To expand students understanding of the mathematical concepts of Algebra 1 as specified by the California State Standards for Algebra 2.

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1 Morgan Hill Unified School District Course Outline Course Title: Algebra II CP Course Length: One Year Credits: 10 Credits Grades: 9-12 Course Goal: To expand students understanding of the mathematical concepts of Algebra 1 as specified by the California State Standards for Algebra 2. Texts and Supplemental Instructional Materials Holliday, Luchin, Cuevas, Carter, Marks, Day, Casey, Hayek, Algebra 2 Concepts, Skills, and Problem Solving. New York: Glencoe, McGraw-Hill, Text resources Teacher made resources Manipulatives TI 83 plus graphing calculator Course Objectives by Essential Standards Standard 1: Students will be able to solve equations and inequalities involving absolute value. Standard 2: Students will be able to solve systems of linear equations and inequalities (in two or three variables) simultaneously, by substitution, or with graphs. Standard 3: Students will be able to perform operations of polynomials, including long division. Standard 4: Students will be able to factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes. Standard 5: Students will be able to describe the algebraic relationships of real and complex numbers. Standard 6: Students will demonstrate knowledge of adding, subtracting, multiplying, and dividing complex numbers.

2 2 Standard 7: Students will be able to perform all operations and simplify rational expressions with monomials and polynomial denominators, and simplify complicated fractions including fractions with negative exponents in the denominator. Standard 8: Students will be able to solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students will apply these techniques in solving word problems, and in solving quadratic equations in the complex number system. Standard 9: Students will be able to explain the effect changing a coefficient has on the graph of quadratic functions. That is, students will be able to determine how the graph of a parabola changes as a, b, and c vary in the equation y = a (x - b)² + c. Standard 10: Students will demonstrate knowledge of graphing quadratic functions and how to determine the maxima, minima, and zeros of the function. Standard 11: Students will demonstrate that they know how to prove the simple laws of logarithms including: 11.1 Students will be able to demonstrate the use of the inverse relationship between exponents and logarithms, a use this relationship to solve problems involving logarithms and exponents Students will be able to determine the validity of an argument based on sequential application of the properties of real numbers, exponents, and logarithms. Standard 12: Students will be able to show understanding of the laws of exponents and exponential functions, and use these functions in problems involving exponential growth and decay. Standard 13: Students will be able to apply the definition of logarithms and of the product formula for logs to translate between logarithms in any bases. Standard 14: Students will be able to use of properties of logarithms to simplify logarithmic numeric expressions and identify their approximate values. Standard 15: Students will be able to determine whether a specific algebraic statement involving rational expressions, radical expressions, logarithmic or exponential functions, is sometimes true, always true, or never true.

3 3 Standard 16: Students will be able to demonstrate how the geometry of the graph of a conic section (e.g. asymptotes, foci, eccentricity) depends on the coefficients of the quadratic equation representing it. Standard 17: Given a quadratic of the form ax² + by² + cx + dy + e = 0, students will be able to use the method of completing the square to transform an equation into standard form and can recognize whether its graph is a circle, ellipse, parabola, or hyperbola and be able to graph the equation. Standard 18: Students will be able to use the fundamental counting principles for computing combinations and permutations. Standard 19: Students will be able to use combinations and permutations for computing probabilities. Standard 20: Students will be able to use the Binomial Theorem and expand binomial expressions that are raised to positive integer powers. Standard 21: Students will be able to apply the method of mathematical induction to prove general statements about the positive integers. Standard 22: Students will be able to find the sums of arithmetic series and both finite and infinite geometric series. Standard 23: Students will be able to derive the summation formulas for arithmetic series and both finite and infinite geometric series. Standard 24: Students will be able to solve problems involving functional concepts such as composition, inverse, and arithmetic operations on functions. Standard 25: Students will be able to use the properties from number systems to justify steps in combing and simplifying functions.

4 4 Outline of Course Major Units First Degree Equations and Inequalities Solving Equations and Inequalities Linear Relationships and Functions Systems of Equations and Inequalities Graphing Calculators: Lines of Regression, Systems of Linear Inequalities, Augmented Matrices Polynomial and Radical Equations and Inequalities Polynomials Quadratic Functions and Inequalities Polynomial Functions Graphing Calculators: Solving Radical Equations and Inequalities, Graphing Families of Parabolas Advanced Functions and Relations Conic Sections Rational Expressions and Equations Exponential and Logarithmic Relations Graphing Calculators: Graphing Rational Functions, Solving Rational Equations by Graphing, solving Exponential and Logarithmic Equations and Inequalities Discrete Mathematics Sequences and Series Probability and Statistics Methods of Instruction Investigations/Explorations Group/Individual Activities Collaborative Learning (pairs/groups) Lecture/Discussion Use of Manipulatives/games Building Content Vocabulary Writing Assignments/Portfolio Audio Visual Materials Guest Speakers/Field Trips Notebooks

5 5 Assessment methods and/or tools Assessment methods include formative assessment, which will promote learning throughout the course or summative assessments, such as benchmarks, final exams, which document student progress toward meeting standards. These methods include: Selected response, e.g. multiple-choice, true/false, matching, and short answer fill-in items, which can appear on quizzes, traditional tests, homework assignments, and practice exercises, benchmark tests, semester and final exam. Essay assessments evaluating students knowledge, reasoning, skills, products, and predispositions. Performance, e.g. student projects, performances, debates, and presentations. Personal communication, e.g. teacher/student conference and interviews, teacher observation, classroom discussions, oral examinations, journals and logs. Participation in Peer Group Assignments.