人教版初中數(shù)學(xué)七年級(jí)上冊(cè)第一二章知識(shí)點(diǎn)總結(jié)及典型例題剖析

人教版初中數(shù)學(xué)七年級(jí)上冊(cè)第一二章知識(shí)點(diǎn)總結(jié)及典型例題剖析人教版七年級(jí)數(shù)學(xué)知識(shí)點(diǎn)第一章有理數(shù)1.1正數(shù)和負(fù)數(shù)?把0以外的數(shù)分為正數(shù)和負(fù)數(shù)。0是正數(shù)與負(fù)數(shù)的分界。(既不是正數(shù)也不是負(fù)數(shù))?負(fù)數(shù):比0小的數(shù)正數(shù):比0大的數(shù)0既不是正數(shù)，也不是負(fù)數(shù)1.2有理數(shù)1.2.1有理數(shù)?正整數(shù)，0，負(fù)整數(shù)，正分?jǐn)?shù)，負(fù)分?jǐn)?shù)都可以寫(xiě)成分?jǐn)?shù)的形式，這樣的數(shù)稱(chēng)為有理數(shù)。?所有正整數(shù)組成正整數(shù)集合，所有負(fù)整數(shù)組成負(fù)整數(shù)集合。正整數(shù)，0，負(fù)整數(shù)統(tǒng)稱(chēng)整數(shù)。1.2.2數(shù)軸?具有原點(diǎn)，正方向，單位長(zhǎng)度的直線叫數(shù)軸。1.2.3相反數(shù)?只有符號(hào)不同的數(shù)叫相反數(shù)。?0的相反數(shù)是0正數(shù)的相反數(shù)是負(fù)數(shù)負(fù)數(shù)的相反數(shù)是正數(shù)1.2.4絕對(duì)值?絕對(duì)值,a,?性質(zhì):正數(shù)的絕對(duì)值是它的本身負(fù)數(shù)的絕對(duì)值的它的相反數(shù)0的絕對(duì)值的01.2.5數(shù)的大小比較?數(shù)學(xué)中規(guī)定:在數(shù)軸上表示有理數(shù)，它們從左到右的順序，就是從小到大的順序，即左邊的數(shù)小于右邊的數(shù)。一般取右為正方向totalheavymodelnumber(m)weight(t)1gatedamflatworkdoordoorleaves6.2x2.022.50slidingblock7.0013.00fixedtypewinchopeningandclosingmachine2x1005.002electricalequipment2-containingplateworkinggateslotofsluiceanddam6.2x2.0of22.502.004.003flataccessdoorleafofsluiceanddam6.2x2.07.007.00electrichoist12.50slider2x801.001.505.001I50jackedwithelectricalequipment4flatemergencygateslotofsluiceanddam6.2x2.0of22.502.004.005sandspillwaygatedoorleaf1.5x1.511.501.50to3.00sliderscrewhoistelectricalequipment650.002.501sandsluiceworkinggateslotofoverflowdam1.5x1.513.002.002.007waterinlettrashrackgateleaf2.0FixedX3.513.003.003.008waterinletdoorleaf2.0x2.5slider13.003.003.00screwhoist80.003.501.009electricalequipmentworkinggateslotoftheintake2.0x2.513.00...Table1-1themaincharacteristicsofthepenstocknumberitemparametertypecontrollersizeheadalongpipediameterpipelength11hydropowerstationpenstockopen-airexposedpipe,singlepipejointwatersupply1.3M931m0.8M8.3*2m22hydropowerstationpenstockopen-airexposedpipe,singlepipejointwatersupply1.4m1063.506m0.8M10*2mtable1-2hydropowerstationHydraulicmetalstructuremaincharacteristicstablenumberprojectnamegate,andstoppeddirtgate,anddoor(Gate)slotopeningandclosingmachinetracknotesholemouthsize(widexhigh)(MXM)number(sets)designhead(m)supportstypetypesingleheavy(t)totalheavy(t)typetypeopeningandclosingcapacity(KN)head(trip)(m)number(sets)singleheavytotalheavymodelnumber(m)weight(t)1gatedamflatworkdoordoorleaves6.2x2.022.50slidingblock7.0013.00fixedtypewinchopeningandclosingmachine2x1005.002electricalequipment2-containingplateworkinggateslotofsluiceanddam6.2x2.0of22.502.004.003flataccessdoor?