Mater Academy Charter High School



Mater Academy Charter High School

Employee # 920457

AP Calculus AB

Syllabus

Teacher and students are going to cover all topics associated with Functions, their Graphs, and Limits; Derivatives and Integrals, according to the Calculus AB topics outline in the AP Calculus AB Course Description.

Students and Teacher must work hard in order to be successful in the course to accomplish the material’s goals and passing the AP exam. As a teacher, I want to encourage students to appreciate topics related to Calculus as a helpful tool for future studies in college.

As a part of a course, students should have a graphing calculator of their own and are expected to use it in classes and on assessments. I would prefer if they used the TI-83 Plus. However, the school library could provide students with the TI-80.

Objectives of the Course According to the Course Description

• Providing students with knowledge to work with functions, represented in different ways.

• Providing students with tools to solve real world situations by using mathematical language to interpret and support the solutions.

• Using the graphing calculator to help them solve problems, interpret the answers, and analyze their conclusions.

• Understanding the meaning of the derivative as a rate of change and local linear approximation to be able to solve a variety of problems.

• Understanding the meaning of the definite integral both as a limit of Riemann Sums and as the net accumulation of changes in solving a variety of problems.

• Understanding the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.

• Being able to communicate in mathematical terms, both orally and in well-written sentences, to be able to explain solutions of the problems.

• Modeling a written description of a physical situation with a function, a differential equation, or an integral.

• Being able to determine reasonable solutions, including sign, size, relative accuracy, and units of measurement.

• Developing an appreciation of Calculus as a coherent body of knowledge

Course Planner

Pre-Requesites

Students were assigned Pre-Calculus materials to work on over the summer.

|textbook section |description |week# |

|Functions, Graphs and Limits (C 2) |

|1.2 -1.3-1.4 |Analysis of Functions and their Graphs. |1 |

|Review of precalculus topics |Domain and Range of a Function. |1 |

|1.1 |Four Ways to Represent a Function. |2 |

|notes and complementary material./ 7.5 |A Library of Essential Functions. Trigonometric Functions. |3 |

| |Inverse of Trigonometric Functions. | |

|additional material |Parametric Relations. |3 |

|Review of precalculus topics |Analysis of Graphs. Asymptotic and unbounded behavior. |4 |

| |Understanding Asymptotes in Terms of Graphical Behavior. | |

| |Describing Asymptotic Behavior in Terms of Limits Involving | |

| |Infinity. | |

|2.2-2.3 |Limits of Function. |4 |

|2.5 |Continuity. |5 |

|2.5 |Intermediate and Extreme Value Theorems. |5 |

|Derivatives (C2) |

|3.1 |Concept of the Derivative. |6 |

|3.2 |Derivative Presented Graphically, numerically, and analytically.|6 |

|3.4 |Derivative Interpreted as an Instantaneous Rate of Change. |6 |

|3.2 |Derivatives Define as the Limit of the Difference Quotient. |7 |

|3.4 |Relationship Between Differentiability and Continuity. |7 |

|3.4 |Derivative at a Point. Slope of a Curve at a Point. Tangent Line|8 |

| |to a Curve at a Point and Local Linear Approximation. | |

|4.3 |Instantaneous Rate of Change as the Limit of Average Rate of |8 |

| |Change. Approximate Rate of Change From Graphs and Tables of | |

| |Values. | |

|4.3 |Derivative as a Function. Corresponding Characteristics of |9 |

| |Graphs of f and f’. Relationship Between the Increasing and | |

| |Decreasing behavior of f and the Sign of f’. | |

|4.3 |The Mean Value Theorem and its Geometric Consequences. |9 |

|3.3 |Differentiation Rules. |10 & 11 |

|3.7 |Equations Involving Derivatives (Verbal Descriptions are |12 |

| |translated into Equations Involving Derivatives and Vice Versa).| |

|3.8 |Second Derivatives. |13 |

|4.6 |Relationship between the Concavity Changes. |14 |

|4.8 |Applications of Derivatives. |14 |

|4.7 |Optimization Both Absolute (Global) and Relative (Local) |15 |

| |Extrema. | |

|2.7 |Modeling Rates of Change, Including Related Rate Problems. |15 |

|3.7 |Use of Implicit Differentiation to Find the Derivative of an |16 |

| |Inverse Function | |

|3.2 |Interpretation of the Derivative as a Rate of Change in Varied |17 |

| |Applied Context, Including Velocity, Speed and Acceleration. | |

|3.9, 4.10, 10.1, 10.2 |Geometric Interpretation of Differential Equations Via Slope |18 |

| |Fields and the Relationship Between Slope Fields and Solution | |

| |Curves for Differential Equations. | |

|3.3, 7.2, 7.3, 7.4, 7.5 |Knowledge of Derivatives of Basic Function, Including Power, |18 |

