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890461com:云南省重点中学高一数学寒假作业(3) Word版 含答案

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云南省 2013-2014 学年高一寒假作业(3)数学 Word 版含答案 第 I 卷(选择题) 请点击修改第 I 卷的文字说明 评卷人 得分 一、选择题(题型注释) 1.下列函数中,既是偶函数又在区间(0,+ ? )上单调递减的是 A. f ? x ? ? x 3 B. f ? x ? ? e ?x C. f ? x ? ? ln x D. f ? x ? ? ?x ? 1 2 2 2 2. 若直线 2ax ? by ? 2 ? 0.(a ? 0, b ? 0) 被圆 ( x ? 1) ? ( y ? 2) ? 4 截得的弦长为 4 ,则 1 1 ? 的最小值为( a b A.1 D.4 ) B.2 C.3 3.顶点在原点,始边与 x 轴正方向重合的角 ? ? ? A.第一象限 B.第二象限 19? 的终边在( 6 ). D.第四象限 C.第三象限 f ?x ? ? 4.函数 1 ? lg?1 ? x ? 1? x 的定义域是:( ) B.(1,+∞) D.(-∞,+∞) A.(-1,1)∪(1,+∞) C.(-∞,-1) 5.下列式子中成立的是( A. log0.4 4 ? log0.4 6 C. 3.5 0.3 ) B. 1.01 3.4 ? 1.013.5 ? 3.4 0.3 D. log7 6 ? log6 7 ) 6.函数 y ? loga ( x ?1)(a ? 1) 的大致图像是( 7.已知 f ( x ) 是定义在 (??, ??) 上的偶函数,且在 ? ??,0? 上是增函数,设 a ? f (log4 7) , b ? f (log 1 3) , c ? f (0.2?0.6 ) ,则 a, b, c 的大小关系是( 2 ) A. c ? a ? b B. c ? b ? a C. b ? c ? a D. a ? b ? c 8.已知 P(x,y)是直线 kx ? y ? 4 ? 0(k ? 0) 上一动点,PA,PB 是圆 C: x 2 ? y 2 ? 2 y ? 0 的两条切线,A、B 是切点,若四边形 PACB 的最小面积是 2,则 k 的值为( A.3 B. ) 21 2 C. 2 2 D.2 第 II 卷(非选择题) 请点击修改第 II 卷的文字说明 评卷人 得分 二、填空题(题型注释) 9.函数 的奇偶性为( )(填:奇函数,偶函数,非奇非偶函数) 10.已知 tan ? =2,求 sin ? ? 3 cos ? = sin ? ? cos ? ; 11.若幂函数 y ? (m2 ? m ? 1) xm 2 ? 2m?1 在 (0,??) 上是增函数,则 m =___________ 12.已知角 ? 的终边上一点的坐标为 _____________。 (sin 5? 5? , cos ) 6 6 ,则角 ? 的最小正值为 13.设 f ( x) ? ? ?lg x, x ? 0 x ?10 , x ? 0 ,则 f ( f (?2)) = . 14.如图所示,AB∥α ,CD∥α ,AC,BD 分别交 α 于 M,N 两点, =2,则 =________. AM MC BN ND 评卷人 得分 三、解答题(题型注释) 15.(本小题 12 分)已知函数 y ? 2 x ?1 , (1)判断函数在区间 (1, ??) 上的单调性; (2)求函数在区间是区间[2,6]上的最大值和最小值. 16.(本小题 12 分)设定义在 R 上的函数 f ? x ? ,满足当 x ? 0 时, f ? x ? ? 1 ,且对任意 x, y ? R ,有 f ? x ? y ? ? f ? x ? f ? y ? , f ?1? ? 2 2 (1)解不等式 f 3 x ? x ? 4 ? ? (2)解方程 ? ? f ? x ?? ? ? 2 1 f ? x ? 3? ? f ? 2 ? ? 1 2 17.(本小题满分 12 分)已知函数 f ( x) 是定义在 R 上的偶函数,已知当 x ? 0 时, f ( x) ? x2 ? 4 x ? 3 . (1)求函数 f ( x) 的解析式; (2)画出函数 f ( x) 的图象,并写出函数 f ( x) 的单调递增区间. 18.(本小题满分 10 分) (1) 计算: 3 (?4) 3 ? ( ) 0 ? 0.252 ? ( 4 1 2 1 ?1 2 ) ?4 ; (2)计算: log3 27 ? 2log510 ? log5 0.25 ? 71?log7 2 。 3 x 19.(本题 8 分)已知函数 f(x)= a , (1) 若 f(x)=2,求 f(3x); (2) y=f(x)的图象经过点(2,4),g(x)是 f(x)反函数,求 g(x)在[ 1 ,2 ]区间上的值域 2 20.(本题共 8 分)已知角 a 满足 (1)求 tan a 的值; sin ? ? cos ? ?2; 2sin ? ? cos ? 2 2 (2)求 sin ? ? 2cos ? ? sin ? cos ? 的值. 试卷答案 1.D 2.D 3.B 4.A 5.D 6.B 7.B 8.B 9.偶函数 10.- 5 3 11.-1 2? 12. 3 13. ?2 14.2 15. 16 17. (1)当 x >0 时,-x<0 ∴f(-x)=(-x) +4(-x)+3=x -4x+3 2 ∴f(-x)为 R 上的偶函数 ∴f(-x)= f(x)= x -4x+3 2 x -4x+3 x>0 2 ∴f(x)=﹛x +4x+3 x≤ 0 2 2 (2)f(x)单调增区间(-2,0),(2,+∞) 18. (1)原式= ?4 ? 1 ? 1 ? ( 2) 4 =-3;…………………

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