2019南方科技大学机试样题练习

2019机试样题练习第一单元 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：1335233=+第2次操作：55331333=++第3次操作：2505533=+如此反复操作，则第2017次操作后得到数是（ ）A ．55B ．133C ．250D ．2602．已知数列}{n a 满足11=a ，n a a n n 21-=++，则201S =（ ）A ．20100-B ．20200-C ．20199-D ．20099-3．在ABC ∆中，,,a b c 分别是角,,A B C 对边，若cos 3,cos 1a Bb A ==，则c=4．在平面直角坐标系中，点)0,5(),0,0(),6,3(C B A ，则=∠BAC （ ）5．在△ABC 中，若42cos 52cos 322=+-C B A ，则C tan 的最大值为( ) A ．－34 B ．－43 C ．－24D ．－226．ABC ∆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CB 方向上的投影为（ ）A ．12B ．23C ． 12-D ．23- 7．已知a 、b 为非零向量，则下列命题中真命题个数为（ ） ①若b a b a +=+，则a 与b 方向相同； ②若b a b a -=+，则a 与b 方向相反；③若b a b a -=+，则a 与b 有相等模；④若b a b a -=-，则a 与b 方向相同．A. 0B. 1C. 2D. 38．对任意向量a 、b ，下列关系式中不恒成立的是( )A ．b a b a ||≤⋅B ．b a b a ||-≤-C ．22||b a b a -≤-）（D ．22))((b a b a b a -=-+9．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A B C D10．已知圆222:()()2(0)C x a y a a a -+-=>及其外一点)2,0(A .若圆C 上存在点T 满足4π=∠CAT ，则实数a 的取值范围是（ ）A. ()1,∞-B. [31,1)-C. [31,1]-D. [31,)-+∞11．双曲线142222=-b y a x 的右焦点F 与抛物线)0(42>=p px y 的焦点重合，且在第一象限的交点为M ，MF 垂直于x 轴，则双曲线的离心率是A ．222+B ．22C ．12+D ．22+12.抛物线C ：28y x =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 正前方A B C D AO C于点Q ，若4||||5PF PQ =，则||QF =（ ） A ．3 B ．4 C ．5 D ．613．椭圆22221(0)x y a b a b+=>>的左、右焦点分别是12,F F ，点P 在椭圆上，21F PF ∆的角平分线PM 交轴于点M ，若2122||||||PM PF PF =，则该椭圆的离心率为( )．提示：内角平分线定理为||||||||2121M F M F PF PF =．A ．22B ．2C ．4D ． 414.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,sin 2:1θρ=C θρcos 32:2=C ，则1C 与2C 交点的坐标为（ ）A ．），（3π3B ．），（6π3C ．），（00D ．），（3π3或），（0016. 若复数z 满足|34|)i 43(i z +=-，则z 的虚部为( ).（A ）4- （B ）54- （C ）4 （D ）54 17．将离心率为1e 的双曲线1C 的实半轴长a 和虚半轴长()b a b ≠同时增加(0)m m >个单位长度，得到离心率为2e 的双曲线2C ，则（ ）A ．对任意的,a b ，12e e >B ．当a b >时，12e e >；当a b <时，12e e <C ．对任意的,a b ，12e e <D ．当a b >时，12e e <；当a b <时，12e e >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53B ．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x x f 2)(=，ax x x g +=2)(（其中R a ∈）.对于不相等的实数21,x x ，设2121)()(x x x f x f m --=，2121)()(x x x g x g n --=.则下列命题是真命题是（ ）. （A ）对于任意不相等的实数21,x x ，都有0>m ；（B ）对于任意的a 及任意不相等的实数21,x x ，都有0>n ；（C ）对于任意的a ，存在不相等的实数21,x x ，使得n m =；（D ）对于任意的a ，存在不相等的实数21,x x ，使得n m -=.3. 已知m ，n 是两条不同直线，α，β是两个不同平面，则下列命题正确是（ ）.（A ）若α，β垂直于同一平面，则α与β平行（B ）若m ，n 平行于同一平面，则m 与n 平行（C ）若α，β不平行，则在α内不存在与β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图12图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.tanθ D.2tanθ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，左侧调压装置可视为理想变压器，负载电路中55 Ω，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，电压表示数为110V，下列表述正确是（）A.电流表的示数为2AB.原、副线圈匝数比为1∶2C.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 4questions 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 it’s important to distinguish television’s influences on children from those of the family. We tend to blame TV, he says, for problems it doesn’t really cause, ignoring our own roles in shaping children’s minds.One traditional belief about television is that it reduces a child’s 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 doesn’t 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 child’s reading. “A child’s 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 it’s the other way around. “If you’re smart young, you’ll watch less TV when you’re 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 ownB. with other kidsC. with his parentsD. with his teachers2. Which of the following is most related to children’s reading ability?A. Radio-listeningB. Television-watchingC. Parents’ reading listD. Parents’ educational background3. 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 TV’s harmful effects on children.C. To explain traditional views on TV influences.D. To present Anderson’s un traditional ideas.。