Course Title: Algebra 2 Course Description This course is designed to be the third year of high school mathematics. The material covered is roughly equivalent to that covered in the first Algebra course in college. Students successfully completing Algebra II will be well prepared for any of the next three high school math courses. Major topics include mathematical modeling, linear functions, exponential functions, quadratic functions, logarithmic functions, radical functions, polynomial and radical functions, and solving systems of equations. Students are required to maintain a comprehensive three ring notebook. TI 84 graphing calculators are used extensively and students are expected to master this technology. Students are strongly urged to have their own. Prerequisite: Algebra I (C or better), Geometry (C or better) District Competencies in Content Area District Competencies in and across Content Areas Students and teachers will collaborate on students learning to: Problem Solving: Students can solve a range of well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. Communicating Reasoning: Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. Concepts and Procedures: Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency. Mathematical Modeling: Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. Students and teachers will collaborate on students becoming a: Learner Demonstrate flexibility, adaptability, and accountability throughout the learning process. Communicator Communicate clearly using the most appropriate and effective means. Thinker Think critically, creatively, and systemically to define and solve problems. Collaborator Demonstrate respect, collaboration, and leadership in working with others. Contributor Demonstrate global pride through community service, acceptance and tolerance of diverse people, and responsibility for the environment.
Technology User Use technology respectfully and apply it effectively. Evaluator Access, evaluate, use, and manage information. Producer Manage projects, produce results, and create media products. School Based Course Competency Statements 1. Students will understand that one of the keys to solving problems lies in the understanding of basic skills such as simplifying algebraic expressions and solving equations and inequalities. Problem Solving, Communicating Reasoning, Concepts and Procedures, Mathematical Modeling 2. Students will understand that linear functions can be used to model relationships between many real-world quantities. Problem Solving, Communicating Reasoning, Concepts and Procedures, Mathematical Modeling 3. Students will understand that systems of linear equations and inequalities can be used to model real-world situations in which many different conditions must be met. Problem Solving, Communicating Reasoning, Concepts and Procedures, Mathematical Modeling 4. Students will understand that quadratic functions can be used to model some non-linear behaviors. Problem Solving, Communicating Reasoning, Concepts and Procedures, Mathematical Modeling 5. Students will understand that operations can be used to simplify polynomial expressions, solve polynomial equations, and graph polynomial functions Problem Solving, Communicating Reasoning, Concepts and Procedures, Mathematical Modeling 6. Students will understand that operations can be used to simplify radical expressions, solve radical equations, and graph radical functions. Problem Solving, Communicating Reasoning, Concepts and Procedures 7. Students will understand that rational expressions can be simplified and rational equations can be solved by applying previously learned rules of operations with fractions in conjunction with properties of exponents and operations with polynomials. Problem Solving, Communicating Reasoning, Concepts and Procedures 8. Students will understand that exponential and logarithmic functions model growth and decay. Problem Solving, Communicating Reasoning, Concepts and Procedures, Mathematical Modeling
Course Units First Degree Equations and Inequalities Linear Relations and Functions Systems of Linear Equations Quadratic Functions and Equations Polynomial Functions and Equations Radical Functions and Equations Rational Expressions and Equations Exponential and Logarithmic Functions and Equations Course Unit Content and Skills Students will be able to solve first degree equations and inequalities. 1. Simplify and evaluate algebraic expressions. 2. Understand properties of Real numbers. 3. Solve and graph linear equations. 4. Solve and graph linear inequalities. 5. Solve absolute value equations 6. Solve and graph compound and absolute value inequalities. Students will be able to write, graph, and analyze linear relations and functions. 1. Analyze and graph functions. 2. Find functional values. 3. Identify, write and graph linear equations in standard form. 4. Find the slope of a line. 5. Understand the relationship between parallel and perpendicular lines. 6. Write and graph linear equations in slope-intercept form. 7. Draw scatterplots and identify the line of best fit and use it to make predictions. 8. Use the graphing calculator to perform a linear regression. 9. Graph absolute value functions. 10. Graph linear inequalities. Students will be able to write and solve systems of linear equations and inequalities. 1. Solve systems of linear equations by graphing.
2. Solve systems of linear equations using substitution. 3. Solve systems of linear equations using elimination. 4. Solve real-world problems using systems of equations. 5. Solve systems of inequalities by graphing. 6. Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities. 7. Find the maximum and minimum values of a function over a region. 8. Use linear programming to solve real-world problems. 9. Solve systems of linear equations in three variables. 10. Solve real-world problems using systems of linear equations in three variables. Students will be able to analyze and graph quadratic functions and solve quadratic equations. 1. Graph quadratic functions. 2. Find and interpret the maximum and minimum values of a quadratic function. 3. Understand the relationship between zeros of a quadratic function and solutions to the related equation. 4. Solve quadratic equations by factoring. 5. Simplify square roots. 6. Perform operations with imaginary and complex numbers. 7. Solve quadratic equations by completing the square. 8. Solve quadratic equations using the quadratic formula. Students will be able to perform operations on polynomial expressions, solve polynomial equations, and graph polynomial functions. 1. Use properties of exponents to multiply and divide monomials. 2. Add, subtract, and multiply polynomials. 3. Divide polynomials with long division. 4. Divide polynomials with synthetic division. 5. Analyze the graphs of polynomial functions. 6. Factor polynomials. 7. Solve polynomial equations by factoring. 8. Find the zeros of a polynomial function. Students will be able to perform operations on radical expressions, solve
radical equations, and graph radical functions. 1. Find the sum, difference, product, and quotient of functions. 2. Find the composition of functions. 3. Find the inverse of a function or relation. 4. Graph and analyze square root functions. 5. Simplify radicals. 6. Add, subtract, multiply, and divide radical expressions. 7. Solve equations containing radicals. Students will be able to perform operations on rational expressions and solve rational equations. 1. Add and subtract rational expressions with monomial denominators. 2. Add and subtract rational expressions with polynomial denominators. 3. Multiply and divide rational expressions with monomial denominators. 4. Multiply and divide rational expressions with polynomial denominators. 5. Solve rational equations. Instructional Strategies Clear Articulation of Instructional Strategies Students will be able to graph exponential and logarithmic functions and solve exponential and logarithmic equations. 1. Graph and analyze exponential functions. 2. Solve exponential equations. 3. Evaluate logarithmic expressions. 4. Solve equations using the properties of logarithms. 5. Solve exponential equations using common logs. 6. Evaluate expressions involving natural base and logarithms. 7. Use logarithms to solve real-world problems using exponential growth and decay. Individual and group learning through lecture, discussions, demonstrations, research, and investigation. Assessment Strategies Homework, class participation, quizzes, unit tests, projects, midterms and finals
Approved Revised 8/29/12