The New York State Algebra 2 Regents exam can feel daunting, but with the right preparation and a solid understanding of key concepts, you can conquer it! This cheat sheet provides a concise overview of crucial topics, formulas, and strategies to help you ace the test. Remember, this is a supplement to your studies, not a replacement for thorough learning.
I. Essential Formulas & Concepts
This section outlines the core formulas and concepts you'll need to be comfortable with for the Algebra 2 Regents. Mastering these will significantly improve your performance.
A. Functions & Their Graphs
- Domain & Range: Understand how to find the domain and range of various functions (linear, quadratic, exponential, logarithmic, rational, etc.). Pay close attention to restrictions, such as denominators not equaling zero and values under square roots being non-negative.
- Function Notation: Be fluent in using function notation (f(x), g(x), etc.) and interpreting its meaning.
- Transformations: Know how transformations (shifts, stretches, reflections) affect the graph of a function. This includes understanding the relationship between a function and its transformations in equation form.
- Inverse Functions: Understand how to find the inverse of a function and its graphical relationship to the original function. Remember the test for inverse functions: f(f⁻¹(x)) = x and f⁻¹(f(x)) = x.
- Piecewise Functions: Be able to evaluate and graph piecewise functions. Understand the implications of different function definitions for various intervals of the domain.
B. Equations & Inequalities
- Solving Equations: Master techniques for solving various types of equations: linear, quadratic (factoring, quadratic formula, completing the square), radical, exponential, and logarithmic.
- Systems of Equations: Know how to solve systems of equations using substitution, elimination, and graphing methods. Understand how to solve systems involving linear and non-linear equations.
- Inequalities: Be able to solve and graph linear and quadratic inequalities. Understand compound inequalities (AND/OR) and absolute value inequalities.
C. Polynomials & Rational Expressions
- Factoring Polynomials: Practice factoring various types of polynomials: greatest common factor (GCF), difference of squares, trinomials, sum/difference of cubes.
- Polynomial Division: Understand long division and synthetic division of polynomials.
- Rational Expressions: Be comfortable simplifying, adding, subtracting, multiplying, and dividing rational expressions. Know how to find the domain of rational expressions.
- Roots & Zeros: Understand the relationship between the roots (or zeros) of a polynomial and its factors. Use the Remainder Theorem and Factor Theorem.
D. Exponential & Logarithmic Functions
- Exponential Growth & Decay: Understand the formulas for exponential growth and decay and how to apply them to real-world problems.
- Logarithms: Know the properties of logarithms and how to use them to solve logarithmic and exponential equations. Be familiar with changing between exponential and logarithmic forms.
- Common & Natural Logarithms: Understand the difference between common logarithms (base 10) and natural logarithms (base e).
E. Trigonometry
- Unit Circle: Thorough understanding of the unit circle, including angles, coordinates, and trigonometric function values.
- Trigonometric Identities: Familiarize yourself with key trigonometric identities (Pythagorean identities, reciprocal identities, etc.).
- Solving Trigonometric Equations: Practice solving trigonometric equations using identities and algebraic techniques.
II. Test-Taking Strategies
Beyond mastering the content, effective test-taking strategies are crucial:
- Time Management: Practice pacing yourself to ensure you have enough time for all sections.
- Read Carefully: Pay close attention to the wording of each question.
- Show Your Work: Even if you get the correct answer, showing your work helps you earn partial credit if there's a minor error.
- Check Your Answers: If time permits, review your work to catch any mistakes.
III. Practice Makes Perfect
This cheat sheet provides a framework. Consistent practice is key to success. Use practice tests, review exercises, and seek help when needed. Good luck!
