Mathematics Prince George s County Public Schools SY

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1 ALGEBRA 2/TRIGONOMETRY Mathematics Prince George s County Public Schools SY Prerequisites: Geometry with a grade of B or higher Credits: 1.0 Math, Merit CLASS MEETS: Every other day for 90 minutes TEXT: Algebra and Trigonometry, Prentice Hall Algebra 2/Trigonometry provides students with the application of skills and concepts related to expressions and functions, graphs of functions, algebraic manipulations of functions, matrices, systems of equations, linear, quadratic, exponential, logarithmic, polynomial, and rational functions and the study of the complex number system. This course also covers topics in trigonometry and the algebraic analysis of the conic sections. Students will be asked to solve real life problems and make connections to other disciplines. INTRODUCTION: Typically in a Math class, to understand the majority of the information it is necessary to continuously practice your skills. This requires a tremendous amount of effort on the student s part. Each student should expect to dedicate 2-3 hours of studying for every hour in class. Some hints for success in a Math class include: attending class daily, asking questions in class, and thoroughly completing all the homework problems with detailed solutions as soon as possible after each class session. CALCULATORS The use of a graphing calculator is required. While participants may use any graphing calculator, the instruction in the course requires the TI-83. The TI-84 is very similar and can be used as well. Knowledge and competence for use of other graphing calculators will be the sole responsibility of the student. GRADING: Your grade will be computed from the following categories: class work, homework, and assessment. The following weighted average will be used to calculate your grade. Category Brief Description Grade Percentage CLASS WORK/ GROUP PARTICIPATION HOMEWORK ASSESSMENT THIS INCLUDES ALL WORK COMPLETED IN THE CLASSROOM SETTING. INCLUDING: NOTEBOOKS, WARM-UPS, VOCABULARYWRITTEN RESPONSES TO CONSTRUCTED RESPONSES (BCR/ECR) WHERE APPLICABLE, GROUP DISCUSSION, ACTIVE PARTICIPATION IN MATH PROJECTS, COMPLETION OF ASSIGNMENTS THIS INCLUDES ALL WORK COMPLETED OUTSIDE THE CLASSROOM TO BE GRADED ON ITS COMPLETION AND STUDENT S PREPARATION FOR CLASS (MATERIALS, SUPPLIES, ETC.) ASSIGNMENTS CAN INCLUDE, BUT NOT LIMITED TO: PROBLEM OF THE WEEK, FRIDAY NIGHT HOMEWORK THIS CATEGORY ENTAILS BOTH THE TRADITIONAL (EXAMS AND QUIZZES) AND ALTERNATIVE (PRESENTATIONS, PROJECTS, PORTFOLIOS) METHODS OF ASSESSING STUDENT LEARNING. EXAMS, QUIZZES, PORTFOLIOS, RESEARCH/UNIT PROJECTS, ORAL PRESENTATIONS SUGGESTED CRITERIA FOR GRADING PRESENTATIONS, PROJECTS, PORTFOLIOS: CONCEPTS/OBJECTIVES HAVE BEEN MET COMPLETION OF PROJECT CREATIVITY, ORIGINALITY 30% 20% 50%

