Overview
This lecture reviews key Algebra 2 concepts through practice problems, including simplification, solving equations, factoring, and graphing.
Simplifying Expressions and Evaluating
- Substitute given values to evaluate algebraic expressions.
- Use arithmetic operations to simplify numerical expressions, including those with exponents.
- Apply the distributive property to expand and simplify expressions.
- Combine like terms in polynomials when adding or subtracting.
Solving Equations
- Isolate the variable to solve linear equations.
- Formulate equations from word problems by translating relationships into algebraic expressions.
- Determine for which values algebraic expressions are undefined by setting denominators to zero.
Factoring and Polynomial Operations
- Factor out common terms and use patterns (e.g., difference of squares, trinomials) to factor polynomials completely.
- Recognize and use factors to simplify and divide polynomials and rational expressions.
Working with Fractions and Rational Expressions
- Reduce fractions to lowest terms by canceling common factors.
- Perform operations (addition, subtraction, multiplication, division) on algebraic fractions.
Graphing and Coordinate Geometry
- Find missing coordinates in ordered pairs that satisfy a linear equation.
- Identify x- and y-intercepts by substituting zero for the appropriate variable.
- Use intercepts to graph lines.
- Determine which ordered pairs are not solutions to a given linear equation.
Word Problems and Translating to Algebra
- Translate real-world problems into algebraic equations involving perimeters, relationships, and totals.
- Set up and solve equations to find unknown side lengths or amounts.
Systems of Equations
- Solve systems of equations by elimination or substitution to find variable values.
Key Terms & Definitions
- Distributive Property — Expanding a(b + c) as ab + ac.
- Polynomial — An algebraic expression with multiple terms combined by addition or subtraction.
- Factoring — Rewriting an expression as a product of its factors.
- Undefined Expression — An algebraic expression that has division by zero for some values.
- Intercept — The point where a graph crosses the x-axis (x-intercept) or y-axis (y-intercept).
Action Items / Next Steps
- Review the solutions provided for each problem in the practice test.
- Practice solving similar algebraic expressions and equations for mastery.
- Graph more lines using intercepts and solve additional systems of equations.