Instructor: Mr. D. Goodrich Office: Room 203 Office Hours: By Appointment Phone: 773-534-8130 xt48588 Email: dmgoodrich@cps.edu

COURSE OVERVIEW AND OBJECTIVE This course was designed with two main objectives in mind. The first objective is to provide the student with a competent working knowledge of calculus; the course content provides adequate coverage of the traditional topics and techniques, especially those that will be needed in courses such as differential equations, physics, chemistry and other science. The second objective is to prepare the student to score to the best of their abilities on the Advanced Placement Exam. The following is a tentative schedule for the year and includes time to evaluate student knowledge at the end of each unit. Changes may be made in the time allotted to increase student understanding and to account for varying bell schedules (i.e. faculty bell, extended division, standardized testing, etc.) Additionally this schedule leaves approximately four weeks for review and preparation for the AP Exam in May.

Unit 1: Limits, Derivatives, Integrals and Integrals (6 Days) 1-1 The Concept of Instantaneous Rate 1-2 Rate of Change by Equation, Graph of Table 1-3 One Type if Integral of a Function 1-4 Definite Integrals by Trapezoids, from Equations and Data Unit 2: Properties of Limits (10 Days) 2-2 Graphical and Algebraic Approach to the Definition of Limit 2-3 The Limit Theorems 2-4 Continuity 2-5 Limits involving Infinity 2-6 The Intermediate Value Theorem and Its Consequences Unit 3: Derivatives, Antiderivatives, and Indefinite Integrals (17 Days) 3-2 Difference Quotients and One Definition of the Derivative 3-3 Derivative Functions Numerically and Graphically 3-4 Derivatives of the Power Functions and Another Definition of Derivative 3-5 Displacement, Velocity, and Acceleration 3-6 Introduction to Sine, Cosine, and Composite Function 3-7 Derivatives of Composite Functions – The Chain Rule 3-8 Proof and Applications of Sine and cosine Derivatives 3-9 Exponential and Logarithmic Functions

Unit 4: Products and Quotients (17 Days) 4-2 Derivative of a Product of Two Functions 4-3 Derivative of a Quotient of Two Functions 4-4 Derivatives of the Other Trigonometric Functions 4-5 Derivatives of Inverse Trigonometric Functions 4-6 Differentiability and Continuity 4-8 Graphs and Derivatives of Implicit Relations 4-9 Related Rates

Unit 5: Definite and Indefinite Integrals (19 Days) 5-2 Linear Approximations and Differentials 5-3 Formal Definition of Antiderivative and Indefinite Integral 5-4 Riemann Sums, and the Definition of Definite Integral 5-5 The Mean Value Theorem and Rolle’s Theorem 5-6 The Fundamental Theorem of Calculus 5-7 Definite Integral Properties and Practice 5-8 Definite Integrals Applied to Area and Other Problems 5-9 Volume by Plane Slicing 5-10 Definite Integrals Numerically by Grapher

Unit 6: The Calculus of Exponential and Logarithmic Functions (15 Days) 6-2 Antiderivatives of the reciprocal function and Another Form of the Fundamental Theorem 6-3 The Uniqueness Theorem and Properties of Logarithmic Functions 6-4 The number e, Exponential Functions, and Logarithmic Differentiation 6-6 Derivative and Integral Practice for Transcendental Functions

Unit 7: The Calculus of Growth and Decay (10 Days) 7-2 Exponential Growth and Decay 7-3 Other Differential Equations for Real World Applications 7-4 Graphical Solution of Differential Equations Using Slope Fields

Unit 8: The Calculus of Plane and Solid Figures (14 Days) 8-2 Critical Points and Points of Inflection 8-3 Maxima and Minima in Plane and Solid Figures 8-4 Volume of a Solid of Revolution by Cylindrical Shells

Unit 9: Algebraic Techniques for the Elementary Functions (3 Days) 9-11 Miscellaneous Integrals and Derivatives

