【全国百强校】上海市复旦附中2018-2019学年高二上学期期中考试数学试题
【全国百强校】上海市复旦附中2018-2019学年高
二上学期期中考试数学试题
学校_________ 班级__________ 姓名__________ 学号__________
一、填空题
1. 直线的倾斜角是____________.
2. 若矩阵，，则__________．
3. 行列式的元素的代数余子式的值为，则______．
4. 已知是增广矩阵为的二元一次方程组的解，则
________
5. 直线的一个单位方向向量是________.
6. 已知直线，若，则
.
7. 已知点在直线上，且点到、两点的距离相等，则点的坐标是__________.
8. 若，则实数t的取值范围是_____________.
9. 已知，则“”是“两直线与
平行”的___________条件（填“充分非必要”、“必要非充分”、“充要”、“既不充分也不必要”）.
10. 过点且与直线的夹角为的直线的一般式方程是____________.
11. 已知实数满足：，且
其中，则以向量为法向量的直线的倾斜角的取值范围是__________.
12. 如图，边长为4的正方形中，半径为1的动圆Q的圆心Q在边CD和DA上移动（包含端点A,C,D），P是圆Q上及其内部的动点，设，
则的取值范围是
_____________.
二、单选题
13. 函数的图像如图所示，在区间上可找到个不同的数
使得，则的取值范围为（）
，
A．B．
C．D．
14. 给出下列命题:
①非零向量满足，则和的夹角为30°；
②将函数的图像按向量平移，得到函数的图像；
③在三角形ABC中，若，则三角形ABC为等腰三角形；其中正确命题的个数是（）
A．0 B．1 C．2 D．3
15. 在平面直角坐标系中,经过原点的直线将
分成左、右两部分,记左、右两部分的面积分别为 ,则取得最小值时,直线的斜率（）
A．等于1 B．等于
D．不存在
C．等于
16. 如图所示，已知，对任何，点按照如下方式生成：，且按逆时针排列，记
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(完整版)历年上海复旦附中自招英语试题及答案解析
1. You should pay attention to the way _____ you stand and sit. A. of B. that C. which D. how 【正确选项】B 【考查内容】定语从句 【试题分析】本题考察the way 后接定语从句的用法。the way 后接定语从句有三种形式： 1.不用引导词； 2.用that 做引导词； 3.用in which 做引导词。本题的考察点是第2 种。同学们根据汉语思维可能误选D。总而言之，同学们对这三种形式一定要牢记！ 2. Lack of eye contact can _____ nervousness. A. signal B. mark C. sigh D. design 【正确选项】A 【考查内容】词语辨析 【试题分析】本题考察高中英语词汇的辨析。根据句子意思：缺少眼神交流可以说明一个人很紧张。A 选项signal 有“表示；表明；预示”的意思，符合题意。B 选项mark 是“做记号，做标记”的意思；C 选项sigh 是“叹气”的意思，单词拼写与signal 类似，同学们可能误选。D 选项design 是“设计”的意思。总而言之，只有A 选项符合题意！ 3. Miss Yang is _____ a good shop assistant because she greets every customer cheerfully. A. looked upon B. regarded C. viewed D. considered 【正确选项】D 【考查内容】词语辨析 【试题分析】本题考察高中英语词汇及词组的辨析。本题难度较大，根据句意：杨小姐被认为是一名优秀的商店售货员因为她会愉快地与每一位顾客打招呼。题目的四个选项都有“被视为，被看成是”的意思，所以本题的难点在于这些词语的搭配的辨析！A, B, C 三个选项的错误之处在于应在单词后加上as 才正确。例如：Miss Yang is looked upon/regarded/viewed as a good shop assistant because she greets every customer cheerfully. 本题只有considered 才可以直接用在题干中。总而言之，同学们务必重视词语的搭配！ 4. Skimming is an important way of understanding a text faster and more _____. A. efficiently B. effectively C. sufficiently D. conveniently 【正确选项】A 【考查内容】词语辨析 【试题分析】本题考察高中英语词汇的辨析。本题选项的四个单词非常容易弄混淆。单词之间的拼写，后缀都有类似的地方。A 选项是“有效率地”的意思；B 选项是“有效果地， 有影响地”的意思；C 选项是“足够地，充足地”的意思；D 选项是“方便地”的意思。根据句意：浏览是一种更快更有效的理解文本的重要方法。总而言之，只有A 符合题意。