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Course Description
Course Description
Prerequisites:
Scores of 80 or above on all 3 Regents exams and an overall average of 80 or higher in Geometry, Algebra I, Algebra II, and Pre-Calculus and
Teacher recommendation.
This is a first course in calculus for students in mathematics, science, computer science and engineering. Topics include basic analytic geometry, functions, limits and continuity, derivatives of algebraic and trigonometric functions, chain rule, implicit differentiation, antiderivatives, definite integrals, Fundamental Theorem, applications of derivatives and integrals. A graphing calculator is required.
Quarter 1
Sep - Nov
Unit or Topic Skills
I can:
LO 1.1A(a): Express limits symbolically using correct notation.
LO 1.1A(b): Interpret limits expressed symbolically.
LO 1.1C: Determine limits of functions.
LO 1.1D: Deduce and interpret behavior of functions using limits.
LO 1.2A: Analyze functions for intervals of continuity or points of discontinuity.
LO 1.2B: Determine the applicability of important calculus theorems using continuity.
LO 2.1A: Identify the derivative of a function as the limit of a difference quotient.
LO 2.1B: Estimate derivatives.
LO 2.1C: Calculate derivatives.
Quarter 2
Nov - Jan
Unit or Topic Skills
I can:
LO 2.1D: Determine higher order derivatives.
LO 2.2A: Use derivatives to analyze properties of a function.
LO 2.2B: Recognize the connection between differentiability and continuity.
LO 2.3A: Interpret the meaning of a derivative within a problem.
LO 2.3B: Solve problems involving the slope of a tangent line.
LO 2.3C: Solve problems involving related rates and optimization.
Quarter 3
Jan - Apr
Unit or Topic Skills
I can:
LO 3.1A: Recognize antiderivatives of basic functions.
LO 3.2A(a): Interpret the definite integral as the limit of a Riemann sum.
LO 3.2A(b): Express the limit of a Riemann sum in integral notation.
LO 3.2B: Approximate a definite integral.
LO 3.2C: Calculate a definite integral using areas and properties of definite integrals.
LO 3.3A: Analyze functions defined by an integral.
LO 3.3B(a): Calculate antiderivatives.
LO 3.3B(b): Evaluate definite integrals.
LO 3.4A: Interpret the meaning of a definite integral within a problem.
LO 3.4B: Apply definite integrals to problems involving the average value of a function.
LO 3.4C: Apply definite integrals to problems involving motion.
Quarter 4
Apr - Jun
Unit or Topic Skills
I can:
LO 3.4D: Apply definite integrals to problems involving area and volume.
LO 3.4E: Use the definite integral to solve problems invarious contexts.
LO 3.5A: Analyze differential equations to obtain general and specific solutions.
LO 3.5B: Interpret, create, and solve differential equations from problems in context.
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