Precalculus Grade 10, 11, or 12 Prerequisites: Algebra I, Geometry, and Algebra II Credit Value: 5

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1 Office of Curriculum and Instruction Prerequisites: Algebra I, Geometry, and Algebra II Credit Value: 5 ABSTRACT is designed to prepare students for high school or college calculus. Topics include a detailed study of composite and applications using exponential, logarithmic, and trigonometric and their applications. Sequences and series and the concept of limits are also studied. Adopted by the Somerville Board of Education on September 27, 2011

2 Month/ Marking Period 2010 Common Core Content Standards (CCCS)* Essential Question: Content: September October November December January F-BF.1.b-c, F-BF.3, F-BF.4.a-d, F-IF.1-2, F-IF.8a What is the relationship between the graph of a function and its algebraic rule? Functions Skills and Topics: analyze and explain the general properties and behavior of of one variable using appropriate graphing techniques: o domain and range o intercepts o roots of equations o maximum and minimum o points that lie on the graph of a function compare the properties of different classes of, including symmetry perform operations on, including composite find inverse function if the inverse exists A-CED.2, A-REI.2, A- SSE.3c, F-BF.5, F-IF.8.b, F-LE.2, F-LE.4-5 How do exponential and logarithmic relate to each other? Exponential and Logarithmic Functions define and apply the Law of Exponents evaluate the inverse relationship between exponential and logarithmic understand the value of e and apply to problem-solving situations demonstrate the ability to evaluate integral and rational exponents apply natural logs to growth and decay identify and apply the Law of Logarithms demonstrate the ability to convert between logs of different bases solve equations containing logs of different bases A-CED.2, F-Tf.1-4, F-TF.8, G-C5 What is the relationship between the measure of angles and the sine and cosine? Trigonometric Functions determine the measure of angles in both radians and degrees identify co-terminal angles calculate arc lengths and areas of a sector of a circle solve problems involving apparent size use sine, cosine, and the unit circle to solve simple trigonometric equations connect the concept of an angle s location on the coordinate plane to the sign of its trigonometric value F-TF.8 How are special angles and reference angles used to simplify trigonometric expressions? Special Reference Angles recognize special angles by both radian and degree measures identify the significance of special angles (e.g., 0 o, 30 o, 45 o, 60 o, 90 o ) as reference angles use reference angles to evaluate and graph sine and cosine use reference angles to determine the values of trigonometric to aid in higher-level problem-solving situations F-BF.4.a-d, F-TF.6-8, G-SRT.6 What is the relationship between trigonometric, their inverse trigonometric, and their reciprocal trigonometric? Reciprocal and Inverse Trigonometric Functions recognize the reciprocal nature between pairs of trigonometric (e.g., sine = 1/cosecant) discuss signs and relationships between trigonometric compare and contrast the graphs of trigonometric determine the values of inverse trigonometric

3 Month/ Marking Period Integration of Technology: Writing: Formative Summative Performance Interdisciplinary Connections: September October November December January Internet, Web Quests, wireless laptop computers, SMART Boards, multimedia presentations, Excel spreadsheets, graphing calculators, overhead graphing calculator unit, student communicators, geometer sketchpad, video streaming, podcasting Open-ended responses, conclusions and analysis of exploratory activities Warm-up activities, exploratory activities, class discussions, student participation Projects, presentations Authentic assessments *ELA: RST , WHST , WHST Science: A.1-3, B.1-4, C.1-3, D.1-3 Arts: Health/PE: Technology: A.1, C.1, E.1-2, F.1 World Language: 7.1.AL.A.3 Social Studies: 21 st Century Life/Careers: A.1, B.1-3, F.2 21 st Century Themes: Global Awareness Civic Literacy Financial, Economic, Business, and Entrepreneurial Literacy Health Literacy 21 st Century Skills: Creativity and Innovation Media Literacy Critical Thinking and Problem Solving Life and Career Skills Resources: Careers: Information and Communication Technologies Literacy Communication and Collaboration Information Literacy Brown, R. (2000). Advanced Mathematics with Discrete Mathematics & Data Analysis. Evanstown, IL: McDougal Littell. HSPA prep problems. Applicable career options are discussed as they arise throughout the mathematics program. Career options include, but are not limited to, the following career clusters: Agriculture, Food, and Natural Resources Career Cluster; Architecture and Construction Career Cluster; Arts, A/V Technology, and Communications Career Cluster; Business, Management, and Administration Career Cluster; Education and Training Career Cluster; Finance Career Cluster; Government and Public Administration Career Cluster; Health Science Career Cluster; Hospitality and Tourism Career Cluster; Human Services Career Cluster; Information Technology Career Cluster; Law, Public Safety, Correction, and Security Career Cluster; Manufacturing Career Cluster; Marketing Career Cluster; Science, Technology, Engineering and Mathematics Career Cluster; Transportation, Distribution, and Logistics Career Cluster.

