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1、暑期培優(yōu)教材暑期培優(yōu)教材初一升初二(數(shù)學(xué))編者:張老師成都·2013.5目錄第一部分——溫故知新專題一整式運算·················································1專題二乘法公式·················································3專題三平行線的性質(zhì)與判定·······································9專題四三角形的基本性質(zhì)·········································11專題五全等三角形·······················
2、························14專題六如何做幾何證明題·········································17專題七軸對稱···················································22第二部分——提前學(xué)習(xí)專題一勾股定理·················································25專題二平方根與算數(shù)平方根·······································29專題三立方根·································
3、··················32專題四平方根與立方根的應(yīng)用····································35專題五實數(shù)的分類1···············································39專題六最簡二次根式及分母有理化··································42專題七非負(fù)數(shù)的性質(zhì)及應(yīng)用·······································46專題八二次根式的復(fù)習(xí)···········································491第一部分——溫故知新
4、專題一整式運算1.由數(shù)字與字母組成的代數(shù)式叫做單項式。單獨一個數(shù)或字母也是單項式。單項式中的叫做單項式的系數(shù)單項式中所有字母的叫做單項式的次數(shù)2.幾個單項式的和叫做多項式多項式中叫做這個多項式的次數(shù)3.單項式和多項式統(tǒng)稱為4.整式加減實質(zhì)就是后5.同底數(shù)冪乘法法則:(m.n都是正整數(shù));逆運算6.冪的乘方法則:(m.n都是正整數(shù));逆運算7.積的乘方法則:(n為正整數(shù));逆運算8.同底數(shù)冪除法法則:(a≠0,m.n都是正整數(shù));逆運算9.零指數(shù)的意義:;10.負(fù)指數(shù)的意義:11.整式乘法:(1)單項式乘以單項式;(2)單項式乘以多項式;(3)多項式乘以多項式12.整式除法:(1)單項式除以單
5、項式;(2)多項式除以單項式知識點1.單項式多項式的相關(guān)概念歸納:在準(zhǔn)確記憶基本概念的基礎(chǔ)上,加強對概念的理解,并靈活的運用例1.下列說法正確的是()A.沒有加減運算的式子叫單項式B.的系數(shù)是C.單項式-1的次數(shù)是0D.是二次三項式例2.如果多項式是關(guān)于x的二次二項式,求m,n的值知識點2.整式加減歸納:正確掌握去括號的法則,合并同類項的法則例3.多項式中不含xy項,求k的值3知識點3.冪的運算歸納:冪的運算一般情況下,考題的類型均以運算法則的逆運算為主,加強對冪的逆運算的練習(xí),是解決這類題型的核心方法。例4.已知求(1)的值(2)的值例5.計算(1)(2)知識點4.整式的混合運算歸納:整式
6、的乘法法則和除法法則是整式運算的依據(jù),注意運算時靈活運用法則。例6.先化簡,再求值:,其中知識點5.運用冪的法則比較大小歸納:根據(jù)冪的運算法則,可以將比較大小的題分為兩種:①化為同底數(shù)比較;②化為同指數(shù)比較例7.比較大?。?)(2)1.若A是五次多項式,B是三次多項式,則A+B一定是()A.五次整式B.八次多項式C.三次多項式D.次數(shù)不能確定2.已知,,,則、、的大小關(guān)系是()A.>> B.>>C.<<D.>>3.若,,則等于()A.-5B.-3C.-1D.134.下列敘述中,正確的是()A.單項式的系數(shù)是0,次數(shù)是3B.a、π、0、22都是單項式C.多項式是六次三項式D.是二次二項式5.下
7、列說法正確的是()A.任何一個數(shù)的0次方都是1B.多項式與多項式的和是多項式C.單項式與單項式的和是多項式D.多項式至少有兩項6.下列計算:①②③④⑤⑥正確的有()A.2個B.3個C.4個D.5個7.在的積中,不想含有項,則必須為.8.若中不含有項,則,.9.比較大?。?)(2)(3)10.計算(1)(2)專題二乘法公式1.平方差公式:平方差公式的一些變形:(1)位置變化:(2)系數(shù)變化:(3)指數(shù)變化:(4