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     22 12
    發新話題
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    高中數學知識口訣(超全)

    高中數學知識口訣(超全)

    根據多年的實踐,總結規律繁化簡;概括知識難變易,高中數學巧記憶。
    言簡意賅易上口,結合課本勝一籌。始生之物形必丑,拋磚引得白玉出。
    一、《集合與函數》
    內容子交并補集,還有冪指對函數。性質奇偶與增減,觀察圖象最明顯。
    復合函數式出現,性質乘法法則辨,若要詳細證明它,還須將那定義抓。
    指數與對數函數,兩者互為反函數。底數非1的正數,1兩邊增減變故。
    函數定義域好求。分母不能等于0,偶次方根須非負,零和負數無對數;
    正切函數角不直,余切函數角不平;其余函數實數集,多種情況求交集。
    兩個互為反函數,單調性質都相同;圖象互為軸對稱,Y=X是對稱軸;
    求解非常有規律,反解換元定義域;反函數的定義域,原來函數的值域。
    冪函數性質易記,指數化既約分數;函數性質看指數,奇母奇子奇函數,
    奇母偶子偶函數,偶母非奇偶函數;圖象第一象限內,函數增減看正負。
    二、《三角函數》
    三角函數是函數,象限符號坐標注。函數圖象單位圓,周期奇偶增減現。
    同角關系很重要,化簡證明都需要。正六邊形頂點處,從上到下弦切割;
    中心記上數字1,連結頂點三角形;向下三角平方和,倒數關系是對角,
    頂點任意一函數,等于后面兩根除。誘導公式就是好,負化正后大化小,
    變成稅角好查表,化簡證明少不了。二的一半整數倍,奇數化余偶不變,
    將其后者視銳角,符號原來函數判。兩角和的余弦值,化為單角好求值,
    余弦積減正弦積,換角變形眾公式。和差化積須同名,互余角度變名稱。
    計算證明角先行,注意結構函數名,保持基本量不變,繁難向著簡易變。
    逆反原則作指導,升冪降次和差積。條件等式的證明,方程思想指路明。
    萬能公式不一般,化為有理式居先。公式順用和逆用,變形運用加巧用;
    1加余弦想余弦,1 減余弦想正弦,冪升一次角減半,升冪降次它為范;
    三角函數反函數,實質就是求角度,先求三角函數值,再判角取值范圍;
    利用直角三角形,形象直觀好換名,簡單三角的方程,化為最簡求解集;
    三、《不等式》
    解不等式的途徑,利用函數的性質。對指無理不等式,化為有理不等式。
    高次向著低次代,步步轉化要等價。數形之間互轉化,幫助解答作用大。
    證不等式的方法,實數性質威力大。求差與0比大小,作商和1爭高下。
    直接困難分析好,思路清晰綜合法。非負常用基本式,正面難則反證法。
    還有重要不等式,以及數學歸納法。圖形函數來幫助,畫圖建模構造法。
    四、《數列》
    等差等比兩數列,通項公式N項和。兩個有限求極限,四則運算順序換。
    數列問題多變幻,方程化歸整體算。數列求和比較難,錯位相消巧轉換,
    取長補短高斯法,裂項求和公式算。歸納思想非常好,編個程序好思考:
    一算二看三聯想,猜測證明不可少。還有數學歸納法,證明步驟程序化:
    首先驗證再假定,從 K向著K加1,推論過程須詳盡,歸納原理來肯定。
    五、《復數》
    虛數單位i一出,數集擴大到復數。一個復數一對數,橫縱坐標實虛部。
    對應復平面上點,原點與它連成箭。箭桿與X軸正向,所成便是輻角度。
    箭桿的長即是模,常將數形來結合。代數幾何三角式,相互轉化試一試。
    代數運算的實質,有i多項式運算。i的正整數次慕,四個數值周期現。
    一些重要的結論,熟記巧用得結果。虛實互化本領大,復數相等來轉化。
    利用方程思想解,注意整體代換術。幾何運算圖上看,加法平行四邊形,
    減法三角法則判;乘法除法的運算,逆向順向做旋轉,伸縮全年模長短。
    三角形式的運算,須將輻角和模辨。利用棣莫弗公式,乘方開方極方便。
    輻角運算很奇特,和差是由積商得。四條性質離不得,相等和模與共軛,
    兩個不會為實數,比較大小要不得。復數實數很密切,須注意本質區別。
    六、《排列、組合、二項式定理》
    加法乘法兩原理,貫穿始終的法則。與序無關是組合,要求有序是排列。
    兩個公式兩性質,兩種思想和方法。歸納出排列組合,應用問題須轉化。
    排列組合在一起,先選后排是常理。特殊元素和位置,首先注意多考慮。
    不重不漏多思考,捆綁插空是技巧。排列組合恒等式,定義證明建模試。
    關于二項式定理,中國楊輝三角形。兩條性質兩公式,函數賦值變換式。
    七、《立體幾何》
    點線面三位一體,柱錐臺球為代表。距離都從點出發,角度皆為線線成。
    垂直平行是重點,證明須弄清概念。線線線面和面面、三對之間循環現。
    方程思想整體求,化歸意識動割補。計算之前須證明,畫好移出的圖形。
    立體幾何輔助線,常用垂線和平面。射影概念很重要,對于解題最關鍵。
    異面直線二面角,體積射影公式活。公理性質三垂線,解決問題一大片。
    八、《平面解析幾何》
    有向線段直線圓,橢圓雙曲拋物線,參數方程極坐標,數形結合稱典范。
    笛卡爾的觀點對,點和有序實數對,兩者—一來對應,開創幾何新途徑。
    兩種思想相輝映,化歸思想打前陣;都說待定系數法,實為方程組思想。
    三種類型集大成,畫出曲線求方程,給了方程作曲線,曲線位置關系判。
    四件工具是法寶,坐標思想參數好;平面幾何不能丟,旋轉變換復數求。
    解析幾何是幾何,得意忘形學不活。圖形直觀數入微,數學本是數形學。

    TOP

    高中數學知識口訣(超全)

    雖嘫萇ㄋ嚸 但媞の確佷佺錒 

    TOP

    嫌長!不好記!!!!

    TOP

    挺全,但是感覺挺難懂的,O(∩_∩)O~
      你的夕陽、我 的容顏、誰的三分之一年.....

    TOP

    確實,太長了啊

    TOP

    好嗜好,就是內容有點長,不過很全面哦
    我個性,我張揚

    TOP

    可以
    有點不好記

    TOP

    是呀

    好難呀~~

    TOP

    的確

    TOP

    難弄懂,好長啊········
    從壹滴水裏,看到了整個海洋!

    TOP

    學習了。。。。。

    TOP

    抄下來就好記啦嘿嘿
    {綠燈亮起,,{{我站在人群裏卻不知道、{{梺﹃埗,該怎嚒赱℅

    TOP

    這要怎么被?
    讀出下面的字,你將獲得月薪2000000的工作,試題如下:簟璁醭歙艽绱癀穡魍旃傯彘硪钚鰣硐。

    TOP

    太多了就會少了點重點

    TOP

    可憐我不看不懂是些什么

    TOP

     22 12
    發新話題

    當前時區 GMT+8, 現在時間是 2019-6-26 01:00
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