TOP28福建省福州市2016届高三数学毕业班3月质量检查试题文.doc文档免费在线阅读

„„„„„„分连接，由知为的外接圆直径，，故的外接圆半径为„„„„„„„„„„„„„„分本小题满分分选修坐标系与参数方程解Ⅰ因为，所以，所以，即为圆的普通方程„„„„„„„„„„„„„分所以所求的圆的参数方程为为参数„„„„„„„„„分Ⅱ由Ⅰ可得，„„„„„„„„„„分当时，即点的直角坐标为，时，„„„„„„„„„„„分取到最大值为„„„„„„„„„„„„„分本小题满分分选修„„„„„„„分由得平面点到平面的距离为„„„„„„„„„„分即点到平面的距离为„„„„„„„„„„„本小题满分分解，，，又正方形，，„„„„„„„„„„分的面积等于„„„„„„„„„„„„分，当时，的周长取得最大值为„„„„„„„„„„„„„分„„„„„„„„„„„„„„„分解由得，由正弦定理得所以的周长„„„„„„分法二由及余弦定理，得„„„„„„„„„„„„„„分整理，得，„„„„„„„„„分，，„„„„„„„„„„„题本大题共小题，共分解答应写出文字说明证明过程或演算步骤本小题满分分解法由及正弦定理，得„„„„„„„中有且只有个答案是正确的把正确选项涂在答题卡的相应位置上第Ⅱ卷非选择题共分二填空题本大题共小题，每小题分，共分，把答案填在答题卡的相应位置上④三解答对满足条件的所有，都成立，求实数的取值范围年福州市普通高中毕业班质量检查数学文科答案第Ⅰ卷选择题共分选择题本大题共小题，每小题分，共分在每小题所给的四个答案是圆上动点，试求的最大值，并求出此时点的直角坐标本小题满分分选修不等式选讲已知，都是实数，，若，求实数的取值范围若分选修坐标系与参数方程在极坐标系中，圆的极坐标方程为若以极点为原点，极轴所在直线为轴建立平面直角坐标系Ⅰ求圆的参数方程Ⅱ在直角坐标系中，点，以端点为圆心的圆交直线于两点，交圆于，两点，过点作垂直于的直线，交直线于点Ⅰ求证，四点共圆Ⅱ若，，求外接圆的半径本小题满分三题中任选题做答，如果多做，则按所做的第题计分作答时，先用铅笔在答题卡上把所选题目对应的题号涂黑，并将所选题号填入括号中本小题满分分选修几何证明讲如图，已知为圆的条直径，Ⅰ当时，求函数在，处的切线方程Ⅱ当时，若函数有两个极值点，，不等式恒成立，求实数的取值范围本题有方程Ⅱ过点，作斜率为的直线，交椭圆于两点，为中点，请说明存在实数，使得以为直径的圆经过点，不要求求出实数本小题满分分已知函数面求证平面求点到面的距离本小题满分分已知椭圆经过点离心率为，且分别为椭圆的左右焦点Ⅰ求椭圆的机抽取个不超过的数据记为，从班的样本数据中随机抽取个不超过的数据记为，求的概率本小题满分分如图，平行四边形中，，，，正方形，且面机抽取个不超过的数据记为，从班的样本数据中随机抽取个不超过的数据记为，求的概率本小题满分分如图，平行四边形中，，，，正方形，且面面求证平面求点到面的距离本小题满分分已知椭圆经过点离心率为，且分别为椭圆的左右焦点Ⅰ求椭圆的方程Ⅱ过点，作斜率为的直线，交椭圆于两点，为中点，请说明存在实数，使得以为直径的圆经过点，不要求求出实数本小题满分分已知函数Ⅰ当时，求函数在，处的切线方程Ⅱ当时，若函数有两个极值点，，不等式恒成立，求实数的取值范围本题有三题中任选题做答，如果多做，则按所做的第题计分作答时，先用铅笔在答题卡上把所选题目对应的题号涂黑，并将所选题号填入括号中本小题满分分选修几何证明讲如图，已知为圆的条直径，以端点为圆心的圆交直线于两点，交圆于，两点，过点作垂直于的直线，交直线于点Ⅰ求证，四点共圆Ⅱ若，，求外接圆的半径本小题满分分选修坐标系与参数方程在极坐标系中，圆的极坐标方程为若以极点为原点，极轴所在直线为轴建立平面直角坐标系Ⅰ求圆的参数方程Ⅱ在直角坐标系中，点，是圆上动点，试求的最大值，并求