南方科技大学机试样题练习.pdf

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：2第 2 次操作：135313333335553 250C250D2603第 3 次操作：53如此反复操作，则第 2017 次操作后得到的数是（）A55B1332已知数列an满足a11，an an1 2n，则S201=（）A20100B20200C20199D200993在ABC中，a,b,c分别是角A,B,C的对边，若acosB 3,bcos A 1，则c=A2B4C12D3yA A4在平面直角坐标系中，点A(3,6),B(0,0),C(5,0)，则BAC（）7CD3124C2A B5在ABC 中，若3cos5cos2 4，则tanC的最大值为()22A6BB BC C342ABCD2 2434xuuu ruuu ruuu ruuu ruuu r6ABC的外接圆的圆心为O，半径为 1，2AO AB AC，且|OA|AB|，则向量AC在向量uu u rCB方向上的投影为（）1133 B C D22227已知a a、b b为非零向量，则下列命题中真命题的个数为（）A若若若若Aa a b b a ab b，则a a与b b方向相同；a a b b a ab b，则a a与b b方向相反；a a b b a ab b，则a a与b b有相等的模；a a b b a ab b，则a a与b b方向相同B.12BOCA.0AC.2D.38对任意向量a a、b b，下列关系式中不恒成立的是()a ab b a a|b b2Ba a b b a a|b bD(a ab b)(a ab b)a a2（a ab b）|a ab b|Cb b29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AB10已知圆C C:(x x a a)2 2BCD正前方D(y y a a)2 2 2 2a a2 2(a a 0)0)及其外一点A(0,2).若圆C上存在点T满足CAT 4AC，则实数a的取值范围是（）A.,1B.3 3 1,1)1,1)C.3 3 1,11,1D.3 3 1,1,)x2y22y 4px(p 0)的焦点重合，且在第一象限的交点为111双曲线的右焦点与抛物线F224abM，MF垂直于x轴，则双曲线的离心率是A2 2 22B2 2C2 1D2 212.抛物线C：y 8x的焦点为F，准线为l，P是l上一点，连接PF并延长交抛物线C于点Q，若|PF|A34|PQ|，则|QF|（）5B4C5D6x2y213 椭圆221(a b 0)的左、右焦点分别是F1,F2，点P在椭圆上，PF1F2的角平分线PMab交轴于点M，若2|PM|2|PF1|PF2|，则该椭圆的离心率为()提示：内角平分线定理为|PF1|F1M|PF2|F2M|CA22B3224D3414.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C1:2sin,A（3，）C2:2 3cos，则C1与C2交点的坐标为（）C（0，0）D或（0，0）（3，）3B（3，）6316.若复数z满足(34i)z|43i|，则z的虚部为().（A）4（B）45（C）4（D）4517将离心率为e1的双曲线C1的实半轴长a和虚半轴长b(a b)同时增加m(m 0)个单位长度，得到离心率为e2的双曲线C2，则（）A对任意的a,b，e1 e2B当a b时，e1 e2；当a b时，e1 e2C对任意的a,b，e1 e2D当a b时，e1 e2；当a b时，e1 e2二、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a升水时，水面恰好经过正四棱锥的顶点P如果将容器倒置，水面也恰好过点P（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35B将容器侧面水平放置时，水面也恰好过点PC任意摆放该容器，当水面静止时，水面都恰好经过点PD若往容器内再注入a升水，则容器恰好能装满2.已知函数f(x)2，g(x)x ax（其中aR）.对于不相等的实数x1,x2，设m x2PP图1图2f(x1)f(x2)g(x1)g(x2)，n.则下列命题是真命题的是（）.x1 x2x1 x2（A）对于任意不相等的实数x1,x2，都有m 0；（B）对于任意的 a 及任意不相等的实数x1,x2，都有n0；（C）对于任意的 a，存在不相等的实数x1,x2，使得mn；（D）对于任意的 a，存在不相等的实数x1,x2，使得mn.3.已知m，n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m，n平行于同一平面，则m与n平行（C）若，不平行，则在内不存在与平行的直线（D）若m，n不平行，则m与n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（）AB.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 orunfinished statements.For each of them there are four choices marked A,B,C and D.Youshould 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 onchildren from those of the family.We tend to blame TV,he says,for problems it doesnt really cause,ignoringour own roles in shaping childrens minds.One traditional belief about television is that it reduces a childs ability to think and to understand theworld.While watching TV,children do not merely absorb words and images(影像).Instead,they learn bothclear and hidden meanings from what they see.Actually,children learn early the psychology of characters inTV shows.Furthermore,as many teachers agree,children understand far more when parents watch TV withthem,explaining new words and ideas.Yet,most parents use an educational program as a chance to put theirkids 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 toAnderson,the amount of time spent watching television is not related to reading ability.TV doesnt take theplace of reading for most children;it takes the place of similar sorts of recreation,such as listening to the radioand 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 schoolperformance.But here,too,Anderson notes that no studies have proved it.In fact,research suggests that its theother way around.“If youre smart young,youll watch less TV when youre older,”Anderson says.Yet,peopleof lower IQ tend to be lifelong television viewers.For years researchers have attempted to show that television is dangerous to children.However,byshowing that television increases none of the dangerous effects as believed before,Anderson suggests thattelevision cannot be criticized without considering other influences.1.An educational program is best watched by a child _.A.on his ownB.with other kidsC.with his parentsD.with his teachers2.Which of the following is most related to childrens reading ability?A.Radio-listeningB.Television-watchingD.Parents educational backgroundC.Parents reading list3.Anderson believed that _.A.the more a child watches TV,the smarter he isB.the younger a child is,the more he watches TVC.the smarter a child is,the less likely he gets addicted to TVD.the less a child watches TV,the better he performs at school4.What is the main purpose of the passage?A.To advise on the educational use of TV.B.To describe TVs harmful effects on children.C.To explain traditional views on TV influences.D.To present Andersons untraditional ideas.第四单元 附加题附加题包括数学、物理、化学、生物、信息共五组，考生需选做其中一组。每组 5 分。样题（略）