Algebra 1: EOC Review Notes

Solving for Variables: Use inverse operations to isolate the variable $n$ in equations like $2(2n + 3) + n = -5n + 1$ and $\frac{n}{4} - 3 = 7 - n$ .
Literal Equations: Rearrange formulas to solve for a specific variable, such as solving $F + V = E + 2$ for $E$ , $A = \pi r^2$ for $r$ , or $ax^2 + bx + c = 0$ for $x$ .

Simplification: Apply product and power rules to simplify expressions like $9x^4y \cdot 3x^5y^{-8}$ .
Rational Exponents: Work with fractional powers such as $2x^{\frac{1}{2}}y^{\frac{2}{3}} \cdot 3x^{\frac{3}{4}}y$ .

Rate of Change: Calculate slope ( $m$ ) between two points ( $x_1, y_1$ ) and ( $x_2, y_2$ ) using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ . For points $(5, -4)$ and $(-10, -20)$ , the rate of change is required.
Parallel Lines: Identify lines with identical slopes; examples provided include $y - 4 = \frac{2}{5}(x - 8)$ , $2x - 5y = 10$ , and $y = \frac{2}{5}x - 4$ .
Equation Writing: Generate linear equations from coordinate tables ( $x$ : $-16$ , $-12$ , $-8$ , $-4$ ; $y$ : $-22$ , $-19$ , $-16$ , $-13$ ).

Algebraic Solutions: Solve systems such as $3x + 2y = -1$ and $5x + 6y = -15$ using substitution or elimination.
Word Problems: - Ticket Pricing: A hall sold $300$ tickets ( $50$ military at half price) for $\$6050$ . Find the normal price. - Number Sums: The sum of two numbers is $24$ ; twice the smaller is $3$ less than the larger. - Coins: Find the number of nickels in a set of $13$ coins (nickels and dimes) totaling $\$0.85$ . - Supply Costs: Compare $9$ packs of colored paper and $4$ packs of white paper ( $\$99.50$ ) against $3$ packs of colored and $10$ packs of white ( $\$51.00$ ).

Finding the Inverse: For $f(x) = 2x - 10$ , determine $f^{-1}(x)$ .
Matching: Link functions to their inverses, such as mapping $y = x + 5$ to $y = x - 5$ , $y = x^2 + 5$ to $y = \pm\sqrt{x - 5}$ , and $y = \log_{5}(x)$ to $y = 5^x$ .

Factoring Methods: - Trinomials: $x^2 - 2x - 15$ , $6x^2 - 13x - 5$ , and $8x^2 - 52x + 24$ . - Binomials: GCF ( $3x^2 + 15x$ ) and Difference of Squares ( $16x^2 - 9$ ).
Solving Quadratics: Solve equations such as $x^2 = 100$ , $4x^2 - 9 = 0$ , and $2x^2 + 26 = 12x$ .
Characteristics of Parabolas: Determine the Axis of Symmetry ( $x = \frac{-b}{2a}$ ), Vertex, $x$ - and $y$ -intercepts, Domain, and Range for equations like $y = x^2 - 4x - 12$ .
Number Products: Systems involving product and sum, e.g., product is $-144$ and sum is $-7$ .

Classification: Group by degree (e.g., cubic, quartic) and terms (monomial, binomial, trinomial).
Operations: Perform addition, subtraction, distribution, and expansion ( $(x - 2)^4$ ).
Composition: Evaluate function operations such as $f(g(x))$ and $(g \circ f)(x)$ for $f(x) = x + 4$ and $g(x) = x^2 - 2x + 1$ .

Square Roots: Simplify radicals such as $\sqrt{200}$ , $\sqrt{50x^2}$ , and $\sqrt{9x^4y^2}$ .
Box and Whisker Plots: Plot data sets ( $4, 4, 5.5, 6, 6.5, 6.5, 7, 8, 9.5, 12$ ).
Data Analysis: Calculate the Inter Quartile Range (IQR) and determine percentiles (e.g., percent of data greater than or equal to $8$ ).