Syllabus

Period 5 Google Class Code: 65deg5c

Pre-AP Calculus

Course Syllabus

Instructor: Mr. Sweigard

Course Overview:

The Reynolds School District’s Pre-AP Calculus course prepares students for the AP Calculus and other college-level mathematics courses. The course focuses on the skills students will need to be successful at Calculus. Calculus skills will be introduced at the end of this course.

Grading:

Your homework, quizzes, notes, AP practice problems, and class participation are 40% of your grade. Tests are 50% of your grade. Citizenship will be 10% of your grade.

Grading uses this scale:

• 92-100 = A

• 84-91 = B

• 72-83 = C

• 60-71 = D

• Below 60 = F

Citizenship:

Every student is to be ready to learn: Bring book, pencil, calculator, and notebook to class every day unless told otherwise. Participate in all class activities. The highest standard of conduct and integrity is required at all times. Disruption of instruction cannot be tolerated.

Course Topics/Tentative Outline:

Review of Algebra and Geometry: (Approximately 10 days)

Unit 1: Exponential and Logarithmic Functions (Approximately 10 days)

• Exponential and Logarithmic Functions and Their Graphs

• Logarithmic Functions and their Graphs

• Properties of Logarithms

• Exponential and Logarithmic Equations and Models

Unit 2: Trigonometry and Analytic Trigonometry (Approximately 35 Days)

• Angles and Measures

• Right Triangle Trigonometry

• Trigonometric Functions of Any Angle

• Graphs of Trigonometric Functions

• Inverse Trigonometric Functions

• Using Fundamental Identities

• Verifying Trigonometric Identities

• Solving Trigonometric Equations

• Sum and Difference Formulas

• Multiple-Angle and Product-to-Sum Formulas

• Law of Sines and Cosines

• Trigonometric Form of a Complex Number

Unit 3: Algebra Skills Needed for Calculus (Approximately 40 Days)

• Piecewise Functions

• Asymptotes of Functions

• Zeros of Functions

• Complex Fractions

• Sign Charts

• Composition of Functions

• Solving Rational Equations

Unit 4: Limits and Continuity (Approximately 15 Days)

• What is a Limit?

• Limits of Polynomials

• Limits of Trigonometric Functions

• The Definition of Continuity

• Types of Discontinuities

Unit 5: Definition of the Derivative and Basic Differentiation (Approximately 30 Days)

• Deriving the Formula

• The Slope of a Curve

• The Secant and the Tangent

• Differentiability

• Notation

• The Power Rule

• Higher Order Derivatives

• The Product Rule

• The Quotient Rule

• The Chain Rule

• Derivatives of Trig Functions

Unit 6: Implicit Differentiation and Basic Applications of the Derivative (Approximately 30 Days)

• How to Do It

• Second Derivatives

• Equations of Tangent Lines and Normal Lines

• The Mean Value Theorem for Derivatives

• Rolle’s Theorem

GOOGLE CLASSROOM

This school year, Reynolds JSHS students will have the opportunity to use Google Classroom and Google Apps For Education, a multimedia learning management system (LMS) that will allow them to create and submit assignments digitally.  Each teacher will have a Google Classroom where students will be able to see and submit assignments for the week, classroom announcements, and online discussions questions posted by their instructor.  Students can gain access to their teacher’s Google Classroom via any internet connected device by simply signing into their Reynolds School District Google Account.

As a guardian, you can receive email summaries showing your student’s progress in classroom. You can choose the frequency of the emails, such as daily or weekly, and you can unsubscribe or remove yourself from Classroom at any time. Guardian email summaries include:

• Missing work—Work that’s late at the time the email was sent

• Upcoming work—Work that’s due today and tomorrow (for daily emails) or work that’s due in the upcoming week (for weekly emails)

• Class activity—Announcements, assignments, and questions recently posted by teachers.

STUDENT AND PARENT ACKNOWLEDGEMENT

I hereby acknowledge that I have read the syllabus for this class and agree to the course outline, classroom rules, and obligations as set forth by the instructor.

Student Name ________________________________________

Student Signature _____________________________________ Date ___________________

Parent Name _________________________________________

Parent Signature ______________________________________ Date ___________________

• As the guardian of this student, I request access to Google Classroom Email Summaries to know what missing work, upcoming work, and class activity is happening in my student’s classrooms.

Parent Email _________________________________________________________________

Period 6 Google Class Code: hckaag6

AP Calculus (AB)

Mr. Jeff Sweigard Room 21

Course Description: AP Calculus offers students their first opportunity to attempt collegiate

level mathematics. This course has two distinct goals: First, to learn and appreciate Calculus as a

significant mathematical and scientific tool and as a human achievement. Second, to prepare for

the College Board’s Advanced Placement Examination in Calculus (AB) . Passing this examination may earn the student college credit when they enroll in a four year institution in the Fall. 

