Algebra 1 Formula Reference Sheet

Need to ace your next algebra test? These formulas are your secret weapons! Learning to recognize and use these patterns will make solving problems much faster.

Factoring patterns save tons of time when simplifying expressions. Remember that perfect square trinomials follow predictable forms: $a^2 + 2ab + b^2 = (a+b)^2$ and $a^2 - 2ab + b^2 = (a-b)^2$. The difference of squares formula $a^2 - b^2 = (a-b)(a+b)$ is a quick way to break down expressions.

Properties of exponents let you manipulate expressions with ease. When multiplying powers with the same base, add the exponents: $a^m a^n = a^{m+n}$. For division, subtract: $a^m/a^n = a^{m-n}$. Other key properties include power of power $(a^m)^n = a^{mn}$, rational exponents $a^{m/n} = \sqrt[n]{a^m}$, and negative exponents $a^{-n} = 1/a^n$.

When working with linear equations, you'll use three main forms: standard form $Ax + By = C$, slope-intercept form $y = mx + b$, and point-slope form $y - y₁ = m(x - x₁)$. The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Pro Tip: For quadratic equations, memorize both the standard form f(x) = ax² + bx + c and vertex form f(x) = a$x - h$² + k. The quadratic formula x = $\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ helps you find solutions, while the axis of symmetry is at x = $\frac{-b}{2a}$.