The New York State Algebra 2 Regents exam can be daunting, but with the right preparation and resources, you can conquer it! This cheat sheet provides a concise overview of key concepts and formulas to help you ace the test. Remember, this is a supplement to thorough study—not a replacement for understanding the underlying principles.
I. Essential Equations & Formulas
This section covers the fundamental formulas you'll need to know for various topics within the Algebra 2 curriculum.
A. Quadratic Equations:
- Quadratic Formula: For equations of the form ax² + bx + c = 0, the solutions are: x = [-b ± √(b² - 4ac)] / 2a
- Discriminant: b² - 4ac. Determines the nature of the roots:
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0: Two distinct real roots
- = 0: One real root (repeated)
- < 0: Two complex conjugate roots
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- Vertex Form: y = a(x - h)² + k, where (h, k) is the vertex.
- Standard Form: y = ax² + bx + c
- Factored Form: y = a(x - r₁)(x - r₂), where r₁ and r₂ are the roots.
B. Exponential & Logarithmic Functions:
- Exponential Growth/Decay: A = P(1 ± r)^t, where A is the final amount, P is the principal amount, r is the rate, and t is the time.
- Compound Interest: A = P(1 + r/n)^(nt), where n is the number of times interest is compounded per year.
- Logarithmic Properties:
- logₐ(mn) = logₐm + logₐn
- logₐ(m/n) = logₐm - logₐn
- logₐ(mⁿ) = n logₐm
- logₐa = 1
- logₐ1 = 0
- Change of Base Formula: logₐb = (logₓb) / (logₓa)
C. Trigonometry:
- Unit Circle: Memorizing the unit circle is crucial for understanding trigonometric values.
- SOH CAH TOA: sin θ = Opposite/Hypotenuse, cos θ = Adjacent/Hypotenuse, tan θ = Opposite/Adjacent
- Pythagorean Identity: sin²θ + cos²θ = 1
- Reciprocal Identities: csc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ
D. Systems of Equations:
Remember methods for solving systems of equations, including substitution and elimination. Be prepared to solve systems with both linear and non-linear equations.
II. Key Concepts & Strategies
Beyond formulas, mastering these concepts is vital for success.
A. Function Transformations:
Understand how transformations (shifts, stretches, reflections) affect the graph of a function.
B. Polynomial Functions:
Know how to find roots, determine end behavior, and identify key features of polynomial graphs.
C. Rational Functions:
Understand asymptotes (vertical, horizontal, slant), domain, and range of rational functions.
D. Sequences and Series:
Familiarize yourself with arithmetic and geometric sequences and series, including their formulas for the nth term and sum.
E. Probability and Statistics:
Review concepts like permutations, combinations, probability distributions (normal, binomial), and hypothesis testing (if applicable to your curriculum).
III. Test-Taking Tips
- Practice, Practice, Practice: Work through past Regents exams to familiarize yourself with the question format and identify your weak areas.
- Manage Your Time: Allocate appropriate time to each section of the exam.
- Show Your Work: Clearly show all steps in your calculations to earn partial credit.
- Check Your Answers: If time permits, review your work for any errors.
- Stay Calm: Take deep breaths and approach the exam with confidence.
This cheat sheet provides a foundational overview. Consult your textbook, class notes, and practice materials for a more comprehensive review. Good luck on your exam!
