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 $y = \log_b(x)$ 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 2: 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 3: 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 4: What is $V$ when you solve Ohm's law $V = IR$ for $V$?

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

Flashcard 5: 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 6: 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 7: 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 8: What is $x$ when you solve $y = \ln(x)$ for $x$?

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

Flashcard 9: What is $h$ when you solve $y = a(x - h)^2 + k$ for $h$ (assume $a \ne 0$)?

Answer: $h = x \pm \sqrt{\frac{y - k}{a}}$. Isolate the squared term, take square root, then solve for $h$.

Flashcard 10: What is $x$ when you solve $y = a(x - h)^2 + k$ for $x$ (with $a \ne 0$)?

Answer: $x = h \pm \sqrt{\frac{y - k}{a}}$. Isolate the squared term, take square root, then add $h$.

Flashcard 11: 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 12: What is $r_2$ when you solve $A = \pi(r_1^2 - r_2^2)$ for $r_2$ (assume $r_2 \ge 0$)?

Answer: $r_2 = \sqrt{r_1^2 - \frac{A}{\pi}}$. Solve for $r_2^2$ and take the square root.

Flashcard 13: What is $x$ when you solve $\frac{1}{x} = a$ (with $a \ne 0$) for $x$?

Answer: $x = \frac{1}{a}$. Take the reciprocal of both sides.

Flashcard 14: What is $x$ when you solve $y = \sqrt{x - h}$ for $x$?

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

Flashcard 15: 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 16: What is $m$ when you solve $y = mx + b$ (with $x \neq 0$) for $m$?

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

Flashcard 17: What is $x$ when you solve $ax + b = c$ (with $a \ne 0$) for $x$?

Answer: $x = \frac{c - b}{a}$. Divide both sides by $a$ after isolating $ax$.

Flashcard 18: 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 19: 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 20: 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 21: What is $b$ when you solve $y = mx + b$ for $b$?

Answer: $b = y - mx$. Subtract $mx$ from both sides.

Flashcard 22: What is $R$ when you solve Ohm's law $V = IR$ for $R$ (with $I \ne 0$)?

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

Flashcard 23: 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 24: What is $x$ when you solve $a(x + h) = k$ (with $a \ne 0$) for $x$?

Answer: $x = \frac{k}{a} - h$. Divide by $a$, then subtract $h$ from both sides.

Flashcard 25: 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 26: 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 27: 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 28: What is the correct first step to isolate $x$ in $ax + b = c$ (with $a \ne 0$)?

Answer: Subtract $b$: $ax = c - b$. Use inverse operations to isolate the term with $x$.

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

Answer: $x = ab$. Multiply both sides by $a$ to eliminate the fraction.

Flashcard 30: What is $x$ when you solve $a = \frac{b}{x}$ (with $a \ne 0$) for $x$?

Answer: $x = \frac{b}{a}$. Cross-multiply to get $ax = b$, then divide by $a$.

Flashcard 31: 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 32: 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 33: 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 34: 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 35: 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 36: What is $c$ when you solve the Pythagorean theorem $a^2 + b^2 = c^2$ for $c$?

Answer: $c = \sqrt{a^2 + b^2}$. Take the square root of both sides.

Flashcard 37: What is $x$ when you solve $a(x - h) = k$ (with $a \ne 0$) for $x$?

Answer: $x = \frac{k}{a} + h$. Divide by $a$, then add $h$ to both sides.

Flashcard 38: What is $x$ when you solve $ax = b$ (with $a \ne 0$) for $x$?

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

Flashcard 39: 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 40: 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 41: 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 42: What is $x$ when you solve $y = mx + b$ (with $m \ne 0$) for $x$?

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