福建省福安市第一中学2018-2019学年高一上学期期中考试数学含答案练习题

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这是一份福建省福安市第一中学2018-2019学年高一上学期期中考试数学含答案练习题，共10页。试卷主要包含了每小题选出答案后，填入答案卷中等内容，欢迎下载使用。
www.ks5u.com2018—2019学年福安一中第一学期期中考高一数学试卷(满分:150分; 时间:120分钟)注意事项：1.答卷前，考生务必将班级、姓名、座号填写清楚。2.每小题选出答案后，填入答案卷中。3.考试结束，考生只将答案卷交回，试卷自己保留。第I卷（选择题共60分）一、选择题：本小题共12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，. 则集合= A． B． C． D．2．函数的定义域是 A． B． C. D．3．下列各组函数中，表示同一函数的是 A. B. C. D．4．已知函数, 若则实数的值为 A． B． C．或 D．或或 5．下列函数是奇函数且在上单调递减的是 A. B. C. D. 6．函数的零点所在的区间为 A. B. C. D. 7．三个数的大小顺序是 A．a>c>b B．a>b>c C．b>a>c D．c>a>b8．函数与（）在同一坐标系中的图象可以是 9．已知定义在上的函数满足:，若, 则 A. B. C. D. 10．双“十一”要到了，某商品原价为元，商家在节前先连续次对该商品进行提价且每次提价.然后在双“十一”期间连续次对该商品进行降价且每次降价.则最后该商品的价格与原来的价格相比 A．相等 B．略有提高 C．略有降低 D．无法确定11．已知是定义域为的奇函数, 当时, ，那么不等式的解集是 A. B. C. D. 12．已知方程的两根为，且，则 A． B. C. D. 第II卷（非选择题共90分）二、填空题：本大题共4小题，每小题5分，共20分．把答案填在答题卡相应位置．13．幂函数的图像过点，则= ． 14．函数的单调递减区间为． 15．设实数满足：，则_________. 16．给出下列说法①函数为偶函数；②函数与是互为反函数； ③ 函数在上单调递减；④函数的值域为.其中所有正确的序号是___________ . 三、解答题：本大题共6小题，共70分．解答应写出文字说明、证明过程或演算步骤．17．（本小题满分10分）求下列各式的值：（Ⅰ）+；（Ⅱ） . 18．（本小题满分12分）已知全集，集合，集合. （Ⅰ）求；（Ⅱ）若集合，且, 求实数的取值范围. 19． (本小题满分12分)已知是定义在上的偶函数，当时，（Ⅰ）在给定的坐标系中画出函数在上的图像（不用列表）；（Ⅱ）直接写出当时的解析式；（Ⅲ）讨论直线与的图象的交点个数． 20．(本小题满分12分)已知定义在上的函数是奇函数.（Ⅰ）求实数的值；（Ⅱ）判断的单调性，并用定义证明. 21．(本小题满分12分)水葫芦原产于巴西，年作为观赏植物引入中国. 现在南方一些水域水葫芦已泛滥成灾严重影响航道安全和水生动物生长. 某科研团队在某水域放入一定量水葫芦进行研究，发现其蔓延速度越来越快，经过个月其覆盖面积为，经过个月其覆盖面积为. 现水葫芦覆盖面积（单位）与经过时间个月的关系有两个函数模型与可供选择.（参考数据：）（Ⅰ）试判断哪个函数模型更合适，并求出该模型的解析式；（Ⅱ）求原先投放的水葫芦的面积并求约经过几个月该水域中水葫芦面积是当初投放的倍. 22．（本小题满分12分）已知函数的图象过点.（Ⅰ）求实数的值;（Ⅱ）若不等式恒成立，求实数的取值范围；（Ⅲ）若函数，，是否存在实数使得的最小值为，若存在请求出的值；若不存在，请说明理由. 高一数学试卷答案与评分标准一.选择题：题号123456789101112答案CCDCDBABDCBA 13. 4 16. ①②③三、解答题：本大题共6小题，共70分．解答应写出文字说明、证明过程或演算步骤．17．（本小题满分10分）解：（Ⅰ）原式=+ ++1················································4分=+ ++1 =··························································5分（Ⅱ）原式= ························································8分 = =2-·························································9分 =··························································10分 18．（本小题满分12分）解：（Ⅰ） ······························································2分 ······························································4分··································································6分（Ⅱ） ·································································7分·································································11分·································································12分（有讨论C=的情况，过程正确，不扣分）19． (本小题满分12分)1（Ⅰ）解：函数图象如图： ··································································4分（Ⅱ）·····························································6分（Ⅲ）设交点个数为当时，；当时，；当时，；当时，；当时，； ……………………………………………………..12分综上所述， (没有写出分段形式答案不扣分).（I）是定义在上的奇函数即 ································································1分得 ································································2分由得······························································3分经检验：时，是定义在上的奇函数········································4分 ·································································5分解法二：···························································1分由得 ······························································3分, ·································································5分（II）在上单调递减. ··················································6分证明如下：由（I）知设是上的任意两个实数，且，···········································7分则 ·································································10分即在上单调递减. ····················································12分解法二：···························································6分在上单调递减. ·······················································7分设是上的任意两个实数，且，则·········································8分 ·································································10分即在上单调递减. ····················································12分21．(本小题满分12分)解：的增长速度越来越快，的增长速度越来越慢. ····························2分则有， ···························································4分解得，································································6分（Ⅱ）当时，·······················································7分该经过个月该水域中水葫芦面积是当初投放的倍. 有··································································9分·································································10分·································································11分答：原先投放的水葫芦的面积为8m2, 约经过17个月该水域中水葫芦面积是当初投放的倍. 12分 22．（本小题满分12分）（I）函数的图象过点 ··································································2分（II）由（I）知恒成立即恒成立令，则命题等价于而单调递增即 ·································································6分（III）， ·································································7分令当时，对称轴①当，即时，不符舍去. ························································9分②当时,即时符合题意. ·························································11分综上所述：························································12分