AP Calculus AB

Hello AP Calculus Students and Parents!

2025-2026

Advanced Placement Calculus AB                                                                 Paradise High School

Charlotte Manning                                                                                              cmanning@pisd.net

Course Description

This course emphasizes the study of functions, graphs, limits and theory, techniques, and applications of derivatives and integrals.  A scientific calculator with graphing capabilities is required.  Instruction and assessment of instruction will be based on the interpretation of the calculus graphically, numerically, analytically, and using written explanation.  The instructor will model these elements and expect the students to use these elements daily in their own preparation for the course and in assessment.  Daily preparation is required for success in Calculus.  This course fulfills the requirements for preparation for the Advanced Placement Calculus AB exam.

Textbooks and Materials

Calculus of a Single Variable, Eighth Edition (Larson; Houghton/Mifflin, 2006) is the text for this course.  Supplemental texts will also be used.  Students should bring a 2-inch to 3-inch three-ring binder, loose-leaf notebook paper, a pencil, and a graphing calculator (TI-84 CE graphing calculators will be provided for those students who need one) to class every day.  We will be utilizing the AP Classroom at apcentral.collegeboard.org. We will make sure you can log onto this site the first few days of school.

Grading Policy

The final grade for each grading period will be based on various methods of assessment.  These methods may include, but are not limited to: tests, homework assignments, quizzes (announced and unannounced), and class participation.  Classroom participation is mandatory for success in this course.  I encourage questions, comments, alternative approaches, new ideas for solutions, and old ideas for solutions.

The grade for this course will be determined by 60% tests and 40% daily grades.  Some tests will be given over a period of two days.  One day of the test will include problems for which the student is expected to use a graphing calculator to solve problems and the second day of the test will include problems for which a calculator is not permissible.  This format is designed to model the assessment format of the AP exam.  All cumulative unit assessments will include problems for which the student will be required to explain in written words the solution or the justification for a problem.

Students are responsible for any work missed due to an absence, whether excused or unexcused.  Students who miss a test must make arrangements for a makeup. 

Essential Functions

To be successful in this class, students must be able to perform the following:

·       Communicate effectively in written and spoken English and be able to read and comprehend technical and mathematical sentences and symbols

·       Keep up with the pace of instruction

·       Actively participate in and follow class discussions, respond to verbal questions, work problems on the board, and explain solutions

·       Keep a well-organized notebook that includes accurate and useful notes, written assignments, all graded papers, corrections to problems missed on graded papers, and a copy of the course syllabus

·       Work cooperatively with the teacher and other students in the classroom

·       Use and apply mathematical skills from previous courses

Exam Review

Prior to the AP exam, a comprehensive review for the exam will be given to prepare students not only for the curriculum they are required to know, but also for the grading standards and the formats for which solutions can be written.  The material used for this review includes the supplemental material listed above along with released exams and released free response questions.

Some of these review sessions may take place outside of the normal school day, either in the evenings or on the weekends. The teacher and students will determine this schedule in the spring so that as many students as possible can attend these sessions.

Graphing Calculator

The use of a graphing calculator is essential to success in this course and to success on the Advanced Placement Exam.  From the first week of the course when students will learn how to use the graphing calculator to use a regression to predict behavior based on a set of data, students will integrate technology into the calculus.  Limits, increasing behavior, extrema, concavity, and domain are all elements that will be discussed from that first regression curve.  The lab manuals mentioned above (Calculus Calculator Labs) will be used throughout the course to help students integrate technology more formally with investigative processes and comparison techniques (e.g., in the topics of Mean Value Theorem, Differential Equations, and the Integral Function).  The calculators, though, will be used in instruction to solve problems (e.g., finding zeros, calculating numerical derivatives, definite integration), and to interpret results and support conclusions (e.g. using tables with incrementally small delta x values to predict limit behavior, using graphs of functions to predict first and second derivative behavior, using graphs to interpret velocity, acceleration, and speed). Assessments in the course will be designed so that the calculators are not tools of calculation as much as they are tools of a thought process.

General Information

Homework/Class work:

  Homework will be given every night.  You should work the problems on a clean sheet of paper with the assignment   

   written at the top of the page.  Failure to do this could result in a grade of zero for the assignment.

  Homework may be checked using any of these methods:

           1. Looking to see if the assignment was attempted.

           2. Checking certain problems for accuracy.

3. Completing a worksheet with similar problems after questions have been answered.

  Each homework check is worth 10 points.

  Class notes should be kept in your three-ringed binder.  Anything I write on the board should be copied into your

     notebook.

Extra help:

  You are accountable for all notes and textbook material.  If you fall behind for any reason, you should come see me.  The times I am available are:  7:30 – 7:55am, and after school, by appointment.

Communication:

           My e-mail address is cmanning@pisd.net.  Parents who wish to contact me can use e-mail or may call the school.

Class Rules:

·   Come to class prepared with the necessary items – notebook, pencil, etc.

·   Arrive on time

·   Respect the others in the classroom

·   Follow directions the first time given

·   Ask questions!!

·   Engage in class activities and work hard

 Course Topics:

The following outline shows the sequence of topics covered within this course over the year by semester.   Each unit of instruction lasts approximately two to three weeks after which an assessment is given.  The exact time for each unit varies from year to year depending on various factors, including the mathematical maturity and the work ethic of the students.   The chapter divisions correspond to the textbook used by the students.  Each unit of instruction includes the presentation and eventual assessment of all material graphically, numerically, analytically, and using written explanation. 

First Semester

Chapter P  Preparation for Calculus

               Transformations of Functions

               Function Characteristics

               Domain and Range

               Increasing and Decreasing Intervals

               Concavity and Points of Inflection

               Asymptotic Behavior

               Exponential Functions and Logarithms

           Graphing Calculator Review

Chapter 1  Limits

           Rates of Change

           Tangent Lines and Velocity

           Limits

           Continuity      

           Derivative (Limit Definition)

           Linear Approximations

Chapter 2  Differentiation

           Derivative Graphs

           Derivatives of Polynomial and Rational

                Exponent Functions

           Derivatives of Exponential Functions

           Product and Quotient Rules

           Derivatives of Trigonometric Functions

           Chain Rule

Chapter 2B  More Derivatives

           Implicit Differentiation

           Derivatives of Inverse Trigonometric

              Functions

           Derivatives of Logarithmic Functions

Chapter 3A  Extrema

           Rolle’s Theorem

           Mean Value Theorem

           Absolute Extrema

           First and Second Derivative Tests for

               Extrema

           Concavity and Points of Inflection

           Curve Sketching

Second Semester

Chapter 3B  Applications of Derivatives

           Related Rates

           Optimization

           Basic Indeterminate Forms of Limits 

                L’Hopital’s Rule

Chapter  Approximation Methods

           Linear Approximations and Differentials

           Left/Right and Midpoint Reimann Sums

           Trapezoidal Approximations

Chapter 4  Integration

           Antiderivatives (Analytical)

           Areas and Total Change

           Fundamental Theorem of Calculus

           Definite and Indefinite Integration

           Substitution

Chapter 7  Applications of Integration

           Areas Between Curves

           Volumes by Disc and Washer

           Volume by Shell

           Volumes by Slicing

           Average Value

Chapter 6

           Differential Equations

           Separable Differential Equations

           Slope Fields

           Exponential Growth and Decay

AP Exam Review

AP TEST