Overview
This lecture reviewed Part 1 (multiple choice) of the January 2025 Algebra 1 Regents Exam, focusing on core algebra concepts, formulas, and problem-solving strategies for 24 questions.
Factoring and Simplifying Expressions
- Factoring requires identifying common terms and rewriting in parentheses form.
- The difference of squares formula: (a^2 - b^2 = (a+b)(a-b)).
- Distributive property is used to simplify expressions and combine like terms.
Linear Equations and Slope
- Equation of a line: (y = mx + b), where (m) is slope and (b) is y-intercept.
- Slope formula: (m = \frac{y_2 - y_1}{x_2 - x_1}).
- Solve for y-intercept by plugging one point into the line equation.
Sequences: Geometric and Arithmetic
- Geometric sequence: next term = previous term × common ratio.
- Common ratio = last term ÷ previous term.
- Arithmetic sequence: next term = previous term + common difference.
- Common difference = (term3 - term1) / 2.
Constants and Terms
- The constant term in a polynomial has no variable attached.
Functions and Graphs
- The term in front of (x) in (y = mx + b) is the rate; the constant is the set fee.
- Solution to a system of inequalities is the overlapping shaded region.
- Domain of a function is all x-values where the function exists.
- Mode is the most frequent value; median is the middle value.
Exponents and Properties
- Product of exponents with same base: (x^a × x^b = x^{a+b}).
- Addition property of equality: add the same value to both sides to maintain equality.
Percentages, Units, and Conversions
- Percent = (part/whole) × 100.
- Speed: numerator is distance, denominator is time.
- Use unit cancellation to check for correct conversion expressions.
Solving Equations and Inequalities
- Set variable alone on one side by inverse operations.
- For inequalities, use solid dots for "or equal to" and open dots for strict inequalities.
Statistics
- Interquartile range (IQR) = third quartile (Q3) – first quartile (Q1).
Key Terms & Definitions
- Slope (m) — measures the steepness of a line; change in y over change in x.
- Y-intercept (b) — the point where the line crosses the y-axis.
- Geometric sequence — sequence with constant multiplication factor (ratio).
- Arithmetic sequence — sequence with constant addition/subtraction (difference).
- Constant term — term with no variable (unchanging).
- Domain — all possible input (x) values for a function.
- Mode — most frequent number in a data set.
- Product of exponents — when multiplying, add exponents if bases are equal.
- IQR (Interquartile Range) — spread between Q1 and Q3 in a data set.
Action Items / Next Steps
- Review and memorize key algebraic formulas (difference of squares, slope, exponents).
- Practice factoring, simplifying, and solving equations.
- Use graphing calculator tools for statistics questions (IQR, regression).
- Complete assigned homework or review the next video for Part 2 of the exam.