PREREQUISITE : Note: Advanced Functions, Grade 12, University Preparation, must be taken prior to or concurrently with Calculus and Vectors.
GRADE : 12 (University)
THE ONTARIO CURRICULUM : Mathematics
MCV4U online at Profectus builds on students’ previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in three dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these concepts and skills to the modelling of real-world relationships. In MCV4U online, students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who choose to pursue careers in fields such as science, engineering, economics, and some areas of business, including those students who will be required to take a university-level calculus, linear algebra, or physics course.
UNIT 1 :
Rate of Change (27.5hrs)
Students will be able to:
Demonstrate an understanding of rate of change by making connections between average rate of change over an interval and instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of the limit.
Graph the derivatives of polynomial, sinusoidal, and exponential functions, and make connections between the numeric, graphical, and algebraic representations of a function and its derivative.
Verify graphically and algebraically the rules for determining derivatives; apply these rules to determine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related problems.
UNIT 2 :
Derivatives and Their Applications (27.5hrs)
Students will be able to:
Make connections, graphically and algebraically, between the key features of a function and its first and second derivatives, and use the connections in curve sketching.
Solve problems, including optimization problems, that require the use of the concepts and procedures associated with the derivative, including problems arising from real-world applications and involving the development of mathematical models.
UNIT 3 :
Geometry and Algebra of Vectors (27.5hrs)
Students will be able to:
Demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications.
Perform operations on vectors in two-space and three-space, and use the properties of these operations to solve problems, including those arising from real-world applications.
Distinguish between the geometric representations of a single linear equation or a system of two linear equations in two-space and three-space, and determine different geometric configurations of lines and planes in three-space.
Represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections.
FINAL 30%
Course Culmination (27.5hrs)
The Culminating Unit incorporates all four strands of the Mathematics Curriculum, and covers the four achievement chart categories. It consists of two parts:
Culminating Project worth 15% and a
Final Exam worth 15%
Online Course Policies
Listed below are various mandatory policies as you take on this course.
Attendance is regularly tracked through student contributions to online discussion boards, assignment completion, and learning logs. Failure to complete allocated activities may challenge the student’s ability to attain the credit.
This course will be presented using an asynchronistic model whereby work will be posted on the Google Classroom and it is the student’s responsibility to complete it on their own time.
ALL portions of this course are intended to be learned and completed online.
Final Exams and Tests will be written on site at Profectus Academy of Toronto. Course instructors will relay this information to students and families.
The integrity of student work will be checked on an ongoing basis using Quetext or Turnitin. Plagiarism is not tolerated.
Assessment & Evaluation Policies
The primary purpose of assessment and evaluation is to improve student learning. The Achievement Chart for Mathematics will guide all assessment and evaluation.
Knowledge and Understanding
17.5%
Thinking
17.5%
Communication
17.5%
Application
17.5%
The final grade will be determined as follows:
70% based on Assessment OF Learning (including conversations, observations and products) conducted throughout the course.
30% based on Culminating Tasks administered at or towards the end of the course.
Assessment and evaluation is divided into two important parts. The grade the student receives on a midterm or final report indicates achievement/ proficiency in Curriculum Expectations. A level of competence (Needs Improvement, Satisfactory, Good or Excellent) will be assessed and reported in the area of Learning Skills and Work Habits: Independent Work, Collaboration, Responsibility, Initiative, Self-Regulation, and Organization.
