This course prepares New York high school students for the Regents Examination in Algebra I by teaching the underlying curriculum and the specific exam skills required for success. It is designed for students who need to master the tested standards, fill knowledge gaps, improve mathematical explanations, and practice with original Regents-style questions. The program begins with exam orientation and a standards-mapped diagnostic so students can identify exactly which topics need the most attention. From there, it builds core Algebra I knowledge step by step, covering expressions, equations, inequalities, graphing, functions, systems, exponents, polynomials, factoring, quadratics, exponential models, statistics, and mathematical modeling. Each part of the course connects conceptual understanding to practical test performance. Students do not just memorize procedures; they learn how to interpret graphs and tables, choose appropriate models, explain reasoning in writing, and complete both multiple-choice and constructed-response tasks under Regents-style expectations. Standards-aligned review: Lessons are organized around the Algebra I content and reporting categories students are expected to know for the New York Regents. Concrete skill development: Students practice solving equations, graphing functions, interpreting slope and intercepts, factoring quadratics, comparing function types, and analyzing statistical displays. Exam-format practice: The course includes original multiple-choice and constructed-response questions modeled on Regents item types, with attention to partial-credit reasoning and clear written work. Error analysis and remediation: Students learn to classify mistakes by concept, procedure, vocabulary, and reading errors, then use a mistake log and targeted review to improve weak areas. Pacing and readiness: Timed drills, mixed review sets, and a full mock exam help students build speed, accuracy, and confidence before test day. By the end of the course, students should be able to solve and explain Algebra I problems across the full tested range of standards, move efficiently between equations, graphs, tables, and contexts, manage time on the exam, and respond effectively to both selected-response and written-response questions. Understand the Regents Algebra I exam format, scoring, and performance expectations. Master foundational algebra skills needed for equations, inequalities, functions, and modeling. Analyze and interpret linear, exponential, and quadratic relationships in multiple forms. Use statistics and regression tools to read data displays and make justified conclusions. Complete state-test-style practice and apply detailed feedback to improve performance.
- How the New York Regents Algebra I Exam Works
- Regents Standards and Reporting Categories
- Diagnostic Pre-Assessment by Standard
- Analyzing Diagnostic Results
- Building a Personal Regents Study Plan
- Order of Operations and Real Number Properties
- Variables, Terms, Coefficients, and Expressions
- Evaluating Algebraic Expressions
- Combining Like Terms and Simplifying
- The Distributive Property and Factoring Out a Common Factor
- Representing Quantities with Algebra
- Common Expression Errors and Precision Checks
- Solving One-Step and Two-Step Equations
- Multi-Step Equations with Distribution
- Equations with Variables on Both Sides
- Literal Equations and Rearranging Formulas
- Checking Solutions and Interpreting Meaning
- Regents-Style Equation Problems
- Writing and Solving One-Variable Inequalities
- Multi-Step Inequalities and Distribution
- Multiplying or Dividing by a Negative
- Graphing Solutions on a Number Line
- Compound Inequalities
- Interpreting Inequalities in Context
- The Coordinate Plane and Plotting Points
- Slope as Rate of Change
- Positive, Negative, Zero, and Undefined Slope
- Finding Slope from Two Points
- Comparing Rates of Change Across Representations
- Graph Reading for Regents Questions
- What Makes a Relationship Linear
- Slope-Intercept Form
- Point-Slope Form
- Standard Form
- Writing Linear Equations from Graphs, Tables, and Situations
- Graphing Linear Functions
- Interpreting Parameters in Context
- Comparing Linear Models
- Understanding Solutions to a System
- Solving Systems by Graphing
- Solving Systems by Substitution
- Solving Systems by Elimination
