南方科技大學機試樣題練習教學提綱

1、<<<<<雜品資料 »»»»2017機試樣題練習特別提示機試環(huán)節(jié)依次包括數(shù)學、物理、英語、附加題四個單元，每單元用時分別為 40、45、25、10分鐘，共2小時。每一 單元考完規(guī)定時間方能進入下一單元，進入下一單元后，不 能再返回前一單元進行操作。機試題型包括單項選擇題和不定項選擇題兩種。第一單元數(shù)學一、單項選擇題（每題所設選項中只有一個正確答案，多選、錯選或不選均不得分；每題 1.5分）1.觀察下列操作：第1次操作：23 +53 = 133第 2 次操作：13 +33 +33 = 55第3次操作：53 +53 = 250如

2、此反復操作，則第 2017次操作后得到的數(shù)是（）A. 55B. 133C. 250 D. 2602 .已知數(shù)列an滿足 a =1 , an +an+ = -2n ,則 S201 =（）A. -20100B. -20200C. -20199 D. -200993 .在 &ABC 中，a,b,c分別是角 A, B,C 的對邊，若 acosB = 3,bcosA = 1 ,則 c =A. 2B. 4C. 1 D. 332<<<<<雜品資料 »»»»4.在平面直角坐標系中，點A(3,6), B(0,0),C(5,0),則 /

3、 BAC =()5.在 ABC 中,A. -3 B.4B.C.D.7冗12c 23 cosA-B +5cos2 C =4 ,貝U tanC 的最大值為(4 C-22C-4 D-226. AABC的外接圓的圓心為1, 2AO = AB 十 AC ,且 |,則向量AC在向量CB方向上的投影為（）A.7 .已知a、b為非零向量，則下列命題中真命題的個數(shù)為（）若a +|b| =|a +b ,則a與b方向相同；若a +|b| =|a b ,則a與b方向相反；若a + b =|a b ,則a與b有相等的模；若a b =|ab ,則a與b方向相同.A. 0B. 1C. 2D. 38 .對任意向量a、b,下列

4、關系式中不恒成立的是()A. ab|<|a |bB. a-b|a | -| bC. (a-b)2W|a -b |2d, (a + b)(a-b) =a2 -b29.如圖，三棱錐A-BCD的頂點A、B、D為正方體的頂點,C為正方體棱的中點，現(xiàn)在正方體的網(wǎng)格紙上用粗線 畫出的它的三視圖，正確的是A22210.已知圓C :(xa)2+(y a)2 = 2a2(aA0)及其外一點A(0,2).若圓C上存在點T滿足 冗/CAT 一,則實數(shù)a的取值范圍是()4A. 一：二,1 B. 3 -1,1) C. 3 -1,1 D. 3-1,)22x y211 .雙曲線 一2=1的右焦點F與拋物線y =4px

5、(p >0)的焦點重合，且在第一象 4a b限的交點為 M , MF垂直于x軸，則雙曲線的離心率是A. 2.2 2 B, 2.2C. 、2 1 D. .2212 .拋物線C : y2 =8x的焦點為F ,準線為l , P是l上一點，連接PF并延長交拋物線 C4于點 Q,若 |pf |= |PQ| ,則 |QF 卜() 5A3B. 4C. 5D. 62213 .橢圓 與+4=1何Ab >0)的左、右焦點分別是 匕下2,點P在橢圓上，APFF2的角 a b平分線PM交軸于點M ,若21PM |2二| PF11| PF2 |,則該橢圓的離心率為().提示：內(nèi)角平分線定理為 J_PF=JL

6、FMJ|PF2| |F2M|A -2B.3C2D.3A.BCD14 .有6名同學參加校園歌手總決賽，觀眾中有四名同學猜測結果，其中甲同學猜測：4號或5號選手得第一名；乙同學猜測：3號選手不可能得第一名；丙同學猜測： 1,2,6號選手中的一位獲得第一名；丁同學猜測：4,5,6號選手都不可能獲得第一名.比賽后發(fā)現(xiàn)沒有并列名次，且甲、乙、丙、丁中只有 1人猜對比賽結果，此人是()A.甲、B.乙、C.丙、D.丁15 .在極坐標系中，曲線C1 : P=2sin& C2: P=2J3cosH，則Ci與C2交點的坐標為D.(內(nèi),/)或(0,0)3(D)A.(內(nèi),壬B.(伺壬 C. (0,0)3616

