Все формулы для ОГЭ по математике

$a^m \cdot a^n = a^{m+n}$

$\dfrac{a^m}{a^n} = a^{m-n}$

$\left(a^m\right)^n = a^{mn}$

$(ab)^n = a^n b^n$

$\left(\dfrac{a}{b}\right)^n = \dfrac{a^n}{b^n}$

$a^0 = 1$

$a^{-n} = \dfrac{1}{a^n}$

$\sqrt{ab} = \sqrt{a}\cdot\sqrt{b}$

$\sqrt{\dfrac{a}{b}} = \dfrac{\sqrt{a}}{\sqrt{b}}$

$\sqrt{a^2} = |a|$

$\left(\sqrt{a}\right)^2 = a$

$(a+b)^2 = a^2 + 2ab + b^2$

$(a-b)^2 = a^2 - 2ab + b^2$

$a^2 - b^2 = (a-b)(a+b)$

$(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$

$(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$

$a^3 + b^3 = (a+b)(a^2 - ab + b^2)$

$a^3 - b^3 = (a-b)(a^2 + ab + b^2)$

$ax^2 + bx + c = 0$

$D = b^2 - 4ac$

$x_{1,2} = \dfrac{-b \pm \sqrt{D}}{2a}$

$x = -\dfrac{b}{2a}$

$\text{корней нет}$

$x^2 + px + q = 0$

$x_1 + x_2 = -p$

$x_1 \cdot x_2 = q$

$x_1 + x_2 = -\dfrac{b}{a},\quad x_1 x_2 = \dfrac{c}{a}$

$ax + b > 0 \;\Rightarrow\; x > -\dfrac{b}{a}$

$-a x > b \;\Rightarrow\; x < -\dfrac{b}{a}$

$ax^2 + bx + c > 0$

$x_1, x_2 \text{ — корни}$

$a_n = a_1 + (n-1)d$

$d = a_{n+1} - a_n$

$S_n = \dfrac{a_1 + a_n}{2}\cdot n$

$S_n = \dfrac{2a_1 + (n-1)d}{2}\cdot n$

$a_n = \dfrac{a_{n-1} + a_{n+1}}{2}$

$b_n = b_1 \cdot q^{\,n-1}$

$q = \dfrac{b_{n+1}}{b_n}$

$S_n = \dfrac{b_1\left(q^n - 1\right)}{q - 1}$

$S_n = b_1 \cdot n$

$\dfrac{p}{100}\cdot a$

$\dfrac{a}{b}\cdot 100\%$

$a\left(1 + \dfrac{p}{100}\right)$

$a\left(1 - \dfrac{p}{100}\right)$

$a\left(1 + \dfrac{p}{100}\right)^{n}$

$y = kx + b$

$y = ax^2 + bx + c$

$x_{\text{в}} = -\dfrac{b}{2a}$

$y = \dfrac{k}{x}$

$P = a + b + c$

$P = 2(a + b)$

$P = 4a$

$P = 2(a + b)$

$S = \dfrac{1}{2}\,a h_a$

$S = \dfrac{1}{2}\,a b$

$S = a b$

$S = a^2$

$S = a h_a$

$S = \dfrac{1}{2}\,d_1 d_2$

$S = \dfrac{a + b}{2}\cdot h$

$c^2 = a^2 + b^2$

$\sin\alpha = \dfrac{a}{c}$

$\cos\alpha = \dfrac{b}{c}$

$\tan\alpha = \dfrac{a}{b}$

$\tan\alpha = \dfrac{\sin\alpha}{\cos\alpha}$

$\sin^2\alpha + \cos^2\alpha = 1$

$\sin 30^\circ = \dfrac{1}{2},\; \cos 30^\circ = \dfrac{\sqrt{3}}{2},\; \tan 30^\circ = \dfrac{\sqrt{3}}{3}$

$\sin 45^\circ = \cos 45^\circ = \dfrac{\sqrt{2}}{2},\; \tan 45^\circ = 1$

$\sin 60^\circ = \dfrac{\sqrt{3}}{2},\; \cos 60^\circ = \dfrac{1}{2},\; \tan 60^\circ = \sqrt{3}$

$\alpha + \beta + \gamma = 180^\circ$

$m = \dfrac{1}{2}\,a$

$2 : 1$

$S = \dfrac{\sqrt{3}}{4}\,a^2$

$S = \dfrac{1}{2}\,a b \sin\gamma$

$C = 2\pi r = \pi d$

$S = \pi r^2$

$l = \dfrac{\pi r \alpha}{180^\circ}$

$S = \dfrac{\pi r^2 \alpha}{360^\circ}$

$\beta = \dfrac{1}{2}\,\alpha$

$\beta = 90^\circ$

$\beta_1 = \beta_2$

$90^\circ$

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$\left(\dfrac{x_1 + x_2}{2},\; \dfrac{y_1 + y_2}{2}\right)$

$S = \text{В} + \dfrac{\text{Г}}{2} - 1$