# PreCalculus B: Functions & Graphical Analysis

## Course Description:

This course is the second in a two-course sequence that broadens student understanding of functions and mathematical models of real-world phenomena. Designed to prepare a student for Calculus, this course will build on student understanding of algebra, extending their knowledge to new mathematical topics, while deepening their knowledge in others. The course contains units on polynomial, rational, logarithmic and exponential functions, sequences, series, conics and limits, as well as systems and vectors. The majority of the course is asynchronous with a few synchronous elements.

## Course Details:

Course Title (District): PreCalculus B: Functions & Graphical Analysis
Course Title (NCES SCED) : Pre-Calculus
Course Provider : Michigan Virtual
Content Provided By : Michigan Virtual
Online Instructor Provided By : Michigan Virtual
Standards Addressed : CCSS, MMC, NCAA
Academic Terms : Accelerated, Semester, Trimester
NCES SCED Code :
 Subject Area : Mathematics Course Identifier : Pre-Calculus Course Level : (G) General or Regular Available Credit : 0.5 Sequence : 2 of 2

## How To Enroll:

Enrollment Website : https://slp.michiganvirtual.org/ [email protected] (888) 889-2840

Students and Parents: It is important to work closely with your local school counselor or registrar to follow the school's enrollment procedures. By clicking the "Start Registration Request" button below, you will be able to notify the school of your interest in registering for the online course. However, it is the responsibility of the district or school to review the registration request and approve or deny the request. Please make a note to follow up with your school after submitting a registration request.

Upon completion of this course, students will be able to…

• Perform algebraic operations (including compositions) on functions and apply transformations.
• Write an expression for the composition of one given function with another and find the domain, range, and graph of the composite function. Recognize components when a function is composed of two or more elementary functions.
• Identify and describe discontinuities of a function and how these relate to the graph.
• Use the idea of limit to analyze a graph as it approaches an asymptote. Compute limits of simple functions informally.
• Use the inverse relationship between exponential and logarithmic functions to solve equations and problems.
• Graph logarithmic functions. Graph translations and reflections of these functions.
• Compare the large-scale behavior of exponential and logarithmic functions with different bases and recognize that different growth rates are visible in the graphs of the functions.
• Solve exponential and logarithmic equations when possible. For those that cannot be solved analytically, use graphical methods to find approximate solutions.
• Explain how the parameters of an exponential or logarithmic model relate to the data set or situation being modeled. Find an exponential or logarithmic function to model a given data set or situation. Solve problems involving exponential growth and decay.
• Solve quadratic-type equations by substitution.
• Apply quadratic functions and their graphs in the context of motion under gravity and simple
optimization problems.
• Explain how the parameters of an exponential or logarithmic model relate to the data set or situation being modeled. Find a quadratic function to model a given data set or situation.
• Solve polynomial equations and inequalities of degree greater than or equal to three. Graph polynomial functions given in factored form using zeros and their multiplicities, testing the sign-on intervals and analyzing the function’s large-scale behavior.
• Recognize and apply fundamental facts about polynomials: the Remainder Theorem, the Factor Theorem, and the Fundamental Theorem of Algebra.
• Solve equations and inequalities involving rational functions. Graph rational functions given in factored form using zeros, identifying asymptotes, analyzing their behavior for large x values, and testing intervals.
• Given vertical and horizontal asymptotes, find an expression for a rational function with these features.
• Recognize and apply the definition and geometric interpretation of difference quotient. Simplify difference quotients and interpret difference quotients as rates of change and slopes of secant lines.
• Perform operations (addition, subtraction, and multiplication by scalars) on vectors in the plane.
• Solve applied problems using vectors.
• Recognize and apply the algebraic and geometric definitions of the dot product of vectors.
• Multiply a vector by a matrix.
• Represent rotations of the plane as matrices and apply to find the equations of rotated conics.
• Define the inverse of a matrix and compute the inverse of two-by-two and three-by-three matrices when they exist.
• Explain the role of determinants in solving systems of linear equations using matrices and compute determinants of two-by-two and three-by-three matrices.
• Write systems of two and three linear equations in matrix form. Solve such systems using Gaussian elimination or inverse matrices.
• Represent and solve systems of inequalities in two variables and apply these methods in linear
programming situations to solve problems.
• Recognize, explain, and use sigma and factorial notation.
• Given an arithmetic, geometric, or recursively defined sequence, write an expression for the nth term when possible. Write a particular term of a sequence when given the nth term.
• Explain, and use the formulas for the sums of finite arithmetic and geometric sequences.
• Compute the sums of infinite geometric series. Apply the convergence criterion for geometric series.
• Convert between polar and rectangular coordinates. Graph functions given in polar coordinates.
• Write complex numbers in polar form. Know and use De Moivre’s Theorem.
• Evaluate parametric equations for given values of the parameter.
• Convert between parametric and rectangular forms of equations.
• Graph curves described by parametric equations and find parametric equations for a given graph.
• Explain and apply the locus definitions of parabolas, ellipses, and hyperbolas and recognize these conic sections in applied situations.
• Identify parabolas, ellipses, and hyperbolas from equations, write the equations in standard form, and sketch an appropriate graph of the conic section.
• Derive the equation for a conic section from given geometric information. Identify key characteristics of a conic section from its equation or graph.