7、 .若復數(shù)z滿足(34i)z =|4+3i |,則z的虛部為().，、，、4，、(A)-4(B)-(C)417 .將離心率為e的雙曲線Ci的實半軸長a和虛半軸長b(a*b)同時增加m(m>0)個單位 長度，得到離心率為 金的雙曲線Q ,則()A.對任意的 a, b, e >e2B.當 a >b 時，e >e2 ;當 a cb 時，e caC.對任意的 a, b , e <e2D.當 a >b 時，e<Q；當 acb 時，gab、不定項選擇題(每題所設選項中至少有一個正確答案, 多選、少選、錯選或不選均不得分；每題 2分)i .如圖1, 一個正四棱柱形的

8、密閉容器底部鑲嵌了同底的正四棱錐形實心裝飾塊，容器內(nèi) 盛有a升水時，水面恰好經(jīng)過正四棱錐的頂點 P.如果將容器倒置， 水面也恰好過點(圖2).則下列四個命題正確的是 3A.正四棱錐的高等于正四棱柱高的-5B.將容器側面水平放置時，水面也恰好過點PC.任意擺放該容器，當水面靜止時，水面都恰好經(jīng)過點PD.若往容器內(nèi)再注入 a升水，則容器恰好能裝滿圖12.已知函數(shù)f(x)=2x, g(x)=x2+ax (其中aR) .對于不相等的實數(shù)x1, x2,設m =""尸f(x2), n = g(x1) - g(x2).則下列命題是真命題的是 ( x1 x2x1 x2(A)對于任意不相等的

9、實數(shù) x1,x2,都有m A 0 ；(B)對于任意的a及任意不相等的實數(shù) x1, x2,都有n a 0 ；(C)對于任意的a,存在不相等的實數(shù) x1,x2,使得m = n；(D)對于任意的a,存在不相等的實數(shù) x1,x2,使得m = -n.3.已知m, n是兩條不同直線，口，P是兩個不同平面，則下列命題正確的是(A)若口，P垂直于同一平面，則 支與P平行(B)若m, n平行于同一平面，則 m與n平行(C)若a , P不平行，則在口內(nèi)不存在與P平行的直線(D)若m, n不平行，則 m與n不可能垂直于同一平面第二單元物理一、單項選擇題（每題所設選項中只有一個正確答案，多選、錯選或不選均不得分；每題

10、 1.5分）1 .質量和電荷量都相等的帶電粒子和，以不同的速率經(jīng)小孔垂直進入勻強磁場，運行的半圓軌跡如圖附3-1-1中虛線所示，下列表述正確的是（）A.帶負電，帶正電B.的速率小于的速率C.洛倫茲力對、做正功D.的運行時間大于的運行時間2 . 一水平拋出的小球落到一傾角為的斜面上時，其速度方向與斜面垂直，運動軌跡如圖2-3-8中虛線所示.小球在豎直方向下落的距離與在水平方向通過的距離之比為（）A.B. C.tan 0 D.2tan 0、不定項選擇題（每題所設選項中至少有一個正確答案,多選、少選、錯選或不選均不得分；每題 2分）1 .如圖所示，物體P靜止于固定白斜面上，P的上表面水平.現(xiàn)把物體Q

11、輕輕地疊放在 P上,則（）A.P向下滑動B.P靜止不動C.P所受的合外力增大D.P與斜面間的靜摩擦力增大2 .如圖，左側的調壓裝置可視為理想變壓器，負載電路中 55 , A、V為理想電流表和電壓表，若原線圈接入如圖（b）所示的正弦交變電壓，電壓表的示數(shù)為110V,下列表述正確的是（）A.電流表的示數(shù)為2 AB原、副線圈匝數(shù)比為 1 : 2C.電壓表的示數(shù)為電壓的有效值D.原線圈中交變電壓的頻率為100Hz第三單元英語Reading Comprehension （4 passages,20 scores）Directions: There are 4 passagesin this part.

12、Each passageis 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.SampleDaniel Anderson, a famous psychologist, believes it ' inaportant to dis

13、tinguish television ' s influences on children from those of the family. We tend to blame TV, he says, for problems it doesn ' t really causignoring our own roles in shaping children' s minds.One traditional belief about television is that it reduces a child 'ability to think and to

14、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

15、 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 accor

16、ding to Anderson, the amount of time spent watching television is not related to reading ability. TV doesn ' t take the placadofgr 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 h

17、ave a stronger influence on a child 'reading. "Achild '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

18、 no studies have proved it. In fact, research suggests that it ' the other way around. " Ifyou ' remart young, you ' 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 sh

19、ow 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 teachers2. Which of the following is most related to children' s readi