正數(shù)大于0，0大于負(fù)數(shù)，正數(shù)大于負(fù)數(shù)。兩個(gè)負(fù)數(shù)，絕對(duì)值大的反而小。1.3有理數(shù)的加減法1.3.1有理數(shù)的加法?同號(hào)兩數(shù)相加，取相同的符號(hào)，并把絕對(duì)值相加。1+1=2(-2)+(-2)=-4?絕對(duì)值不相等的異號(hào)兩數(shù)相加，取絕對(duì)值較大的加數(shù)的符號(hào)，并用較大的絕對(duì)值減去較小的絕對(duì)值，互為相反數(shù)的兩個(gè)數(shù)相加得0。(-4)+3=-1(-3)+(+3)=0?一個(gè)數(shù)同0相加，仍得這個(gè)數(shù)。?加法交換律:兩個(gè)數(shù)相加，交換加數(shù)的位置，和不變。a+b=b+a?加法結(jié)合律:三個(gè)數(shù)相加，先把前兩個(gè)數(shù)相加，或者先把后兩個(gè)數(shù)相加，和不變。(a+b)+c=(a+c)+b1.3.2有理數(shù)的減法?減去一個(gè)數(shù)，等于加這個(gè)數(shù)的相反數(shù)。a-b=a+(-b)1.4有理數(shù)的乘除法1.4.1有理數(shù)的乘法?兩數(shù)相乘，同號(hào)得正，異號(hào)的負(fù)，并把絕對(duì)值相乘。?任何數(shù)同0相乘，都得0。?乘積是1的兩個(gè)數(shù)互為倒數(shù)。?幾個(gè)不是0的數(shù)相乘，負(fù)因數(shù)的個(gè)數(shù)的偶數(shù)時(shí)，積是正數(shù);負(fù)因數(shù)的個(gè)數(shù)是奇數(shù)時(shí)，積是負(fù)數(shù)。(-2)×(-3)×(4)(-2)×(-3)×(4)×(-1)?乘法交換律:兩個(gè)數(shù)相乘，交換因數(shù)的位置，積相等。ab=ba?乘法結(jié)合律:三個(gè)數(shù)相乘，先把前兩個(gè)數(shù)相乘，或者先把后兩個(gè)數(shù)相乘，積相等。(ab)c=(ac)b?乘法分配律:一個(gè)數(shù)同兩個(gè)數(shù)的和相乘，等于把這個(gè)數(shù)分別同這兩個(gè)數(shù)相乘，再把積相加。a(b+c)=ab+ac1.4.2有理數(shù)的除法?除以一個(gè)不等0的數(shù)，等于乘以這個(gè)數(shù)的倒數(shù)。a?b=a×(1/b)?兩數(shù)相除，同號(hào)得正，異號(hào)得負(fù)，并把絕對(duì)值相除。0除以任何一個(gè)不等于0的數(shù)，都得0?乘除混合運(yùn)算往往先將除法化成乘法，然后確定積的符號(hào)，最后求出結(jié)果。?有理數(shù)的加減乘除混合運(yùn)算，如無(wú)括號(hào)指出先做什么運(yùn)算，則按照‘先乘除，后加減’的順序進(jìn)行。totalheavymodelnumber(m)weight(t)1gatedamflatworkdoordoorleaves6.2x2.022.50slidingblock7.0013.00fixedtypewinchopeningandclosingmachine2x1005.002electricalequipment2-containingplateworkinggateslotofsluiceanddam6.2x2.0of22.502.004.003flataccessdoorleafofsluiceanddam6.2x2.07.007.00electrichoist12.50slider2x801.001.505.001I50jackedwithelectricalequipment4flatemergencygateslotofsluiceanddam6.2x2.0of22.502.004.005sandspillwaygatedoorleaf1.5x1.511.501.50to3.00sliderscrewhoistelectricalequipment650.002.501sandsluiceworkinggateslotofoverflowdam1.5x1.513.002.002.007waterinlettrashrackgateleaf2.0FixedX3.513.003.003.008waterinletdoorleaf2.0x2.5slider13.003.003.00screwhoist80.003.501.009electricalequipmentworkinggateslotoftheintake2.0x2.513.00...Table1-1themaincharacteristicsofthepenstocknumberitemparametertypecontrollersizeheadalongpipediameterpipelength11hydropowerstationpenstockopen-airexposedpipe,singlepipejointwatersupply1.3M931m0.8M8.3*2m22hydropowerstationpenstockopen-airexposedpipe,singlepipejointwatersupply1.4m1063.506m0.8M10*2mtable1-2hydropowerstationHydraulicmetalstructuremaincharacteristicstablenumberprojectnamegate,andstoppeddirtgate,anddoor(Gate)slotopeningandclosingmachinetracknotesholemouthsize(widexhigh)(MXM)number(sets)designhead(m)supportstypetypesingleheavy(t)totalheavy(t)typetypeopeningandclosingcapacity(KN)head(trip)(m)number(sets)singleheavytotalheavymodelnumber(m)weight(t)1gatedamflatworkdoordoorleaves6.2x2.022.50slidingblock7.0013.00fixedtypewinchopeningandclosingmachine2x1005.002electricalequipment2-containingplateworkinggateslotofsluiceanddam6.2x2.0of22.502.004.003flataccessdoor1.5有理數(shù)的乘方1.5.1乘方n?