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Ms. Shashi Rai Soldan International Studies High School

Room: 203 Syllabus

Email: shashi.rai@ AP( Calculus AB

(UMSL Math 1800)

Course Description: This course provides an introduction to differential and integral calculus. Topics include limits, derivatives, related rates, Newton's method, the Mean-Value Theorem, Max-Min problems, the integral, the Fundamental Theorem of Integral Calculus, areas, volumes, and average values.

UMSL Dual College Credit Option: This course is available to students who meet the criteria for dual credit at the University of Missouri, St. Louis. When you successfully complete this course with a “C” or above, you will have earned five college credit hours if you have enrolled with the University of Missouri St. Louis. You can enroll for the course online at umsl.edu/acp.

Please note that SLPS will pay for the dual credit only if you get an ‘A’ or ‘B’ in the course.

Final Grade for UMSL credit will be determined by averaging BOTH semester grades.

Text: Calculus of a Single Variable AP* Edition 10e by Ron Larson and Bruce Edwards

Also, supplementary material from online resources like will be used throughout the course.

Materials: Pencil, Spiral Notebook, laptop, internet connection.

Useful Websites:

Consider using these if you need extra help!

•

Videos for a variety of topics

•

Tutorials and worked-out solutions to odd-numbered problems

•

Paul’s Online Math Notes

•

Online graphing calculators

Course Overview:

Unit 1: Limits

In this unit students develop an understanding of limits as the foundational building block for both derivatives and integration. One goal of this unit is to ensure that students are comfortable solving limit problems using the Rule of Four. The Rule of Four is a method where students can solve problems using:

1. A graphical approach

2. A numerical/tabular approach

3. An algebraic approach

4. A verbal or written approach, communicating effectively what their final answer means in the context of the problem

Unit 2: Differentiation: Definition and Fundamental Properties

In these units, students use their understanding of limits to explore the meaning of a derivative and instantaneous rate of change. Building on the limit definition of the derivative, students will explore and begin to use the basic rules for taking a derivative. One goal of this unit is for students to use the Rule of Four to solve for derivatives of many different types of functions.

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

In this unit, students expand on their understanding of derivatives by learning more advanced algebraic techniques for solving complex derivatives including composite functions. Students explore how to take derivatives of equations that are not mathematical functions using implicit differentiation. They will be able to identify the correct procedure to use when approaching any type of derivative.

Unit 4: Interpreting the Meaning of the Derivative in Context

In this unit, students then expand on their understanding the meaning of derivatives and their use in real-world problems including, but not limited to, straight line motions. One goal of this unit is for students to take derivatives of an expression with relation to any variable, typically time with related rates problems. Other applications of derivatives including linearization and L’Hopital’s Rule will also be included in this unit.

Unit 5: Analytical Applications of Differentiation

In this unit, students discover how we can use the first and second derivatives of functions to describe the function’s behavior and sketch it accurately. One goal of this unit is for students to understand how to apply the Existence Theorems (which include the Intermediate Value Theorem, Extreme Value Theorem, Rolle’s Theorem, and the Mean Value Theorem) to help problem solve and justify their conclusions. They will also learn how to use calculus to solve optimization problems.

Unit 6: Integration and Accumulation of Change

In this unit, students discover the relationship between differentiation and integration as inverse operations. Students learn how to integrate functions and then, using the definite integral, learn how to “accumulate” in various real-world settings. As the unit progresses they learn the importance of the Fundamental Theorem of Calculus and its many applications.

Unit 7: Differential Equations

In this unit, students discover how to “read” a slope field and see how a function (or other equations that are not mathematical functions) behave. Slope fields are the graphical interpretation of a differential equation (DE) and tie in nicely to the Rule of Four. Students will also build upon their knowledge of integration, using separation of variables to solve more complicated differential equations.

Unit 8: Applications of Integration

In this unit students discover the real power and beauty of calculus in a variety of integration problems. Building upon their knowledge of accumulation (and specifically area under a curve), students will be able to find the area between two curves given two functions. Students also learn to find volume of a solid where a function (or two functions) is rotated around a horizontal line or vertical line. Using a variety of geometric shapes, students will also be able to find the volume of a 3-D solid using known cross-sectional areas.

Unit 9: AP Test Review

Once students have learned all the material we will review for the AP Exam (Given on Tuesday, May 4 at 8:00 a.m.). This review will include a practice exam to be used as the final exam for the course.

Grading Policy: Grades will be determined by a cumulative total of the points scored during the semester. The following components and designated weight assigned to each will determine a student’s grade.

Participation (Do Now, Exit Slip and 10%

in-class participation)

Classwork/ Homework 40%

Tests/ Quizzes 50%

Final exam is mandatory at the end of each semester.

Grading Scale: The following ranges of letter grades will be assigned:

90 – 100% A; 80 – 89% B; 70 – 79% C; 60 – 69% D; Below 60% F

Classroom Participation is crucial to success in this class.

Do Now: ‘Do Now’s are short, 5-10 minute exercises that will be given at the beginning of each class. Each do now is worth 5 points. If you are late or absent, you will miss the “Do Now” points.

Exit Slip: ‘Exit Slip’ are short, 5-10 minute exercises that will be given at the end of each class. Each exit slip is worth 5 points. If you are absent, you will miss the “Exit Slip” points.

Classwork: Classwork will be the assignments that I give you in class to practice a skill. These will be usually due by the end of class and will be graded on completion. In order to receive full credit, you must show ALL your work for every problem. Each assignment must be submitted via Teams assignments. Assignments with no work shown will receive a zero.

Homework: Expect to have homework after every class, usually due the following class period.

• It is the student's responsibility to determine the assignments missed due to an absence.

Check our class Teams page for handouts, assignments, and links to work you may have missed.

Notebook : YOUR SPIRAL NOTEBOOK WILL BE WHERE YOU WILL DO all of your work for each assignment, as well as maintain all notes from class. You need your notebook in every class. All assignments must be labeled and your work should be legible

Tests & Quizzes: Just completing your work will not be enough to pass this class with a good grade. You must do well in your tests and quizzes as well.

Absences: You will be given one day per excused absence to complete your missing work.

Late work is never accepted in the final week of a grading period.

Cheating: In this class, cheating includes...

1. turning in another’s work as one’s own,

2. copying work from a friend in class, before class, or while in another class.

What happens when you cheat . . .? 

• The first time 

– Assume there is some type of misunderstanding, a conversation with the student happens. The student will be allowed to redo the assignment with the understanding that this will not happen again.  

• The second time 

– If this happens again, you will get a zero for the assignment, and will need to complete the alternative assignment for the work. Also, your parents will be notified via e-mail or a phone call.  

Classroom Expectations: In this class we L.E.A.R.N.

• L- Listen to instructions. (Strong Academic Habit)

• E - Enter and exit prepared. (Come to class on time, prepared with materials, ready to learn.)

• A - Always try our best. (Be proactive and persistent about your academic success. Never give up on mastering new concepts.)

• R - Respect teacher and classmates. (Advocate respectfully for yourself and others when there is a need.)

• N - No excuses. (Maintain integrity in all that you do. It is likely that you will make mistakes. Be honest, learn from them, and you will be a better student because of them).

Technology Use: Your laptop is required every day. The goal is to use your devices to support your learning. During class try to limit your distractions and use your devices for the teacher assigned use.

Students will check their email and Teams frequently for important information from the teacher and will respond to the teacher’s emails when needed.

Phones may be taken and stored for the remainder of the hour if those are being used during the class for non-instructional purposes.

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