Overview
This lecture reviewed the January 2025 Algebra 1 Regents Exam, covering key formulas, problem-solving strategies, and step-by-step solutions for multiple-choice and free-response questions, emphasizing core Algebra 1 concepts.
Formula Sheet Essentials
- The formula sheet provides the quadratic formula, axis of symmetry for parabolas, slope formula, and arithmetic sequence formula.
- The most used formulas on this exam are the quadratic formula, arithmetic sequence formula, and slope formula.
Factoring and Equations
- Always factor out the greatest common factor before using other factoring methods (difference of squares, trinomials).
- To find a line through two points: calculate the slope, then use point-slope or slope-intercept form to find the equation.
- Geometric sequences multiply by a common ratio; arithmetic sequences add a common difference.
Functions and Terminology
- The constant term in a polynomial has no variable (e.g., 2x³ - x + 5 + 4x² → constant term is 5).
- In cost functions like C(x) = 55x + 80, the coefficient of x is the rate (slope), and the constant is the set fee (y-intercept).
Algebraic Manipulation
- When simplifying expressions, distribute negatives and combine like terms carefully.
- For inequalities, remember to reverse the inequality sign when dividing/multiplying by a negative.
Sequences and Patterns
- Arithmetic sequence formula: nth term = first term + (n−1) × common difference.
- In geometric sequences, the common ratio = (next term)/(previous term).
Data Analysis
- To find percentages: (part/whole) × 100.
- The interquartile range (IQR) = Q3 - Q1, found using statistics functions on calculators.
Solving Equations
- To solve for a variable in a literal equation (e.g., solve P = 2L + 2W for W): isolate W step by step.
- Use calculators for complex arithmetic and statistics calculations.
Graphing and Systems
- The domain is all valid x-values; an open circle excludes that value, a closed circle includes it.
- For system solutions, look for overlap in shaded areas for inequalities or intersection points for equations.
- Always label axes and use accurate scales when graphing functions.
Key Terms & Definitions
- Quadratic Formula — Used to solve ax² + bx + c = 0: x = [-b ± √(b²-4ac)]/(2a)
- Common Ratio — The multiplier between terms in a geometric sequence.
- Constant Term — The term without a variable in a polynomial.
- Slope — Rate of change, (y₂ - y₁)/(x₂ - x₁), defines the steepness of a line.
- Arithmetic Sequence — Sequence where each term increases/decreases by a constant difference.
- Interquartile Range (IQR) — Q3 minus Q1, measures data spread in statistics.
- Domain — Set of all possible x-values (inputs) for a function.
Action Items / Next Steps
- Review the formula sheet, especially the quadratic formula and sequence formulas.
- Practice graphing functions and systems of equations.
- Ensure calculator proficiency for statistical and regression calculations.
- Prepare scrap/graph paper for the test and attempt all questions—no penalty for guessing.