求n個(gè)相同因數(shù)的積的運(yùn)算，叫做乘方，乘方的結(jié)果叫做冪。在a中，a叫做底數(shù)，n叫做指數(shù)。?負(fù)數(shù)的奇次冪是負(fù)數(shù)，負(fù)數(shù)的偶次冪的正數(shù)。?正數(shù)的任何次冪都是正數(shù)，0的任何正整數(shù)次冪都是0。?做有理數(shù)的混合運(yùn)算時(shí)，應(yīng)注意以下運(yùn)算順序:1.先乘方，再乘除，最后加減;2.同級(jí)運(yùn)算，從左到右進(jìn)行;3.如有括號(hào)，先做括號(hào)內(nèi)的運(yùn)算，按小括號(hào)，中括號(hào)，大括號(hào)依次進(jìn)行。totalheavymodelnumber(m)weight(t)1gatedamflatworkdoordoorleaves6.2x2.022.50slidingblock7.0013.00fixedtypewinchopeningandclosingmachine2x1005.002electricalequipment2-containingplateworkinggateslotofsluiceanddam6.2x2.0of22.502.004.003flataccessdoorleafofsluiceanddam6.2x2.07.007.00electrichoist12.50slider2x801.001.505.001I50jackedwithelectricalequipment4flatemergencygateslotofsluiceanddam6.2x2.0of22.502.004.005sandspillwaygatedoorleaf1.5x1.511.501.50to3.00sliderscrewhoistelectricalequipment650.002.501sandsluiceworkinggateslotofoverflowdam1.5x1.513.002.002.007waterinlettrashrackgateleaf2.0FixedX3.513.003.003.008waterinletdoorleaf2.0x2.5slider13.003.003.00screwhoist80.003.501.009electricalequipmentworkinggateslotoftheintake2.0x2.513.00...Table1-1themaincharacteristicsofthepenstocknumberitemparametertypecontrollersizeheadalongpipediameterpipelength11hydropowerstationpenstockopen-airexposedpipe,singlepipejointwatersupply1.3M931m0.8M8.3*2m22hydropowerstationpenstockopen-airexposedpipe,singlepipejointwatersupply1.4m1063.506m0.8M10*2mtable1-2hydropowerstationHydraulicmetalstructuremaincharacteristicstablenumberprojectnamegate,andstoppeddirtgate,anddoor(Gate)slotopeningandclosingmachinetracknotesholemouthsize(widexhigh)(MXM)number(sets)designhead(m)supportstypetypesingleheavy(t)totalheavy(t)typetypeopeningandclosingcapacity(KN)head(trip)(m)number(sets)singleheavytotalheavymodelnumber(m)weight(t)1gatedamflatworkdoordoorleaves6.2x2.022.50slidingblock7.0013.00fixedtypewinchopeningandclosingmachine2x1005.002electricalequipment2-containingplateworkinggateslotofsluiceanddam6.2x2.0of22.502.004.003flataccessdoor1.5.2科學(xué)記數(shù)法n?把一個(gè)大于10的數(shù)表示成a×10的形式(其中a是整數(shù)數(shù)位只有一位的數(shù)，n是正整數(shù))，使用的是科學(xué)記數(shù)法。1.5.3近似數(shù)?一個(gè)數(shù)只是接近實(shí)際人數(shù)，但與實(shí)際人數(shù)還有差別，它是一個(gè)近似數(shù)。?近似數(shù)與準(zhǔn)確數(shù)的接近程度，可以用精確度表示。比如0.345是精確到小數(shù)點(diǎn)后第三位或者說(shuō)是精確到0.001?