Contents of the Course The following course contents are approximate; the number of days per unit may have to be adjusted due to school wide testing days, weather conditions and other unforeseen events. [C2] Unit 1 Review, Limits & Continuity (appr. 8 days) 1 Test – – -1.7 Selected Topics Limits (An Intuitive Approach) Computing Limits Limits at Infinity; End Behavior of a Function Limits (Discussed More Rigorously) Continuity Unit 2 Derivative Mechanics (appr. 12 days) 2 – – Tangent Lines, Velocity, and General Rates of Change The Derivative Function Techniques of Differentiation The Product Rule and Quotient Rules Derivatives of Trigonometric Functions The Chain Rule Implicit Differentiation Derivatives of Logarithmic Functions Derivatives of Exponential and Inverse Trigonometric Functions L’Hopital’s Rule; Indeterminate Forms Unit 3 Derivative Applications (appr. 12 days) 1 Test (2 days) – – Analysis of Functions I: Increase, Decrease, and Concavity Analysis of Functions II: Relative Extrema; Graphing Polynomials More on Curve Sketching: Rational Functions; Curves with Cusps and Vertical Tangent Lines Absolute Maxima and Minima Applied Maximum and Minimum Problems Related Rates Local Linear Approximation; Differentials Rolle’s Theorem; Mean-Value Theorem Rectilinear Motion Limits, Continuity & Derivatives Final 2 day Test – Semester Final AP style Multiple Choice Questions – Unit 4 Integration Mechanics (appr. 9 days) 2 Tests (1 Test overlaps Unit 4 & 5) – – (We actually start this unit during the first semester, between the Derivatives Final and Semester Final) An Overview of the Area Problem The Definition of Area as a Sigma Notation The Definite Integral The Indefinite Integral The Fundamental Theorem of Calculus Integration by Substitution Rectilinear Motion Revisited Using Integration Evaluating Definite Integrals by Substitution Logarithmic Functions from the Integral Point of view Unit 5 Integration Applications (appr. 8 days) 1 Test – –
Contents of the Course The following course contents are approximate; the number of days per unit may have to be adjusted due to school wide testing days, weather conditions and other unforeseen events. [C2] Unit 1 – Review, Limits & Continuity (appr. 8 days) – 1 Test -1.7 Selected Topics Limits (An Intuitive Approach) Computing Limits Limits at Infinity; End Behavior of a Function Limits (Discussed More Rigorously) Continuity Unit 2 – Derivative Mechanics (appr. 12 days) – 2 Tangent Lines, Velocity, and General Rates of Change The Derivative Function Techniques of Differentiation The Product Rule and Quotient Rules Derivatives of Trigonometric Functions The Chain Rule Implicit Differentiation Derivatives of Logarithmic Functions Derivatives of Exponential and Inverse Trigonometric Functions L’Hopital’s Rule; Indeterminate Forms Unit 3 – Derivative Applications (appr. 12 days) – 1 Test (2 days) Analysis of Functions I: Increase, Decrease, and Concavity Analysis of Functions II: Relative Extrema; Graphing Polynomials More on Curve Sketching: Rational Functions; Curves with Cusps and Vertical Tangent Lines Absolute Maxima and Minima Applied Maximum and Minimum Problems Related Rates Local Linear Approximation; Differentials Rolle’s Theorem; Mean-Value Theorem Rectilinear Motion Limits, Continuity & Derivatives Final – 2 day Test Semester Final – AP style Multiple Choice Questions Unit 4 – Integration Mechanics (appr. 9 days) – 2 Tests (1 Test overlaps Unit 4 & 5) (We actually start this unit during the first semester, between the Derivatives Final and Semester Final) An Overview of the Area Problem The Definition of Area as a Sigma Notation The Definite Integral The Indefinite Integral The Fundamental Theorem of Calculus Integration by Substitution Rectilinear Motion Revisited Using Integration Evaluating Definite Integrals by Substitution Logarithmic Functions from the Integral Point of view Unit 5 – Integration Applications (appr. 8 days) – 1 Test
BC%20Syllabus.docx