Honors Algebra II / Trigonometry 2013-2014 Instructor: Busselmaier Room: 158 Academic Support Location: Room 158 or Office 152 E-mail: cbusselmaier@regisjesuit.com (email is the best way to get in touch with me) Web Link: http://regisjesuithighschool.instructure.com Course Description This course advances the student s algebraic skills and will allow students to be able to work with a variety of types of functions in several different ways: graphical, analytical, numerical, literal. Students will focus on polynomial, exponential, logarithmic, conic and trigonometric functions and their graphs. The topics prepare the student for precalculus/ trigonometry-math analysis. We endeavor to develop students as effective and creative problem solvers. The use of graphing calculators in this course will enable each student to adapt to the increasing demands of the workplace and today s technological world. This course is intended for students performing at an advanced level entering from Honors Geometry with departmental recommendation. Prerequisite: Honors Algebra 1, Honors Geometry and/or departmental recommendation. Essential Questions Chapters 1-2: How can you apply numerical relationships and algebraic properties to solve real world problems? Chapter 3: How can you represent linear equations and inequalities in the coordinate plane and interpret the results? Chapter 4: What is a polynomial? How is it represented algebraically and graphically? Chapter 5: What is a rational expression? What known processes are used to simplify and solve? Chapter 6: How do irrational and complex numbers relate to rational numbers? Chapter 7: What methods can you use to determine the roots and vertex of a quadratic function? Chapter 8: What is variation? Chapter 9: What is a conic section? What are its properties? Chapter 10: What is a logarithm? How does it relate to exponents? Chapter 12: What is trigonometry? How is it used to solve triangles? Chapter 13: How is trigonometry used with circles? How are trigonometric functions represented graphically? Chapter 14: How are inverse trigonometric functions represented graphically? Learning Outcomes 1. Students will be able to understand, graph, and analyze a variety of functions including linear, quadratic, higher order polynomials, exponential, logarithmic, rational, irrational, and trigonometric. 2. Students will develop the ability to reason logically and accurately, apply mathematical knowledge to model and solve real-life problems.
3. Students will recognize correlations among mathematical ideas and connections to mathematics within other fields of study. 4. Students will understand numbers, ways of representing numbers, relationships among numbers and number systems. 5. Students will be able to effectively communicate their knowledge of mathematics. 6. Students will be able to apply technology to interrupt, analyze and solve mathematical data. Scheduled Units (Days are approximate) SEMESTER 1 I. Chapter 12: Triangle Trigonometry (8 days) 12.1 Angles and Degree Measure 12.2 Trigonometric Functions of Acute Angles 12.3 Trigonometric Functions of General Angles 12.4 Values of Trigonometric Functions 12.5 Solving Right Triangles 12.6 The Law of Cosines 12.7 The Law of Sines 12.8 Solving General Triangles 12.9 Areas of Triangles II. III. IV. Chapter 13: Trigonometric Graphs; Identities (6 days) 13.1 Radian Measure 13.2 Circular Functions 13.3 Periodicity and Symmetry 13.4 Graphs of the Sine and Cosine 13.5 Graphs of the Other Functions 13.6 The Fundamental Identities Chapter 14: Trigonometric Applications (4 days, no quiz) 14.6 The Inverse Cosine and Inverse Sine 14.7 Other Inverse Functions 14.8 Trigonometric Equations Chapter 1: Basic Concepts of Algebra (4 days) 1.1 Real Numbers and Their Graphs 1.2 Simplifying Expressions 1.3 Basic Properties of Real Numbers 1.4 Sums and Differences 1.5 Products 1.6 Quotients 1.7 Solving Equations in One Variable 1.8 Words into Symbols 1.9 Problem Solving with Equations V. Chapter 2: Inequalities and Proof (4 days) 2.1 Solving Inequalities in One Variable
