Phineas Banning High School

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AP Calculus

Course Description

Course Description: AP Calculus offers students their first opportunity to attempt collegiate level mathematics. This course has two distinct goals: First, to learn and appreciate Calculus as a significant mathematical and scientific tool and as a human achievement. Second, to prepare for the College Board’s Advanced Placement Examination in Calculus (AB) to be given on Wednesday, May 8, 2013. Passing this examination may earn the student college credit when they enroll in a four year institution in the Fall of 2013.

Calculus A Course Outline

Chapter 1: Limits and Continuity

1.1 Limits – An intuitive (geometric) approach (2.1)
1.2 Limits – Computational Techniques (algebraic) (2.1 and 2.2)
1.3 Continuity (2.3)
1.4 Trigonometric limits (2.1 and 2.2)

Chapter 2: Derivatives/Differentiation

2.1 The Derivative(Definition) (3.1 and 3.2)
2.2 Differentiation Rules (3.3)
2.3 Average and Instantaneous Rates of Change (2.4 and 3.4)
2.4 The Chain Rule (3.6)
2.5 Derivatives of Trigonometric Functions (3.5)
2.6 Evaluating Limits as Derivatives
2.7 Implicit Differentiation (3.7)
2.8 Derivatives of Inverse Functions; Inverse Trig (3.8)
2.9.a Getting a Derivative Graph (3.1 and 4.3)
b. Getting the Function Graph from a Derivative Graph

Chapter 3: Applications of Derivatives
3.1 Tangent Lines (2.4, 3.3)
3.2 Tangent Line Approximations(Linearizations) (3.2 and 4.5)
3.3.a Motion along a line: A Graphical look (3.4)
b. Motion along a line: Using Equations
3.4 Intervals of Increase and Decrease; Concavity (4.1)
3.5 Relative Extrema: First and Second Derivative Tests (4.3)
3.6 Getting information about f from an graph (4.3)
3.7 Maximum and Minimum Values of a Function (4.1 and 4.3)
3.8 Applied Maximum and Minimum Problems (4.4)
3.9 Related Rates (4.6)
3.10 Rolle’s Theorem; Mean Value Theorem (4.2)

Calculus B Course Outline

Chapter 4: Integration and Area

4.1 Anti Derivative Basics (5.2)
4.2 Anti Derivative by Substitution (6.2)
4.3.a Differential Equations (Simple Separable Type) (6.1)
b. Slope Fields (6.1)
4.4 Area under a Curve (by dividing into rectangles) (5.1 and 5.2)
4.5 Area by Calculus (the Fundamental Theorem), The Definite Integral (5.3 and 5.4)
4.6.a The Area Function (5.3 and 5.4)
b. More on the Fundamental Theorem
4.7.a The Area under a Velocity Curve and its Relationship to Distance Travelled (5.1)
b. Area under other Rate Curves
4.8 The Average Value of a Function (5.3)
4.9 The Trapezoid Rule (5.5)

Chapter 5: Area and Volume

5.1 Areas between Curves (7.2)
5.2 Volumes by Revolving: Disks, Washers (7.3)
5.3 Volumes by Cross Sections (7.3)

Chapter 6: Logarithms and Exponents

6.1 Derivatives and Integrals of Natural Logarithms (3.9)
6.2 Derivatives and Integrals of and (3.9)
6.3 Natural Growth and Decay (6.4)
6.4 L’Hopital’s Rule (8.2)

During First and Second semester all students are invited to form groups to do homework, study for class exams and the AP test and are welcome to meet in my classroom during Nutrition, Lunch and after school.

Starting mid-February we will begin focusing on the AP Exam, the style of its questions, the intent of its questions, and the expectations of the AP Test Development Committee for student success on the exam. Also to get you ready for the AP Calculus Exam we will take THREE full length practice exams throughout the school year.