Our textbook is Calculus of a Single Variable, by Ron Larson, Robert Hostetler, and Bruce

Edwards (Eighth Edition), 2006.

Supplemental materials include: Cracking the AP Calculus AB Exams 2016 by David S. Kahn, The Princeton Review.

A graphing calculator (the TI-83 or TI-84 is particularly recommended) is required. Students

who are unable to obtain their own calculator may check out a calculator for the year in a manner

somewhat similar to that of checking out textbooks. We will use the calculator in a variety of ways including:

• Graph functions within arbitrary windows.

• Solve equations numerically

• Analyze and interpret results.

• Conduct explorations.

• Justify and explain results of graphs and equations.

The “Rule of Four” will be emphasized in the approach and solving of problems. The four parts are:

• Numerical analysis(where data points are known, but not an equation)

• Graphical analysis(where a graph is known, but not an equation)

• Analytic/algebraic analysis(traditional equation and variable manipulation)

• Verbal/written method of representing problems(classic story problems as well as written justification of one’s thinking in solving a problem)

Throughout the course, students will be asked to explain how they solved a problem to the class. Student will regularly work in groups. I find that some students feel more comfortable asking fellow students for help. An atmosphere where students are comfortable asking questions is of great importance and will be emphasized. My hope is to build confidence and motivate students to do their best. 

Student will have an opportunity after a test and some quizzes to get partial credit for missed questions. The student will write what they did wrong and what they should have done to get the correct answer. They can earn back up to half of the points lost.

Grading: Your homework, quizzes, notes, AP practice problems, and class participation are

40% of your grade. Tests are 50% of your grade. Citizenship will be 10% of your grade.

Grading uses this scale:

92 - 100 = A

84 - 91 = B

72 - 83 = C

60 - 71 = D

below 60 = F

Citizenship:

Every student is to be ready to learn: Bring book, pencil, paper, and notebook to class every day unless told otherwise. You will need a graphing calculator. Participate in all class activities.

This is a college level course offered in the high school. The highest standard of conduct and

integrity is required at all times. Disruption of instruction cannot be tolerated.

Topics of Study:

Summer Assignment: review topics in trigonometry and pre-calculus. (Approximately 5 days)

Unit 1: Limits and Continuity (Approximately 10 days)

• What is a Limit?

• Limits of Polynomials

• Limits of Trigonometric Functions

• The Definition of Continuity

• Types of Discontinuities

Unit 2: Definition of the Derivative and Basic Differentiation (Approximately 15 days)

• Deriving the Formula

• The Slope of a Curve

• The Secant and the Tangent

• Differentiability

• Notation

• The Power Rule

• Higher Order Derivatives

• The Product Rule

• The Quotient Rule

• The Chain Rule

• Derivatives of Trig Functions

Unit 3: Implicit Differentiation and Basic Applications of the Derivative (Approximately 10 days)

• How to Do It

• Second Derivatives

• Equations of Tangent Lines and Normal Lines

• The Mean Value Theorem for Derivatives

• Rolle’s Theorem

Unit 4: Maxima and Minima, Motion (Approximately 5 days)

• Applied Maxima and Minima Problems

** Sketch graphs and label all extrema, points of inflection, and asymptotes. Students will check their work using their graphic calculator.

• Position, Velocity, and Acceleration

** A CBL experiment is conducted with students tossing a ball into the air. Students graph the height of the ball versus the time the ball is in the air. The calculator is used to find a quadratic equation to model the motion of the ball over time. Average velocities are calculated over different time intervals and students are asked to approximate instantaneous velocity. The tabular data and the regression equation are both used in these calculations. These velocities are graphed versus time on the same graph as the height versus time graph.

Unit 5: Exponential and Logarithmic Functions, Differential Calculus (Approximately 15 days)

• The Derivative of ln x

• The Derivative of ex

• The Derivative of logax

• The Derivative of ax

• The Derivative of an Inverse Function

• Derivatives of Parametric Functions

• L’Hopital’s Rule

• Differentials

• Logarithmic Differentiation

Unit 6: The Integral (Approximately 10 days)

• The Antiderivative

• Integrals of Trig Functions

• Addition and Subtraction

• U-Substitution

Unit 7: Definite Integrals, Exponential and Logarithmic Functions (Approximately 16 days)

