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四川省雅安市天全中学2017-2018学年高一上学期期中考试数学试题 Word版含答案

天全中学 2017-2018 学年高一上学期半期测试 数 学 试 卷 一、选择题(每小题 5 分,共 60 分,每小题有且只有一个正确答案)最新试卷十年寒窗苦,踏上高考路,心态放平和, 信心要十足,面对考试卷,下笔如有神,短信送祝福,愿你能高中,马到功自成,金榜定题名。 1.已知全集 U={1,2,3,4,5,6,7},A={2,4,6},B={1,3,5,7},则 A∩(?UB)等 于( ) B.{1,3,5} C.{2,4,5} D.{2,5} A.{2,4,6} 2.已知集合 A.0 或 3.函数 f(x)= ,B={1,m},A∪B=A,则 m=( B.0 或 3 C.1 或 ) ) D.1 或 3 1 +lg(1+x)的定义域是( 1? x A. (﹣∞,﹣1)B. (1,+∞)C. (﹣1,1)∪(1,+∞)D. (﹣∞,+∞) 4、已知 x ? x A. 7 5、 log 2 3 ? log 2 A 4 ?1 ? 3 ,则 x 2 ? x ?2 等于( B. 9 ) C. 11 D. 13 1 1 ? log 5 - lg100 = ( ) 3 25 B 1 ) B. = ) C. = D. ( ) =n m 7 7 C -1 D -4 6.下列各式成立的是( A. = ( x ? y) 4 3 7.设 a=log35,b=log34,c=log22,则( A.a>b>c B.c>a>b C.b>a>c D.b>c>a 8.函数 f(x)= ax +bx+ +5,满足 f(﹣3)=2,则 f(3)的值为( A.﹣2 9.函数 B.8 的图象大致形状是( C.7 ) 3 ) D.2 A. B. C. D. 10.已知函数 是 R 上的增函数,则 a 的取值范围是 ( ) B.﹣3≤a≤﹣2 C.a≤ ﹣2 D.a<0 A.﹣3≤a<0 11.若 f(x)是奇函数,且在(0,+∞)上是增函数,又 f(﹣3)=0,则(x﹣1)f(x)< 0 的解是( ) B. (﹣3,0)∪(0,3) A. (﹣3,0)∪(1,+∞) C. (﹣∞,﹣3)∪(3,+∞) D. (﹣3,0)∪(1,3) 12、已知偶函数 f(x)在区间上的单调性,并证明; (2)求函数 21. (本题满分 12 分)已知函数 的最大值和最小值. f ( x) ? loga ( x ? 1) ? loga (1 ? x), a ? 0 且 a ? 1 . (1)求 f ( x ) 的定义域; (2)判断 f ( x ) 的奇偶性并予以证明; (3)若 a ? 1 时,求使 f ( x) ? 0 的 x 的解集. 2 22、 (本题满分 12 分) 已知二次函数 f ( x) ? ax ? bx(a ? 0) , 并且满足 f (1 ? x) ? f (1 ? x) , 且方程 f ( x) ? x 有等根。 (1)求 f ( x) 的解析式; (2)若对任意的 x ? [ ?2,1] ,不等式 f ( x) ? m ? 3 2 x 恒成立,求 m 的取值范围。. 2 高一半期考试数学参考答案 1A2B3C4A5D6C7A8B9B10B11D12A 13.26 14.(1,2) 15.(0,4/5)U (1,+无穷) 16. -2 17.CR(A∩B)= [3,7) CR(A∪B)=x《2 或 x》10 18.41/72 19.5/4 根号 10 或 3/4 20.(1) 减函数 (2)最大值-2 21.解析 最小值-4 所以-1<x<1,所以 f(x )的定义域为(-1,1). ?x+1>0, ? (1)因为? ?1-x>0, ? (2)f(x)为奇函数.因为 f(x)定义域为(-1,1),且 f(-x)=loga(-x+1)-loga(1+x)=- f(x),所以 f(x)为奇函数. x+1 (3 )因为当 a>1 时,f(x)在(-1,1)上单调递增,所以 f(x)>0? >1,解得 0<x<1. 1-x 所 以使 f(x)>0 的 x 的取值范围是(0,1). 22. f ( x) ? ? 1 2 x ?x 2 m》2

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