Passaic County Technical Institute ALGEBRA 2 HONORS

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1 Passaic County Technical Institute ALGEBRA 2 HONORS September 2012

2 Course Description Algebra 2 Honors The Algebra honors curriculum is design for academically motivated students who are proficient in mathematics. This course takes a different approach than the standard Algebra ll course, requiring students to perform at a high level of abstraction. There will be substantially more rigorous questions, mathematical analysis, projects, and real-life problems. This course should bring students to a high level of confidence in their ability to derive and effectively use some of the most fundamental relationships of mathematics. Student s GPA for this course is calculated as 1 point more than a regular course. Algebra is the language we use to understand, describe and manipulate the world in which we live. Therefore, it is imperative that today s students fully understand the fundamentals of this language, and use this knowledge as a tool to further their education and/or successfully compete in today s global market place by effectively utilizing the expertise they have gained by the study of this subject. Students need to understand how quantities are related to one another and how algebra can be used to concisely express and analyze those relationships. Algebra has been referred to as a gatekeeper for the future study of the higher mathematics, the sciences, the social sciences, business, and a host of other areas. In the past, algebra has served as a filter, screening people out of these opportunities. It is important that algebra play a major role in a mathematics program that opens the gates for all students. By the end of the course students will have learned how to work with functions that are represented in a variety of ways graphically, numerically, analytically and verbally. These techniques support each other, and add to a clearer understanding of algebra, enabling the student to use algebra to model and solve real-life problems. The course teaches students how to use graphing calculators to help solve problems, experiment, interpret results, and support conclusions. The course also teaches students how to communicate with mathematics and explain solutions to problems both verbally and in written sentences. Modern technology provides tools for supplementing the traditional focus on algebraic procedures, such as solving equations, with a more visual approach through graphs of equations displayed on a screen. Students can then focus on understanding the relationship between the equation(s) and the graph, and on what the graph represents in a real-life situation.

3 COURSE OBJECTIVES/OUTLINE Note to Teachers: Review topics from Algebra 1 should be completed by the end of the 2nd week of the new school year. Please utilize the graphing calculator for the topics that the textbook indicate as an extra tool. S Supplemental Material I. QUADRATIC FUNCTIONS AND FACTORING 1. Graphing Quadratic Functions in Standard Form. (F-IF 7a) 2. Graphing Quadratic Functions in Vertex or Intercept Form. (F-IF 7a) 3. Solving Quadratic Equations by Factoring. (A-SSE 3a) 4. Solving Quadratic Equations by Factoring. (A-SSE 3a) 5. Solving Quadratic Equations by Finding Square Roots. (A-REI 4b) 6. Perform Operations with Complex Numbers. (N-CN 2) 7. Completing the Square. (A-REI 4a) 8. The Quadratic Formula and the Discriminant. (N-CN 7) 9. Graphing and Solving Quadratic Inequalities. (A-REI 4b) S. Modeling with Quadratic Functions. (F-LE 1) End of MP 1 II. POLYNOMIALS AND POLYNOMIAL FUNCTIONS 1. Use Properties of Exponents. (A-RN 1) 2. Evaluating and Graphing Polynomial Functions. (F-IF 7c) 3. Adding, Subtracting, and Multiplying Polynomials. (A-APR 1) 4. Factoring and Solving Polynomial Equations. (A-SSE 2) 5. Remainder and Factor Theorems. (A-APR 2) 6. Find Rational Zeros. (A-APR 2) 7. Apply the Fundamental Theorem of Algebra (N-CN 9) S. Modeling with Polynomials Functions. (F-LE 1) III. RATIONAL EXPONENTS AND RADICAL FUNCTIONS 1. nth Roots and Rational Exponents. (N-RN 1) 2. Properties of Rational Exponents. (N-RN 2) 3. Perform Function Operations and Composition. (F-BF 1) 4. Inverse Functions. (F-BF 4) 5. Graphing Square Root Function and Cube Root Functions. (F-BF 4) 6. Solving Radical Equations. (A-REI 2) End of MP 2

