algebra 2 regents cheat sheet

2 min read 01-02-2025

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 succeed. Remember, this is a supplement to your studies, not a replacement for thorough understanding.

I. Fundamental Concepts

A. Real Numbers and Operations

Number Sets: Know the relationships between natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. Understanding set notation is crucial.
Absolute Value: $|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}$
Properties of Real Numbers: Commutative, associative, distributive, identity, and inverse properties are essential for simplifying expressions and solving equations.

B. Exponents and Radicals

Exponent Rules: $a^m \cdot a^n = a^{m+n}$ , $\frac{a^m}{a^n} = a^{m-n}$ , $(a^m)^n = a^{mn}$ , $(ab)^n = a^n b^n$ , $(\frac{a}{b})^n = \frac{a^n}{b^n}$ (assuming $a, b \ne 0$ where applicable). Also understand zero and negative exponents.
Radicals: $\sqrt[n]{a} = a^{\frac{1}{n}}$ , $\sqrt[n]{a^m} = a^{\frac{m}{n}}$ ; be able to simplify radicals and rationalize denominators.

C. Polynomials and Factoring

Polynomial Operations: Addition, subtraction, multiplication, and division of polynomials. Long division and synthetic division are important for factoring and finding roots.
Factoring Techniques: Greatest Common Factor (GCF), difference of squares, perfect square trinomials, grouping, and factoring by using the quadratic formula.

II. Equations and Inequalities

A. Solving Equations

Linear Equations: $ax + b = c$
Quadratic Equations: $ax^2 + bx + c = 0$ (solve using factoring, quadratic formula, or completing the square). The quadratic formula is: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Systems of Equations: Solve using substitution, elimination, or graphing. Understand how to solve systems with three variables.
Radical and Exponential Equations: Know how to isolate the radical or exponential term and solve. Check for extraneous solutions.

B. Solving Inequalities

Linear Inequalities: Solve similar to linear equations, but remember to flip the inequality sign when multiplying or dividing by a negative number.
Quadratic Inequalities: Find the roots and test intervals.
Absolute Value Inequalities: $|x| < a$ means $-a < x < a$ , and $|x| > a$ means $x < -a$ or $x > a$ .

III. Functions

A. Function Notation and Transformations

Function Notation: $f(x)$ , $g(x)$ , etc. Understand composition of functions ( $f(g(x))$ ) and inverse functions ( $f^{-1}(x)$ ).
Transformations: Shifts, stretches, and reflections of graphs (vertical and horizontal shifts, vertical and horizontal stretches/compressions, reflections across the x-axis and y-axis).

B. Types of Functions

Linear Functions: $f(x) = mx + b$
Quadratic Functions: $f(x) = ax^2 + bx + c$ (parabolas)
Polynomial Functions: Functions with multiple terms and varying exponents.
Rational Functions: Functions in the form $f(x) = \frac{p(x)}{q(x)}$ , where $p(x)$ and $q(x)$ are polynomials. Identify vertical and horizontal asymptotes.
Exponential Functions: $f(x) = a \cdot b^x$ (growth and decay).
Logarithmic Functions: Inverse of exponential functions. Understand properties of logarithms.

C. Analyzing Functions

Domain and Range: The set of all possible input and output values.
Intercepts: x-intercepts and y-intercepts.
Asymptotes: Vertical, horizontal, and slant asymptotes.
Increasing and Decreasing Intervals: Where the function is increasing or decreasing.
Maxima and Minima: Local and global maximum and minimum values.

IV. Data Analysis and Probability

Statistical Measures: Mean, median, mode, range, standard deviation, quartiles.
Probability: Basic probability rules (independent and dependent events).
Regression: Linear regression and correlation.

This cheat sheet is intended as a quick reference. For a thorough understanding, review your class notes, textbook, and practice problems extensively. Good luck on your exam!