2017年南方科技大學(xué)機(jī)試樣題練習(xí)

1、2017年南方科技大學(xué)機(jī)試樣題 練習(xí)2017年南方科技大學(xué)機(jī)試樣題練習(xí)特別提示機(jī)試環(huán)節(jié)依次包括數(shù)學(xué)、物理、英語、附加題四個(gè)單元，每單元用時(shí)分別為 40、45、25、10分鐘，共2小時(shí)。每一 單元考完規(guī)定時(shí)間方能進(jìn)入下一單元，進(jìn)入下一單元后，不 能再返回前一單元進(jìn)行操作。機(jī)試題型包括單項(xiàng)選擇題和不定項(xiàng)選擇題兩種。第一單元數(shù)學(xué)一、單項(xiàng)選擇題（每題所設(shè)選項(xiàng)中只有一個(gè)正確答案，多選、錯(cuò)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如此反復(fù)操作，則第2017次操作后得到的數(shù) 是（）A 55 B 133 C

2、. 250 D 2602.已知數(shù)列an滿足 a1 1）an an1 2n）則 $201=（）A .20100 B .20200 C .20199 D .200993.在ABC中）a,b,c分別是角A,B,C的對(duì)邊）若acosB 3,b cos A 1）貝c =4 .在平面直角坐標(biāo)系中，點(diǎn)A（3,6）,B.A. 2 B. 4 C. ； D OA.5.在4ABC中，若3cos2甘 5co吟4,則tanC的最 大值為（）A. -3 B. -4 C.乎 D. 2/2 4346. ABC的外接圓的圓心為O,半徑為1/UAO UAB髭, 且iOAiiabi,則向量AC在向量CB方向上的投影 為（）A 2

3、B t c 1D<qb17.已知a、b為非零向量，則下列命題中真命題的個(gè)數(shù)為()若la 1b 1ab)則a與b方向相同;若a b la 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 |a b ,則a與b方向相同.A. 0 B. 1 C. 2 D. 38 .對(duì)任意向量a、b,下列關(guān)系式中不恒成立的 是()A . a b| a |b|B . a b |a| |b|C . (a b)2 |a b|2D. (a b)(a b) a2 b29 .如圖，三棱錐 A-BCD的頂點(diǎn)A、B、D為正 方體的頂點(diǎn)，C為正方體棱的中點(diǎn)，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

4、是正、心 刖方10.已知圓 C：(x a)2 (y a)2 2a2(a 0)及其外一點(diǎn) A(0,2). 若圓C上存在點(diǎn)T滿足CAT 則實(shí)數(shù)a的取 值范圍是()A. ,1B, b/3 1.1) C, h/3 1,1 D.V3 1,)22，,，、 k，一11 .雙曲線 J 七1的右焦點(diǎn)f與拋物線y2 4Px(p 0) 4a b的焦點(diǎn)重合，且在第一象限的交點(diǎn)為M , MF 垂直于x軸，則雙曲線的離心率是A. 272 2 B , 2 J2C, J2 1 D e J2 212 .拋物線C： y2 8x的焦點(diǎn)為F,準(zhǔn)線為l, P是l上 一點(diǎn)，連接PF并延長交拋物線C于點(diǎn)Q,若|PF| |PQI )貝UlQ

5、FI () 5A. 3B. 4 C. 5D 62213 ,橢圓x251(a b 0)的左、右焦點(diǎn)分別是燈2, a b7點(diǎn)P在橢圓上，PF1F2的角平分線PM交軸于點(diǎn)M）若21PM |2 IPFJIPF2I）則該橢圓的離心率為 （）.提示：內(nèi)角平分線定理為四A.B.吏C.D.14 .有6名同學(xué)參加校園歌手總決賽，觀眾中有 四名同學(xué)猜測結(jié)果，其中甲同學(xué)猜測：4號(hào) 或5號(hào)選手得第一名；乙同學(xué)猜測：3號(hào)選 手不可能得第一名；丙同學(xué)猜測：1,2,6號(hào) 選手中的一位獲得第一名；丁同學(xué)猜測： 4,5,6號(hào)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(duì)比賽結(jié)果，此人是（）A

6、 甲、 B.乙、 C.丙、 D.丁15 .在極坐標(biāo)系中,曲線Ci : 2sin , C2 :273cos）則Cl與C2交點(diǎn)的坐標(biāo)為（）A. 33,；）B. （J3,，）C. （0,0）D. F）或（0Q16.若復(fù)數(shù)z滿足（3 4i）z |4 3i|則z的虛部為().(A)4(B)g(C) 4(D):5517.將離心率為ei的雙曲線G的實(shí)半軸長a和虛半軸長b (a b)同時(shí)增加m(m 0)個(gè)單位長度，得到離心率為&的雙曲線C2,則()A .對(duì)任意的a,b, ee2B,當(dāng)a b時(shí),e G；當(dāng)ab時(shí),e GC.對(duì)任意的a.b, e e2D.當(dāng)a b時(shí)e e Q ；當(dāng)a b時(shí)e e e2二、不