從一個(gè)數(shù)的左邊第一個(gè)非0數(shù)字起，到末位數(shù)字止，所有的數(shù)字都是這個(gè)數(shù)的有效數(shù)字。totalheavymodelnumber(m)weight(t)1gatedamflatworkdoordoorleaves6.2x2.022.50slidingblock7.0013.00fixedtypewinchopeningandclosingmachine2x1005.002electricalequipment2-containingplateworkinggateslotofsluiceanddam6.2x2.0of22.502.004.003flataccessdoorleafofsluiceanddam6.2x2.07.007.00electrichoist12.50slider2x801.001.505.001I50jackedwithelectricalequipment4flatemergencygateslotofsluiceanddam6.2x2.0of22.502.004.005sandspillwaygatedoorleaf1.5x1.511.501.50to3.00sliderscrewhoistelectricalequipment650.002.501sandsluiceworkinggateslotofoverflowdam1.5x1.513.002.002.007waterinlettrashrackgateleaf2.0FixedX3.513.003.003.008waterinletdoorleaf2.0x2.5slider13.003.003.00screwhoist80.003.501.009electricalequipmentworkinggateslotoftheintake2.0x2.513.00...Table1-1themaincharacteristicsofthepenstocknumberitemparametertypecontrollersizeheadalongpipediameterpipelength11hydropowerstationpenstockopen-airexposedpipe,singlepipejointwatersupply1.3M931m0.8M8.3*2m22hydropowerstationpenstockopen-airexposedpipe,singlepipejointwatersupply1.4m1063.506m0.8M10*2mtable1-2hydropowerstationHydraulicmetalstructuremaincharacteristicstablenumberprojectnamegate,andstoppeddirtgate,anddoor(Gate)slotopeningandclosingmachinetracknotesholemouthsize(widexhigh)(MXM)number(sets)designhead(m)supportstypetypesingleheavy(t)totalheavy(t)typetypeopeningandclosingcapacity(KN)head(trip)(m)number(sets)singleheavytotalheavymodelnumber(m)weight(t)1gatedamflatworkdoordoorleaves6.2x2.022.50slidingblock7.0013.00fixedtypewinchopeningandclosingmachine2x1005.002electricalequipment2-containingplateworkinggateslotofsluiceanddam6.2x2.0of22.502.004.003flataccessdoor第二章整式的加減2.1整式23?單項(xiàng)式:表示數(shù)或字母積的式子100t,6a,a,2.5x,vt,-n?單項(xiàng)式的系數(shù):單項(xiàng)式中的數(shù)字因數(shù)100t,vt,-n100,1,-1?單項(xiàng)式的次數(shù):一個(gè)單項(xiàng)式中，所有字母的指數(shù)和100t字母t指數(shù)是1，100t是一次單項(xiàng)式vt字母v和t的指數(shù)和是2，vt是二次單項(xiàng)式?幾個(gè)單項(xiàng)式的和叫做多項(xiàng)式。每個(gè)單項(xiàng)式叫做多項(xiàng)式的項(xiàng)，不含字母的項(xiàng)叫做常數(shù)項(xiàng)。2X-32X和-3都是它的項(xiàng)，其中-3是常數(shù)項(xiàng)?多項(xiàng)式里次數(shù)最高項(xiàng)的次數(shù)，叫做這個(gè)多項(xiàng)式的次數(shù)。22X+2X+18次數(shù)最高的項(xiàng)是X，這個(gè)多項(xiàng)式的次數(shù)是2?單項(xiàng)式與多項(xiàng)式統(tǒng)稱(chēng)整式。2.2整式的加減22?同類(lèi)項(xiàng):所含字母相同，而且相同字母的次數(shù)相同的單項(xiàng)式。3ab和-4ab?把多項(xiàng)式中的同類(lèi)項(xiàng)合并成一項(xiàng)，叫做合并同類(lèi)項(xiàng)。?合并同類(lèi)項(xiàng)后，所得項(xiàng)的系數(shù)是合并前各同類(lèi)項(xiàng)的系數(shù)的和，且字母部分不變。