-1}\) is even and \(a_n = 3a_{n-1} +1\) if \(a_{n-1}\) is odd. For how many positive integers \(a_1 \le 2008\) is it true that \(a_1\) is less thatn each of \(a_2 , \; a_3 ,\) and \(a_4\) ? (A) \(250\) (B) \(251\) (C) \(501\) (D) \(502\) (E) \(1004\) 정답 (D)