伤城文章网 >  > 2017-2018学年四川省广安市高二上学期期末数学试卷含解析(文科)

2017-2018学年四川省广安市高二上学期期末数学试卷含解析(文科)


2017-2018 学年四川省广安市高二上学期期末数学试卷(文科) 一、选择题:本大题共 12 个小题,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.(5 分)直线 3x﹣ y﹣1=0 的倾斜角是( ) A. B. C. D. 2.(5 分)重庆市 2013 年各月的平均气温(℃)数据的茎叶图如,则这组数据的中位数是 () A.19 B.20 C.21.5 D.23 3.(5 分)圆(x+1)2+y2=2 的圆心到直线 y=x+3 的距离为( ) A.1 B.2 C. D.2 4.(5 分)某中学有高中生 3500 人,初中生 1500 人,为了解学生的学习情况,用分层抽样 的方法从该校学生中抽取一个容量为 n 的样本,已知从高中生中抽取 70 人,则 n 为( ) A.100 B.150 C.200 D.250 5.(5 分)如图的正方体 ABCD﹣A1B1C1D1 中,异面直线 A1B 与 B1C 所成的角是( ) A.30° B.45° C.60° D.90° 6.(5 分)原命题:“设 a、b、c∈R,若 a>b,则 ac2>bc2”,以及它的逆命题、否命题、逆 否命题中,真命题共有( ) A.0 个 B.1 个 C.2 个 D.4 个 7.(5 分)四进制数 123(4)化为十进制数为( ) A.30 B.27 C.23 第 1 页(共 13 页) D.18 8.(5 分)已知 5 件产品中有 2 件次品,其余为合格品.现从这 5 件产品中任取 2 件,恰有 一件次品的概率为( ) A.0.4 B.0.6 C.0.8 D.1 9.(5 分)执行如图的程序,如果输出的结果是 4,则输入的只可能是( ) A.2 B.﹣4 C.2 或﹣4 D.±2 或﹣4 10.(5 分)设点 A(﹣2,3),B(3,2),若直线 ax+y+2=0 与线段 AB 没有交点,则 a 的 取值范围是( ) A. B. C. D. 11.(5 分)若 l,m 是两条不同的直线,m 垂直于平面 α,则“l⊥m”是“l∥α”的( ) A.充分而不必要条件 B.必要而不充分条件 C.充分必要条件 D.既不充分也不必要条件 12.(5 分)已知 A,B 为双曲线 E 的左,右顶点,点 M 在 E 上,△ABM 为等腰三角形,顶 角为 120°,则 E 的离心率为( ) A. B.2 C. D. 二、填空题(每题 5 分,满分 20 分,将答案填在答题纸上) 13.(5 分)抛物线 y2=﹣8x 的焦点坐标是 . 14.(5 分)过点(1,2)且与直线 2x﹣y﹣1=0 平行的直线方程为 . 15.(5 分)在长方体 ABCD﹣A1B1C1D1 中,AB=3,AD=2,AA1=1,三棱椎 B1﹣A1BC 的 第 2 页(共 13 页) 体积为 . 16.(5 分)在区间[0,5]上随机地选择一个数 p,则方程 x2+2px+3p﹣2=0 有两个负根的概 率为 . 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.(10 分)设 p:实数 x 满足 x2﹣4ax+3a2<0;q:实数 x 满足|x﹣3|<1. (1)若¬q 为假,求实数 x 的取值范围; (2)若 a>0 且 q 是 p 的充分不必要条件,求实数 a 的取值范围. 18.(12 分)某企业为了解下属某部门对本企业职工的服务情况,随机访问 50 名职工,根 据这 50 名职工对该部门的评分,绘制频率分布直方图(如图所示),其中样本数据分组 区间为[40,50],[50,60],…,[80,90],[90,100] (1)求频率分布图中 a 的值; (2)估计该企业的职工对该部门评分不低于 80 的概率; (3)从评分在[40,60]的受访职工中,随机抽取 2 人,求此 2 人评分都在[40,50]的概 率. 19.(12 分)已知,圆 C:x2+y2﹣8y+12=0,直线 l:ax+y+2a=0. (1)当 a 为何值时,直线 l 与圆 C 相切; (2)当直线 l 与圆 C 相交于 A、B 两点,且 AB=2 时,求直线 l 的方程. 20.(12 分)下表是高三某位文科生连续 5 次月考的历史、政治的成绩,结果统计如下: 月份 9 10 11 12 1 历史(x 分) 79 81 83 85 87 第 3 页(共 13 页) 政治(y 分) 77 79 79 82 83 (1)求该生 5 次月考历史成绩的平均分和政治成绩的方差 (2)一般来说,学生的历史成绩与政治成绩有较强的线性相关,根据上表提供的数据, 求两个变量 x、y 的线性回归方程 = x+ (附: = = , =y﹣ x) 21.(12 分)如图,在三棱椎 P﹣ABC 中,D,E,F 分别为棱 PC,AC,AB 的中点,已知 PA⊥AC,PA=6,BC=8,DF=5,求证: (1)直线 PA∥平面 DEF; (2)平面 BDE⊥平面 ABC. 22.(12 分)已知椭圆 的离心率为 ,短轴长为 . (1)求椭圆 C 的方程; (2)设 P(4,0),A,B 是椭圆 C 上关于 x 轴对称的任意两个不同的点,连接 PB 交椭 圆 C 于另一点 E,证明直线 AE 与 x 轴相交于定点 Q; (3)在(2)的条件下,过点 Q 的直线与椭圆 C 交于 M,N 两点,求 的取值范围. 第 4 页(共 13 页) 2017-2018 学年四川省广安市高二上学期期末数学试卷 (文科) 参考答案与试题解析 一、选择题:本大题共 12 个小题,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

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