Unit 10: The Calculus of Motion – Averages and Extremes (9 Days) 10-2 Distance, Displacement, and Acceleration for Linear Motion 110-3 Average Value Problems in Motion and Elsewhere 10-4 Minimal Path Problems 10-5 Maximum and Minimum Problems in Motion and Elsewhere

PEDAGOGICAL ISSUES AND METHODOLOGY The course methodology grew out of the strong conviction that incorporating technology into the calculus curriculum better prepares students for further study in mathematics and science This calculator or computer based graphing approach empowers students to explore problems that arise from real world situations and learn from their experiences. The result is a “mathematical laboratory” with an interactive instructional approach that focuses on problem solving. As a natural outgrowth of this experience, students complete the course with a better understanding of mathematics and a solid intuitive foundation in calculus. Furthermore, the course will attune to the two outstanding mathematical trends of our time – the computer revolution and the burgeoning use of mathematical models in real world situations. All the material will be presented in a variety or methods. A majority of the topics will be taught using lecture but some will be elaborated upon using “laboratory” style explorations in which the students experience the material first hand. For example the students might explore a volume of revolution by cutting circles out of cardboard and stacking them to form the solid required. The dimensions of these slices would be tabulated and either entered into their graphing calculator or spreadsheet. The use of technology will then allow the students to explore the limit of the slices as the number grows without bound. This type of exploration allows the students to experience the calculus through equations, graphs, tables and applications to the real world. All of the results from these explorations, as well as class work, will be presented using complete sentences, algebraic verifications, and correct labels. Students might be required to verbally explain there thought process that led them to their conclusion.

CALCULATOR USE Students are required to purchase and use a graphing calculator on a daily basis; calculators may made available for students that can not afford to purchase their own. Students are required to perform the following tasks on the graphing calculator:

Graph a function within an arbitrary viewing window

Find roots of functions

Numerically calculate the derivative of a function

Numerically calculate the value of a definite integral

When students answer questions using their calculator they are to write the mathematical expression used to arrive at their conclusion using standard mathematical notation and rounding to at least three decimal places. Calculator syntax is never to be written on any assignment, quiz, or test.

MATHEMATICS AS A LANGUAGE

Mathematics is a complex language that incorporates many different symbols and syntax. Translating the mathematics into a language that everyone can understand and contribute to is an essential part of the learning process. Throughout this course students are expected to express their solutions and processes to each other in both written and verbal forms. Many aspects of the class structure require that students work in small groups and discuss difficult problems and arrive at a consensus. These conclusions are presented to the whole class in an effort to promote whole class discussions. Additionally, students might be asked to explain their reasoning to the class while demonstrating their solution on an overhead projector.

One of the most powerful uses of Calculus is to explain real world phenomena. Quite often these experiences are expressed verbally. Students taking calculus are required to translate these real world problems into mathematics, solve the problem, and then express the solution in a manner that is easily understood. This communication could be done in either a verbal or written form. Being fluent in the language of mathematics and being able to communicate the concepts to others in both a written and verbal form is essential to fully understanding the concepts of calculus.

TEXTBOOK

Foerster, Paul A. Calculus: Concepts and Applications. Emeryville, CA: Key Curriculum Press. 2005. 2nd Edition. Replacement cost is $60.GRADING SYSTEMSemester grades will be approximately based on the following system:

Assessment Tool

Approximate Percent ofFinal Semester Grade

Point Distributions PerAssignment

Homework (HW)

See Homework Section

Homework Quizzes (HQ)

5%

5 Points Each

Quizzes (Q)

25%

10-30 Points Each

Unit Exams (T)

30%

100 Points Each

Projects (P)

20%

50 Points Each

Final (F)

20%

A total points scheme may be used but the approximate percentages are accurate. The following grading scale will be used on ALL assessments:

A

90% to 100%

B

80% to 89.9%

C

70% to 79.9%

D

60% to 69.9%

F

59.9% or below

GRADE NOTIFICATIONParents and students will be notified of their progress in the class on a regular basis. This will be done by accessing Parent/Student Portal which is available at www.cps.edu. Parents without access to the Internet should request that the student print out the grade reports at school in the computer lab or at any public library and bring them home for the parent to review and discuss with the student. Additionally, progress reports will be mailed to the house at the 5, 15, 25 and 35 week marks.