| |Exponential, Logarithmic, Trigonometric, and Inverse | |

| |Trigonometric Functions. | |

|3.3 |Basic Rules for the Derivative of Sums, Products, and Quotients |19 |

| |of Functions. | |

|3.3 |Chain Rule and Implicit Differentiation. |19 |

|Integrals (C 2) |

|4.10, 5.1 |Interpretations and Properties Of Definite Integrals. |20 |

|5.2 |Computation of Riemann Sums Using Left, Right, and Midpoint |21 |

| |Evaluation Points. | |

|5.2 |Definite Integrals as a Limit of Riemann Sums Over Equal |21 |

| |Subdivisions. | |

|5.3 |Definite Integral Rate of Change of a Quantity Over an Interval |22 |

| |Interpreted as the Change of the Quantity Over the Interval. | |

|5.2 |Basic Properties of Definite Integrals (Examples Include |23 |

| |Additivity and Linearity). | |

|6.1-6.5 |Applications of Integrals. |23 |

|5.3 |Fundamental Theorem of Calculus. |24 |

|5.3-5.4 |Use of Fundamental Theorem to Evaluate Definite Integrals. |24 |

|5.3-5.5 |Use of the Fundamental Theorem to Represent a Particular |25 |

| |Antiderivative, and the Analytical and Graphical Analysis of | |

| |Function so Derived. | |

|4.10 |Techniques of Antidifferentiation. |26 |

|4.10 |Antiderivatives by Substitution of Variables (Including Change |27 |

| |of Limits for Definite integrals), Parts, and Simple Partial | |

| |Fractions (Nonrepeating Linear Factors Only). | |

|Review of chapter 6 |Applications of Antidifferentiation. Finding Specific |28 |

| |Antiderivatives Using Initial Conditions, Including Applications| |

| |to Motion Along a Line. | |

|7.1, 7.3-7.4 |Solving Separable Differential Equations and Using them in |29 |

| |Modeling. In Particular, Studying the Equations y’ = ky and | |

| |Exponential Growth. | |

|Applications of 5.2 |Use of Riemann and Trapezoidal Sums to Approximate Definite |30 |

| |Integrals of Functions Represented Algebraically, Graphically, | |

| |and by Tables of Values. | |

This schedule leaves about 20 hours to teach topics that students find most difficult. The remaining time will be used to review the main topics before the AP Exams.

TEACHER STRATEGIES

Expectations from faculty members and Universities are considerably high. With today’s teaching resources, classroom tools, and proficient programs students are expected to follow the syllabus thoroughly, completing all assignments with enough time to be prepared for the AP exam. All the materials and course topics are provided to the students on the first day of class. The instructor will coach the progress of the students and will work on every point on the course planner to achieve the common goal of doing well on the AP Exam.

We are going to spend 3 weeks at the beginning of the course to review topics on functions and their graphs in order to familiarize students with the basic functions, and be able to represent the functions in a variety of ways (graphically, numerically, analytically, and verbally) It is important that students can identify the connection among these representations. (C3).

The course will teach the students how to use graphing calculators to help them solve different problems from the real world. The concepts learned will not only be applied in Math class but also in real life situations. During the first three weeks of the course I will spend extra time if necessary (through after school tutoring) familiarizing the student with their graphing calculator. Also I would like to use the graphing calculator to help students to form an intuitive concept prior developing the algebraic procedures, for example, to understand a function behavior before sketching the curve by applying the derivative concepts. (C5)

To stress communication as a main purpose, this course includes a diversity of teaching strategies to encourage students to expand their vocabulary and explanation skills. It is important to increase the student’s class participation by solving problems on the board and explaining his/her conclusion to other classmates. In addition, students are going to prepare a Power Point presentation (working in teams) about selected topics to discuss in class, as well as encouraging them to study in groups. Every teacher knows that students learn more when they tutor themselves. (C4)

MAJOR ASSESSMENTS

Students could assess by using different methods.

The following examples demonstrate ways to help students gain and increase their knowledge and understanding of Calculus.

• Discussions on:

A. “Functions defined By Integrals” By Ray Cannon

B. “Exploring the FTC from numerical and graphical points of view” By Mark Howell

C. “Using the Fundamental Theorem of Calculus in a variety of AP Questions” By Larry Riddle

These 3 articles will help students understand and assess the fundamental Theorems of Calculus. These materials give excellent examples of concepts that require some special attention when taking a first year calculus class. Every chapter focuses on a special topic and its connection to the FTC. This activity enriches the students’ communication skills and teaches them how to work in groups in order to prepare for the discussion.

• Students will receive sets of questions in AP format for each topic to help them prepare for the AP exam.

• Students will use “Preparing for the Calculus AP Exam with Calculus: Graphical, Numerical, Algebraic” By: Barton, Brunsting, Diehl, Hill, Tyler, Wilson Pearson Education, Inc.  Publishing as Pearson Addison-Wesley.  Boston. 2006. ISBN: 0-321-29265-0.

This book will be used for learning and practicing the material.

• Students must complete selected questions from the Chapter Review at the end of each chapter.

• Students will be required to take a Mid-Term that is in the AP Exam format.

TECHNOLOGY

Students are expected to use a graphing calculator throughout the course.

It is also useful for the students to consult the following website for further references regarding the AP Exam:

• .

• for free online tutoring.

• calculus-

• calculus/fr.html to find questions and solutions from previous AP Exams

• this will allow the students to explore excellent visual presentations, and it is a great graphing utility.

• as a fun way to learn about derivatives

PRIMARY TEXTBOOK

• Stewart, James. Calculus Concepts & Contexts. 3rd Edition. Thomson Books/Cole, 2005

ALTERNATIVE TEXTBOOKS AND SOURCES

• Stewart, James. Calculus Concepts & Contexts. 3rd Edition. Thomson Books/Cole, 2005.

• Finney, Ross L. Demana, F. Waits, B Kennedy, D. Calculus: Graphical, Numerical, Algebraic Prentice Hall 2003

• Handley AP Calculus Web Site:



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