This comprehensive cheat sheet covers key concepts for your Algebra 2 midterm. Remember, this is a tool for review and should supplement, not replace, your studying. Understanding the underlying principles is crucial for success!
I. Fundamental Concepts
A. Real Numbers & Operations
- Number Sets: Know the relationships between natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.
- Order of Operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
- Properties of Real Numbers: Commutative, associative, distributive, identity, and inverse properties. Understanding how these properties apply to solving equations is vital.
B. Exponents and Radicals
- Exponent Rules: Master the rules for multiplying, dividing, raising powers to powers, and dealing with negative and zero exponents. This is a cornerstone of Algebra 2.
- Radical Expressions: Simplify radicals, rationalize denominators, and add, subtract, multiply, and divide radical expressions. Remember the relationship between exponents and radicals.
- Rational Exponents: Understand the connection between fractional exponents and radicals (e.g., x^(1/2) = √x).
II. Equations and Inequalities
A. Solving Equations
- Linear Equations: Solve one-variable and multi-variable linear equations. Practice techniques like combining like terms and using the distributive property.
- Quadratic Equations: Solve quadratic equations using factoring, the quadratic formula, and completing the square. Know how to identify the discriminant and interpret its meaning.
- Systems of Equations: Solve systems of linear equations using substitution, elimination, and graphing. Understand how to represent systems graphically and interpret solutions.
B. Solving Inequalities
- Linear Inequalities: Solve one-variable and multi-variable linear inequalities. Remember to flip the inequality sign when multiplying or dividing by a negative number.
- Quadratic Inequalities: Solve quadratic inequalities by factoring or using a sign chart. Graphing these inequalities on a number line is crucial for understanding solutions.
- Systems of Inequalities: Graph systems of linear inequalities and identify the solution region (feasible region).
III. Functions and Their Graphs
A. Function Notation and Operations
- Function Notation: Understand function notation (f(x)) and how to evaluate functions for given inputs.
- Function Operations: Perform operations on functions (addition, subtraction, multiplication, division, and composition).
- Inverse Functions: Find the inverse of a function and understand the relationship between a function and its inverse.
B. Graphing Functions
- Identifying key features of graphs: x-intercepts, y-intercepts, domain, range, asymptotes, and vertex (for parabolas).
- Transformations of Functions: Understand how transformations (shifts, stretches, reflections) affect the graph of a function. Master how to apply these transformations based on the function's equation.
- Common Function Types: Become familiar with the graphs of linear, quadratic, exponential, logarithmic, and rational functions.
IV. Polynomials
A. Operations with Polynomials
- Adding, Subtracting, Multiplying, and Dividing Polynomials: Practice these operations with both monomials and polynomials. Long division and synthetic division are essential techniques.
- Factoring Polynomials: Factor various types of polynomials, including greatest common factor (GCF), difference of squares, perfect square trinomials, and others.
B. Polynomial Theorems
- Remainder Theorem: Understand how to use the Remainder Theorem to find the remainder when a polynomial is divided by a linear factor.
- Factor Theorem: Know how the Factor Theorem relates to finding roots or zeros of a polynomial.
V. Other Important Topics (Check your syllabus for specifics)
- Sequences and Series: Arithmetic and geometric sequences and series. Be prepared to find terms, sums, and apply formulas.
- Matrices: Basic matrix operations (addition, subtraction, multiplication). This section may or may not be on your midterm; check your syllabus.
- Logarithms and Exponentials: Properties of logarithms, solving exponential and logarithmic equations.
This cheat sheet provides a broad overview. Refer to your textbook, class notes, and completed homework assignments for detailed explanations and examples. Good luck on your midterm!