HOMEWORK POLICYHomework is your responsibility! There is a lot of it! It will take you a great deal of time to compete it. You should be working on it EVERY DAY. It gives you the practice that you need to pass the quizzes, tests, and most importantly the AP Exam. I expect everyone to do the homework and I will ask to see it at the end of each unit. Answers without supporting work will not be accepted. In general: All answers must be reproducible from the work shown. The solutions manual will be available and will only be available under my direct supervision. You man NOT photocopy or take pictures of the manual. Students wishing to see the solutions must come in during their lunch periods or before / after school only. Passes will be available if needed. MAKE-UP POLICYOnly students with excused absences will be allowed to make up assignments. It is the student's responsibility to inquire about missing work on the first day back from their excused absence. Excused absences are only as follows: religious holiday, family emergency, illness, or death in the family. Phone calls will be made or emails will be sent to verify student absences. Assessments must be made up within a timely manner upon returning from an excused absence. Students are responsible to schedule a time to make up assessments upon the FIRST day back from an excused absence. Assessments not made up by the agreed upon date will be recorded as zero (0) and no further make up opportunities will be allowed.

TARDY POLICY Students that are not in the classroom when the bell rings will be marked tardy and will be required to obtain an entry permit from the closest swipe machine. Students that have a note justifying their tardiness will be exempt. Three (3) tardies will result in a detention. Any material covered prior to entry into class will be marked as zero and no extra time will be given on tests and quizzes unless deemed by an individual education plan.

UNEXCUSED ABSENCE POLICY Any student with an unexcused absence will receive a permanent zero on any assignments that are due and/or assigned for that day. Any student with unexcused absences will be referred to the discipline office.

REQUIRED MATERIALS / FEESAll students are required to attend class daily with the appropriate textbook, calculator, notebook, and supplies. All students are required to take the College Board AP Calculus (AB) exam. The cost for this exam is approximately $90.00. Registration will begin sometime after the first of the year. Students that do not take the AP Exam will not receive AP course credit. DISCLAIMER
The instructor reserves the right to change anything on this page at any time.
Notification of changes will be given as changes are made.

## AP Calculus AB Syllabus

Instructor: Mr. D. Goodrich

Office: Room 203

Office Hours: By Appointment

Phone: 773-534-8130 xt48588 Email: dmgoodrich@cps.edu

COURSE OVERVIEW AND OBJECTIVEThis course was designed with two main objectives in mind. The first objective is to provide the student with a competent working knowledge of calculus; the course content provides adequate coverage of the traditional topics and techniques, especially those that will be needed in courses such as differential equations, physics, chemistry and other science.

The second objective is to prepare the student to score to the best of their abilities on the Advanced Placement Exam. The following is a tentative schedule for the year and includes time to evaluate student knowledge at the end of each unit. Changes may be made in the time allotted to increase student understanding and to account for varying bell schedules (i.e. faculty bell, extended division, standardized testing, etc.) Additionally this schedule leaves approximately four weeks for review and preparation for the AP Exam in May.

Unit 1: Limits, Derivatives, Integrals and Integrals (6 Days)

1-1 The Concept of Instantaneous Rate

1-2 Rate of Change by Equation, Graph of Table

1-3 One Type if Integral of a Function

1-4 Definite Integrals by Trapezoids, from Equations and Data

Unit 2: Properties of Limits (10 Days)

2-2 Graphical and Algebraic Approach to the Definition of Limit

2-3 The Limit Theorems

2-4 Continuity

2-5 Limits involving Infinity

2-6 The Intermediate Value Theorem and Its Consequences

Unit 3: Derivatives, Antiderivatives, and Indefinite Integrals (17 Days)