- No Solution and Infinitely Many Solutions in Systems
- Modeling with Systems of Equations
- Graphing Systems of Linear Inequalities
- Feasible Regions and Context-Based Constraints
- Exponent Rules for Integer Exponents
- Zero and Negative Exponents
- Simplifying Exponential Expressions
- Square Roots and Radical Basics
- Simplifying Radicals
- Scientific Notation
- Operations with Scientific Notation
- Classifying Polynomials by Terms and Degree
- Adding and Subtracting Polynomials
- Multiplying a Polynomial by a Monomial
- Multiplying Binomials and Polynomials
- Special Products
- Interpreting Polynomial Expressions in Context
- Common Errors in Polynomial Work
- Factoring Out the Greatest Common Factor
- Factoring Trinomials with Leading Coefficient 1
- Factoring Trinomials with Leading Coefficient Greater Than 1
- Factoring Difference of Squares
- Factoring by Grouping
- Choosing the Best Form of an Expression
- Using Factoring to Reveal Zeros and Intercepts
- Recognizing Quadratic Relationships
- Solving Quadratic Equations by Factoring
- Solving Quadratic Equations by Square Roots
- Completing the Square Conceptually
- The Quadratic Formula
- The Discriminant
- Graphing Parabolas
- Standard, Vertex, and Factored Forms of Quadratics
- Interpreting Key Features of Quadratic Graphs
- Modeling with Quadratic Functions
- Recognizing Exponential Relationships
- Writing Exponential Functions from Tables and Situations
- Graphing Exponential Functions
- Comparing Exponential and Linear Functions
- Percent Growth and Percent Decay
- Interpreting Parameters in Exponential Models
- Choosing Between Linear, Quadratic, and Exponential Models
- What a Function Is
- Functions in Tables, Graphs, Equations, and Sets of Ordered Pairs
- Domain and Range
- Function Notation
- Independent and Dependent Variables
- Comparing Functions in Different Forms
- Key Features from Graphs and Tables
- Types of Data and Measurement Contexts
- Dot Plots, Histograms, and Box Plots
- Mean, Median, and Measures of Center
- Range, Interquartile Range, and Variability
- Scatter Plots and Association
- Line of Best Fit and Linear Regression
- Correlation Versus Causation
- Residuals and Model Fit
- Using Statistics in Regents-Style Questions
- Translating Words into Algebraic Models
- Units, Labels, and Reasonable Answers
- Linear Modeling in Real Situations
- Exponential Modeling in Real Situations
- Quadratic Modeling in Real Situations
- Choosing and Defending a Model
- Interpreting Solutions, Intercepts, and Constraints
- Showing Algebraic Work Clearly
- Writing Complete Mathematical Explanations
- Justifying Why a Method Works
- Using Evidence from Graphs, Tables, and Equations
- Partial Credit Strategies for Constructed Response
- Revising Explanations for Accuracy and Precision
- Expressions and Equations Review
- Inequalities and Systems Review
- Linear Functions Review
- Exponential Functions Review
- Quadratic Functions Review
- Statistics and Regression Review
- Modeling and Application Review
- Reading Multiple-Choice Questions Efficiently
- Using Estimation and Elimination
- Avoiding Trap Answers
- When to Solve Fully and When to Test Choices
- Mixed Multiple-Choice Practice by Topic
- Reviewing Multiple-Choice Mistakes
- Understanding Multi-Part Constructed-Response Tasks
- Setting Up Work for Maximum Credit
- Using Graphs and Tables in Written Responses
- Solving Application-Based Constructed Responses
- Scoring Sample Responses
- Constructed-Response Practice with Detailed Review
- Algebra and Number Concepts Mixed Review
- Functions and Graphs Mixed Review
- Modeling and Application Mixed Review
- Statistics and Regression Mixed Review
- Calculator and Non-Calculator Mixed Sets
- Cumulative Spiral Review
- Identifying Recurring Error Patterns
- Sign Errors, Distribution Errors, and Arithmetic Slips
- Graph and Table Misinterpretations
- Misunderstanding Function Types
- Creating and Using a Mistake Log
- Targeted Remediation by Standard
- Pacing for the Full Regents Exam
- Timed Mini-Sets by Topic
- Timed Mixed Practice Sets
- Calculator Use Under Time Limits
- Checking Work Efficiently
- Managing Test Stress and Staying Focused
- Preparing for a Full Regents Simulation
- Full-Length Mock Regents Exam
- Scoring and Performance Analysis
- Detailed Review of Every Question
- Final Targeted Review Plan
- Last-Week and Last-Day Preparation