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AP Calculus AB - CURRICULUM GUIDE AP Calculus AB CEDAR...

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CURRICULUM GUIDE AP Calculus AB CEDAR GROVE PUBLIC SCHOOLS 520 Pompton Avenue Cedar Grove, New Jersey 07009 Approved by the Cedar Grove Board of Education 12 June 2007 Dr. Gene Polles, Superintendent Thomas J. Altonjy, Administrative Assistant to the Superintendent Elizabeth Toriello, Supervisor Janine Miscia, Teacher Board of Education Jean Jaeger, President Frank Mandala, Vice – President Anthony Palma, Joseph Racaniello
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Description This is a college-level course that is designed primarily for students who have demonstrated a strong mathematical ability in all previous math courses and are independent workers. AP Calculus AB encompasses the two branches of a typical Calculus course: derivatives and integrals along with associated applications. Students will have an understanding of all topics analytically, graphically, numerically, and verbally. All students enrolled in the class are expected to take the College Board AP Exam in May. Assessments include quizzes, tests, group work and presentations. Activities are completed throughout the year in addition to practicing problems from supplementary AP Exam materials. Prerequisites: A minimum grade of “B” in Precalculus Honors and teacher recommendation. AP application must be submitted.
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UNIT 1 – Pre-Calculus Review Course Objective(s) Student Objectives NJ CCCS Strands & Indicators Suggested Timeframe (in blocks) Review all components of the coordinate graph and linear functions Define all terms associated with the coordinate plane Use the distance formula and reflections with respect to the axes and origin in problem-solving Find the slope of a line, and determine the relationship between parallel and perpendicular lines Write the equation of a line in slope- intercept, point-slope and standard forms 4.1 4.2 4.3 4.5 A,B,C A1,A3,C,D A,B1,B2 C ,D B,C,D,E,F 1 Identify basic terminology and properties associated with functions Classify functions (polynomial, rational, root, quadratic, cubic, reciprocal, composite), and determine all associated characteristics Find the domain and range of a function Determine if a function is odd or even with respective types of symmetry Perform a composition of functions Identify all the characteristics of the inverse of a function 4.1 4.2 4.3 4.5 A,B,C A1,A3,C,D A,B1,B2,C,D C (all) D (all) B,C,D,E,F 3
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Course Objective(s) Student Objectives NJ CCCS Strands & Suggested Indicators Timeframe (in blocks) Present “unique” functions and accompanying properties Understand all characteristics of the following functions both graphically and algebraically: absolute value, greatest integer, piecewise 4.1 4.2 4.3 4.5 A,B,C A1,A3,C,D A,B1,B2,B4, C,D B,C,D,E,F 1 Identify all properties of exponential and logarithmic functions Establish connections between exponential functions of the form c x Apply properties of e x and ln x when algebraically manipulating exponential and logarithmic equations functions 4.1 4.2 4.3 4.5 A,B,C A1,A3,C,D A,B1,B2,B4, C,D B,C,D,E,F 2 Present the three basic trigonometric functions
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