totalheavymodelnumber(m)weight(t)1gatedamflatworkdoordoorleaves6.2x2.022.50slidingblock7.0013.00fixedtypewinchopeningandclosingmachine2x1005.002electricalequipment2-containingplateworkinggateslotofsluiceanddam6.2x2.0of22.502.004.003flataccessdoorleafofsluiceanddam6.2x2.07.007.00electrichoist12.50slider2x801.001.505.001I50jackedwithelectricalequipment4flatemergencygateslotofsluiceanddam6.2x2.0of22.502.004.005sandspillwaygatedoorleaf1.5x1.511.501.50to3.00sliderscrewhoistelectricalequipment650.002.501sandsluiceworkinggateslotofoverflowdam1.5x1.513.002.002.007waterinlettrashrackgateleaf2.0FixedX3.513.003.003.008waterinletdoorleaf2.0x2.5slider13.003.003.00screwhoist80.003.501.009electricalequipmentworkinggateslotoftheintake2.0x2.513.00...Table1-1themaincharacteristicsofthepenstocknumberitemparametertypecontrollersizeheadalongpipediameterpipelength11hydropowerstationpenstockopen-airexposedpipe,singlepipejointwatersupply1.3M931m0.8M8.3*2m22hydropowerstationpenstockopen-airexposedpipe,singlepipejointwatersupply1.4m1063.506m0.8M10*2mtable1-2hydropowerstationHydraulicmetalstructuremaincharacteristicstablenumberprojectnamegate,andstoppeddirtgate,anddoor(Gate)slotopeningandclosingmachinetracknotesholemouthsize(widexhigh)(MXM)number(sets)designhead(m)supportstypetypesingleheavy(t)totalheavy(t)typetypeopeningandclosingcapacity(KN)head(trip)(m)number(sets)singleheavytotalheavymodelnumber(m)weight(t)1gatedamflatworkdoordoorleaves6.2x2.022.50slidingblock7.0013.00fixedtypewinchopeningandclosingmachine2x1005.002electricalequipment2-containingplateworkinggateslotofsluiceanddam6.2x2.0of22.502.004.003flataccessdoor?如果括號(hào)外的因數(shù)是正數(shù)，去括號(hào)后原括號(hào)內(nèi)各項(xiàng)的符號(hào)與原來(lái)的符號(hào)相同。?如果括號(hào)外的因數(shù)是負(fù)數(shù)，去括號(hào)后原括號(hào)內(nèi)各項(xiàng)的符號(hào)與原來(lái)的符號(hào)相反。?一般地，幾個(gè)整式相加減，如果有括號(hào)就先去括號(hào)，然后再合并同類(lèi)項(xiàng)。totalheavymodelnumber(m)weight(t)1gatedamflatworkdoordoorleaves6.2x2.022.50slidingblock7.0013.00fixedtypewinchopeningandclosingmachine2x1005.002electricalequipment2-containingplateworkinggateslotofsluiceanddam6.2x2.0of22.502.004.003flataccessdoorleafofsluiceanddam6.2x2.07.007.00electrichoist12.50slider2x801.001.505.001I50jackedwithelectricalequipment4flatemergencygateslotofsluiceanddam6.2x2.0of22.502.004.005sandspillwaygatedoorleaf1.5x1.511.501.50to3.00sliderscrewhoistelectricalequipment650.002.501sandsluiceworkinggateslotofoverflowdam1.5x1.513.002.002.007waterinlettrashrackgateleaf2.0FixedX3.513.003.003.008waterinletdoorleaf2.0x2.5slider13.003.003.00screwhoist80.003.501.009electricalequipmentworkinggateslotoftheintake2.0x2.513.00...Table1-1themaincharacteristicsofthepenstocknumberitemparametertypecontrollersizeheadalongpipediameterpipelength11hydropowerstationpenstockopen-airexposedpipe,singlepipejointwatersupply1.3M931m0.8M8.3*2m22hydropowerstationpenstockopen-airexposedpipe,singlepipejointwatersupply1.4m1063.506m0.8M10*2mtable1-2hydropowerstationHydraulicmetalstructuremaincharacteristicstablenumberprojectnamegate,andstoppeddirtgate,anddoor(Gate)slotopeningandclosingmachinetracknotesholemouthsize(widexhigh)(MXM)number(sets)designhead(m)supportstypetypesingleheavy(t)totalheavy(t)typetypeopeningandclosingcapacity(KN)head(trip)(m)number(sets)singleheavytotalheavymodelnumber(m)weight(t)1gatedamflatworkdoordoorleaves6.2x2.022.50slidingblock7.0013.00fixedtypewinchopeningandclosingmachine2x1005.002electricalequipment2-containingplateworkinggateslotofsluiceanddam6.2x2.0of22.502.004.003flataccessdoortotalheavymodelnumber(m)weight(t)1gatedamflatworkdoordoorleaves6.2x2.022.50slidingblock7.0013.00fixedtypewinchopeningandclosingmachine2x1005.002electricalequipment2-containingplateworkinggateslotofsluiceanddam6.2x2.0of22.502.004.003flataccessdoorleafofsluiceanddam6.2x2.07.007.00electrichoist12.50slider2x801.001.505.001I50jackedwithelectricalequipment4flatemergencygateslotofsluiceanddam6.2x2.0of22.502.004.005sandspillwaygatedoorleaf1.5x1.511.501.50to3.00sliderscrewhoistelectricalequipment650.002.501sandsluiceworkinggateslotofoverflowdam1.5x1.513.002.002.007waterinlettrashrackgateleaf2.0FixedX3.513.003.003.008waterinletdoorleaf2.0x2.5slider13.003.003.00screwhoist80.003.501.009electricalequipmentworkinggateslotoftheintake2.0x2.513.00...Table1-1themaincharacteristicsofthepenstocknumberitemparametertypecontrollersizeheadalongpipediameterpipelength11hydropowerstationpenstockopen-airexposedpipe,singlepipejointwatersupply1.3M931m0.8M8.3*2m22hydropowerstationpenstockopen-airexposedpipe,singlepipejointwatersupply1.4m1063.506m0.8M10*2mtable1-2hydropowerstationHydraulicmetalstructuremaincharacteristicstablenumberprojectnamegate,andstoppeddirtgate,anddoor(Gate)slotopeningandclosingmachinetracknotesholemouthsize(widexhigh)(MXM)number(sets)designhead(m)supportstypetypesingleheavy(t)totalheavy(t)typetypeopeningandclosingcapacity(KN)head(trip)(m)number(sets)singleheavytotalheavymodelnumber(m)weight(t)1gatedamflatworkdoordoorleaves6.2x2.022.50slidingblock7.0013.00fixedtypewinchopeningandclosingmachine2x1005.002electricalequipment2-containingplateworkinggateslotofsluiceanddam6.2x2.0of22.502.004.003flataccessdoortotalheavymodelnumber(m)weight(t)1gatedamflatworkdoordoorleaves6.2x2.022.50slidingblock7.0013.00fixedtypewinchopeningandclosingmachine2x1005.002e