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CHARLES P. ALLEN HIGH SCHOOL ∞ MATHEMATICS DEPARTMENT ∞ MATH 12 PRECALCULUS COURSE OUTLINE Teaching Staff 2014 – 2015: A. Woods [email protected] B. Richardson [email protected] Room 230 Room 333 Prerequisite: Successful completion of Advanced Mathematics 11 and Advanced Mathematics 12 OR Successful completion of Mathematics 11 and Mathematics 12 AND demonstrated very good to outstanding performance in relation to the curriculum outcomes prescribed for Mathematics 11 and Mathematics 12 Textbook: Mathematical Modeling , Book 4 (Thomson Nelson 2002) Course Overview: This course is designed for students who intend on pursuing science, engineering and medical related degree programs. This is a challenging course that is suited to students who have a keen interest in mathematics. This course is designed to prepare students for Calculus. Course content includes the study of sequences, polynomial, rational, irrational, absolute value, exponential, logarithmic and trigonometric functions. As well, an introductory look at complex numbers and polar graphing. Course Outline: Sequences and Series Functions - a new Perspective Assessment: 25% Combine functions using addition, subtraction, and/or multiplication. Interpret and analyze these combined functions and use their graphs to solve problems. Apply transformations to functions Find the equations of combined functions from graphs Solve polynomial equations and inequalities Form, interpret, and analyze composite functions. Use graphs of composite functions to solve problems. Interpret slope to find average and instantaneous rate of change Find the slope of the tangent to a graph at a point using a derivative Compare the graph of a function to the corresponding graph of the slope of the tangent Find the equation of a polynomial function from given points and/or intercepts Use the power rule to find the derivative of a polynomial function Sketch the graph of polynomial functions using intercepts and critical points Solve maximum/minimum problems using a derivative Functions, Part II Assessment: 20% Demonstrate an understanding of recursive formulas Represent sequences graphically Develop, analyze and apply procedures to describe sequences algebraically Develop, analyze and apply procedures to evaluate the sums of series Develop proofs of mathematical statements using mathematical induction Demonstrate an understanding of the concept of limit in the context of sequences and series Demonstrate an understanding of the concepts of convergence and divergence Apply convergence in a variety of contexts Demonstrate an understanding of how to find the area of a region under a curve Assessment: 25% Plot the graphs of the functions in the transformational form and use these functions to model real-world phenomena. Identify the zeros, the vertical, horizontal, and oblique asymptotes, and the points of discontinuity of rational functions, and sketch the graphs of these functions. Simplify rational expressions and complex fractions Solve problems that involve rational equations Analyze the effect of taking the square root of polynomial and rational functions, plot the graphs of irrational functions, and use these functions to model real world phenomena. Analyze the effect of taking the absolute value of polynomial, rational, and irrational functions, determine the domain and range of these absolute-value functions, and plot their graphs. Analyze and plot the graphs of piecewise functions. Review exponential and logarithmic functions and use these functions to model real-world phenomena. Determine the value of e, plot the graph of ex, and use this natural exponential function to model real-world phenomena. Analyze and plot the graph of y = ln x, and use this natural logarithmic function to model real-world phenomena. Solve inequalities involving rational expressions and absolute values. Trigonometry Express angle measures in terms of arc length Model periodic behaviour and solve problems using periodic functions Identify equivalent trigonometric relations Describe transformations of periodic functions to model situations Combine trigonometric functions to create models Use matrix multiplication to rotate images Prove trigonometric identities Solve trigonometric equations Identify the graphs of the reciprocal trigonometric functions Use reciprocal and inverse trigonometric functions and their graphs to solve problems Complex Numbers Assessment: 25% Assessment: 5% Explain the connections between real numbers and complex numbers Represent complex numbers in a variety of ways Construct and examine graphs in the complex and polar planes Develop and evaluate mathematical arguments and proofs Apply operations on complex numbers in both rectangular and polar forms Translate between polar and rectangular representations, and investigate the relationships in the operations using graphs Apply De Moivre's Theorem Assessment: Assessment is the process of gathering, from a variety of sources, information that accurately reflects how well a student is achieving the learning outcomes in a subject or course. A) Formative assessment is to show growth over time, determine student needs, plan next steps in instruction, and provide students with descriptive feedback. B) Summative assessment is to determine the extent to which learning has occurred for students. Evaluation is the process of analyzing, reflecting upon, and summarizing assessment information and making judgements and / or decisions based on the information gathered. Unit assessments will consist of multiple opportunities for a student to demonstrate their understanding of the outcomes. Such opportunities include (but are not limited to) tests, quizzes, in-class assignments, portfolios, comprehension questions, and projects. Teachers will employ both formative and summative assessments in gathering information to determine a student grade. No one method of assessment will be worth more than 50% of the unit. Throughout the semester, students may feel that they have not successfully demonstrated their understanding of particular outcomes and would like another opportunity to demonstrate that they now “Get It”. Please refer to the Multiple Opportunities document on teacher/school website for more details. Mathematics courses require commitment and students must take responsibility for achieving the outcomes. Students need to make sure that they keep up with the work and seek help early if they encounter difficulties before they become insurmountable. Extra help is available, please check with your teacher for times. Students are NOT permitted to exempt the final exam. Final Assessment: 80% Course Outline 20% Final Exam Communication of Student Achievement: A collaborative effort of all stakeholders (student / parent/ teacher) is important to ensure student academic success. In an effort to maintain communications, a number of avenues are available. Class Web sites are updated daily Marks and attendance can be checked at any time on the Parent/ Student Portal of Powerschool. (If you do not have a password for the portal, please contact the main office) The Auto-dialer calls home regarding unexcused absences and upcoming events. Parents and students are encouraged to contact the teacher via email if they have any concerns regarding academic progress. Important dates include: o Curriculum night: February 10, 2015 o Parent/teacher interviews: April 22 , 2015 o Multiple Opportunity Testing week: June 1 - 12, 2015