• Area Under a Curve

• Tabular Riemann Sums

• The Fundamental Theorem of Calculus

• The Trapezoid Rule

• The Mean Value Theorems for Integrals

• The Second Fundamental Theorem of Calculus

• Integrals of Trig Functions

• Integrating ex and ax 

Unit 8: The Area Between Two Curves, The Volume of a Solid of Revolution (Approximately 10 days)

• Vertical Slices

• Horizontal Slices

• Washer and Disks

• Cylindrical Shells

• Volumes of Solids with Known Cross-Sections

Unit 9: Integration by Parts, Trig Functions (Approximately 10 days)

• The Formula

• Inverse Trig Functions

• Advanced Integration of Trig Functions

Unit 10: Differential Equations (Approximately 10 days)

• Separation of Variables

• Euler’s Method

• Slope Fields

Review for AP Exam (Approximately 20 days)

Unit 11: Other Applications of the Integral (Approximately 10 days) 

• Length of a Curve

• Parametric Functions

• The Method of Partial Fractions

• Improper Integrals

• Calculus of Polar Curves

Unit 12: Infinite Series (Approximately 18 days)

• Sequences and Series

• Geometric Series

• The Ratio Test

• Alternating Series

• Integral Test

• Comparison Test

• Power Series

• Taylor Series and Polynomials

GOOGLE CLASSROOM

This school year, Reynolds JSHS students will have the opportunity to use Google Classroom and Google Apps For Education, a multimedia learning management system (LMS) that will allow them to create and submit assignments digitally.  Each teacher will have a Google Classroom where students will be able to see and submit assignments for the week, classroom announcements, and online discussions questions posted by their instructor.  Students can gain access to their teacher’s Google Classroom via any internet connected device by simply signing into their Reynolds School District Google Account.

As a guardian, you can receive email summaries showing your student’s progress in classroom. You can choose the frequency of the emails, such as daily or weekly, and you can unsubscribe or remove yourself from Classroom at any time. Guardian email summaries include:

• Missing work—Work that’s late at the time the email was sent

• Upcoming work—Work that’s due today and tomorrow (for daily emails) or work that’s due in the upcoming week (for weekly emails)

• Class activity—Announcements, assignments, and questions recently posted by teachers.

STUDENT AND PARENT ACKNOWLEDGEMENT

I hereby acknowledge that I have read the syllabus for this class and agree to the course outline, classroom rules, and obligations as set forth by the instructor.

Student Name ________________________________________

Student Signature _____________________________________ Date ___________________

Parent Name _________________________________________

Parent Signature ______________________________________ Date ___________________

• As the guardian of this student, I request access to Google Classroom Email Summaries to know what missing work, upcoming work, and class activity is happening in my student’s classrooms.

Parent Email _________________________________________________________________

Advanced Algebra/Trigonometry Syllabus

Google Class Code: opivbhf

Course Description: This year-long course combines study of Advanced Algebra and Trigonometry.

Students will investigate multiple representations of functions through mathematical modeling of

real-world situations. Trigonometry will be investigated through the study of trigonometric

definitions, applications, graphing and solving trigonometric equations and inequalities. Students

will be working collaboratively to communicate using the language of mathematics, logic of

procedure and interpretation of results. Virginia College and Career Mathematical Proficiency skills

will be developed on an individualized basis based on college placement test results.

At the end of Advanced Algebra, the student is expected to:

● Demonstrate a knowledge of algebraic functions including

– Polynomial functions

– Rational functions

– Absolute value functions

– Graphing techniques

– Exponential functions

– Inverse functions

– Conics

– Sequences, counting principles, and probability

● Demonstrate algebra skills needed for calculus, life skills, and/or technical

skills

● Demonstrate an understanding of graphs/functions

● Possess an increased number of solution techniques so that when a new

problem is posed, the student has more tools to use for solution

● Demonstrate an understanding of technology with an emphasis on

interpretation

● Demonstrate knowledge of various algebra topics through mathematical

modeling and real world problem solving.

At the end of Trigonometry, the student is expected to:

● Demonstrate a knowledge of the six trigonometric functions

● Demonstrate the ability to determine the value of any trigonometric function

given one trigonometric value

● Demonstrate the knowledge of the trigonometric values of special angles and

their related angles

● Demonstrate the ability to convert from radians to degrees and vice versa

● Demonstrate the understanding of any trigonometric function value and

inverse trigonometric function value

● Identify the domain and range of inverse trigonometric functions and

recognize their graphs

● Demonstrate an understanding of the trigonometric identities by verifying and

using them in substitutions

● Demonstrate the ability to graph trigonometric functions by identifying their

domain, range, amplitudes, period, phase shift, and vertical shift

● Demonstrate an understanding in solving trigonometric equations including

infinite solutions and restricted domain and basic trigonometric inequalities

● Demonstrate an understanding of trigonometric functions by creating and

solving practical problems using Pythagorean Identities, Law of Sines, and

Law of Cosines

● Demonstrate knowledge of various trigonometric topics through mathematical

modeling and real world problem solving.