4 *2010 Common Core Content Standards: RST: Reading in Science and Technical Subjects WHST: Writing in History, Science, and Technical Subjects SL: Speaking and Listening L: Language N: Real Number System N-VM: Vector and Matrix Quantities G-CO: Congruence A: Algebra A- SSE: Seeing Structure in Expressions G-SRT: Similarity, Right Triangles, and Trigonometry F: Functions A-REI: Reasoning with Equations and Inequalities G-C: Circles G: Geometry F-IF: Interpreting Functions G-GPE: Expressing Geometric Properties with Equations S: Statistics and Probability F-BF: Building Functions S-ID: Interpreting Categorical and Quantitative Data MD: Measurement and Data F-LE: Linear, Quadratic, and Exponential Models S-IC: Making Inferences and Justifying Conclusions N-Q: Quantities F-TF: Trigonometric Functions S-CP: Conditional Probability and the Rules of Probability S-MD: Using Probability to Make Decisions

5 Month/ Marking Period 2010 Common Core Content Standards (CCCS)* Essential Question: Content: February March April May June A-CED.2, F-IF.9, F-TF.5 F-TF.8, G-SRT.7-8 A-SSE.4, F-BF.1.a, F-BF.2, F-Ir.3, F-LE.2, F-TF.9 How does the domain of a function affect its solutions? Solving Trigonometric Equations Skills and Topics: solve trigonometric equations on a specified interval determine the slope of a line using the angle of inclination determine the period and amplitude of sine and cosine curves, graphs, and equations graph sine and cosine of varying periods and amplitudes perform transformations on sine and cosine (e.g., translations, reflections, dilations) How are trigonometric used to solve for unknown parts of a triangle? Trigonometric Ratios investigate relationships between trigonometric (e.g., negative, Pythagorean, cofunctional) simplify trigonometric expressions express complex trigonometric fractions composed of simple trigonometric fractions in lowest terms solve complex trigonometric equations recognize multiple solutions to problems occurring over predetermined intervals use trigonometric to find unknown sides or angles of right triangles How are sequences and series represented by algebraic formulas? Trigonometry Addition Formulas and Sequences and Series apply the sum and difference formulas for sine, cosine, and tangent apply double and half angle formulas for sine, cosine, and tangent recognize arithmetic and geometric sequences and series determine explicit formulas for the n th term find terms of recursive sequences determine recursive sequence formulas find the sums of finite arithmetic and geometric series estimate the limit of an infinite geometric sequence F-BF.3, F-TF.1-3, F-TF.7.d How do limits serve as a means to better understand and their behavior? Introduction to Limits recognize the use of asymptotes in determining limits define the concept represented by the terms, convergent and divergent find the sum of an infinite geometric series interpret limit notation of a sequence or series use partial sums to determine limits represent series using sigma notation use the properties of finite sums to evaluate a given series find the limit of a function determine the limit of the quotient of two A-REI.11 How is the limit of a function related to its graph? Limits apply the properties of limits to aid in problem solving formulate a definition of continuity using limits including lefthand and right-hand determine the location of asymptotes using limits recognize continuity at a point of a function predict how the limit of a function relates to its continuity

6 Month/ Marking Period February March April May June Skills and Topics: recognize and solve applications using the angle of depression (e.g., descent) and the angle of elevation determine the area of a triangle given the lengths of two sides and the measure of the included angle use the Laws of Sines and Cosines to solve for unknown parts of a triangle apply trigonometry to navigation and surveying Integration of Technology: Internet, Web Quests, wireless laptop computers, SMART Boards, multimedia presentations, Excel spreadsheets, graphing calculators, overhead graphing calculator unit, student communicators, geometer sketchpad, video streaming, podcasting Writing: Open-ended responses, conclusions and analysis of exploratory activities Formative Warm-up activities, exploratory activities, class discussions, student participation Summative Projects, presentations Performance Authentic assessments Interdisciplinary Connections: *ELA: RST , WHST , WHST Science: A.1-3, B.1-4, C.1-3, D.1-3 Technology: A.1, C.1, E.1-2, F.1 World Language: 7.1.AL.A.3 21 st Century Life/Careers: A.1, B.1-3, F.2

