Trigonometry and Precalculus
This course is the year long course in Precalculus and Trigonometry. This course will broaden student understanding of functions and mathematical models of real-world phenomena. This course will build on student understanding of geometry and algebra, extending their knowledge in the field of trigonometry. The first semester contains units on functions and their properties, geometric foundations and right triangle trigonometry, applications of trigonometric and circular functions and their graphs, as well as trigonometric function properties, identities, and equations. the second semester 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 Title (District):||Trigonometry and Precalculus|
|Course Title (NCES SCED) :||Pre-Calculus|
|Course Provider :||Montague Area Public Schools|
|Content Provided By :||Michigan Virtual|
|Online Instructor Provided By :||Montague Area Public Schools|
|Standards Addressed :||Michigan Merit Curriculum, Common Core State Standards, National Collegiate Athletic Association|
|Alignment Document :||https://drive.google.com/file/d/118C2qyx63hRl-OU9WkKLryecT5DTPhUr/view?usp=sharing|
|Academic Terms :||Year Long|
|NCES SCED Code :||
How To Enroll:
|Enrollment Website :||https://docs.google.com/forms/d/1U-YFSFkRlPHVqrFpNQGgj8H1oEmGhaYSV6i3kIbYlMY/edit?ts=611abbc8|
|Email :||[email protected]|
|Phone :||(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.
Additional Course Information:
- Email: [email protected]
- Phone: (888) 889-2840
- Define function and use a function to decide if a given relation is a function
- Perform algebraic operations (including compositions) on functions and apply transformations
- Know basic properties of the inverse trigonometric functions and recognize their graphs
- Determine whether a function has an inverse and express the inverse if it exists. Express and interpret the function notation for inverses
- Solve trigonometric equations using basic identities and inverse trigonometric functions
- Prove trigonometric identities and derive some of the basic ones
- Find a sinusoidal function to model a given data set or situation and explain how the parameters of the model relate to the data set or situation.
- 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.
- Define matrix addition and multiplication. Add, subtract, and multiply matrices.
- 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.
Additional Cost: $0.0
Additional Cost Description:
A graphing calculator, such as the TI-84 Plus, TI-83, or TI-83 Plus, is needed for both Pre-Calculus A and Pre-Calculus B. Students will be required to participate in one or more synchronous, live session(s) with the instructor.
Upon completion of this course, students will be able to...
iNACOL National Standards for Quality Online Courses
|Academic Content Standards and Assessments||Rating||Comments|
|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.||Pilot: Review Pending|
|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.||Pilot: Review Pending|
|The course content and assignments are of sufficient rigor, depth and breadth to teach the standards being addressed.||Pilot: Review Pending|
|Information literacy and communication skills are incorporated and taught as an integral part of the curriculum.||Pilot: Review Pending|
|Multiple learning resources and materials to increase student success are available to students before the course begins.||Pilot: Review Pending|
|Course Overview and Introduction||Rating||Comments|
|Clear, complete course overview and syllabus are included in the course.||Pilot: Review Pending|
|Course requirements are consistent with course goals, are representative of the scope of the course and are clearly stated.||Pilot: Review Pending|
|Information is provided to students, parents and mentors on how to communicate with the online instructor and course provider.||Pilot: Review Pending|
|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.||Pilot: Review Pending|
|Expectations for academic integrity, use of copyrighted materials, plagiarism and netiquette (Internet etiquette) regarding lesson activities, discussions, and e-mail communications are clearly stated.||Pilot: Review Pending|
|Privacy policies are clearly stated.||Pilot: Review Pending|
|Online instructor resources and notes are included.||Pilot: Review Pending|
|Assessment and assignment answers and explanations are included.||Pilot: Review Pending|
|Accessing Course Effectiveness||Rating||Comments|
|The course provider uses multiple ways of assessing course effectiveness.||Pilot: Review Pending|
|The course is evaluated using a continuous improvement cycle for effectiveness and the findings used as a basis for improvement.||Pilot: Review Pending|
|The course is updated periodically to ensure that the content is current.||Pilot: Review Pending|
|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.||Pilot: Review Pending|
|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.||Pilot: Review Pending|
|The course provider offers technical support and course management assistance to students, the course instructor, and the school coordinator.||Pilot: Review Pending|
|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.||Pilot: Review Pending|
|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.||Pilot: Review Pending|
|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.||Pilot: Review Pending|
