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Formulalar

Formulalar va qoidalar

SAT'ning rasmiy formula varag'i va savollarda eng ko'p kerak bo'ladigan qoidalar.

Algebra

Qiyalik$m=\dfrac{y_2-y_1}{x_2-x_1}$
To'g'ri chiziq$y=mx+b$, $y-y_1=m(x-x_1)$
Parallel / perpendikulyar$m_1=m_2$ / $m_1\cdot m_2=-1$
Sistema: yechim yo'q$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\ne\dfrac{c_1}{c_2}$
Sistema: cheksiz yechim$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$

Advanced Math

Kvadrat tenglama$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$
Diskriminant$D=b^2-4ac$: $D>0$ ikki, $D=0$ bitta, $D<0$ haqiqiy yechim yo'q
Viyet$x_1+x_2=-\dfrac ba$, $x_1x_2=\dfrac ca$
Parabola uchi$x=-\dfrac{b}{2a}$; $y=a(x-h)^2+k$ da uch $(h,k)$
Qisqa ko'paytirish$a^2-b^2=(a-b)(a+b)$, $(a\pm b)^2=a^2\pm2ab+b^2$
Darajalar$a^ma^n=a^{m+n}$, $(a^m)^n=a^{mn}$, $a^{-n}=\dfrac1{a^n}$, $a^{\frac mn}=\sqrt[n]{a^m}$
Eksponensial o'sish/kamayish$y=a(1\pm r)^t$
Qoldiq teoremasi$p(x)$ ni $x-a$ ga bo'lgandagi qoldiq $=p(a)$

Problem Solving

Foiz o'zgarishi$\dfrac{\text{yangi}-\text{eski}}{\text{eski}}\cdot100\%$
Ketma-ket foizlar$x(1+p)(1-q)$
O'rtacha qiymat$\dfrac{\text{yig'indi}}{\text{soni}}$
Ehtimollik$P=\dfrac{\text{qulay holatlar}}{\text{barcha holatlar}}$
Xatolik chegarasi$p\pm e$ oralig'ida

Geometry & Trig

Doira$A=\pi r^2$, $C=2\pi r$, $360^\circ=2\pi$ radr
Yoy va sektor$s=r\theta$; $s=\dfrac{\alpha}{360}\cdot2\pi r$, $A=\dfrac{\alpha}{360}\cdot\pi r^2$αrs
Aylana tenglamasi$(x-h)^2+(y-k)^2=r^2$r(h, k)hkxy
Uchburchak$A=\dfrac12bh$, $a^2+b^2=c^2$hbbca
Maxsus uchburchaklar$30^\circ$-$60^\circ$-$90^\circ$: $x,\,x\sqrt3,\,2x$; $45^\circ$-$45^\circ$-$90^\circ$: $x,\,x,\,x\sqrt2$2xxx√330°60°xxx√245°45°
Hajmlar$V_{\text{quti}}=lwh$, $V_{\text{silindr}}=\pi r^2h$, $V_{\text{shar}}=\dfrac43\pi r^3$ℓwhrhr
Konus va piramida$V=\dfrac13\pi r^2h$, $V=\dfrac13lwh$hrhℓw
Piramida sirtiAsosi kvadrat ($a$): $s^2=h^2+\left(\dfrac a2\right)^2$, $S_{\text{yon}}=\dfrac12Ps=2as$ ($P$ — asos perimetri), $S_{\text{to'la}}=a^2+2as$hsaaha/2s
Konus sirti$l^2=r^2+h^2$, $S_{\text{yon}}=\pi rl$, $S_{\text{to'la}}=\pi r^2+\pi rl$hrl
Ichki burchaklar$(n-2)\cdot180^\circ$123n = 5 tomon3 ta uchburchak3 · 180° = 540°
Trigonometriya$\sin=\dfrac{\text{qarshi}}{\text{gip.}}$, $\cos=\dfrac{\text{yopishgan}}{\text{gip.}}$, $\tan=\dfrac{\text{qarshi}}{\text{yopishgan}}$θgipotenuzaqarshiyopishgan
Bog'lanishlar$\sin x^\circ=\cos(90-x)^\circ$, $\sin^2x+\cos^2x=1$x°(90−x)°
O'xshash shakllarMasshtab $k$ bo'lsa: yuzalar $k^2$, hajmlar $k^3$ martaabkakb× k