Instructor: April Cruz
Room: 226
Phone: 239-369-2932 ext. 1226
Email: aprildc@leeschools.net
URL: http://deriverswanted.wikispaces.com
AP Exam Date: Wednesday, May 9, 2012
Introduction
Calculus is the crowning achievement of 17th century mathematics. It is the branch of mathematics used to describe
motion and change – velocities and accelerations. Calculus is also deals with tangent lines, slopes, areas, volumes,
arc lengths, centroids, curvatures, and a variety of other concepts that have enabled scientists, engineers, and
economists to model real-life situations with applications in mathematics, the physical sciences, engineering, and the
social and biological sciences.
Course Content
This Advanced Placement Calculus syllabus is consistent with the College Board's publication. The design of the
course is to provide students with the knowledge necessary to enable them to score sufficiently high on the AP
Calculus AB Exam to award them college credit if they so desire.
This course is intended to be exciting and intellectually challenging for all participants. This course will embrace the
key ideas of calculus -- function, limit, derivative, integral, and fundamental theorem -- from multiple perspectives and
in great depth. An increased responsibility is placed on the learner to help develop and extend his/her own
mathematical knowledge under the guidance of an instructor.
Participants will take from this course not only mathematical information but also a host of information-management
skills. Problem solving, heuristic strategies, and computer/calculator assistance will be emphasized throughout. We
will use both computers and graphing calculators (TI-83 and TI-Nspire) to support and attack problems from three
perspectives -- numerical, graphical, and symbolic. Students will develop abilities to think and reason
mathematically, to communicate technical ideas effectively, to visualize calculus as a network of related ideas from
which lots of information can be generated, to recognize when and how to use technical support, to pose and solve
problems, and to construct, interpret, and evaluate calculus models in the context of real applications!
Course Objectives
∞ Work with functions represented in a variety of ways: graphical, numerical, analytical, and verbal
∞ Understand the meaning of the derivative in terms of a rate of change and local linear approximation
∞ Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation
of a rate of change
∞ Understand the relationship between the derivative and the definite integral as expressed in both parts of the
Fundamental Theorem of Calculus
∞ Communicate mathematics both orally and in well-written sentences
∞ Model a written description of a physical situation with a function, a differential equation, or an integral
∞ Use technology to help solve problems, experiment, interpret results, and verify conclusions
∞ Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement
∞ Give a geometric interpretation of differential equations via slope fields
Textbook and Resources
Larson, Ron and Edwards, Bruce. AP* Edition Calculus 9th ed. Brooks/Cole, Cengage Learning, 2010
AP Calculus AB Course Home Page
http://www.collegeboard.com/student/testing/ap/sub_calab.html?calcab
Course Outline:
Unit P: Preparation For Calculus
P.1 Graphs and Models
P.2 Linear Models and Rates of Change
P.3 Functions and their Graphs
P.4 Fitting Models to Data
*** Supplemental Review:
Logarithmic and Exponential Functions
Trigonometric Functions and Identities
Unit One: Limits and Their Properties
1.1
1.2
1.3
1.4
1.5
A Preview of Calculus
Finding Limits Graphically and Numerically
Evaluating Limits Analytically
Continuity and One-Sided Limits
Infinite Limits
Unit Two: Differentiation
2.1
2.2
2.3
2.4
2.5
2.6
The Derivative and the Tangent Line Problem
Basic Differentiation Rules and Rates of Change
The Product and Quotient Rules and Higher-Order Derivative
The Chain Rule
Implicit Differentiation
Related Rates
Unit Three: Applications of Differentiation
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
Extrema on an Interval
Rolle’s Theorem and the Mean Value Theorem
Increasing and Decreasing Functions and the First Derivative
Concavity and the Second Derivative Test
Limits at Infinity
A Summary of Curve Sketching
Optimization Problems
Newton’s Method
Differentials
Unit Four: Integration
4.1
4.2
4.3
4.4
4.5
4.6
Antiderivatives and Indefinite Integration
Area
Riemann Sums and Definite Integrals
Fundamental Theorem of Calculus
Integration by Substitution
Numerical Integration
Unit Five: Logarithmic, Exponential, and Other Transcendental Functions
5.1
5.2
5.3
5.4
5.6
5.7
5.8
5.9
Natural Logarithmic Function: Differentiation
Natural Logarithmic Function: Integration
Inverse Functions
Exponential Functions: Differentiation and Integration
Differential Equations: Growth and Decay
Differential Equations: Growth and Decay
Inverse Trigonometric Equations: Differentiation
Inverse Trigonometric Equations: Integration
Unit Six: Differential Equations
6.1 Slope Fields and Euler’s Method
Unit Seven: Applications of Integration
7.1 Area of a Region Between Two Curves
7.2 Volume: The Disk Method
Unit Eights: Integration Techniques, L’Hopital’s Rule, and Improper Integrals
8.1 Basic Integration Rules
Review and Preparation for AP Exam
Students are given a mock test prior to the exam. The tests are scored and analyzed by using the AP Scoring
Guidelines posted on the College Board website.
Post AP Exam
Final Project
Choose one of the following topics to explore and present a lesson. A rubric with be provided.
8.2
8.5
8.6
8.7
8.8
9.1
9.2
9.7
6.2
6.3
6.4
Integration by Parts
Partial Fractions
Integration by Tables and Other Integration Techniques
Indeterminate Forms and Hopitals’s Rule
Improper Integrals
Sequences
Series and Convergence
Taylor Polynomials and Approximations
Differential Equations: Growth and Decay
Separation of Variables and the Logistic Function
First-Order Linear Differential Equations
Technology
Classroom demonstrations are presented using either a TI-84 Plus or TI-Nspire Calculator. Students in the course
should own a graphing calculator. A class set is available for use at school only. In addition, students should use
the internet frequently for this course. If a student does not have access to the internet at home, arrangements can
be made with the instructor or media specialist.
Teaching Strategies
∞
Lessons are designed using around the acronym, TAPS, where students will experience instruction via the
total group, working alone, working in pairs, and working in small groups
∞
Differentiated strategies are utilized for mastery learning.
∞
Each lesson begins with a brief quiz over the previous night’s homework.
∞
Quizzes may consist of rote homework type questions and/or AP sample test questions.
∞
Tests consist of mainly AP sample test questions and include a calculator portion and a non-calculator
portion.
∞
Homework assignments include a variety of tasks. Problems from the textbook are expected to be completed
daily, as well as frequent postings onto our class wikispace.
∞
Major projects encompass graphical, analytical, numerical and written solutions and explanations, allowing
students to show deeper understanding using alternative assessments.
∞
The midterm and final exam consists of problems from previous AP exams with emphasis on making
connections to the content graphically, analytically, numerically, and verbally.
Student Evaluation
Summative Items (50%)
∞
Consists of unit tests, cumulative exams, and comprehensive projects.
∞
Students must be thorough with all work and explanations in order to receive full credit.
∞
Summative assessments are announced in advance.
Formative Items (50%)
∞
30% consists of quizzes and 20% consists of homework, class-work, projects, and participation.
∞
Homework and class-work are graded for completion and quizzes are graded for accuracy.
∞
No credit will be given for problems that do not show all explanations and calculations necessary to
determine an answer.
Grading Scale
A
90 – 100
B
80 – 89
C
70 – 79
D
60 – 69
F
0 – 59