Course Title: Grade 12 Calculus and Vectors
Course Code: MCV4U
Course Type: University Preparation
Format: Online School Course
Prerequisite: MCR3U, Functions, Grade 11, University Preparation
Tuition Fee (CAD): $499
Course Description for MCV4U Grade 12 Calculus and Vectors Online Course
Grade 12 Calculus & Vectors (MCV4U) 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. 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.
Summary of Units and Timelines for Grade 12 Calculus and Vectors
Below is the suggested sequence of course unit delivery as well as the recommended number of hours to complete the respective unit. For complete details of targeted expectations within each unit and activity, please see each Unit Overview found in the MCV4U course profile.
|Unit Order||Unit Name||Suggested Time|
|Unit 0||Prerequisite Review||10 hours|
|Unit 1||Rates of Change||15 hours|
|Unit 2||Derivatives||15 hours|
|Unit 3||Curve Sketching and Optimization||15 hours|
|Mid Semester Point|
|Unit 4||Trig & Exponential Functions||20 hours|
|Unit 5||Geometric & Cartesian Vectors||20 hours|
|Unit 6||Lines & Planes||20 hours|
|Final||Course Culminating Activity||5 hours|
Throughout this course, students will:
- Problem Solving – develop, select, apply, compare, and adapt a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding
- Reasoning and Proving – develop and apply reasoning skills (e.g., use of inductive reasoning, deductive
reasoning, and counter-examples; construction of proofs) to make mathematical
conjectures, assess conjectures, and justify conclusions, and plan and construct
organized mathematical arguments;
- Reflecting – demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions)
- Selecting Tools and Computational Strategies – select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems
- Connecting – make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports)
- Representing – create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems
- Communicating – communicate mathematical thinking orally, visually, and in writing, using precise mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions
- Address both what students learn and how well they learn
- Are based both on the categories of knowledge and skills and on the achievement level descriptions given in the achievement chart
- Are varied in nature, administered over a period of time, and designed to provide opportunities for students to demonstrate the full range of their learning
- Are appropriate for the learning activities used, the purposes of instruction, and the needs and experiences of the students
- Are fair to all students
- Accommodate students with special education needs, consistent with the strategies outlined in their Individual Education Plan
- Accommodate the needs of students who are learning the language of instruction
- Ensure that each student is given clear directions for improvement
- Promote students’ ability to assess their own learning and to set specific goals
- Include the use of samples of students’ work that provide evidence of their achievement
- Are communicated clearly to students and parents at the beginning of the school year and at other appropriate points throughout the school year.
The achievement chart for mathematics outlines four categories of knowledge and skills. They include; knowledge and understanding, thinking, communication and application. Teachers will ensure that student work is assessed and/or evaluated in a balanced manner with respect to the four categories, and that achievement of particular expectations is considered within the appropriate categories. A final grade is recorded for this course, and a credit is granted and recorded for this course if the student’s grade is 50% or higher. The final grade for this course will be determined as follows:
- Seventy percent of the grade will be based on evaluations conducted throughout the course. This portion of the grade should reflect the student’s most consistent level of achievement throughout the course, although special consideration should be given to more recent evidence of achievement.
- Thirty percent of the grade will be based on a final evaluation in the form of an examination and administered towards the end of the course.
Examples of accommodations (but not limited to) include:
- Adjustment and or extension of time required to complete assignments or summative tasks
- Providing alternative assignments or summative tasks
- Use of scribes and/or other assistive technologies
- Simplifying the language of instruction
- Erdman, Wayne. McGraw-Hill Ryerson Calculus and Vectors 12. Toronto: McGraw-Hill Ryerson, 2008.
- D’Agostino, Santo. McGraw-Hill Ryerson Calculus & Advanced Functions. [Whitby, Ont.]: McGraw-Hill Ryerson, 2002.
- Calculus.org – The Calculus Page. Web.
Sample Lesson Video: Grade 12 Calculus and Vectors (MCV4U)
Frequently Asked Questions
Co-requisite: MHF4U, Advanced Functions, Grade 12, University Preparation