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    初中階段涉及的數學公式有哪些?

    初中階段涉及的數學公式有哪些?

      初中的數學公式比較多,想要牢牢記住可能對大多數同學來說,有點困難。所以,現在同學們的福利來了。
      今天小編把初中數學函數、幾何,最基礎而且是常考的知識點的口訣做了一個簡單的歸納。希望不擅長數學的同學們能夠把這些公式、口訣記牢、理解,并實際運用。
      1、最簡根式的條件
      最簡根式三條件,
      號內不把分母含,
      冪指(數)根指(數)要互質,
      冪指比根指小一點。
      2、去、添括號法則
      去括號、添括號,關鍵看符號。
      括號前面是正號,去、添括號不變號。
      括號前面是負號,去、添括號都變號。
      3、因式分解
      因式分一提(公因式)二套(公式)三分組,
      細看幾項不離譜,兩項只用平方差,
      三項十字相乘法,陣法熟練不馬虎,
      四項仔細看清楚,若有三個平方數(項),
      就用一三來分組,否則二二去分組,
      五項、六項更多項,二三、三三試分組,
      以上若都行不通,拆項、添項看清楚。
      4、分式方程的解法步驟
      同乘最簡公分母,化成整式寫清楚,
      求得解后須驗根,原(根)留、增(根)舍別含糊,
      5、特殊點的坐標特征
      坐標平面點(x,y),橫在前來縱在后;
     (+,+),(-,+),(-,-)和(+,-),四個象限分前后;
      x軸上y為0,x為0在y軸。
      6、象限角的平分線
      象限角的平分線,
      坐標特征有特點,
      一、三橫縱都相等,
      二、四橫縱確相反。
      7、平行某軸的直線
      平行某軸的直線,點的坐標有講究,
      直線平行x軸,縱坐標相等橫不同;
      直線平行于y軸,點的橫坐標仍照舊。
      8、對稱點的坐標
      對稱點坐標要記牢,相反數位置莫混淆,
      x軸對稱y相反,y軸對稱,x前面添負號;
      原點對稱最好記,橫縱坐標變符號。
      9、自變量的取值范圍
      分式分母不為零,偶次根下負不行;
      零次冪底數不為零,整式、奇次根全能行。
      10、函數圖象的移動規律
      若把一次函數解析式寫成y=k(x+0)+b,二次函數的解析式寫成y=a(x+h)2+k的形式,則可用下面的口訣:
      左右平移在括號,上下平移在末稍,
      左正右負須牢記,上正下負錯不了。
      11、一次函數圖象與性質
      一次函數是直線,圖象經過三象限;
      正比例函數更簡單,經過原點一直線;
      兩個系數k與b,作用之大莫小看,
      k是斜率定夾角,b與y軸來相見,
      k為正來右上斜,x增減y增減;
      k為負來左下展,變化規律正相反;
      k的絕對值越大,線離橫軸就越遠。
      12、二次函數圖象與性質
      二次函數拋物線,圖象對稱是關鍵;
      開口、頂點和交點,它們確定圖象現;
      開口、大小由a斷,c與y軸來相見,
      b的符號較特別,符號與a相關聯;
      頂點位置先找見,y軸作為參考線,
      左同右異中為0,牢記心中莫混亂;
      頂點坐標最重要,一般 式配方它就現,
      橫標即為對稱軸,縱標函數最值見。
      若求對稱軸位置,符號反,
      一般、頂點、交點式,不同表達能互換。
      13、反比例函數圖象與性質
      反比例函數有特點,雙曲線相背離得遠;
      k為正,圖在一、三(象)限,
      k為負,圖在二、四(象)限;
      圖在一、三函數減,兩個分支分別減。
      圖在二、四正相反,兩個分支分別增;
      線越長越近軸,永遠與軸不沾邊。
      14、三角函數定義
      三角函數有正弦、余弦、正切、余切,
      它們實際是直角三角形的邊的比值,
      可以把兩個字用/隔開,再一句話記定義:
      正對魚磷(余鄰)直刀切
      正:正弦或正切,
      對:對邊即正是對;
      余:余弦或余弦,
      鄰:鄰邊即余是鄰;
      切是直角邊。
      15、合并同類項
      合并同類項,法則不能忘,
      只求系數和,字母、指數不變樣。
      16、特殊三角函數值
      三十,四五,六十度,三角函數記牢固;
      分母弦二切是三,分子要把根號添;
      一二三來三二一,切值三九二十七;
      遞增正切和正弦,余弦函數要遞減。
      17、平行四邊形的判定
      要證平行四邊形,兩個條件才能行,
      一證對邊都相等,或證對邊都平行,
      一組對邊也可以,必須相等且平行。
      對角線,是個寶,互相平分“跑不了”,
      對角相等也有用,“兩組對角”才能成。
      18、梯形問題的輔助線
      移動梯形對角線,兩腰之和成一線;
      平行移動一條腰,兩腰同在“△”現;
      延長兩腰交一點,“△”中有平行線;
      作出梯形兩高線,矩形顯示在眼前;
      已知腰上一中線,莫忘作出中位線。
      19、添加輔助線歌
      輔助線,怎么添?找出規律是關鍵,
      題中若有角(平)分線,可向兩邊作垂線;
      線段垂直平分線,引向兩端把線連,
      三角形兩邊中點,連接則成中位線;
      三角形中有中線,延長中線翻一番。
      20、圓的證明歌
      圓的證明不算難,常把半徑直徑連;
      有弦可作弦心距,它定垂直平分弦;
      直徑是圓最大弦,直圓周角立上邊,
      它若垂直平分弦,垂徑、射影響耳邊;
      還有與圓有關角,勿忘相互有關聯,
      圓周、圓心、弦切角,細找關系把線連;
      同弧圓周角相等,證題用它最多見,
      圓中若有弦切角,夾弧找到就好辦;
      圓有內接四邊形,對角互補記心間,
      外角等于內對角,四邊形定內接圓;
      直角相對或共弦,試試加 個輔助圓;
      若是證題打轉轉,四點共圓可解難;
      要想證明圓切線,垂直半徑過外端,
      直線與圓有共點,證垂直來半徑連,
      直線與圓未給點,需證半徑作垂線;
      四邊形 有內切圓,對邊和等是條件;
      如果遇到圓與圓,弄清位置很關鍵,
      兩圓相切作公切,兩圓相交連公弦。
      21、圓中比例線段
      遇等積,改等比,橫找豎找定相似;
      不相似,別生氣,等線等比來代替,
      遇等比,改等積,引用射影和圓冪,
      平行線,轉比例,兩端各自找聯系。
      22、正多邊形
      份相等分割圓,n值必須大于三,
      依次連接各分點,內接正n邊形在眼前。
      經過分點做切線,切線相交n個點。
      n個交點做頂點,外切正n邊形便出現。
      正n邊形很美觀,它有內接、外切圓,
      內接、外切都唯一,兩圓還是同心圓,
      它的圖形軸對稱,n條對稱軸 都過圓心點,
      如果n值為偶數,中心對稱很方便。
      正n邊形做計算,邊心距、半徑是關鍵,
      內切、外接圓半徑,邊心距、半徑分別換,
      分成直角三角形2n個整,依此計算便簡單。
      23、函數學習口決
      二次函數拋物線,選定需要三個點,
      a的正負開口判,c的大小y軸看,
      △的符號最簡便,x軸上數交點,
      a、b同號軸左邊拋物線平移a不變,
      頂點牽著圖象轉,三種形式可變換,
      配方法作用最關鍵。
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