AP Calculus AB syllabus
East Early College High School
Houston, Texas
Room #242
Mr. Park, Y
Phone: 713.847.4809
E-mail: ypark@houstonisd.org
Conference Time: A:12:30-1:30; B: 2:00-3:15
Tutoring Schedule: Tuesday, Thursday: 3:30 pm
Course Description: Calculus AB focuses on in-depth understanding of the
concepts of calculus as a whole by providing a multi-representational approach to
various calculus topics.
Course objectives: The students will develop the knowledge and understanding of
calculus as a coherent body of concepts and demonstrate their competency in AP
Calculus examination.
Prerequisites: The students should complete Algebra 1, Geometry, Algebra 2, and
Pre-calculus with trigonometry that are designed for college- bound students.
Resource and Materials:
- Textbook: Calculus with analytic geometry by Larson, 5th edition, D. C. Heath.
- TI- 83 Graphing Calculator
- Supplementary materials from various sources including the past AP calculus
exams.
AP Calculus AB course Outline:
Scarborough high school uses an eight- period, alternate block schedule. Each class
period is 90 minutes long. The students are assigned homework in every class period
including the problems from the AP exams. A quiz is given after each calculus topic
and two tests are given on each unit. The tests will be formatted as AP exam
whenever possible. The graphing calculator is used liberally for the assignments and
tests as well as class work. The graphing calculator helps students develop an
intuitive feel for concepts before algebra approach is performed. Throughout the
school year, Algebra approach will also be emphasized and practiced. There will be
one mandatory AP practice exam on the last week of April.
Unit 1: Limit and Continuity: 3 weeks
-An introduction of limit concept by graphically and numerically.
-Language of limits: notation, one-sided, and two-sided limit.
-Finding limits algebraically such as 0/0, infinity/infinity forms etc.
-Horizontal asymptote with limits involving infinity.
-Limit of exponential and logarithmic function.
-Continuous functions in terms of limits.
-Discontinuous functions (removable and non-removable discontinuity) in terms of
limits.
- The intermediate value and Extreme value theorems.
Unit 2: Derivatives: 4 weeks.
-Linear function and local linearity.
-Definition of the derivative as the limit of the difference quotient.
-Find the slope of a curve at a point.
-Tangent line to a curve at a point and local linear approximation.
-Derivative as a rate of change-constant, average, and instantaneous rate of change.
-Relationship between differentiability and continuity.
-Basic differentiation rules for finding derivatives of various functions including
trigonometric, logarithmic, and exponential functions; power, product, quotient,
and chain rules.
-Implicit differentiation.
Unit 3: Application of Derivatives: 6 weeks.
-Related rates problems.
-Extrema of a function.
-Increasing and decreasing behavior.
-Critical values and local extrema.
-The mean value theorem.
-The first and second derivative tests.
-Concavity and point of inflection.
-Curve sketching.
-Relationship between f’, f, and f “.
-Optimization problems.
Unit 4: The definite Integral: 4 weeks.
-Definition of antiderivative and slope field.
-Basic integration rules.
-Summation notation and partition.
-Computation of Riemann sums using left. right, and midpoint evaluation point.
-Definition of the definite integral as the limit of a Riemann sum over equal
subdivision.
-Numerical integration method; Trapezoid rule.
-The first and Second Fundamental Theorem of Calculus.
-Integral of a rate of change produces net change.
-The average value theorem.
Unit 5: Differential equations and Modeling: 3 weeks
-Integration by substitution.
-Solve differential equations by using separation of variables.
-Growth and decay problems.
-Slope fields.
-General differential equations.
Unit 6: Applications of definite integrals: 3 weeks
-Find specific antiderivatives using initial conditions, including applications to
motion along a line.
-Areas in the plane.
-Volumes of solids of revolution by Disk method and Washer method.
-Volumes of solids with known cross-sections.
* Comprehensive review for AP Calculus AB examination for 5-6 weeks.