# Honors Precalculus (A)

## Course Description:

This course is a rigorous and challenging preparation for AP Calculus AB. Topics covered include matrices, vectors, conic sections, limits, polar coordinates, and difference quotients. The focus is problem solving techniques and real world applications.

## Course Details:

Course Title (District): Honors Precalculus (A)
Course Title (NCES SCED) : Pre-Calculus
Course Provider : Novi Community School District
Content Provided By : Novi Community School District
Online Instructor Provided By : Novi Community School District
NCES SCED Code :
 Subject Area : Mathematics Course Identifier : Pre-Calculus Course Level : High School (Secondary) Available Credit : 0.5 Sequence : 1 of 2

## How To Enroll:

Email : [email protected] 248-675-3159

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.

• (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. 5.
•  (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.
• Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems
• (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).
• (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
• (+) Solve problems involving velocity and other quantities that can be represented by vectors.
• (+) Add and subtract vectors.
• a. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
• b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
• c. 5. Understand vector subtraction v– w as v + (–w), where–w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
•  (+) Multiply a vector by a scalar.
• a. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx , vy ) = (cvx , cvy ).
• b. Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
• (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
• (+) Add, subtract, and multiply matrices of appropriate dimensions.
• (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
• Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context
• Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
• Graph the solutions to a linear inequality in two variables as a half plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
• Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

#### 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
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: Novi Community School District
Date of Review: 05/26/2022

• Unit 1:  Linear & Quadratic Functions
• Unit 2:  Polynomials
• Unit 3:  Rational Functions
• Unit 4:  Exponential and Logarithmic Functions
• Unit 5:  Trigonometry
• Unit 6:  Analytic Trigonometry
• Unit 7:  Vectors
• Unit 8:  Conic Sections
• Unit 9:  Parametric & Polar Equations
• Unit 10:  Systems
• Unit 11:  Matrices
• Unit 12:  Series & Sequences
• Unit 13:  Introduction to Calculus
Term Type Enrollment Opens Enrollment Ends Random Draw Date Enrollment Drop Date Course Starts Course Ends # of Seats Course Fee Potential Additional Costs
Semester 09/05/2023 09/30/2023 09/05/2023 01/26/2024 30 \$0
Drop Policy Completion Policy Term Type Enrollment Opens Enrollment Ends
Per District Policy Per District Policy Semester 09/05/2023 09/30/2023
Instructor will provide daily, live instruction and also a mix of independent and on demand learning options, in a structured, virtual classroom setting. Students are expected to regularly check school email, reply accordingly, and schedule meetings with instructors, as needed, during on demand time.

Students will need the following:

• A Chromebook (or similar device) with camera and microphone enabled