7、定項(xiàng)選擇題(每題所設(shè)選項(xiàng)中至少有一個(gè)正確答案，多選、少選、錯(cuò)選或不選均不得分；每題2分)1 .如圖1, 一個(gè)正四棱柱形的密閉容器底部鑲 嵌了同底的正四棱錐形實(shí)心裝飾塊，容器內(nèi) 盛有a升水時(shí)，水面恰好經(jīng)過正四棱錐的頂 點(diǎn)P .如果將容器倒置，水面也恰好過點(diǎn)P(圖 2).則下列四個(gè)命題正確的是圖1圖2A.正四棱錐的高等于正四棱柱高的3B.將容器側(cè)面水平放置時(shí)，水面也恰好過點(diǎn)PC.任意擺放該容器，當(dāng)水面靜止時(shí)，水面都 恰好經(jīng)過點(diǎn)PD.若往容器內(nèi)再注入a升水，則容器恰好能裝 滿2 .已知函數(shù)f(x) 2x, g(x) x2 ax (其中a R).對(duì)于 不相等的實(shí)數(shù)為,xz,設(shè) m f(x1)f(x2)

8、, n g(xi)g(x2).則7x1x2x1x2下列命題是真命題的是().(A)對(duì)于任意不相等的實(shí)數(shù)xi,x2,都有m 0；(B)對(duì)于彳E意的a及任意不相等的實(shí)數(shù)為,x2,都有n 0；(C)對(duì)于彳E意的a,存在不相等的實(shí)數(shù)X,x2,使 得m n;(D)對(duì)于彳E意的a,存在不相等的實(shí)數(shù)使 得m n .3 .已知m , n是兩條不同直線，是兩個(gè)不同 平面，則下列命題正確的是().(A)若，垂直于同一平面，則與平行(B)若m, n平行于同一平面，則m與n平行(C)若，不平行，則在 內(nèi)不存在與 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(xiàng)選擇題(每題所設(shè)選項(xiàng)

9、中只有一個(gè)正確答案，多選、錯(cuò)選或不選均不得分；每題 1.5分)1 .質(zhì)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(jìn)入勻強(qiáng)磁場，運(yùn)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(fù)電，帶正電B.的速率小于的速率C.洛倫茲力對(duì)、做正功D.的運(yùn)行時(shí)間大于的運(yùn)行時(shí)間2 . 一水平拋出的小球落到一傾角為的斜面上時(shí)，其速度方向與斜面垂直，運(yùn)動(dòng)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 0二、不定項(xiàng)選擇題（每題所設(shè)選項(xiàng)中至少有一個(gè)正確答案，多選、少選、錯(cuò)選或不選均不得分；每題 2分）1 .如圖

10、所示，物體 P靜止于固定的斜面上，P 的上表面水平.現(xiàn)把物體Q輕輕地疊放在P上，A.P向下滑動(dòng)B.P靜止不動(dòng)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(cè)的調(diào)壓裝置可視為理想變壓器， 負(fù)載電路中55 Q, 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2AB.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

11、 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.SampleDaniel Anderson, a famous psychologist, beli

12、eves it ' s important to distinguish television influences on children from those of the family. We tend to blame TV, he says, for problems it doesn ' really cause, ignoring our own roles in shaping children ' s minds.One traditional belief about television is that it reduces a child 

13、9;ability to think and to understand the world. While watching TV, children do not merely absorb words andimages （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, c

14、hildren understand far more when parents watch TV with them, explaining new words and ideas. Yet, most parents use ar 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 en

15、tertainment.toofBut according to Anderson, the amount of time spent watching television is not related reading ability. TV doesn' take the place 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 &#

16、39; educational background have a stronger influence on a child ' reading. "A child ;reading ability is best predicted by how much a parent reads. " Anderson says.s the other w;Traditional wisdom also has it that heavy television-watching lowers IQ （ 智商）scores and affects school perfor

17、mance. But here, too, Anderson notes that no studies have proved it.In fact, research suggests that itAnderson says. Yet,around. "If you ' resmart young, you ' lwatch less TV when you ' re older, people of lower IQ tend to be lifelong television viewers.For years researchers have at

18、tempted 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.A. on his own with his parents 2. Which of the1. An educational program is best watched by a child.B. with other kids C.D. with his teachersfollowing is most related toB.children ' s reading ability?A. Radio-listening