INACOL Online Course Quality Standards

The goals and objectives clearly state what the participants will know or be able to do at the end of the course. The goals and objectives are measurable in multiple ways.
The course content and assignments are aligned with the state’s content standards, Common Core curriculum, or other accepted content standards set for Advanced Placement® courses, technology, computer science, or other courses whose content is not included in the state standards.
The course content and assignments are of sufficient rigor, depth and breadth to teach the standards being addressed.
Information literacy and communication skills are incorporated and taught as an integral part of the curriculum.
Multiple learning resources and materials to increase student success are available to students before the course begins.
Course Overview and Introduction Rating Comments
Clear, complete course overview and syllabus are included in the course.
Course requirements are consistent with course goals, are representative of the scope of the course and are clearly stated.
Information is provided to students, parents and mentors on how to communicate with the online instructor and course provider.
Legal and Acceptable Use Policies Rating Comments
The course reflects multi-cultural education, and the content is accurate, current and free of bias or advertising.
Expectations for academic integrity, use of copyrighted materials, plagiarism and netiquette (Internet etiquette) regarding lesson activities, discussions, and e-mail communications are clearly stated.
Privacy policies are clearly stated.
Online instructor resources and notes are included.
Assessment and assignment answers and explanations are included.
Instructional and Audience Analysis Rating Comments
Course design reflects a clear understanding of all students’ needs and incorporates varied ways to learn and master the curriculum.
Course, Unit and Lesson Design Rating Comments
The course is organized by units and lessons that fall into a logical sequence. Each unit and lesson includes an overview describing objectives, activities, assignments, assessments, and resources to provide multiple learning opportunities for students to master the content.
Instructional Strategies and Activities Rating Comments
The course instruction includes activities that engage students in active learning.
The course and course instructor provide students with multiple learning paths, based on student needs that engage students in a variety of ways.
The course provides opportunities for students to engage in higher-order thinking, critical reasoning activities and thinking in increasingly complex ways.
The course provides options for the instructor to adapt learning activities to accommodate students’ needs.
Readability levels, written language assignments and mathematical requirements are appropriate for the course content and grade-level expectations.
The course design provides opportunities for appropriate instructor-student interaction, including opportunities for timely and frequent feedback about student progress.
The course design includes explicit communication/activities (both before and during the first week of the course) that confirms whether students are engaged and are progressing through the course. The instructor will follow program guidelines to address non-responsive students.
The course provides opportunities for appropriate instructor-student and student-student interaction to foster mastery and application of the material.
Student evaluation strategies are consistent with course goals and objectives, are representative of the scope of the course and are clearly stated.
The course structure includes adequate and appropriate methods and procedures to assess students’ mastery of content.
Ongoing, varied, and frequent assessments are conducted throughout the course to inform instruction.
Assessment strategies and tools make the student continuously aware of his/her progress in class and mastery of the content.
Assessment Resources and Materials Rating Comments
Assessment materials provide the instructor with the flexibility to assess students in a variety of ways.
Grading rubrics are provided to the instructor and may be shared with students.
The grading policy and practices are easy to understand.
The course architecture permits the online instructor to add content, activities and assessments to extend learning opportunities.
The course accommodates multiple school calendars; e.g., block, 4X4 and traditional schedules.
Clear and consistent navigation is present throughout the course.
Rich media are provided in multiple formats for ease of use and access in order to address diverse student needs.
Technology Requirements and Interoperability Rating Comments
All technology requirements (including hardware, browser, software, etc...) are specified.
Prerequisite skills in the use of technology are identified.
The course uses content-specific tools and software appropriately.
The course is designed to meet internationally recognized interoperability standards.
Copyright and licensing status, including permission to share where applicable, is clearly stated and easily found.
Course materials and activities are designed to provide appropriate access to all students. The course, developed with universal design principles in mind, conforms to the U.S. Section 504 and Section 508 provisions for electronic and information technology as well as the W3C’s Web Content Accessibility guidelines (WCAg 2.0).
Student information remains confidential, as required by the Family Educational Rights and Privacy Act (FERPA).
The course provider uses multiple ways of assessing course effectiveness.
The course is evaluated using a continuous improvement cycle for effectiveness and the findings used as a basis for improvement.
The course is updated periodically to ensure that the content is current.
Course instructors, whether faceto-face or virtual, are certificated and “highly qualified.” The online course teacher possesses a teaching credential from a state-licensing agency and is “highly qualified” as defined under ESEA.
Instructor and Student Support Rating Comments
Professional development about the online course delivery system is offered by the provider to assure effective use of the courseware and various instructional media available.
The course provider offers technical support and course management assistance to students, the course instructor, and the school coordinator.
Course instructors, whether face-to-face or virtual, have been provided professional development in the behavioral, social, and when necessary, emotional, aspects of the learning environment.
Course instructors, whether face-to-face or virtual, receive instructor professional development, which includes the support and use of a variety of communication modes to stimulate student engagement online.
The provider assures that course instructors, whether face-to-face or virtual, are provided support, as needed, to ensure their effectiveness and success in meeting the needs of online students.
Students are offered an orientation for taking an online course before starting the coursework.

