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dang56:2018高考数学(理)二轮复习闯关导练:基础模拟(一) Word版含解析-数学备课大师【全免费】

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基础模拟(一) 时间:120 分钟 满分:150 分 一、选择题:本题共 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 M={x∈R|0<x<2},N={x∈R|x>1},则 M∩(?RN)=( ) A.[1,2) B.(1,2) C.(0,1] D.[0,1) 2.(导学号:50604164)命题“若 ex+x≤1,则 x≤0”的否命题是( ) x x A.若 e +x≤1,则 x>0 B.若 e +x>1,则 x≤0 C.若 ex+x>1,则 x>0 D.若 ex+x≥1,则 x≥0 1 3.复数 z= 的虚部为( ) 1+2i 2 1 A.- B.-2 C. D.1 5 5 4.一组数据的平均数是 2,方差是 3,若将这组数据中的每一个数据都加上 10,得到 一组新数据,则所得新数据的平均数和方差分别是( ) A.12, 13 B.2, 13 C.2, 3 D.12,3 5.已知数列{an}的前 n 项和 Sn=An2,且 a4=7,则 an=( ) A.2n-1 B.2n+1 C.n+1 D.3n-2 ?x+2y≤6, 6.(导学号:50604165)已知实数 x,y 满足?x-y≤3, ?x≥1, 则 x2+y2 的最大值为( ) A. 5 B.17 C. 17 D.5 7.在空间中,有如下四个命题: ①平行于同一个平面的两条直线是平行直线; ②垂直于同一条直线的两个平面是平行平面; ③若平面 α 内有不共线的三个点到平面 β 距离相等,则 α∥β; ④过平面 α 的一条斜线有且只有一个平面与平面 α 垂直. 其中正确的命题是( ) A.①④ B.②③ C.①③ D.②④ 8.(导学号:50604166)《九章算术》中,将底面为长方形且有一条侧棱与底面垂直的 四棱锥称之为阳马,将四个面都为直角三角形的四面体称之为鳖臑.下图(左)就是阳马与鳖 臑的组合体,如果图中鳖臑的三视图如下图(右)所示(小正方形的边长为 1),则该图中阳马 的体积为( ) A.4 B.8 C.9 D.12 x2 y2 9.已知椭圆 2+ 2=1(a>b>0)的右焦点为 F,过点 F 的直线与椭圆交于点 A,B,若 AB a b 1 中点为(1,- ),且直线 AB 的倾斜角为 45° ,则椭圆方程为( ) 2 “备课大师”全科【9 门】 :免注册,不收费!http://www.eywedu.cn/ x2 y2 x2 y2 2x2 4y2 x2 2y2 A. + =1 B. + =1 C. + =1 D. + =1 9 5 9 4 9 9 9 9 1 2 ?5 10.(导学号:50604167)(x -2)? ?x-1? 的展开式的常数项是( A.8 B.-8 C.12 D.-12 ) π 11.(导学号:50604168)设函数 f(x)= 3sin(ωx+φ)+cos(ωx+φ)(ω>0,|φ|< )的最小正 2 周期为 2π,且其图象关于 y 轴对称,则( ) π π 3π A.f(x)在(0, )上单调递增 B.f(x)在( , )上单调递减 2 4 2 π π 3π C.f(x)在(0, )上单调递减 D.f(x)在( , )上单调递增 2 4 2 1 12.函数 y=- 的图象向右平移 1 个单位之后得到的函数图象与函数 y=2sinπx(- x 2≤x≤4)的图象所有交点的橫坐标之和等于( ) A.2 B.4 C.6 D.8 二、填空题:本题共 4 小题,每小题 5 分,共 20 分. 第 13 题图 13.运行如图所示程序框图,若输入 n=56,则输出结果为________. 14.(导学号:50604169)已知平面向量 a=(1,-2)与 b 的夹角为 θ,且|b|= 5,|a-b| = 2,则 cos θ=________. 15.已知函数 f(x)是定义在 R 上的偶函数,且当 x≥0 时,f(x)=x3+ax2+1,y=f(x)的 图象在点(-1,f(-1))处的切线过点(1,-7),则 a=________. 1 16.(导学号:50604170)已知公比为 q 的等比数列{an}的前 n 项和为 Sn,a1= , 数列 2 12k {anSn+a2 n}也是公比为 q 的等比数列,记数列{4an+1}的前 n 项和为 Tn,若不等式 4+n-Tn ≥2n-7 对任意的 n∈N*恒成立,则实数 k 的取值范围是________. 三、解答题:共 70 分.解答应写出文字说明、证明过程或演算步骤.第 17~21 题为必 考题,每个试题考生都必须作答.第 22、23 题为选考题,考生根据要求作答. (一)必考题:共 60 分. 17.(导学号:50604171)(12 分) 3 在△ABC 中,角 A,B,C 的对边长分别为 a,b,c,已知 a=2,c=5,cosB= . 5 (Ⅰ)求 b 的值; (Ⅱ)求 sinC 的值. “备课大师”全科【9 门】 :免注册,不收费!http://www.eywedu.cn/ 18.(导学号:50604172)(12 分) 东海学校从参加 2016 年迎新百科知识竞赛的同学中, 选取 60 名同学, 将他们的成绩(百 分制)(均为整数)分成 6 组后,得到部分频率分布直方图(如图),观察图形中的信息,回答下 列问题. (Ⅰ)求分数在[70,80)内的频率,并补全这个频率分布直方图; (Ⅱ)若从 60 名学生中随机抽取 2 人, 抽到的学生成绩在[40,70)记 0 分, 在[70,100]记 1 分,用 Χ 表示抽取结束后的总记分,求 Χ 的分布列和数学期望. 19.(导学号:50604173)(12 分) 如图,在三棱柱 ABC-A1B1C1 中,侧面 A1ACC1⊥底面 ABC,侧棱 AA1 与底面所成角为 60° ,AA1=2AC=4,AB=BC. → → → (

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