陕西省西安地区八校高三下学期联考（三）理科数学试题及答案.doc

陕西省西安地区八校联考2015届高三下学期联考（三）数学理试题（word版）题 本试卷分第I卷（选择题）和第卷（非选择题）两部分共150分，考试时间120分钟，注意事项： 1答题前，考生务必先将自己的姓名、准考证号填写在答题纸上，认真核对条形码上的姓名、准考证号，并将条形码粘贴在答题纸上的指定位置上 2选择题答案使用2B铅笔填涂，如需改动，用橡皮擦干净后，再选涂其它答案标号；非选择题答案用05毫米的黑色中性（签字）笔或碳素笔书写，字体工整，笔迹清楚 3请按照题号在各题的答题区域（黑色线框）内作答，超出答题区域书写的答案无效 4保持纸面清洁，不折叠，不破损 5若做选考题时，考生应按照题目要求作答，并用2B铅笔在答题纸上把所选题目对应的题号涂黑第I卷（选择题共60分）一、选择题：本大题共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设集合，则实数a的值为 A0 B1 C2 D42已知复数在夏平面上对应的点位于 A第一象限 B第二象限 C第三象限 D第四象限3已知数列的 A充分不必要条件 B必要不充分条件 C充要条件 D既不充分也不必要条件4对于任意向量a、b、c，下列命题中正确的是 5执行如图所示的程序框图，会输出一列数，则这个数列的第3项是 A870 B30 C6 D36设的展开式的各项系数之和为肘，二项式系数之和为N函数f（x）的图像如图所示，下列数值排序正确的是A4B6C8D107一几何体的三视图如图所示，若主视图和左视图都是等腰直角三角形，直角边长为1，则该几何体外接球的表面积为8已知实数的取值范围是9定义行列式运算的图象向左平移个单位，所得图像对应的函数为偶函数，则n的最小值为10已知两点A（0，2）、B（2，0），若点C在函数的图像上，则使得的面积为2的点C的个数为A4B3C2D111函数f(x)的图像如图所示，下列数值排序正确的是 12已知双曲线的右焦点为F，过F作双曲线C的一条渐近线的垂线，垂足为H，若线段FH的中点肘在双曲线C上，则双曲线C的离心率为第卷（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13已知数列的值为 。14若指数函数在其定义域内是减函数，则口的取值范围是_j15由1，4，5，x可组成没有重复数字的四位数，若所有这些四位数的各位数字之和为288，则x 的值为_16已知函数有解，则实数m的取值范围为_三、解答题：解答应写出文字说明，证明过程或演算步骤（本大题共6小题，共70分）17（本小题满分12分）ABC中，三个内角A，B，C的对边分别为a，b，c，若A，B，C成等差数列，且a，b，c也成等差数列，求证：ABC为等边三角形18（本小题满分12分）19（本小题满分12分）现有4人去旅游，旅游地点有A、B两个地方可以选择但4人都不知道去哪里玩，于是决定通过掷一枚质地均匀的骰子决定自己去哪里琨，掷出能被3整除的数时去A地，掷出其他的则去B地 （I）求这4个人中恰好有1个人去B地的概率； （）求这4个人中去A地的人数大于去B地的人数的概率； （）用X、Y分别表示这4个人中去A、B两地的人数，记求随机变量亭的分布列与数学期望20（本小题满分12分）设P为椭圆离心率为 （I）求椭圆的方程； （）符直线与椭圆交于A、B两点，若线段AB的中点C在直线上，D为坐标原点，求OAB面积S的最大值21（本小题满分12分）已知函数 （I）求函数f（x）的单调区间和极值； （）若的图像上存在P1、P2两点，其横坐标满足，且g（x）的图像在此两点处的切线互相垂直，求a的取值范围 请考生从第（22）、（23）、（24）三题中任选一题作答注意：只能做所选定的题目如果多做，则按所做的第一个题目计分，作答时请用2B铅笔在答题卡上将所选题号后的方框涂黑22（本小题满分10分）选修4-1:几何证明选讲如图，过圆O外一点P分别作圆D的切线PA和割线PBC，其中A为切点过点A作PC的平行线交圆O于点D，BD的延长线交直线PA于点Q （I）求证： （）若求PC的长23（本小题满分10分）选修4-4:坐标系与参数方程在直角坐标系xOy中，以O为极点，x轴正半轴为极轴建立极坐标系圆C和直线l的极坐标方程分别为 （I）求圆C和直线l的直角坐标方程； （）设圆C和直线l相交于点A和B，求以AB为直径的圆D的参数方程24（本小题满分10分）选修4-5:不等式选讲 已知函数 （I）当a=3时，求不等式f（x）4的解集； 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