AP CALCULUS- COURSE SYLLABUS
TEACHER: Ms. Stirling ROOM: 211 PHONE: 610.847.5131 x2335 EMAIL:
MATERIALS:
Texts: Calculus of a Single Variable, Early Transcendental Functions, 4th Edition. Larson, Hostetler, Edwards; Houghton Mifflin, 2007
Supplies: A three ring binder, a notebook with lined paper, pencil, eraser, and a graphing calculator.
Calculator: You will need your own graphing calculator. I recommend TI-84, TI-84+ or TI-Nspire.
COURSE CONTENT:
DESCRIPTION OF COURSE:
This course is designed to develop the conceptual understanding of limits, differential and integral calculus and their applications at a college level. Course content includes analytic geometry, elementary functions, the concept of limits, derivatives and their application, differential equations and slope fields, and indefinite and definite integrals and their applications. The use of technology is integrated throughout the course to provide a balanced approach to the learning of calculus. Calculator usage will be limited. Students will need to be able to approach problems with and without the use of use of technology. The course is structured to prepare students for the AP Calculus AB Exam. Practice with exam items will be imbedded throughout the course.
AP Calculus AB Course Outline
Unit 1: Preparation for Calculus
1.1 Graphs and Models (Summer assignments.)
1. Rule of 4: situation, graph, table and equations
2. Graphs (intercepts, symmetry, intersection)
3. Mathematical models
1.2 Linear Models and Rates of Change (Summer assignments.)
1. Slope and average rates of change
2. Parallel and perpendicular lines
3. Equations of lines (various forms)
1.3 Functions and Their Graphs (Summer assignments.)
1. Functions and relations: dependent & independent variables, real number solution, function notation, explicit & implicit forms.
2. Domain and range
3. Families of functions and transformations: algebraic (polynomial, radical & rational) and transcendental (trigonometric, exponential & logarithmic).
4. Piecewise functions
5. Composition of functions and function properties (sum, difference, product, quotient)
6. Even & odd functions
1.4 Fitting Models to Data (Summer assignments.)
1. Fitting linear, quadratic & trigonometric models.
2. Graphing calculators
1.5 Inverse Functions (Summer assignments.)
1. Inverse functions: rule of 4, existence and writing inverse functions
2. Inverse trigonometric functions
1.6 Exponential and Logarithmic Functions (Summer assignments.)
1. Exponential growth and decay
2. Logarithmic functions
3. Properties of exponents and logarithms
Review/Unit Exam
Unit 2: Limits and Their Properties
1. A Preview of Calculus
2. Finding Limits Graphically and Numerically
3. Evaluating Limits Analytically
4. Continuity and One-Sided Limits
5. Infinite Limits
6. (Section 4.5) Limits at Infinity
Review/Unit Exam
Unit 3: Differentiation
1. The Derivative and the Tangent Line Problem
2. Basic Differentiation Rules and Rates of Change
3. The Product and Quotient Rules and Higher-Order Derivatives
4. The Chain Rule
5. Implicit Differentiation
6. Derivatives of Inverse Functions
7. Related Rates
Review/Unit Exam
Unit 4: Applications of Differentiation
1. Extrema on an Interval
2. Rolle's Theorem and the Mean Value Theorem
3. Increasing and Decreasing Functions and the First Derivative Test
4. Concavity and the Second Derivative Test
5. A Summary of Curve Sketching
6. Optimization Problems
7. Differentials
Review/Unit Exam
Unit 5: Integration
1. Antiderivatives and Indefinite Integration
2. Area
3. Riemann Sums and Definite Integrals
4. The Fundamental Theorem of Calculus
5. Integration by Substitution
6. Numerical Integration
7. The Natural Logarithmic Function & Inverse Trigonometric: Integration
Review/Unit Exam
Unit 6: Differential Equations
1. Slope Fields
2. Differential Equations: Growth and Decay
3. Differential Equations: Separation of Variables
Review/Unit Exam
Unit 7: Applications of Integration
1. Area of a Region Between Two Curves
2. Volume: The Disk Method
Unit 8: Integration Techniques
1. Basic Integration Rules
2. L’Hopital’s Rule
Review/Unit Exam
Cumulative Final Exam
Review sessions for the AP Exam.
EVALUATION:
Quarter Grade: Test, Quizzes, and Performance Tasks: 90%
Homework/Class work: 10%
Course Grade: First Quarter: 40%
Second Quarter: 40%
Exams (Midterm and/or Cumulative Final): 20%
CLASSROOM POLICIES:
· DO your classwork and homework to really learn the material, not just to get it done!! And do it all!
· Help yourself and your classmates by fully participating in class and in your groups. Ask questions and explain your understanding of the concepts fully. Carefully check your work!
· Get help as soon as you start to struggle and be persistent in trying to gain a full understanding of the concepts.
· Absences, lateness, and plagiarism will be dealt with according to school policy. See your student handbook for details.
· If you miss class to participate in a school-approved trip or activity, the assignment is still due. (Student Handbook).
HOMEWORK POLICY:
Homework will be assigned regularly and is due the following day. Late homework will receive no credit. Work must be shown for each problem, answers only is not acceptable! Grades for homework will be determined as follows:
Full credit: All problems are completed and well explained.
Half credit: Partially done, with at least half completed or many explanations are missing.
No credit: Less than half has been attempted.
PORTFOLIO ENTRIES:
Projects and selected performance assessments all make great portfolio entries.
**Course content may vary from this outline to meet the needs of this particular group.**