|Students are offered an orientation for taking an online course before starting the coursework.||Pilot: Review Pending|
|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.||Pilot: Review Pending|
|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.||Pilot: Review Pending|
|Instructional Strategies and Activities||Rating||Comments|
|The course instruction includes activities that engage students in active learning.||Pilot: Review Pending|
|The course and course instructor provide students with multiple learning paths, based on student needs that engage students in a variety of ways.||Pilot: Review Pending|
|The course provides opportunities for students to engage in higher-order thinking, critical reasoning activities and thinking in increasingly complex ways.||Pilot: Review Pending|
|The course provides options for the instructor to adapt learning activities to accommodate students’ needs.||Pilot: Review Pending|
|Readability levels, written language assignments and mathematical requirements are appropriate for the course content and grade-level expectations.||Pilot: Review Pending|
|Communication and Interaction||Rating||Comments|
|The course design provides opportunities for appropriate instructor-student interaction, including opportunities for timely and frequent feedback about student progress.||Pilot: Review Pending|
|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.||Pilot: Review Pending|
|The course provides opportunities for appropriate instructor-student and student-student interaction to foster mastery and application of the material.||Pilot: Review Pending|
|Resources and Materials||Rating||Comments|
|Students have access to resources that enrich the course content.||Pilot: Review Pending|
|Student evaluation strategies are consistent with course goals and objectives, are representative of the scope of the course and are clearly stated.||Pilot: Review Pending|
|The course structure includes adequate and appropriate methods and procedures to assess students’ mastery of content.||Pilot: Review Pending|
|Ongoing, varied, and frequent assessments are conducted throughout the course to inform instruction.||Pilot: Review Pending|
|Assessment strategies and tools make the student continuously aware of his/her progress in class and mastery of the content.||Pilot: Review Pending|
|Assessment Resources and Materials||Rating||Comments|
|Assessment materials provide the instructor with the flexibility to assess students in a variety of ways.||Pilot: Review Pending|
|Grading rubrics are provided to the instructor and may be shared with students.||Pilot: Review Pending|
|The grading policy and practices are easy to understand.||Pilot: Review Pending|
|The course architecture permits the online instructor to add content, activities and assessments to extend learning opportunities.||Pilot: Review Pending|
|The course accommodates multiple school calendars; e.g., block, 4X4 and traditional schedules.||Pilot: Review Pending|
|Clear and consistent navigation is present throughout the course.||Pilot: Review Pending|
|Rich media are provided in multiple formats for ease of use and access in order to address diverse student needs.||Pilot: Review Pending|
|Technology Requirements and Interoperability||Rating||Comments|
|All technology requirements (including hardware, browser, software, etc...) are specified.||Pilot: Review Pending|
|Prerequisite skills in the use of technology are identified.||Pilot: Review Pending|
|The course uses content-specific tools and software appropriately.||Pilot: Review Pending|
|The course is designed to meet internationally recognized interoperability standards.||Pilot: Review Pending|
|Copyright and licensing status, including permission to share where applicable, is clearly stated and easily found.||Pilot: Review Pending|
|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).||Pilot: Review Pending|
|Student information remains confidential, as required by the Family Educational Rights and Privacy Act (FERPA).||Pilot: Review Pending|
Review Conducted By: Michigan Virtual
Date of Review: 04/02/2020
NSQ National Standards for Quality Online Courses
|A1. A course overview and syllabus are included in the online course||Fully Met|
|A2. Minimum computer skills and digital literacy skills expected of the learner are clearly stated.*||Fully Met|
|A3. The instructor’s biographical information and information on how to communicate with the instructor are provided to learners and other stakeholders.||Fully Met|
|A4. Learner expectations and policies are clearly stated and readily accessible within the introductory material of the course.||Fully Met|
|A5. Minimum technology requirements for the course are clearly stated, and information on how to obtain the technologies is provided.*||Fully Met|
|A6. Grading policies and practices are clearly defined in accordance with course content learning expectations.||Fully Met|
|A7. The online course provides a clear description or link to the technical support offered and how to obtain it.*||Fully Met|
|A8. Learners are offered an orientation prior to the start of the online course.||Fully Met|
|B1. The online course objectives or competencies are measurable and clearly state what the learner will be able to demonstrate as a result of successfully completing the course.*||Fully Met|
