2017南方科技大学机试样题练习

2017机试样题练习特别提示机试环节依次包括数学、物理、英语、附加题四个单元，每单元用时分别为40、45、25、10分钟，共2小时。每一单元考完规定时间方能进入下一单元，进入下一单元后，不能再返回前一单元进行操作。机试题型包括单项选择题和不定项选择题两种。第一单元 数学一、单项选择题（每题所设选项中只有一个正确答案，多选、错选或不选均不得分；每题1.5分）1观察下列操作：第1次操作：第2次操作：第3次操作：如此反复操作，则第2017次操作后得到的数是（ ）A55B133C250D2602已知数列满足，则=（ ）ABCD3在中，分别是角的对边，若，则=A2B4CD4在平面直角坐标系中，点，则（ ）ABCD5在ABC中，若，则的最大值为()A B C D26的外接圆的圆心为，半径为1，且，则向量在向量方向上的投影为（ ）A B C D7已知、为非零向量，则下列命题中真命题的个数为（ ）若，则与方向相同；若，则与方向相反；若，则与有相等的模；若，则与方向相同A. 0B. 1C. 2D. 38对任意向量、，下列关系式中不恒成立的是()A BCD9如图，三棱锥A-BCD的顶点A、B、D为正方体的顶点，C为正方体棱的中点，现在正方体的网格纸上用粗线画出的它的三视图，正确的是正前方 A B C D10已知圆及其外一点.若圆上存在点满足，则实数的取值范围是（ ）A. B. C. D. 11双曲线的右焦点与抛物线的焦点重合，且在第一象限的交点为，垂直于轴，则双曲线的离心率是ABCD12.抛物线：的焦点为，准线为，是上一点，连接并延长交抛物线于点，若，则（ ）A3B4C5D6 13椭圆的左、右焦点分别是，点在椭圆上，的角平分线交轴于点，若，则该椭圆的离心率为( ) 提示：内角平分线定理为ABCD 14.有6名同学参加校园歌手总决赛，观众中有四名同学猜测结果，其中甲同学猜测：4号或5号选手得第一名；乙同学猜测：3号选手不可能得第一名；丙同学猜测：1,2,6号选手中的一位获得第一名；丁同学猜测：4,5,6号选手都不可能获得第一名比赛后发现没有并列名次，且甲、乙、丙、丁中只有1人猜对比赛结果，此人是( )A.甲、B.乙、C.丙、D.丁15在极坐标系中，曲线，则与交点的坐标为（ ）ABCD或16. 若复数满足，则的虚部为( ).（A）（B）（C）（D）17将离心率为的双曲线的实半轴长和虚半轴长同时增加个单位长度，得到离心率为的双曲线，则（ ） A对任意的， B当时，；当时，C对任意的， D当时，；当时，二、不定项选择题（每题所设选项中至少有一个正确答案，多选、少选、错选或不选均不得分；每题2分）1如图1，一个正四棱柱形的密闭容器底部镶嵌了同底的正四棱锥形实心装饰块，容器内盛有升水时，水面恰好经过正四棱锥的顶点如果将容器倒置，水面也恰好过点（图2）则下列四个命题正确的是A正四棱锥的高等于正四棱柱高的B将容器侧面水平放置时，水面也恰好过点C任意摆放该容器，当水面静止时，水面都恰好经过点D若往容器内再注入升水，则容器恰好能装满2. 已知函数，（其中）.对于不相等的实数，设，.则下列命题是真命题的是（ ）.（A）对于任意不相等的实数，都有；（B）对于任意的a及任意不相等的实数，都有；（C）对于任意的a，存在不相等的实数，使得；（D）对于任意的a，存在不相等的实数，使得.3. 已知，是两条不同直线，是两个不同平面，则下列命题正确的是（ ）. （A）若，垂直于同一平面，则与平行 （B）若，平行于同一平面，则与平行 （C）若，不平行，则在内不存在与平行的直线 （D）若，不平行，则与不可能垂直于同一平面第二单元 物理一、单项选择题（每题所设选项中只有一个正确答案，多选、错选或不选均不得分；每题1.5分）1. 质量和电荷量都相等的带电粒子和，以不同的速率经小孔垂直进入匀强磁场，运行的半圆轨迹如图附3-1-1中虚线所示，下列表述正确的是（ ）A.带负电，带正电 B.的速率小于的速率C.洛伦兹力对、做正功 D.的运行时间大于的运行时间2. 一水平抛出的小球落到一倾角为的斜面上时，其速度方向与斜面垂直，运动轨迹如图2-3-8中虚线所示.小球在竖直方向下落的距离与在水平方向通过的距离之比为（ ）A B. C.tan D.2tan二、不定项选择题（每题所设选项中至少有一个正确答案，多选、少选、错选或不选均不得分；每题2分）1. 如图所示，物体P静止于固定的斜面上，P的上表面水平.现把物体Q轻轻地叠放在P上，则（ ）A.P向下滑动B.P静止不动C.P所受的合外力增大D.P与斜面间的静摩擦力增大2. 如图，左侧的调压装置可视为理想变压器，负载电路中55 ，A、V为理想电流表和电压表，若原线圈接入如图（b）所示的正弦交变电压，电压表的示数为110V，下列表述正确的是（ ）A.电流表的示数为2AB.原、副线圈匝数比为12C.电压表的示数为电压的有效值D.原线圈中交变电压的频率为100Hz 第三单元 英语Reading Comprehension (4 passages,20 scores)Directions:There are 4 passages in this part. Each passage is followed by 4 questions or unfinished statements. For each of them there are four choices marked A, B, C and D. You should decide on the best choice and write the corresponding letter on the Answer Sheet.【Sample】Daniel Anderson, a famous psychologist, believes its important to distinguish televisions influences on children from those of the family. We tend to blame TV, he says, for problems it doesnt really cause, ignoring our own roles in shaping childrens minds.One traditional belief about television is that it reduces a childs ability to think and to understand the world. While watching TV, children do not merely absorb words and images (影像). Instead, they learn both clear and hidden meanings from what they see. Actually, children learn early the psychology of characters in TV shows. Furthermore, as many teachers agree, children understand far more when parents watch TV with them, explaining new words and ideas. Yet, most parents use an educational program as a chance to put their kids in front of the set and do something in another room. Another argument against television is that it replaces reading as a form of entertainment. But according to Anderson, the amount of time spent watching television is not related to reading ability. TV doesnt take the place of reading for most children; it takes the place of similar sorts of recreation, such as listening to the radio and playing sports. Things like parents educational background have a stronger influence on a childs reading. “A childs reading ability is best predicted by how much a parent reads.” Anderson says.Traditional wisdom also has it that heavy television-watching lowers IQ (智商) scores and affects school performance. But here, too, Anderson notes that no studies have proved it. In fact, research suggests that its the other way around. “If youre smart young, youll watch less TV when youre older,” Anderson says. Yet, people of lower IQ tend to be lifelong television viewers. For years researchers have attempted to show that television is dangerous to children. However, by showing that television increases none of the dangerous effects as believed before, Anderson suggests that television cannot be criticized without considering other influences. 1. An educational program is best watched by a child _. A. on his own B. with other kids C. with his parents D. with his teachers 2. Which of the following is most related to childrens reading ability?A. Radio-listening B. Television-watchingC. Parents reading list D. Parents educational background3. Anderson believed that _. A. the more a child watches TV, the smarter he is B. the younger a child is, the more he watches TV C. the smarter a child is, the less likely he gets addicted to TV D. the less a child watches TV, the better he performs at school 4. What is the main