2.2 Solving Combined Inequalities 2.3 Problem Solving Using Inequalities 2.4 Absolute Value in Open Sentences 2.5 Solving Absolute Value Sentences Graphically VI. VII. Chapter 3: Linear Equations and Functions (6 days) 3.1 Open Sentences in Two Variables 3.2 Graphs of Linear Equations in Two Variables 3.3 The Slope of a Line 3.4 Finding an Equation of a Line 3.5 Systems of Linear Equations in Two Variables 3.6 Problem Solving Using Systems 3.7 Linear Inequalities in Two Variables 3.8 Functions 3.9 Linear Functions 3.10 Relations Chapter 4: Products and Factors of Polynomials (9 days) 4.1 Polynomials 4.2 Using Laws of Exponents 4.3 Multiplying Polynomials 4.4 Using Prime Factorization 4.5 Factoring Polynomials 4.6 Factoring Quadratic Polynomials 4.7 Solving Polynomial Equations 4.8 Problem Solving using Polynomial Equations VIII. Chapter 5:Rational Expressions (8 days) 5.1 Quotients of Monomials 5.2 Zero and Negative Exponents 5.3 Rational Algebraic Expressions 5.5 Products and Quotients of Rational Expressions 5.6 Sums and Differences of Rational Expressions 5.7 Complex Fractions 5.8 Fractional Coefficients 5.9 Fractional Equations SEMESTER 2 IX. Chapter 16: Matrices and Determinants (This chapter will be completed during Junior/Senior service projects) 16.1 Definition of Terms 16.2 Addition and Scalar Multiplication 16.3 Matrix Multiplication 16.4 Applications of Matrices 16.5 Determinants 16.6 Inverses of Matrices 16.7 Expansion of Determinants by Minors
16.8 Properties of Determinants 16.9 Cramer s Rule X. Chapter 6: Irrational and Complex Numbers (7 days) 6.1 Roots of Real Numbers 6.2 Properties of Radicals 6.3 Sums of Radicals 6.4 Binomials Containing Radicals 6.5 Equations Containing Radicals 6.7 The imaginary number i 6.8 The Complex Numbers XI. Chapter 7: Quadratic Equations and Functions (7 days) 7.1 Completing the Square 7.2 The Quadratic Formula 7.3 The Discriminant 7.4 Equations in Quadratic Form 7.5 2 Graphing y k = a( x h) 7.6 Quadratic Functions 7.7 Writing Quadratic Equations and Functions XII. Chapter 8: Variation and Polynomial Equations (9 days) 8.1 Direct Variation and Proportion 8.2 Inverse and Joint Variation 8.3 Dividing Polynomials 8.4 Synthetic Division 8.5 The Remainder and Factor Theorems 8.7 Finding Rational Roots 8.8 Approximating Irrational Roots 8.9 Linear Interpolations XIII. Chapter 9: Analytic Geometry (8 days) 9.1 Distance and Midpoint Formulas 9.2 Circles 9.3 Parabolas 9.4 Ellipses 9.5 Hyperbolas 9.6 More on Central Conics 9.8 Solving Quadratic Systems 9.9 Systems of Linear Equations in Three Variables XIV. Chapter 10: Exponential and Logarithmic Functions (9 days) 10.1 Rational Exponents 10.2 Real Number Exponents 10.3 Composition and Inverses of Functions 10.4 Definition of Logarithms 10.5 Laws of Logarithms
10.6 Applications of Logarithms 10.7 Problem Solving: Exponential Growth and Decay 10.8 The Natural Logarithm Function Required Texts: Algebra and Trigonometry Structure and Method Book 2 Materials: PENCIL (not pen), binder with graph paper, graphing calculator (TI-83 or TI-84), MathXL login Classroom Expectations and Rules: 1. Be on time, prepared, and in dress code. 2. Be respectful of classmates, teacher, and guests. 3. Spend class time working on the day s math assignment. 4. Use technology appropriately. 5. Adhere to the academic honor code as stated in the RJ handbook. Late Work and Makeup Work: Homework: Homework is given electronically. Unexcused late homework may be submitted until the Friday preceding final exams for a 50% penalty. Excused late homework must be submitted within a week of student s return to school for full credit. Students MUST email me when a late assignment has been completed in order to receive credit. Quizzes: Quizzes are given electronically as take-home assignments in lieu of homework. Students have two days to complete a quiz, and may choose to re-take a quiz one time to improve score. Unexcused missing quiz scores will be taken from the chapter test with a 10% penalty. Excused missing quiz scores should make arrangements with me. Tests: Tests are given in class. Any student who misses a test will make up the test on the next day he is in class. If tests have been returned by the student s return to class, he will have to meet with me to discuss options which may include an alternate test, an electronic test or accepting the final exam grade with a 5% penalty. Grading Scale: Work Ethic (homework, class work, notes) 15% Basic Skills 15% Simplifying 20% Solving/Graphing 25% Application 10% Final Exam 15%
Re-assessment Policy: I believe that learning is a process, and that students should be given credit for learning whenever it occurs, therefore, I allow students to re-assess test grades on their final exam with the following conditions in place. Students must meet with me to approve grades for re-assessment No student with a cumulative grade of 93% or better will be allowed to re-assess No student may re-assess a test with a score of 85% or better No student with a work ethic grade below 80% may re-assess Responsible Use Policy: Regis Jesuit High School s Responsible Use Policy regarding the use of technology, especially the ipad, will be enforced at all times. Honor Code: Students at RJHS will pursue education with honesty and integrity. The following may result in a loss of credit for any specific assignment and a disciplinary referral: copying another student s homework cheating on quizzes, tests or any other major assignment plagiarism