|B2. The online course expectations are consistent with course-level objectives or competencies, are representative of the structure of the course, and are clearly stated.||Fully Met|
|B3. The online course content is aligned with accepted state and/or other accepted content standards, where applicable.*||Fully Met|
|B4. Digital literacy and communication skills are incorporated and taught as an integral part of the curriculum.*||Fully Met|
|B5. Supplemental learning resources and related instructional materials are available to support and enrich learning and are aligned to the specific content being delivered.*||Fully Met|
|B6. The online course content and supporting materials reflect a culturally diverse perspective that is free of bias.*||Fully Met|
|B7. The online course materials (e.g., textbooks, primary source documents, OER) that support course content standards are accurate and current.||Fully Met|
|B8. The online course is free of adult content and avoids unnecessary advertisements.*||Fully Met|
|B9. Copyright and licensing status for any third-party content is appropriately cited and easily found.||Fully Met|
|B10. Documentation and other support materials are available to support effective online course facilitation.*||Fully Met|
|C1. The online course design includes activities that guide learners toward promoting ownership of their learning and self-monitoring.||Fully Met|
|C2. The online course’s content and learning activities promote the achievement of the stated learning objectives or competencies.||Fully Met|
|C3. The online course is organized by units and lessons that fall into a logical sequence.||Fully Met|
|C4. The online course content is appropriate to the reading level of the intended learners.*||Fully Met|
|C5. The online course design includes introductory assignments or activities to engage learners within the first week of the course.||Fully Met|
|C6. The online course provides learners with multiple learning paths as appropriate, based on learner needs, that engage learners in a variety of ways.||Fully Met|
|C7. The online course provides regular opportunities for learner-learner interaction.||Fully Met|
|C8. The online course design provides opportunities for learner-instructor interaction, including opportunities for regular feedback about learner progress.*||Fully Met|
|C9. Online course instructional materials and resources present content in an effective, engaging, and appropriate manner.*||Fully Met|
|D1. Learner assessments are linked to stated course, unit, or lesson-level objectives or competencies.||Fully Met|
|D2. Valid course assessments measure learner progress toward mastery of content.||Fully Met|
|D3. Assessment practices provide routine and varied opportunities for self-monitoring and reflection of learning.*||Fully Met|
|D4. Assessment materials provide the learner with the flexibility to demonstrate mastery in a variety of ways.*||Fully Met|
|D5. Rubrics that clearly define expectations for varied levels of proficiency are created and shared with learners.*||Fully Met|
|E1. Online course navigation is logical, consistent, and efficient from the learner’s point of view.*||Fully Met|
|E2. The online course design facilitates readability.*||Fully Met|
|E3. The online course provides accessible course materials and activities to meet the needs of diverse learners.*||Fully Met|
|E4. Course multimedia facilitate ease of use.*||Fully Met|
|E5. Vendor accessibility statements are provided for all technologies required in the course.*||Fully Met|
|F1. Educational tools ensure learner privacy and maintain confidentiality of learner information in accordance with local, state, and national laws for learner data.||Fully Met|
|F2. The online course tools support the learning objectives or competencies.*||Fully Met|
|F3. The online course provides options for the instructor to adapt learning activities to accommodate learners’ needs and preferences.*||Fully Met|
|F4. The course allows instructors to control the release of content.*||Fully Met|
|F5. The course provides the necessary technical functionality to score and record assessments and calculate earned course points or grades.*||Fully Met|
|G1. The online course uses multiple methods and sources of input for assessing course effectiveness.||Fully Met|
|G2. The online course is reviewed to ensure that the course is current.||Fully Met|
|G3. The online course is updated on a continuous improvement cycle for effectiveness based on the findings from ongoing reviews.||Fully Met|
Review Conducted By: Quality Matters
Date of Review: 10/23/2020
Unit 1: Fundamentals and Functions
Unit 2: Define Trigonometric Functions and Angles
Unit 3: Applying Trigonometric Functions
Unit 4: Radian Measures
Unit 5: Graphing Trigonometric Functions
Unit 6: Trigonometric Identities
Unit 7: Inverse Trigonometric Functions & Solving Equations
Unit 8: Solving Right Triangles
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|
|Drop Policy||Completion Policy||Term Type||Enrollment Opens||Enrollment Ends|
|Enrollments must be dropped one or before the enrollment's drop date to receive a refund.||A completion is considered a final score of 60% or higher.||Year Long||08/16/2021||09/17/2021|
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.
Please review the Michigan Virtual Technology Requirements: https://michiganvirtual.org/about/support/knowledge-base/technical-requirements/