2020考研初試將(jiang)于12月下(xia)旬進行,為(wei)了(le)讓大家能夠查缺(que)補漏,沖刺高分,中國教(jiao)育在線考研頻道為(wei)大家整理了(le)考研數學答題技(ji)巧,供各位考生參(can)考!
(1)不要(yao)粗心大意(yi)犯最低級(ji)的(de)錯誤
拿到考(kao)卷以后,先把名字及其他試卷要求(qiu)信(xin)息(xi)寫上,雖然這(zhe)是最基(ji)本的(de)常識(shi),但每年都有不少考(kao)生會(hui)犯這(zhe)個低級錯(cuo)誤。
(2)瀏(liu)覽整套(tao)試卷
將試卷瀏覽一遍,看(kan)看(kan)哪些題目自己比較熟悉,哪些題沒有思路(lu),這(zhe)套(tao)卷子(zi)大(da)概哪部分做(zuo)起來會(hui)比較困難,做(zuo)到心中有數,以(yi)便(bian)合理分配時間。
(3)切忌心中發(fa)慌
如果這套題看(kan)起來有(you)很多陌生(sheng)的題,也不(bu)要心(xin)慌。畢竟有(you)些試題萬變不(bu)離其宗,相(xiang)信只要做到(dao)心(xin)中不(bu)亂、仔細(xi)思考就(jiu)會產生(sheng)思路。
(4)合理(li)掌握時間
如果(guo)一(yi)道考(kao)題(ti)思(si)考(kao)了(le)大約有(you)二十分(fen)鐘仍然沒有(you)思(si)路,可(ke)以先暫(zan)時(shi)放棄這道題(ti)目(mu),不要在一(yi)道試(shi)題(ti)上花費太多的時(shi)間(jian),導致會做(zuo)的題(ti)反而沒有(you)時(shi)間(jian)去做(zuo),那就太可(ke)惜了(le)。
(5)學會適當放棄(qi)
當確實沒(mei)有思路的時候要(yao)暫(zan)時放棄(qi),如果(guo)放棄(qi)的是一道選(xuan)擇題(ti)(ti),建(jian)議大家標記一下此題(ti)(ti),防止因(yin)此題(ti)(ti)使答題(ti)(ti)卡順序涂錯,如果(guo)時間充足還可再(zai)做。
但(dan)是,標(biao)記要慎重,以免被視為作(zuo)弊,可以用(yong)鉛筆標(biao)記,交試卷之(zhi)前用(yong)橡皮察去。
(6)確(que)定做題順(shun)序
在做題順序(xu)上可以采(cai)用選擇、填(tian)空、計算、證明的(de)順序(xu)。完成選擇填(tian)空后,做大題時,先(xian)通觀整個(ge)試題,明確哪些(xie)分數(shu)是(shi)必得的(de),哪些(xie)是(shi)可能得到的(de),哪些(xie)是(shi)根(gen)本(ben)得不到的(de),再采(cai)取不同的(de)對應方式,才能鎮定自如(ru),進退有據,最終從總體上獲勝。
1.函(han)(han)(han)(han)(han)(han)數(shu)(shu)(shu)(shu)(shu)在(zai)(zai)(zai)一(yi)(yi)點(dian)(dian)處極限存(cun)在(zai)(zai)(zai),連(lian)續(xu),可(ke)導(dao)(dao),可(ke)微(wei)之間關(guan)系。對(dui)于一(yi)(yi)元(yuan)函(han)(han)(han)(han)(han)(han)數(shu)(shu)(shu)(shu)(shu)函(han)(han)(han)(han)(han)(han)數(shu)(shu)(shu)(shu)(shu)連(lian)續(xu)是(shi)(shi)函(han)(han)(han)(han)(han)(han)數(shu)(shu)(shu)(shu)(shu)極限存(cun)在(zai)(zai)(zai)的充分條件。若函(han)(han)(han)(han)(han)(han)數(shu)(shu)(shu)(shu)(shu)在(zai)(zai)(zai)某點(dian)(dian)連(lian)續(xu),則(ze)該函(han)(han)(han)(han)(han)(han)數(shu)(shu)(shu)(shu)(shu)在(zai)(zai)(zai)該點(dian)(dian)必有極限。若函(han)(han)(han)(han)(han)(han)數(shu)(shu)(shu)(shu)(shu)在(zai)(zai)(zai)某點(dian)(dian)不(bu)連(lian)續(xu),則(ze)該函(han)(han)(han)(han)(han)(han)數(shu)(shu)(shu)(shu)(shu)在(zai)(zai)(zai)該點(dian)(dian)不(bu)一(yi)(yi)定無極限。