Review Conducted By :
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Date of Review : 04/02/2020

Unit 9: Polynomial Functions

Unit 10: Rational Functions

Unit 11: Exponential & Logarithmic Functions

Unit 12: Sequences & Series

Unit 13: Conics

Unit 14: Limits

Unit 15: Systems

Unit 16: Trigonometry & The Polar Plane

Term Type Enrollment Opens Enrollment Ends Random Draw Date Enrollment Drop Date Course Starts Course Ends # of Seats Course Fee Potential Additional Costs
Trimester 04/01/2020 01/04/2021 06/01/2020 10/23/2020 04/02/2021 100 \$325.0000 0.0000
Semester 04/01/2020 03/29/2021 06/01/2020 11/27/2020 06/18/2021 300 \$325.0000 0.0000
Trimester 04/01/2020 04/12/2021 06/01/2020 01/08/2021 06/18/2021 100 \$325.0000 0.0000
Accelerated 01/26/2021 07/06/2021 04/30/2021 08/13/2021 100 \$325.0000 0.0000
Drop Policy Completion Policy Term Type Enrollment Opens Enrollment Ends
The last day to drop to receive a full refund is either 25 consecutive days after the enrollment's Start Date or the defined refund date, which ever date comes soonest. Students who are enrolled with a Start Date that is in the past, will have a minimum of 5 consecutive calendar days to drop and receive a refund. Students may access their course from their enrollment Start Date to their enrollment End Date. For reporting purposes, a completion is a 60% final score or higher. Trimester 04/01/2020 01/04/2021
The last day to drop to receive a full refund is either 25 consecutive days after the enrollment's Start Date or the defined refund date, which ever date comes soonest. Students who are enrolled with a Start Date that is in the past, will have a minimum of 5 consecutive calendar days to drop and receive a refund. Students may access their course from their enrollment Start Date to their enrollment End Date. For reporting purposes, a completion is a 60% final score or higher. Semester 04/01/2020 03/29/2021
The last day to drop to receive a full refund is either 25 consecutive days after the enrollment's Start Date or the defined refund date, which ever date comes soonest. Students who are enrolled with a Start Date that is in the past, will have a minimum of 5 consecutive calendar days to drop and receive a refund. Students may access their course from their enrollment Start Date to their enrollment End Date. For reporting purposes, a completion is a 60% final score or higher. Trimester 04/01/2020 04/12/2021
The last day to drop to receive a full refund is either 25 consecutive days after the enrollment's Start Date or the defined refund date, which ever date comes soonest. Students who are enrolled with a Start Date that is in the past, will have a minimum of 5 consecutive calendar days to drop and receive a refund. Students may access their course from their enrollment Start Date to their enrollment End Date. For reporting purposes, a completion is a 60% final score or higher. Accelerated 01/26/2021 07/06/2021

Students can use email or the private message system within the Student Learning Portal to access highly qualified teachers when they need instructor assistance. Students will also receive feedback on their work inside the learning management system. The Instructor Info area of their course may describe additional communication options.

Students will require a computer device with headphones, a microphone, webcam, up-to-date Chrome Web Browser, and access to YouTube. Students will also require a graphing calculator, such as TI-84 Plus, TI-83, or TI-83 Plus.