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北京师大附中2013-2014学年上学期高二年级期中考试微积分ab试卷(ap班) 后有答案


北京师大附中 2013—2014 学年上学期高二年级期中考试微积分 AB 试卷(AP 班) 本试卷满分 100 分,考试时间为 120 分钟。不能使用计算器。 Section A 1. Which of the following defines a function f for which f (? x) ? ? f ( x) ? A. f ( x) ? x2 D. f ( x) ? log x B. f ( x) ? sin x E. f ( x) ? e x C. f ( x) ? cos x 2. ln( x ? 2) ? 0 if and only if A. x ? 3 D. x ? 2 B. 0 ? x ? 3 E. x ? 3 C. 2 ? x ? 3 ? 2x ? 5 ? x ? 7 ? f ( x) ? 3. If ? , for x ? 2 , and if f is continuous at x ? 2 , then k= x?2 ? f (2) ? k ? A. 0 B. 1 6 C. 1 3 D. 1 E. 7 5 4. If f ( x) ? 2? | x ? 3 | for all x, then the value of the derivative f ?( x ) at x ? 3 is A. -1 E. nonexistent B. 0 C. 1 D. 2 ?1 ? ?1? 8? ? h ? ? 8? ? ?2 ? ?2? ? 5. What is lim h ?0 h A. 0 B. 8 8 1 2 C. 1 D. The limit does not exist. E. It cannot be determined from the information given. 6. When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units, the radius is A. 1 4? B. t 1 4 C. 1 ? D. 1 E. ? 7. The set of all points ( e , t ), where t is a real number, is the graph of y= A. 1 ex 1 1 B. e x C. xe x D. 1 ln x E. ln x 8. If f ( x ) ? 4 and g ( x) ? 2 x , then the solution set of f ( g ( x)) ? g ( f ( x)) is x ?1 A. ? ? ?1 ? ?3? B. {2} C. {3} D. {?1, 2} E. ? , 2 ? ?1 ?3 ? ? 9. If f ( x) ? x3 ? 3x2 ? 4 x ? 5 and g ( x) ? 5 , then g ( f ( x)) = A. 5 x ? 15 x ? 25 2 B. 5 x ? 15 x ? 20 x ? 25 3 2 C. 1125 ?1 D. 225 E. 5 , the inverse function of f, is 10. If the function f is defined by f ( x) ? x5 ?1 , t

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