The Regents Exam in Mathematics in New York State is a standardized test that assesses students’ proficiency in math. The exam typically consists of various levels, including Algebra 1, Geometry, and Algebra 2, depending on the student’s grade level and progress in their math education.

Here is a general syllabus for each of the math Regents exams:

1. Algebra 1 (Common Core)

• Number and Quantity
  • Operations with real numbers
  • Integer exponents
  • Radicals and rational exponents
  • The real number system
• Algebra
  • Solving linear equations and inequalities
  • Systems of linear equations
  • Quadratic equations (factoring, completing the square, quadratic formula)
  • Polynomial expressions and operations
• Functions
  • Understanding and interpreting functions
  • Linear and exponential functions
  • Graphing functions
• Statistics and Probability
  • Descriptive statistics
  • Probability concepts
  • Data interpretation and analysis

2. Geometry (Common Core)

• Congruence and Similarity
  • Proportions and similarity
  • Geometric transformations (translations, reflections, rotations, dilations)
  • Congruent figures
• Right Triangle Trigonometry
  • Trigonometric ratios
  • Solving right triangles using trigonometric functions
• Coordinate Geometry
  • Distance formula
  • Midpoint formula
  • Slope and equations of lines
• Circles
  • Properties and equations of circles
  • Arc length, sector area, and radian measure
• Geometric Proofs
  • Proving theorems involving geometric shapes and properties
• Area and Volume
  • Area of two-dimensional figures
  • Surface area and volume of three-dimensional solids

3. Algebra 2 (Common Core)

• Polynomial Functions
  • Operations with polynomials
  • Factoring and solving polynomial equations
  • Rational functions and expressions
• Exponential and Logarithmic Functions
  • Properties of exponents and logarithms
  • Solving exponential and logarithmic equations
• Radical Expressions and Rational Exponents
  • Simplifying expressions with roots and exponents
  • Solving radical equations
• Trigonometry
  • Unit circle
  • Graphs of sine, cosine, and tangent functions
  • Trigonometric identities
• Sequences and Series
  • Arithmetic and geometric sequences
  • Sum of series
• Statistics and Probability
  • Descriptive statistics
  • Probability distributions
  • Data analysis

General Tips for Preparing:

• Practice Problem-Solving: Focus on practicing different types of problems and understanding the steps involved.
• Understand Key Concepts: The exams focus on understanding mathematical concepts and their real-world applications, so ensure you’re comfortable with both procedural skills and conceptual understanding.
• Review Previous Regents Exams: Practice with past exams to become familiar with the question format and identify areas where you need improvement.
• Use a Graphing Calculator: Know how to use your calculator efficiently, as it is allowed on most of the Regents exams, and it can be very helpful for graphing and calculations.

This syllabus is a general guideline, and the exact content covered in the exams may vary slightly from year to year, but this should provide a strong foundation for your preparation.