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www.mzc38.com:【全国百强校】吉林省实验中学2016届高三上学期第一次模拟考试文数试题解析(解析版)

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吉林省实验中学 2016 届高三毕业班第一次适应性测试 文科数学 第Ⅰ卷(共 60 分) 一、选择题:本大题共 12 个小题,每小题 5 分,共 60 分.在每小题给出的四个选项中,只有一项 是符合题目要求的. 1.已知集合 A ? {x | x ? 2 ? 0} , B ? {x | x ? a} ,若 A A. B ? A ,则实数 a 的取值范围是 ( D. [2, ??) ) (??, ?2] B. [?2, ??) C. (??, 2] 【答案】D 【解析】 试题分析:∵ A ? {x | x ? 2 ? 0} ? {x | x ? 2} , B ? {x | x ? a} , A 考点:集合的子集关系. 2.若 (a ? 2i )i A.0 【答案】D 2013 B ? A ,∴ A ? B ,∴ a ? 2 . ? b ? i ,其中 a, b ? R , i 是虚数单位,则 a 2 ? b 2 等于( B.2 C. ) 5 2 D.5 考点:复数的运算. 3.已知两条不同的直线 l , m 和两个不同的平面 ? , ? ,有如下命题: ①若 l ? ? , m ? ? , l / / ? , m / / ?,则? / / ? ; ②若 l ? ? , l / / ? , ? ? ? ? m,则l / / m ; ③若 ? ? ? , l ? ?,则l / /? ,其中正确命题的个数是 ( A. 3 【答案】C 【解析】 试题分析:由于一个平面内的两条相交直线与另一个平面平行,则这两个平面平行,所以①错误; B.2 C.1 ) D.0 由于一条直线与一个平面平行,则过这条直线的任一平面与此平面的交线与该直线平行,所以②正确; 因为 ? ? ? , l ? ?, 则 l / /? 或 l ? ? ,所以③错误; 综上可知:②正确. 考点:线面关系. 4.阅读右面的程序框图,若输出的 y ? A. ?1 B. 0 1 ,则输入的 x 的值可能为( 2 C. 1 D. 5 ) 【答案】C 考点:程序框图. 5.将长方体截去一个四棱锥,得到的几何体如下图所示,则该几何体的左视图为 ( ) 【答案】C 考点:简单空间图形的三视图. 6.函数 y ? xa x ? a ? 1? 的图象的大致形状是 ( x ) 【答案】B 【解析】 试题分析:∵ y ? 考点:函数图象. 7.下列说法错误 的是 ( .. ) ? ax , x ? 0 xa x ,所以利用指数函数的图象得到 B 选项. ? a ? 1? ? ? x x ??a , x ? 0 A.命题“若 a ? 0 ,则 ab ? 0 ”的否命题是: “若 a ? 0 ,则 ab ? 0 ” B.如果命题“ ?p ”与命题“ p 或 q ”都是真命题,那么命题 q 一定是真命题. C.若命题 p : ?x ? R, x ? x ? 1 ? 0 ,则 ?p : ?x ? R, x ? x ? 1 ? 0 ; 2 2 D. “ sin ? ? 【答案】D 1 ”是“ ? ? 30? ”的充分不必要条件; 2 考点:否命题、命题的否定、充分必要条件、命题的真假. 8.若数列 {a n } 满足 a1 ? 1 1 , an ? 1 ? (n ? 2且a ? N ) ,则 a2013 等于( 2 a n ?1 1 2 C.1 D.2 ) A.-1 【答案】D 【解析】 试题分析:∵ a1 ? B. 1 1 1 1 , an ? 1 ? (n ? 2且a ? N ) ,∴ a2 ? 1 ? ? ?1 , a3 ? 1 ? ? 2 , 2 a n ?1 a1 a2 a4 ? 1 ? 1 1 1 1 ? , a5 ? 1 ? ? ?1 , a6 ? 1 ? ? 2 ,…,∴ an ?3 ? an ,∴ a2013 ? a3 ? 2 . a3 2 a4 a5 考点:递推公式. 9.在平面直角坐标系中, O 为坐标原点,直线 l : x ? ky ? 1 ? 0 与圆 C : x ? y ? 4 相交于 A, B 两点, 2 2 OM ? OA ? OB .若点 M 在圆 C 上,则实数 k ? ( A. ?2 【答案】C 【解析】 B. ?1 C. 0 ) D. 1 试题分析:设 AB 的中点为 D,有 OM ? OA ? OB ? 2OD ,∴ | OM |? 2 | OD |? R ? 2 ,∴ | OD |? 1 , 由点到直线的距离公式得 1 ? | 0 ? 0 ? 1| k 2 ?1 ,解得 k ? 0 . 考点:直线与圆相交问题、平面向量的基本定理及其意义. 10.已知 cos( x ? ? 6 )?? 3 ? ,则 cos x ? cos( x ? ) ? ( 3 3 ) A. ? 2 3 3 B. ? 2 3 3 C. ? 1 D. ? 1 【答案】C 【解析】 试题分析:∵ cos x ? cos( x ? ? 3 ) ? cos x ? cos x cos ? 3 ? sin x sin ? 1 3 ? cos x ? cos x ? sin x 2 2 3 ? 3 3 3 1 3 ? cos x ? sin x ? 3( cos x ? sin x) ? 3 cos( x ? ) ? 3 ? (? ) . 2 2 2 2 3 6 考点:两角和与差的余弦公式. 1 ,看下面四个结论: ① f ( x) 是奇函数;②当 x ? 2007 时, 2 1 3 1 ( ) f ( x) ? 恒成立;③ f ( x) 的最大值是 ;④ f ( x) 的最小值是 ? .其中正确结论的个数为: 2 2 2 11. 关于函数 f ( x) ? sin 2 x ? ( ) | x| ? A.1 个 【答案】A B.2 个 C.3 个 D

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