高中三年数学必背公式_公式库网

高中三年数学必背公式

一、集合与函数

集合运算：$A \cup B = {x | x \in A \text{ 或 } x \in B}$；$A \cap B = {x | x \in A \text{ 且 } x \in B}$

二次函数顶点：$y = a(x-h)^2+k$，顶点 $(h,k)$，$h=-\dfrac{b}{2a}$，$k=\dfrac{4ac-b^2}{4a}$文章源自公式库网-https://www.gongshiku.com/html/201908/f35691c9e5.html

指数运算：$a^m \cdot a^n = a^{m+n}$；$(a^m)^n = a^{mn}$；$a^{-n} = \dfrac{1}{a^n}$文章源自公式库网-https://www.gongshiku.com/html/201908/f35691c9e5.html

二、三角函数

$\sin^2\theta + \cos^2\theta = 1$文章源自公式库网-https://www.gongshiku.com/html/201908/f35691c9e5.html

$\tan\theta = \dfrac{\sin\theta}{\cos\theta}$文章源自公式库网-https://www.gongshiku.com/html/201908/f35691c9e5.html

$\sin 2\theta = 2\sin\theta\cos\theta$文章源自公式库网-https://www.gongshiku.com/html/201908/f35691c9e5.html

$\cos 2\theta = \cos^2\theta - \sin^2\theta = 2\cos^2\theta - 1 = 1 - 2\sin^2\theta$文章源自公式库网-https://www.gongshiku.com/html/201908/f35691c9e5.html

正弦定理：$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C} = 2R$文章源自公式库网-https://www.gongshiku.com/html/201908/f35691c9e5.html

余弦定理：$a^2 = b^2 + c^2 - 2bc\cos A$文章源自公式库网-https://www.gongshiku.com/html/201908/f35691c9e5.html

三、数列

等差数列：$a_n = a_1 + (n-1)d$；$S_n = \dfrac{n(a_1+a_n)}{2} = na_1 + \dfrac{n(n-1)}{2}d$文章源自公式库网-https://www.gongshiku.com/html/201908/f35691c9e5.html

等比数列：$a_n = a_1 q^{n-1}$；$S_n = \dfrac{a_1(1-q^n)}{1-q}$（$q \neq 1$）文章源自公式库网-https://www.gongshiku.com/html/201908/f35691c9e5.html

四、导数

$(x^n)' = nx^{n-1}$；$(\sin x)' = \cos x$；$(\cos x)' = -\sin x$

$(e^x)' = e^x$；$(\ln x)' = \dfrac{1}{x}$

求导法则：$(uv)' = u'v + uv'$；$\left(\dfrac{u}{v}\right)' = \dfrac{u'v - uv'}{v^2}$

五、概率统计

古典概型：$P(A) = \dfrac{m}{n}$（$m$ 为有利情况数，$n$ 为总情况数）

条件概率：$P(B|A) = \dfrac{P(AB)}{P(A)}$

二项分布：$P(X=k) = C_n^k p^k (1-p)^{n-k}$