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# Mathematics / Calculus (ECE)

 Calculus (ACE):This course is a dual enrollment course offered in collaboration with Westchester Community College (WCC) through its Advanced College Experience (ACE). This course includes topics in differential and integral calculus. The final exam is a departmental exam. Students must pay the (discounted) fee for WCC credit to receive a Westchester Community College transcript.

Please note that the timelines listed below are a guide. Teachers modify their pacing based on student needs in order to ensure concept mastery.

 Unit 1 Pre-calculus Review September Concepts Textbook Resources Factoring Teacher Generated Materials Review Functions Piecewise Functions Finding Zeros of a Polynomial Function Graphing Rational Functions Unit 2 Introduction to Limits Sept - Oct Concepts Resources Intro to Limits Graphically Teacher Generated Materials Limit Laws and Finding Limits Algebraically -piecewise functions Limits to Infinity Limits of Trig Functions Unit 3 Continuity Oct - Nov Concepts Resources Definition of Continuity Teacher Generated Materials Classifying types of Continuities Determining if a function is continuous- using the 3 part definition Domain of compositions of Functions and Continuities End of Quarter 1 Unit 4 The Derivative Nov - Dec Concepts Resources What is the Derivative? Teacher Generated Materials Definition of the Derivative Finding the First Derivative using the definition of the derivative Intro to Rules- Power Rule, Sum and Difference, Product, Quotient, and Chain Rule Midterm Exam Unit 5 Implicit Differentiation Jan - Feb Concepts Resources Differentiating Implicitly-all rules Teacher Generated Materials Higher Order Derivatives Applications of the Derivative Derivatives of Trig Functions End of Quarter 2 Unit 6 Curve Sketching March - April Concepts Resources Relative Maximum and Minimum Teacher Generated Materials Absolute Maximum and Minimum Second Derivative and Concavity Sketching a Graph of a Polynomial Functions Sketching a Graph of Rational Functions End of Quarter 3 Unit 7 Integration April - May Concepts Resources The Antiderivative- the indefinite integral Teacher Generated Materials Left and Right Riemann Sums Approximating using left and right endpoint rectangles Riemann Sums as n approaches infinity The Definite Integral Final Exam Before Memorial Day