2 Your grade will be determined using the following scale: 90% - 100% A 80% - 89% B 70% - 79% C 60% - 69% D 59% and below E SAT/ACT: SAT/ ACT preparation is infused into daily instruction. The curriculum is embedded with standardized test preparation activities and test-taking strategies that will help students be successful on high-stakes tests like the SAT, ACT or college entrance exams. The practice in each lesson will prepare the students for the format as well as for the content. First Quarter at a Glance Throughout first quarter, fundamental concepts of Algebra and linear functions should be emphasized. As students learn linear equations and inequalities, they should be guided through inductive and deductive reasoning procedures in order to learn logical thinking processes on how to solve and graph linear functions. By the end of First Quarter Algebra 2 Trigonometry students should be able to: Unit 1: Linear Equations and Inequality Use fundamental concepts of Algebra Find the union, intersection of sets and recognize subsets of real numbers Graph equations and inequalities in the rectangular coordinate system Interpret information about a graphing utility s viewing rectangular coordinate and table Solve linear equations, linear equations involving fractions, and rational equations Use interval notations in solving linear inequalities and absolute value inequalities Use linear equations to solve real world problems Calculate line s slope and write the different forms of the equation of the line Unit 2: Functions Determine and identify the basics of functions and their graphs Find and verify inverse functions Form composite functions Write functions as compositions Unit 3: Linear Systems and Matrices Solve linear systems by substitution and addition Identify systems that so not have exactly one ordered-pair solution Verify and solve systems of linear equations in three variables Graph systems of inequalities Add and multiple matrices Evaluate determinants Use Cramer s rule in solving systems of linear equations

3 Second Quarter at a Glance Throughout second quarter, radicals and quadratics with the connections in real world should be emphasized. As students learn the rules, procedures and formulas in solving radicals and quadratics, they should be guided through modeling, inductive and deductive reasoning procedures in order to learn logical thinking processes. By the end of Second Quarter Algebra 2 Trigonometry students should be able to: Unit 4: Radical Expressions and Equations Use product rule and quotient rule in simplifying radical expressions Perform operations on radicals by rationalizing denominators Simplify, multiply and divide higher roots Solve radical equations Solve equations with rational exponents Perform operations on complex numbers Use complex conjugates to divide complex numbers Unit 5: Quadratic Functions and Relations Recognize characteristics of parabolas and graph parabolas Use FOIL in multiplying binomials Factor trinomials Solve quadratic equation by completing the square Utilize quadratic formula in solving quadratic equations Solve quadratic inequalities Write the standard form and general form of a circle s equation Use the standard form of a circle s equation to graph a circle Write equations of ellipses in standard form and in general form Graph ellipses centered at the origin or not centered at the origin Write equations of hyperbolas in standard form and in general form Graph hyperbolas centered at the origin or not centered at the origin

4 Third Quarter at a Glance Throughout third quarter, polynomials, rational, exponential and logarithmic functions and the connections to real world should be emphasized. As students learn to solve polynomial, rational, exponential and logarithmic functions, properties and theorems should be highlighted. By the end of Third Quarter Algebra 2 Trigonometry students should be able to: Unit 6: Polynomials and Rational Functions Simplify rational expressions Add and subtract rational expressions that have different denominators Solve rational equations Dividing polynomials using long division and synthetic division Use the rational zero theorem to find zeros of polynomial functions Identify and recognize the characteristics of polynomial functions Solve problems modeled by polynomial inequalities Identify the properties of rational functions Identify slant asymptotes of rational functions Solve problems modeled by rational inequalities Unit 7: Exponential and Logarithmic Functions Simplify exponential expression Evaluate and graph exponential functions Transform exponential functions Define and graph logarithmic functions Use logarithmic properties to expand or condense logarithms Use like bases and logarithms to solve exponential functions Solve applied problems involving exponential and logarithmic equations

5 Fourth Quarter at a Glance Throughout fourth quarter, angle measurement and real world problem connections should be emphasized. As students learn right triangles, trigonometric functions and identities, the prior knowledge should be highlighted in order to assist the student s construction of knowledge. By the end of fourth Quarter Algebra 2 Trigonometry students should be able to: Unit 8: Trigonometry Utilize basics of trigonometry to solve angle measures Use right triangle to evaluate trigonometric functions Recognize and use fundamental identities Use calculator to evaluate trigonometric functions Use a unit circle to define trigonometric functions of real numbers Find and use reference angles to evaluate trigonometric functions Solve right triangles Use law of sine to solve oblique triangles Use law of cosines to solve oblique triangles Verify identities using the fundamental trigonometric identities Use sum and difference formulas for sines, cosines and tangents Use double-angle formulas to find exact values