出此时点的直角坐标本小题满分分选修不等式选讲已知，都是实数，，若，求实数的取值范围若对满足条件的所有，都成立，求实数的取值范围年福州市普通高中毕业班质量检查数学文科答案第Ⅰ卷选择题共分选择题本大题共小题，每小题分，共分在每小题所给的四个答案中有且只有个答案是正确的把正确选项涂在答题卡的相应位置上第Ⅱ卷非选择题共分二填空题本大题共小题，每小题分，共分，把答案填在答题卡的相应位置上④三解答题本大题共小题，共分解答应写出文字说明证明过程或演算步骤本小题满分分解法由及正弦定理，得„„„„„„„„„„„„„„„„分，，„„„„„„„„„„„„„„„„分法二由及余弦定理，得„„„„„„„„„„„„„„分整理，得，„„„„„„„„„„„„„„„分解由得，由正弦定理得所以的周长„„„„„„„„„„„„„分，当时，的周长取得最大值为„„„„„„„„„„„„„分本小题满分分解，，，又正方形，，„„„„„„„„„„分的面积等于„„„„„„„分由得平面点到平面的距离为„„„„„„„„„„分即点到平面的距离为„„„„„„„„„„„分本小题满分分解椭圆经过点离心率为，，解得椭圆的方程为„„„„„„„„„„„„„„„分证明设线段的中点，由题意可得直线的方程为，且联立，化为„„„„„„„„„„„„„分，由，可得，且„„„„„„„„„„„„„„„分，假设存在实数，使得为直径的圆过点，即，则，，，化为，设，则关于的方程存在正解，这样实数存在即存在实数，使得以为直径的圆过点„„„„„„„„„„„„„„分本小题满分分解Ⅰ当时，则，所以切线方程为，即为„„„„„„„„„„„„„„„分Ⅱ令，则当，时，，函数在，上单调递增，无极值点„„„„„„„分当且，时，由得，当变化时，与的变化情况如下表，单调递增极大值单调递减极小值单调递增当时，函数有两个极值点，，则，，„„„„„„„„„„„„„„„分由可得，令„„„„„„„„„„„„„„„分因为，所以，，即在，递减，即有，所以实数的取值范围为，„„„„„„„„„„„„„„„分本题有三题中任选题做答，如果多做，则按所做的第题计分作答时，先用铅笔在答题卡上把所选题目对应的题号涂黑，并将所选题号填入括号中本小题满分分选修几何证明讲证明为圆的条直径，，四点共圆„„„„„„„„„„„„„„分解与圆相切于点，由切割线定理得，即，解得，所以，，又，则，得，„„„„„„„„„„„„„„分连接，由知为的外接圆直径，，故的外接圆半径为„„„„„„„„„„„„„„分本小题满分分选修坐标系与参数方程解Ⅰ因为，所以，所以，即为圆的普通方程„„„„„„„„„„„„„分所以所求的圆的参数方程为为参数„„„„„„„„„分Ⅱ由Ⅰ可得，„„„„„„„„„„分当时，即点的直角坐标为，时，„„„„„„„„„„„分取到最大值为„„„„„„„„„„„„„分本小题满分分选修不等式选讲解，由得或，解得或故所求实数的取值范围为„„分由且得，又，„„„„„„„„„„分，的解集为，的解集为所求实数的取值范围为，„„分年福州市普通高中毕业班质量检查数学文科试卷完卷时间分钟满分分第Ⅰ卷选择题共分选择题本大题共小题，每小题分，共分在每小题所给的四个答案中有且只有个答案是正确的把正确选项涂在答题卡的相应位置上设集合，集合，则已知复数满足，若的虚部为，则已知命题，，则为，，，，若，且则的值为已知，，，④在如右图所示的程序框图中，如果输入，而输出，则在空白处可填入④④已知数列是等差数列，且，，则公差在年全国青运会火炬传递活动中，有编号为的名火炬手若从中任选人，则选出的火炬手的编号相连的概率为几何体的三视图如右图所示，则该几何体的表面积是已知抛物线与直线相交于，两点，为的焦点，若，则已知函数，若关于的方程有两个不同的实根，则实数的取值范围是，，已知双曲线，的左右焦点分别为过的直线与双曲线的右支相交于，两点