Algebra 2 Flashcards: Rearranging Formulas To Highlight Quantities

What this deck covers

This deck focuses on Rearranging Formulas To Highlight Quantities, giving you a quick way to review the definitions, rules, and examples that matter most for Algebra 2.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is $x$ when you solve $y = \frac{ax + b}{c}$ for $x$ (with $a \ne 0$, $c \ne 0$)?

Answer: $x = \frac{cy - b}{a}$. Multiply by $c$, subtract $b$, then divide by $a$.

Flashcard 2: What is $I$ when you solve Ohm's law $V = IR$ for $I$ (with $R \ne 0$)?

Answer: $I = \frac{V}{R}$. Divide both sides by $R$ to isolate current.

Flashcard 3: What is $b$ when you solve triangle area $A = \frac{1}{2}bh$ for $b$ (with $h \ne 0$)?

Answer: $b = \frac{2A}{h}$. Multiply by $2$, then divide by $h$.

Flashcard 4: What is $x$ when you solve $y = \frac{a}{x} + b$ for $x$ (with $y \ne b$)?

Answer: $x = \frac{a}{y - b}$. Subtract $b$, then divide $a$ by the result.

Flashcard 5: What is $x$ when you solve $ax^2 = b$ for $x$ (with $a \ne 0$)?

Answer: $x = \pm\sqrt{\frac{b}{a}}$. Divide by $a$, then take square root with $\pm$.

Flashcard 6: What is $k$ when you solve $y = a(x - h)^2 + k$ for $k$?

Answer: $k = y - a(x - h)^2$. Subtract the squared term from both sides.

Flashcard 7: What is $P$ when you solve $A = P(1 + rt)$ for $P$ (assume $1+rt \ne 0$)?

Answer: $P = \frac{A}{1 + rt}$. Divide both sides by $(1 + rt)$.

Flashcard 8: What is $I$ when you solve Ohm's law $V = IR$ for $I$ (with $R \ne 0$)?

Answer: $I = \frac{V}{R}$. Divide both sides by $R$ to isolate current.

Flashcard 9: What is $V$ when you solve Ohm's law $V = IR$ for $V$?

Answer: $V = IR$. No rearrangement needed; $V$ is already isolated.

Flashcard 10: What is $W$ when you solve $P = 2L + 2W$ for $W$ (treat $P,L$ as constants)?

Answer: $W = \frac{P - 2L}{2}$. Subtract $2L$, then divide by $2$.

Flashcard 11: What is $r$ when you solve the circle area formula $A = \pi r^2$ for $r$?

Answer: $r = \sqrt{\frac{A}{\pi}}$. Divide by $\pi$, then take the square root.

Flashcard 12: What is $h$ when you solve the cylinder volume formula $V = \pi r^2 h$ for $h$?

Answer: $h = \frac{V}{\pi r^2}$. Divide both sides by $\pi r^2$.

Flashcard 13: What is $r$ when you solve $V = \pi r^2 h$ for $r$ (assume $h>0$)?

Answer: $r = \sqrt{\frac{V}{\pi h}}$. Divide by $\pi h$, then take the square root.

Flashcard 14: What is $b$ when you solve triangle area $A = \frac{1}{2}bh$ for $b$ (with $h \ne 0$)?

Answer: $b = \frac{2A}{h}$. Multiply by $2$, then divide by $h$.

Flashcard 15: What is $h$ when you solve triangle area $A = \frac{1}{2}bh$ for $h$ (with $b \ne 0$)?

Answer: $h = \frac{2A}{b}$. Multiply by $2$, then divide by $b$.

Flashcard 16: What is $r$ when you solve circumference $C = 2\pi r$ for $r$?

Answer: $r = \frac{C}{2\pi}$. Divide both sides by $2\pi$.

Flashcard 17: What is $r$ when you solve $d = rt$ for $r$ (with $t \ne 0$)?

Answer: $r = \frac{d}{t}$. Divide both sides by $t$.

Flashcard 18: What is $t$ when you solve $A = P(1 + rt)$ for $t$ (with $Pr \ne 0$)?

Answer: $t = \frac{\frac{A}{P} - 1}{r}$. Divide by $P$, subtract $1$, then divide by $r$.

Flashcard 19: What is $r$ when you solve $A = P(1 + rt)$ for $r$ (with $Pt \ne 0$)?

Answer: $r = \frac{\frac{A}{P} - 1}{t}$. Divide by $P$, subtract $1$, then divide by $t$.

Flashcard 20: What is $P$ when you solve $A = P\left(1 + \frac{r}{n}\right)^{nt}$ for $P$?

Answer: $P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}$. Divide by the compound interest factor.

Flashcard 21: What is $b$ when you solve $y = a(b^x)$ for $b$ (assume $a>0$, $y>0$)?

Answer: $b = \left(\frac{y}{a}\right)^{\frac{1}{x}}$. Take the $x$th root of $\frac{y}{a}$.

Flashcard 22: What is $a$ when you solve $y = a(b^x)$ for $a$ (assume $b^x \ne 0$)?

Answer: $a = \frac{y}{b^x}$. Divide both sides by $b^x$.

Flashcard 23: What is $x$ when you solve $y = \log_b(x)$ for $x$ (assume $b>0$, $b\ne 1$)?

Answer: $x = b^y$. Apply the definition of logarithms: $\log_b(x) = y$ means $b^y = x$.

Flashcard 24: What is $b$ when you solve $y = \log_b(x)$ for $b$ (assume $x>0$, $y \ne 0$)?

Answer: $b = x^{\frac{1}{y}}$. Rewrite as $b^y = x$, then solve for $b$.

Flashcard 25: What is $x$ when you solve $y = \ln(x)$ for $x$?

Answer: $x = e^y$. Apply the inverse relationship between $\ln$ and $e$.

Flashcard 26: What is $x$ when you solve $y = \sqrt{x - h}$ for $x$?

Answer: $x = y^2 + h$. Square both sides, then add $h$.

Flashcard 27: What is $x$ when you solve $y = \sqrt{ax + b}$ for $x$ (with $a \ne 0$)?

Answer: $x = \frac{y^2 - b}{a}$. Square both sides, subtract $b$, then divide by $a$.

Flashcard 28: What is $x$ when you solve $y = (ax + b)^2$ for $x$ (with $a \ne 0$)?

Answer: $x = \frac{\pm\sqrt{y} - b}{a}$. Take square root of both sides, then solve for $x$.

Flashcard 29: What is $x$ when you solve $y = \frac{ax + b}{c}$ for $x$ (with $a \ne 0$, $c \ne 0$)?

Answer: $x = \frac{cy - b}{a}$. Multiply by $c$, subtract $b$, then divide by $a$.

Flashcard 30: What is $x$ when you solve $y = \frac{a}{x} + b$ for $x$ (with $y \ne b$)?

Answer: $x = \frac{a}{y - b}$. Subtract $b$, then divide $a$ by the result.