3-2 Difference Quotients and One Definition of the Derivative

3-3 Derivative Functions Numerically and Graphically

3-4 Derivatives of the Power Functions and Another Definition of Derivative

3-5 Displacement, Velocity, and Acceleration

3-6 Introduction to Sine, Cosine, and Composite Function

3-7 Derivatives of Composite Functions – The Chain Rule

3-8 Proof and Applications of Sine and cosine Derivatives

3-9 Exponential and Logarithmic Functions

Unit 4: Products and Quotients (17 Days)

4-2 Derivative of a Product of Two Functions

4-3 Derivative of a Quotient of Two Functions

4-4 Derivatives of the Other Trigonometric Functions

4-5 Derivatives of Inverse Trigonometric Functions

4-6 Differentiability and Continuity

4-8 Graphs and Derivatives of Implicit Relations

4-9 Related Rates

Unit 5: Definite and Indefinite Integrals (19 Days)

5-2 Linear Approximations and Differentials

5-3 Formal Definition of Antiderivative and Indefinite Integral

5-4 Riemann Sums, and the Definition of Definite Integral

5-5 The Mean Value Theorem and Rolle’s Theorem

5-6 The Fundamental Theorem of Calculus

5-7 Definite Integral Properties and Practice

5-8 Definite Integrals Applied to Area and Other Problems

5-9 Volume by Plane Slicing

5-10 Definite Integrals Numerically by Grapher

Unit 6: The Calculus of Exponential and Logarithmic Functions (15 Days)

6-2 Antiderivatives of the reciprocal function and Another Form of the Fundamental Theorem

6-3 The Uniqueness Theorem and Properties of Logarithmic Functions

6-4 The number e, Exponential Functions, and Logarithmic Differentiation

6-6 Derivative and Integral Practice for Transcendental Functions

Unit 7: The Calculus of Growth and Decay (10 Days)

7-2 Exponential Growth and Decay

7-3 Other Differential Equations for Real World Applications

7-4 Graphical Solution of Differential Equations Using Slope Fields

Unit 8: The Calculus of Plane and Solid Figures (14 Days)

8-2 Critical Points and Points of Inflection

8-3 Maxima and Minima in Plane and Solid Figures

8-4 Volume of a Solid of Revolution by Cylindrical Shells

Unit 9: Algebraic Techniques for the Elementary Functions (3 Days)

9-11 Miscellaneous Integrals and Derivatives

Unit 10: The Calculus of Motion – Averages and Extremes (9 Days)

10-2 Distance, Displacement, and Acceleration for Linear Motion 110-3 Average Value Problems in Motion and Elsewhere

10-4 Minimal Path Problems

10-5 Maximum and Minimum Problems in Motion and Elsewhere

PEDAGOGICAL ISSUES AND METHODOLOGYThe course methodology grew out of the strong conviction that incorporating technology into the calculus curriculum better prepares students for further study in mathematics and science This calculator or computer based graphing approach empowers students to explore problems that arise from real world situations and learn from their experiences. The result is a “mathematical laboratory” with an interactive instructional approach that focuses on problem solving. As a natural outgrowth of this experience, students complete the course with a better understanding of mathematics and a solid intuitive foundation in calculus. Furthermore, the course will attune to the two outstanding mathematical trends of our time – the computer revolution and the burgeoning use of mathematical models in real world situations. All the material will be presented in a variety or methods. A majority of the topics will be taught using lecture but some will be elaborated upon using “laboratory” style explorations in which the students experience the material first hand. For example the students might explore a volume of revolution by cutting circles out of cardboard and stacking them to form the solid required. The dimensions of these slices would be tabulated and either entered into their graphing calculator or spreadsheet. The use of technology will then allow the students to explore the limit of the slices as the number grows without bound. This type of exploration allows the students to experience the calculus through equations, graphs, tables and applications to the real world. All of the results from these explorations, as well as class work, will be presented using complete sentences, algebraic verifications, and correct labels. Students might be required to verbally explain there thought process that led them to their conclusion.