4 IV. EXPONENTIAL AND LOGORITHMIC FUNCTIONS 1. Exponential Growth. (F-IF 7e) 2. Exponential Decay. (F-IF 7e) 3. The number e. (F-IF 7e) 4. Evaluate Logarithms and Graph Logarithmic Functions. (F-IF 7e) 5. Apply properties of Logarithms. (F-BF 5 (+)) 6. Solve Exponential and Logarithmic Equations. (F-LE 4) S. Modeling with Exponential Functions. (F-LE 1) V. RATIONAL FUNCTIONS 1. Inverse and Joint Variation. (A-CED 2) 2. Graphing Simple Rational Functions. (F-IF 7d) 3. Graphing General Rational Functions. (F-IF 7d) 4. Multiplying and Dividing Rational Expressions. (A-APR 7) 5. Addition, Subtraction, and Rational Functions. (A-APR 7) 6. Solving Rational Equations. (A-REI 2) 7. Describe and Compare Function Characteristics. (F-IF 9) End of MP 3 VI. DATA ANALYSIS AND STATISTICS 1. Use Combinations and the Binomial Theorem. (A-APR 5) 2. Construct and Interpret Binomial Distributions. (S-MD 3) 3. Use Normal Distribution. (S-ID 4) 4. Select and Draw Conclusions from Samples. (S-IC 1) 5. Compare Surveys, Experiments, and Observational Studies. (S-IC 3) VII. SEQUENCES AND SERIES 1. Define and Use Sequences and Series. (F-IF 3) 2. Analyze Arithmetic Sequences and Series. (F-BF 2) 3. Analyze Geometric Sequences and Series. (A-SSE 4) 4. Find Sums of Infinite Geometric Series. (A-SSE 3) End of MP 4

5 INSTRUCTIONAL, RESOURCE & SOFTWARE MATERIALS Student Textbook: Algebra 2 Larson, Boswell, Kanold, Stiff ISBN by Houghton Mifflin Harcourt Resource Materials: Algebra 2 Teaching an Essential Algebra 2 Course Chapter Resource Books Standardized Test Practice Workbook Basic Skills Workbook: Diagnosis and Remediation Practice Workbook with Examples Notetaking Guide Teacher s Edition Software: Texas TI-83 or TI-84 or TI-Nspire Graphing Calculators TI-Navigator Ron Larson Test Generator (CD)

6 EVALUATION The student will be evaluated using the following criteria: 1. Test 2. Quizzes 3. Homework 4. Class participation 5. Notebook 6. Projects INSTRUCTIONAL STRATEGIES Various teaching methods are used in this course. Instruction will be given using class notes, power point presentations, and exercises from the book, prepared worksheets and a graphing calculator. Classroom demonstrations will be included. Group activities and cooperative learning will be used. Vocabulary words and word problems will be infuse within each lesson. An understanding of math terms is crucial to students ability to understand and execute math problems. In order to support students comprehension of math terms, vocabulary instruction practices are useful. In particular, instruction of math terms and vocabulary will include: Discussion and repeated exposure to the conceptual base of each term Active exploration of examples for each term Active exploration of the differences between terms

7 PASSAIC COUNTY TECHNICAL INSTITUTE ALGEBRA 2 COURSE OVERVIEW Algebra 2 extends the fundamental concepts and skills of elementary algebra to higher level. Students should study Algebra 1 before they study Algebra 2. Algebra 2 is design to be taught in a full academic school year. Algebra 2 also offers the opportunity to apply algebraic skills and reasoning to the related mathematical areas of Pre-Calculus, Data Analysis, Probability & Statistics, and Discrete Mathematics. Algebra 2 is designed to prepare students with a strong foundation that will give them the tools to succeed in the future and apply it to real-life situations. PROFICIENCES Upon successful completion of the requirements for this course, the student will be able to: Graph quadratic functions and inequalities. Use four methods to solve quadratic equations. See the relationship between the solutions of the quadratic equation, the zeros of the quadratic equation, and the x-intercepts of this function. Perform operations with complex numbers. See how real-life situations are modeled by quadratic functions. Perform operations on polynomials and find the solutions of a polynomial equation, which is the most classical problem in all of algebra. See how real-life situations have been modeled by polynomial functions for hundred of years. Use rational exponents and nth roots of numbers. Perform operations with, and find the inverses of functions. Graph radical functions and solve radical equations. See that quantities increasing by the same percent over equal periods of time are modeled by exponential functions. Graph and use exponential, logarithmic, and logistic growth function. Use the number e and the definition and properties of logarithms. Solve exponential and logarithmic equations. Simplify and perform operations with rational expressions. Graph rational functions and solve rational equations. Use a variety models and rational models to describe real-life situations. Use algebra to establish rules for sequences and series and use summation notation. See how algebra is use in probability and statistics. To count the number of ways an event can happen and to calculate and use probabilities. To fully understand the role and use of the graphing calculator in promoting their full understanding of the algebra.

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