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