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    貴陽博文強化記憶之數學公式的常用記憶步驟和方法
    發布時間:12月22日 瀏覽:1291   [ ] 視力保護色:
    1.弄清公式結構 
    例二項展開式為: 
    (a+b)n 
    對公式右邊作如下分析:(1)共有(n+1)項,全帶正號;(2)每項由三部分的積組成,呈Cab的形式;(3)a的指數從高到低(n 到0);(4)b的指數從低到高(0到n);(5)C的下標恒為n,上示從低到高,明白以上五點后,學生即可逐步寫出這個公式。開始可能慢了些,但熟練后,即可直接寫出二項展開式。

    2.賦予一個名稱,或使用一個記號 
    有時候,為了加深對某個公式的印象,可以自己賦予某一公式的部件以一個合適的名稱,也可以使用一個恰當的記號。經過這種刺激,反而使學生記住這一公式。 
    例如,點(x0,y0)到直線Ax+By+C=0的距離d由下公式計算: 
    此外,分子容易記住:把點代入直線方程一般式的左邊后,再取絕對值。 
    此名稱關系,學生就會記住:還要除以一個叫法化因子的東西――而這正是我們的目的。 
    當然,名稱也并非胡撰的。事實上,直線方程在化為法線方程時,確實 
    數學上有些公式,或是不常用到,或是重要性相對來說較為次要。這些公式,不必一定全部記住,只要記住其大概的推導方向,或推導方法。直到要用時,臨時推導一下即可。

    4.利用圖表 
    某些公式,可以制成一個圖或一個表,借此,可較為輕松地記住這些公式。 
    例如,初學“同角三角函數間關系”對其中關系式可能較難記憶,右圖可以協助記憶: 
    ①對角線上兩個三角函數乘積為1。 
    如sinα cscα=1。 
    ②帶陰影的三角形中,上面兩個頂點上的值的平方和等于下面頂點上的值的平方。 
    如sin2a+cos2α=1。 
    ③六角形任一頂點上的函數值等于與它相鄰的二個頂點函數值的乘積。 
    如sisα=tgα cosα。

    5.代入特殊值 
    r> 例如,對某學生來說,正弦函數的三倍角公式是甲?還是乙 
    甲:sin3α=3sinα-4sin3α, 
    乙:sin3α=4sin3α-3sinα. 
    他記不準了(主要該生把它與cos3α的公式混淆起來了)。這好辦,令成立。 
    這里特別要注意,特殊值必須選好,要能區分,又要易于計算。如選α=60°,則無從區分。

    6.編制口決 
    有時候,為了記住某個公式,或為了正確地使用公式,可以根據公式的特點編制一些口訣,運用口訣就可以較方便地解決這種記憶。 
    例:三角學中有所謂誘導公式,它由54個公式組成。如果記住這54個公式,膾炙人口的口訣“奇變偶不變,符號看象限”就完全解決了這一問題。

    7.記住一般的公式。 
    有些公式,是更一般公式的特例。因此,單獨記住它是不妥的。這似乎是“就事論事”。更主要的是,沒能更深刻地揭示事物的本質,故還不如記住一般的公式為好。 
    (所謂“球臺”是在一個球缺上取下一個球缺后所成的幾何體,但二球缺底面要平行)。 
    理由是簡單的,球缺可以看作是球臺的特例(r2=0)。由球缺的體積公式去推出球臺的體積公式是鍛煉學生智力的一個極好的練習。

    8.推廣公式的意義或使用范圍 
    推廣公式的意義,實際上是多記住了一些公式,推廣公式的使用范圍,有助于減少記憶公式的個數。

    9.用一句話,一種說法記住公式,或公式的關鍵部分,或公式的作用 
    例如,一平面圖形面積為S,該圖形所在平面與某平面M成α角。該圖形在M上射影面積為S',則有S'=Scosα。這個立體幾何中頗為有用的公式,請勿記為S=S'cosα。這只要記住以下簡單事實即可:在雨中一塊木板所能擋住地面不遭受雨淋的面積決不大于木板本身面積。
    相關標簽: 強化記憶
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