7 Month/ Marking Period February March April May June 21 st Century Themes: Global Awareness Civic Literacy Financial, Economic, Business, and Entrepreneurial Literacy Health Literacy 21 st Century Skills: Creativity and Innovation Media Literacy Critical Thinking and Problem Solving Life and Career Skills Resources: Careers: Information and Communication Technologies Literacy Communication and Collaboration Information Literacy Brown, R. (2000). Advanced Mathematics with Discrete Mathematics & Data Analysis. Evanstown, IL: McDougal Littell. HSPA prep problems Applicable career options are discussed as they arise throughout the mathematics program. Career options include, but are not limited to, the following career clusters: Agriculture, Food, and Natural Resources Career Cluster; Architecture and Construction Career Cluster; Arts, A/V Technology, and Communications Career Cluster; Business, Management, and Administration Career Cluster; Education and Training Career Cluster; Finance Career Cluster; Government and Public Administration Career Cluster; Health Science Career Cluster; Hospitality and Tourism Career Cluster; Human Services Career Cluster; Information Technology Career Cluster; Law, Public Safety, Correction, and Security Career Cluster; Manufacturing Career Cluster; Marketing Career Cluster; Science, Technology, Engineering and Mathematics Career Cluster; Transportation, Distribution, and Logistics Career Cluster. *2010 Common Core Content Standards: RST: Reading in Science and Technical Subjects WHST: Writing in History, Science, and Technical Subjects SL: Speaking and Listening L: Language N: Real Number System N-VM: Vector and Matrix Quantities G-CO: Congruence A: Algebra A- SSE: Seeing Structure in Expressions G-SRT: Similarity, Right Triangles, and Trigonometry F: Functions A-REI: Reasoning with Equations and Inequalities G-C: Circles G: Geometry F-IF: Interpreting Functions G-GPE: Expressing Geometric Properties with Equations S: Statistics and Probability F-BF: Building Functions S-ID: Interpreting Categorical and Quantitative Data MD: Measurement and Data F-LE: Linear, Quadratic, and Exponential Models S-IC: Making Inferences and Justifying Conclusions N-Q: Quantities F-TF: Trigonometric Functions S-CP: Conditional Probability and the Rules of Probability S-MD: Using Probability to Make Decisions

8 Course Requirements Grades: 10, 11, or 12 Prerequisites: Algebra I, Geometry, and Algebra II Credit Value: 5 Length of Course: Academic Year Course Description is designed to prepare students for high school or college calculus. Topics include a detailed study of composite and applications using exponential, logarithmic, and trigonometric and their applications. Sequences and series and the concept of limits are also studied. Course Content This course will consist of the following units of study: Functions Exponential and Logarithmic Functions Trigonometric Functions Special Reference Angles Reciprocal and Inverse Trigonometric Functions Solving Trigonometric Equations Trigonometric Ratios Trigonometry Addition Formulas and Sequences and Series Introduction to Limits Limits Course Objectives The student will demonstrate the ability to answer in detail the following essential questions: What is the relationship between the graph of a function and its algebraic rule? How do exponential and logarithmic relate to each other? How are special angles and reference angles used to simplify trigonometric expressions? What is the relationship between trigonometric, their inverse trigonometric, and their reciprocal trigonometric? How does the domain of a function affect is solutions? How are trigonometric used to solve for unknown parts of a triangle? How are sequences and series represented by algebraic formulas?

9 Course Objectives (continued) How do limits serve as a means to better understand and their behavior? How is the limit of a function related to its graph? What are the post-graduation and/or career options that apply to the course content? Evaluation Process A final average of 65% or better is required to be awarded course credit. Throughout the length of this course, students may be evaluated on the basis of, but not limited to: Formative Assessments, such as writing prompts, journals, and portfolios Summative Assessments, such as quizzes, tests, and midterm and final examinations Performance Assessments, such as projects and presentations Technology-based Applications, such as electronic portfolios, Web Quests, ThinkQuest, and podcasting Class Participation Homework Specific weights will be determined by course and level.

10 Student Agreement STUDENT NAME: Last Name First Name GRADE: My signature below indicates that I have received a copy of the Somerville Public Schools Course Requirements for. I acknowledge my responsibility to read and understand all of the information contained in the Course Requirements information and syllabus packet. Student Signature Date Note: Please share the course requirements for with your parents.

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