CALCULATOR USEStudents are required to purchase and use a graphing calculator on a daily basis; calculators may made available for students that can not afford to purchase their own. Students are required to perform the following tasks on the graphing calculator:

When students answer questions using their calculator they are to write the mathematical expression used to arrive at their conclusion using standard mathematical notation and rounding to at least three decimal places. Calculator syntax is never to be written on any assignment, quiz, or test.

MATHEMATICS AS A LANGUAGEMathematics is a complex language that incorporates many different symbols and syntax. Translating the mathematics into a language that everyone can understand and contribute to is an essential part of the learning process. Throughout this course students are expected to express their solutions and processes to each other in both written and verbal forms. Many aspects of the class structure require that students work in small groups and discuss difficult problems and arrive at a consensus. These conclusions are presented to the whole class in an effort to promote whole class discussions. Additionally, students might be asked to explain their reasoning to the class while demonstrating their solution on an overhead projector.

One of the most powerful uses of Calculus is to explain real world phenomena. Quite often these experiences are expressed verbally. Students taking calculus are required to translate these real world problems into mathematics, solve the problem, and then express the solution in a manner that is easily understood. This communication could be done in either a verbal or written form. Being fluent in the language of mathematics and being able to communicate the concepts to others in both a written and verbal form is essential to fully understanding the concepts of calculus.

TEXTBOOKFoerster, Paul A. Calculus: Concepts and Applications. Emeryville, CA: Key Curriculum Press. 2005. 2nd Edition. Replacement cost is $60.GRADING SYSTEMSemester grades will be approximately based on the following system:

A total points scheme may be used but the approximate percentages are accurate.

The following grading scale will be used on ALL assessments:

GRADE NOTIFICATIONParents and students will be notified of their progress in the class on a regular basis. This will be done by accessing Parent/Student Portal which is available at www.cps.edu. Parents without access to the Internet should request that the student print out the grade reports at school in the computer lab or at any public library and bring them home for the parent to review and discuss with the student. Additionally, progress reports will be mailed to the house at the 5, 15, 25 and 35 week marks.HOMEWORK POLICYHomework is your responsibility! There is a lot of it! It will take you a great deal of time to compete it. You should be working on it EVERY DAY. It gives you the practice that you need to pass the quizzes, tests, and most importantly the AP Exam. I expect everyone to do the homework andAnswers without supporting work will not be accepted. In general: All answers must be reproducible from the work shown. The solutions manual will be available and will only be available under my direct supervision. You man NOT photocopy or take pictures of the manual. Students wishing to see the solutions must come in during their lunch periods or before / after school only. Passes will be available if needed.I will ask to see it at the end of each unit.MAKE-UP POLICYOnly students with excused absences will be allowed to make up assignments. It is the student's responsibility to inquire about missing work on the first day back from their excused absence. Excused absences are only as follows: religious holiday, family emergency, illness, or death in the family. Phone calls will be made or emails will be sent to verify student absences.Assessments must be made up within a timely manner upon returning from an excused absence. Students are responsible to schedule a time to make up assessments upon the FIRST day back from an excused absence. Assessments not made up by the agreed upon date will be recorded as zero (0) and no further make up opportunities will be allowed.

TARDY POLICYStudents that are not in the classroom when the bell rings will be marked tardy and will be required to obtain an entry permit from the closest swipe machine. Students that have a note justifying their tardiness will be exempt. Three (3) tardies will result in a detention. Any material covered prior to entry into class will be marked as zero and no extra time will be given on tests and quizzes unless deemed by an individual education plan.

UNEXCUSED ABSENCE POLICYAny student with an unexcused absence will receive a permanent zero on any assignments that are due and/or assigned for that day. Any student with unexcused absences will be referred to the discipline office.

REQUIRED MATERIALS / FEESAll students are required to attend class daily with the appropriate textbook, calculator, notebook, and supplies. All students are required to take the College Board AP Calculus (AB) exam. The cost for this exam is approximately $90.00. Registration will begin sometime after the first of the year. Students that do not take the AP Exam will not receive AP course credit.DISCLAIMER

The instructor reserves the right to change anything on this page at any time.

Notification of changes will be given as changes are made.