伤城文章网 >  > 2011-2012学年山东冠县武训高中高二下第二次模块考试文科数学试卷(带解析)

2011-2012学年山东冠县武训高中高二下第二次模块考试文科数学试卷(带解析)


2011-2012 学年山东冠县武训高中高二下第二次模块考试文科数学试 卷(带解析) 一、选择题 1.“所有金属都能导电,铁是金属,所以铁能导电”这种推理属于 A.演绎推理 【答案】A 【解析】解:因为“所有金属都能导电,铁是金属,所以铁能导电”这种推理属于演绎推理, 从一般到特殊点 思想,选 A 2.已知命题 A. B. C. D. 【答案】B 【解析】解:因为命题 3.复数 A.-1+2 【答案】D 【解析】解:因为复数 4.集合 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 【答案】B 【解析】解:因为 ,那么“ ”是“ ” 必要不充分条件,选 B ,则 ,那么“ ” 是“ ” ,则虚部为 2,选 D ( 是虚数单位),则复数 B.-1 C.2 D.2 ,那么 是 虚部是 ,选 B ,那么 是 B.类比推理 C.合情推理 D.归纳推理 5.如图是 2012 年某大学自主招生面试环节中,七位评委为某考生打出的分数的茎叶图,去掉 一个最高分和一个最低分后,所剩数据的平均数和方差分别是 A.84,4.84 【答案】C B.84,1.6 C.85,1.6 D.85,4 【解析】解:由已知的茎叶图可得七位评委为某参赛选手打出的分数为:79,84,84,86, 84,87,93, 去掉一个最高分 93 和一个最低分 79 后, 所剩数据的平均数 . x =(84+84+86+84+87) 5 =85 所以方差 S = 故答案为 C 6.变量 与 相对应的一组数据为(10, 1), (11.3, 2), (11.8, 3), (12.5, 4), (13, 5);变量 与 相对 应的一组数据为(10,5), (11.3, 4), (11.8, 3), (12.5, 2), (13, 1), 表示变量 与 之间的线性相关系 数, 表示变量 与 之间的线性相关系数,则 A. 【答案】C 【解析】解:∵变量 X 与 Y 相对应的一组数据为(10,1),(11.3,2), (11.8,3),(12.5,4),(13,5), . X =(10+11.3+11.8+12.5+13) 5 =11.72 . Y =(1+2+3+4+5) 5 =3 ∴这组数据的相关系数是 r=7.2 19.172 =0.3755, 变量 U 与 V 相对应的一组数据为 (10,5),(11.3,4), (11.8,3),(12.5,2),(13,1) . U =(5+4+3+2+1) 5 =3, ∴这组数据的相关系数是-0.3755, ∴第一组数据的相关系数大于零,第二组数据的相关系数小于零, 故选 C. 7.已知某生产厂家的年利润 (单位:万元)与年产量 (单位:万件)的函数关系式为 ,则使该生产厂家获取最大年利润的年产量为 A.13 万件 B. 11 万件 C. 9 万件 D.7 万件 B. C. D. 2 [(84-85) +(84-85) +(86-85) +(84-85) +(87-85) ]=1.6 2 2 2 2 2 【答案】C 【解析】解:令导数 y′=-x +81>0,解得 0<x<9; 令导数 y′=-x +81<0,解得 x>9, 所以函数 y=x +81x-234 在区间(0,9)上是增函数, 3 2 2 在区间(9,+∞)上是减函数, 所以在 x=9 处取极大值,也是最大值,故选 C. 8.圆形纸片的圆心为 ,点 是圆内异于 点的一定点,点 是周围上一点,把纸片折叠使 与点 重合,然后展平纸片,折痕与 交于 点,当点 运动时点 的轨迹是 A.圆 B.椭圆 C.双曲线 D.抛物线 【答案】B 【解析】解:如图所示:由题意可得,CD 是线段 AQ 的中垂线, ∴PA=PQ,∴PQ+PO=PA+PO=半径 R, 即点 P 到两个定点 O、Q 的距离之和等于定长 R (R>OQ ), 由椭圆的定义可得,点 P 的轨迹为椭圆, 故选 B 9.设三次函数 的导函数为 ,函数 的图象的一部分如图所示,则 A. B. C. D. 极大值为 极大值为 极大值为 极大值为 ,极小值为 ,极小值为 ,极小值为 ,极小值为 【答案】D 【解析】解:观察图象知,x<-3 时,y=x?f′(x)>0, ∴f′(x)<0. -3<x<0 时,y=x?f′(x)<0, ∴f′(x)>0. 由此知极小值为 f(-3). 0<x<3 时,y=x?f′(x)>0, ∴f′(x)>0. x>3 时,y=x?f′(x)<0, ∴f′(x)<0. 由此知极大值为 f(3). 故选 D. 10.若点 和点 F(-2,0)分别是双曲线 任意一点,则 A. 【答案】B 【解析】解:因为 F(-2,0)是已知双曲线的左焦点, 所以 a +1=4,即 a =3,所以双曲线方程为 设点 P(x0,y0), 则有 (x0≥ ),因为 FP =(x0+2,y0), OP =(x0,y0), x02 +2x0-1, 2 2 的中心和左焦点,点 为双曲线右支上 的取值范围是 B. C. D. , 所以 OP ? FP =x0(x0+2)+y02= x0(x0+2)+ x02 3 -1= 此二次函数对应的抛物线的对称轴为 x0=因为 x0≥ 所以当 x0= , 时, OP ? FP 取得最小值 × ,+∞), , -1= , 故 OP ? FP 的取值范围是[ 二、填空题 1.某校高三有 1000 个学生,高二有 1200 个学生,高一有 1500 个学生,现按年级分层抽样, 调查学生的视力情况,若高一抽取 75 人,则全校共抽取 人. 【答案】.185 【解析】解:∵高三有 1000 个学生,高二有 1200 个学生,高一有 1500 个学生. ∴本校共有学生 1000+1200+1500=3700, ∵按年级分层抽,高一抽取了 75 人, ∴每个个体被抽到的概率是 75: 1500 =

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