GOOGLE CLASSROOM

This school year, Reynolds JSHS students will have the opportunity to use Google Classroom and Google Apps For Education, a multimedia learning management system (LMS) that will allow them to create and submit assignments digitally.  Each teacher will have a Google Classroom where students will be able to see and submit assignments for the week, classroom announcements, and online discussions questions posted by their instructor.  Students can gain access to their teacher’s Google Classroom via any internet connected device by simply signing into their Reynolds School District Google Account.

As a guardian, you can receive email summaries showing your student’s progress in classroom. You can choose the frequency of the emails, such as daily or weekly, and you can unsubscribe or remove yourself from Classroom at any time. Guardian email summaries include:

• Missing work—Work that’s late at the time the email was sent

• Upcoming work—Work that’s due today and tomorrow (for daily emails) or work that’s due in the upcoming week (for weekly emails)

• Class activity—Announcements, assignments, and questions recently posted by teachers.

STUDENT AND PARENT ACKNOWLEDGEMENT

I hereby acknowledge that I have read the syllabus for this class and agree to the course outline, classroom rules, and obligations as set forth by the instructor.

Student Name ________________________________________

Student Signature _____________________________________ Date ___________________

Parent Name _________________________________________

Parent Signature ______________________________________ Date ___________________

• As the guardian of this student, I request access to Google Classroom Email Summaries to know what missing work, upcoming work, and class activity is happening in my student’s classrooms.

Parent Email _________________________________________________________________

Algebra Syllabus  Google Classroom Code: tj7xba6

Course Description:

This algebra course is designed to provide students with a solid foundation in algebraic concepts and skills as outlined by the Pennsylvania Standards. The course will cover a range of topics including linear equations, inequalities, functions, systems of equations, polynomials, factoring, quadratic equations, and more. Emphasis will be placed on problem-solving, critical thinking, and real-world applications of algebraic concepts.

Course Objectives:

By the end of the course, students should be able to:

1. Understand and apply foundational algebraic concepts.

2. Solve linear equations and inequalities in one and two variables.

3. Analyze and graph linear functions and relations.

4. Solve systems of linear equations and inequalities.

5. Manipulate and simplify algebraic expressions and equations.

6. Factor and solve quadratic equations.

7. Perform operations with polynomials and rational expressions.

8. Understand and apply properties of exponents and radicals.

9. Analyze and graph various types of functions, including quadratic and exponential functions.

10. Solve real-world problems using algebraic techniques.

Grading:

- Homework/Classwork: 40%

- Tests: 50%

- Citizenship: 10%

Course Outline:

Unit 1: Introduction to Algebra

- Overview of algebraic concepts

- Order of operations and evaluating expressions

- Properties of real numbers

- Simplifying expressions with variables

Unit 2: Linear Equations and Inequalities

- Solving linear equations

- Writing and solving linear inequalities

- Applications of linear equations and inequalities

Unit 3: Functions and Graphs

- Understanding functions and function notation

- Graphing linear equations and inequalities

- Rate of change and slope

Unit 4: Systems of Equations and Inequalities

- Solving systems of linear equations by graphing, substitution, and elimination

- Applications of systems of equations

- Solving systems of linear inequalities

Unit 5: Polynomials and Factoring

- Adding, subtracting, multiplying, and dividing polynomials

- Factoring quadratic expressions

- Factoring by grouping and special factoring patterns

Unit 6: Quadratic Equations and Functions

- Solving quadratic equations by factoring, completing the square, and using the quadratic formula

- Graphing quadratic functions

- Applications of quadratic equations

Unit 7: Rational Expressions and Equations

- Simplifying rational expressions

- Multiplying, dividing, adding, and subtracting rational expressions

- Solving rational equations

Unit 8: Exponents and Radicals

- Properties of exponents

- Scientific notation

- Simplifying expressions with radicals

Unit 9: Functions and Their Properties

- Characteristics of linear, quadratic, and exponential functions

- Transformations of functions

- Inverse functions

Unit 10: Final Projects and Applications

- Real-world problem-solving using algebraic techniques

- Presentations and discussions of final projects

Note: This syllabus is a general outline and can be adjusted based on the specific curriculum guidelines and pacing requirements of the Pennsylvania Standards. It's important to regularly assess student progress and adapt teaching methods as needed to ensure successful learning outcomes.