CURRICULUM GUIDE Algebra II College-Prep Level Revised Sept 2011 Course Description: This course builds upon the foundational concepts of Algebra I and Geometry, connects them with practical real world applications, and prepares students to meet the challenges of a higher education and practical work in the world. Students will be looking at mathematics from various vantage points as a way of learning to confront problem-solving in new ways and in new situations and will develop mathematical understanding through the solving and guided investigation of both real-world and abstract mathematical problems. Students will learn to formulate solutions to these problems as well as communicate these concepts to others in an understandable manner. The school wide learning expectation for problem solving is addressed throughout the course. Intended Audience: This course is designed to meet the needs of students who are college bound and have successfully completed Algebra I and Geometry, but whose main strength is not in mathematics. While this course contains a treatment of topics from both Algebra I and Algebra II, there is some reinforcement of basic algebraic skills and a review of concepts and methods seen before in Algebra I. Course Goals: Students will learn to Solve problems using a graphing calculator. Find solutions to linear, quadratic, exponential, logarithmic, polynomial, radical and rational equations both algebraically and graphically. Find solutions to systems of linear equations, both algebraically and graphically Analyze and formulate equation models and systems to solve real-world problems algebraically and graphically. Understand the concepts of function and relation and be able to differentiate between these as well as analyze functions algebraically and graphically to determine domain, range, x- and y-intercepts, zeros. Gain a full understanding of quadratic functions and equations including the analysis of graphs of quadratic functions and solutions of quadratic equations using both factoring and the quadratic formula. Develop an understanding of complex numbers and their relationship to the roots of quadratic functions. Gain a full understanding of exponents (positive, negative, fractional) and radicals and the relationship and conversions between these. Gain an understanding of polynomial functions, their zeros and values. Learn to operate fully (addition, subtraction, multiplication and division) with rational expressions including those involving literal expressions to be factored.
Essential Questions/Habits of Mind What is a reasonable answer for this problem? Do I have a reasonable estimate of expected solutions? What method should I use to solve this problem? What is the relationship between the roots of a function and its graph? What is the relationship between a problem and the equations / functions which are used to model and solve it? This course addresses the following school-wide expectation: Demonstrate problem solving and critical thinking skills Collects and evaluates information to identify patterns, make inferences, and draw conclusions Predicts results using conceptual knowledge Identifies and analyzes the possible alternative strategies to solve a problem Develops original and well-thought decisions/solutions that apply appropriate and relevant information First Quarter Course Outline Unit 1: Functions, Equations, and Graphs Relations and Functions Linear Equations Linear function, dependent and independent variables, intercepts Slope Standard form of a linear equation Writing equation given point and slope or two points Slope intercept form of a line Parallel and perpendicular lines Direct Variation Using Linear Models Absolute Value Functions and Graphs Vertical and Horizontal Shifts Two-Variable Inequalities Standards*: [AI.N.1] [AI.N.2] [A1.P.10] [A1.P.5] [10.P.10] CBL Lab: Modeling Motion with Linear Equations Graphing Calculator Absolutely activity Unit 2: Linear Systems
Second Quarter Graphing Systems of Equations Solving Systems Algebraically Systems of Inequalities Linear Programming Standards*: [AII.P.10] [A1.P.12] CBL Lab: Modeling Motion with Linear Systems Unit 3: Quadratic Equations and Functions Modeling Data with Quadratic Models Properties of Parabolas Translating Parabolas Factoring GCF Use Algebra Tiles to show products and factoring Cases where a = 1 and a not Perfect Square Trinomial Difference of Squares Quadratic Equations Standard form quadratic equation Solve by factoring Solve by finding square roots Zero of a function Solve by graphing Golden Rectangle Complex Numbers Graphing Operations on Complex solutions Completing the Square Solve equations by completing the square Rewrite function in vertex form by completing the square The Quadratic Formula Solve equations using Quadratic Formula Derive by completing the square The Discriminant Standards*: [A1.P.9] [A1.P.11][AII.N.1][AII.P.6][AII.P.7][AII.P.8][AII.P.13] CBL Lab: Modeling Motion with Quadratic Equations Graphing calculator Transform activity Area of the Missing Square activity Completing the Square with algebra tiles Video: NOVA Fractals
Second and Third Quarter Unit 4: Polynomials and Polynomial Functions Polynomial Functions Classify by degree and number of terms Modeling data with polynomial functions End behavior Polynomials and Linear Factors Standard form and factored form of a polynomial Relative Maxima/Minima Factors and zeroes of a polynomial function Factor Theorem Writing a polynomial function from its zeroes Dividing Polynomials Polynomial long division (basic) Synthetic division Remainder theorem Solving Polynomial Equations By graphing By factoring Rational, Irrational, and Imaginary Roots of Polynomial Equations Fundamental Theorem of Algebra Permutations and Combinations The Binomial Theorem Expanding binomials Pascal s Triangle Standards*: [AII.P.1] [AII.P.3] [AII.D.3] Third Quarter How to Weigh an Alligator (regression activity) Investigation: Pascal s Triangle and the Binomial Theorem Unit 5: Radical Functions and Rational Exponents Roots and Radical Expressions Simplifying Radical Expressions Rational Exponents Writing in radical and exponential form Simplifying Solving Radical Equations Inverse Functions Function Operations Addition, subtraction, multiplication, division Composition Graphing radical functions.
Standards*: [AII.P.5] [AII.P.6][AII.N.2] Graphs of Inverse Functions Unit 6: Exponential and Logarithmic Functions Fourth Quarter Modeling data with exponential functions Properties of exponential functions Logarithms as inverses Graphs of exponential and logarithmic functions Properties of Logarithms Solving Exponential Equations Using Logs The Natural Logarithm Standards*: [AII.P.4] [AII.P.8][AII.P.11] [AII.P.13] Investigation: Population growth Investigation: Olympic records Unit 7: Sequences and Series Mathematical patterns Arithmetic sequences Geometric series Geometric sequences Arithmetic series Fibonacci sequence Fibonacci Numbers in Nature Unit 8: Rational Functions Inverse variation Rational functions and their graphs Rational expressions Operations on rational expressions Solving rational equations *Standards based on the Massachusetts Mathematics Curriculum Frameworks (November 2000)
Instructional Methods: Teacher-led discussions Pairs and individual work Graphing calculator investigations Whole class and group investigations/labs Use of mathematical software and interactive whiteboard. Texts & Materials Used in Course: Algebra 2, Prentice Hall Mathematics, 2004, Pearson Education Inc. Assessment: Exams done both with and without a graphing calculator Homework Assignments from text Worksheet assignments Mid-Year and Final Exams Course Evaluation Tools: Final Exam