若函(han)(han)(han)(han)(han)(han)數(shu)(shu)(shu)(shu)(shu)在(zai)(zai)(zai)某點(dian)(dian)可(ke)導(dao)(dao),則(ze)函(han)(han)(han)(han)(han)(han)數(shu)(shu)(shu)(shu)(shu)在(zai)(zai)(zai)該點(dian)(dian)一(yi)(yi)定連(lian)續(xu)。但是(shi)(shi)如果函(han)(han)(han)(han)(han)(han)數(shu)(shu)(shu)(shu)(shu)不(bu)可(ke)導(dao)(dao),不(bu)能推出函(han)(han)(han)(han)(han)(han)數(shu)(shu)(shu)(shu)(shu)在(zai)(zai)(zai)該點(dian)(dian)一(yi)(yi)定不(bu)連(lian)續(xu),可(ke)導(dao)(dao)與可(ke)微(wei)等(deng)價。而對(dui)于二(er)元(yuan)函(han)(han)(han)(han)(han)(han)數(shu)(shu)(shu)(shu)(shu),只能又(you)可(ke)微(wei)推連(lian)續(xu)和可(ke)導(dao)(dao)(偏導(dao)(dao)都存(cun)在(zai)(zai)(zai)),其余都不(bu)成立。
2.基本初等(deng)(deng)函(han)(han)數(shu)與初等(deng)(deng)函(han)(han)數(shu)的(de)連(lian)續性(xing):基本初等(deng)(deng)函(han)(han)數(shu)在(zai)其定(ding)義域內是連(lian)續的(de),而初等(deng)(deng)函(han)(han)數(shu)在(zai)其定(ding)義區間上是連(lian)續的(de)。
3.極(ji)(ji)值(zhi)點(dian)(dian)(dian)(dian)(dian),拐(guai)點(dian)(dian)(dian)(dian)(dian)。駐點(dian)(dian)(dian)(dian)(dian)與極(ji)(ji)值(zhi)點(dian)(dian)(dian)(dian)(dian)的關系:在(zai)一元函(han)數中,駐點(dian)(dian)(dian)(dian)(dian)可能是(shi)極(ji)(ji)值(zhi)點(dian)(dian)(dian)(dian)(dian),也可能不是(shi)極(ji)(ji)值(zhi)點(dian)(dian)(dian)(dian)(dian),而(er)函(han)數的極(ji)(ji)值(zhi)點(dian)(dian)(dian)(dian)(dian)必(bi)(bi)是(shi)函(han)數的駐點(dian)(dian)(dian)(dian)(dian)或導數不存(cun)在(zai)的點(dian)(dian)(dian)(dian)(dian)。注意極(ji)(ji)值(zhi)點(dian)(dian)(dian)(dian)(dian)和拐(guai)點(dian)(dian)(dian)(dian)(dian)的定義一充、二充、和必(bi)(bi)要條件。
4.夾逼(bi)定理(li)和(he)(he)用定積分定義(yi)求(qiu)極(ji)限。這兩(liang)種方(fang)法(fa)都可(ke)以用來求(qiu)和(he)(he)式極(ji)限,注意方(fang)法(fa)的選擇。還有(you)夾逼(bi)定理(li)的應用,特(te)別是無窮(qiong)小(xiao)量與有(you)界(jie)量之積仍是無窮(qiong)小(xiao)量。
5.可(ke)導是對定(ding)義域(yu)內(nei)的(de)點而言(yan)的(de),處(chu)處(chu)可(ke)導則(ze)存(cun)在導函數,只要(yao)一個函數在定(ding)義域(yu)內(nei)某一點不可(ke)導,那么就不存(cun)在導函數,即使該(gai)函數在其它(ta)各處(chu)均可(ke)導。
6.泰勒中值(zhi)定理的應用(yong),可用(yong)于計(ji)算(suan)極限以及證(zheng)明(ming)。
7.比(bi)(bi)較積(ji)(ji)分(fen)的大小。定積(ji)(ji)分(fen)比(bi)(bi)較定理的應(ying)用(常用畫(hua)圖法),多重積(ji)(ji)分(fen)的比(bi)(bi)較,特別(bie)注意第二類曲線積(ji)(ji)分(fen),曲面積(ji)(ji)分(fen)不可直接比(bi)(bi)較大小。