Mathematics Department

Essential Knowledge and Skills

Algebra II will start with a review of the fundamental properties and operations of Algebra. After this introduction, the course will cover all the topics of Algebra 2 including systems of equations, operation and use of matrices, quadratic, polynomial and rational functions, analytical geometry (including the study of the conic sections) and an introduction to trigonometry.

Indicators of Student Learning

Upon completion of this course, students will:

• Read, verbalize and write mathematical symbols and ideas including: properties of real numbers, relations and functions, matrices, quadratic functions, polynomial functions, complex numbers, systems of equations, angles and the coordinate plane, even and odd functions and inverse and direct variation relationships.

• Select and describe appropriate problem solving strategies for problems involving: a.) Linear functions, b.) Matrices, c.) Systems of equations, d.) Quadratic functions with real and imaginary solutions using: graphical solutions, factoring, completing the square and the quadratic formula, e.) Polynomial functions using: long division, synthetic division, the Factor Theorem, the Fundamental Theorem of Algebra and the Zero Product property, f.) Triangles and right triangles.

• Use mathematical models to translate real world problems using equations of lines, systems of linear equations and inequalities, quadratic and polynomial functions, systems of circular functions, trigonometric laws and quadratic relations (conics).

• Obtain and graph solutions for: a.) Linear functions, b.) Polynomial functions and relations, c.) Trigonometric functions (including the ability to identify domain restrictions including: asymptotes, holes, and discontinuities) and d.) Quadratic relations (conic sections) of conic sections.

• Utilize graphing calculator technology to: a.) Graph linear equations and scatter plots, b.) Perform curve fitting of linear and quadratic functions, c.) Graph quadratic and polynomial functions, d.) Perform matrix manipulations, e.) Analyze functions and verify algebraic solutions, f.) Evaluate trigonometric function values, g.) Graph trigonometric functions in degree and radian measure, h.) Graph conic sections.

Problem Solving

• Choose from and employ a variety of problem solving strategies including: diagrams lists and tables, looking for and identifying patterns, eliminating possibilities, solving a similar problem, guessing and checking.

• Choose appropriate operations

• Learn to estimate solutions to problems and determine the reasonableness of answers by relating their answers to their estimates.

• Solve a variety of multi-step problems and extended problem-solving projects

Reasoning and Proof

• Explain and justify problem-solving procedures.

• Make and investigate mathematical conjectures.

• Recognize that a mathematical conjecture does not constitute a proof.

• Evaluate and analyze functions

Communication

• Express mathematical concepts to others correctly and clearly in both written and oral form.

• Utilize mathematical symbols, notation and terminology in an appropriate manner.

• Establish and describe connections between mathematical expressions, physical models and real-world situations.

Technology

• Use a graphing calculator efficiently and accurately for computation, graphing and modeling a variety of mathematical concepts

Assessment

Upon completion of this course students will:

• Demonstrate competency in problem solving by using appropriate methods and techniques, generating a solution and checking the reasonableness of the solution.

• Demonstrate competency in communication by expressing mathematical concepts and results, in a clear manner using correct terminology.

• Demonstrate competency in technology by using a graphing calculator to obtain correct solutions to problems in diverse topics that would not be easily solvable manually.