📐 Sổ tay công thức toán THCS

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

$$(-a)\cdot(-b) = a\cdot b, \quad (-a)\cdot b = -(a\cdot b)$$

$$-(a + b - c) = -a - b + c$$

$$\text{ƯCLN}(a,b)\cdot\text{BCNN}(a,b) = a\cdot b$$

$$60 = 2^2\cdot 3\cdot 5, \quad 72 = 2^3\cdot 3^2$$

$$\frac{a}{b} = \frac{c}{d} \Leftrightarrow ad = bc$$

$$\frac{a}{b} : \frac{c}{d} = \frac{a}{b}\cdot\frac{d}{c}$$

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

$$S = a\cdot h$$

$$S = \frac{d_1\cdot d_2}{2}$$

$$S = \frac{(a+b)\cdot h}{2}$$

$$S = a\cdot b,\quad P = 2(a+b)$$

$$|x| = \begin{cases} x & x \ge 0 \\ -x & x < 0 \end{cases}$$

$$\sqrt{a} = x \Leftrightarrow x \ge 0,\ x^2 = a$$

$$x^m\cdot x^n = x^{m+n},\quad (x^m)^n = x^{mn}$$

$$\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc$$

$$\frac{a}{b} = \frac{c}{d} = \frac{a+c}{b+d}$$

$$y = kx$$

$$x\cdot y = a$$

$$P(a) = 0 \Leftrightarrow x = a \text{ là nghiệm}$$

$$a(b + c) = ab + ac$$

$$\hat{A} + \hat{B} + \hat{C} = 180^\circ$$

$$\widehat{ACx} = \hat{A} + \hat{B}$$

$$\hat{A} = 180^\circ - 2\hat{B}$$

$$\overline{x} = \frac{x_1 + x_2 + \dots + x_n}{n}$$

$$P(A) = \frac{n(A)}{n(\Omega)}$$

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

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

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

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

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

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

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

$$ax + b = 0\ (a \ne 0) \Leftrightarrow x = -\frac{b}{a}$$

$$y = ax + b\quad (a \ne 0)$$

$$a = a',\ b \ne b'$$

$$a \ne a'$$

$$BC^2 = AB^2 + AC^2$$

$$AC = \sqrt{BC^2 - AB^2}$$

$$MN \parallel BC \Rightarrow \frac{AM}{AB} = \frac{AN}{AC}$$

$$MN = \frac{BC}{2}$$

$$\frac{S}{S'} = k^2$$

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

$$\sqrt{AB} = \sqrt{A}\cdot\sqrt{B}\ (A, B \ge 0)$$

$$\sqrt{A^2 B} = |A|\sqrt{B}$$

$$\frac{1}{\sqrt{a}} = \frac{\sqrt{a}}{a}$$

$$\begin{cases} ax + by = c \\ a'x + b'y = c' \end{cases}$$

$$\Delta = b^2 - 4ac$$

$$x_{1,2} = \frac{-b \pm \sqrt{\Delta}}{2a}$$

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

$$\sin\alpha = \frac{\text{đối}}{\text{huyền}},\ \cos\alpha = \frac{\text{kề}}{\text{huyền}},\ \tan\alpha = \frac{\text{đối}}{\text{kề}}$$

$$\sin 30^\circ = \tfrac12,\ \sin 45^\circ = \tfrac{\sqrt2}{2},\ \sin 60^\circ = \tfrac{\sqrt3}{2}$$

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

$$\sin\alpha = \cos(90^\circ - \alpha)$$

$$C = 2\pi R,\quad S = \pi R^2$$

$$l = \frac{\pi R n}{180}$$

$$S_{xq} = 2\pi r h,\quad V = \pi r^2 h$$

$$S_{xq} = \pi r l,\quad V = \frac13 \pi r^2 h$$

$$S = 4\pi R^2,\quad V = \frac43 \pi R^3$$