Grade 12 Calculus and Vectors University Preparation MCV4U Course Outline
Department: Math | Course Developer: Canada Online School | Credit value: 1.0 | Credit Hours: 110
Development Date: April 2018 | Revision Date: N/A
Ministry Document: Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007
Prerequisite(s): MHF4U (can be taken concurrently)
This course 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.
|Unit Title||Expected Hours||Final Grade Weighting|
|Limits and Rates of Change||13||70% – Grades and the curriculum strands evaluated are cumulative across the entire term. Specific mark weightings may sometimes be adjusted at teacher’s discretion to better reflect cumulative learning. Learning must be achieved and then retained.|
|Applications of Derivatives||12|
|Derivatives of Exponential and Trigonometric Functions||16|
|Introduction to Vectors||12|
|Applications of Vectors||10|
|Points, Lines and Planes||20|
|Final Assessment||3||30% – An exam which covers all course learning.|
Teaching & Learning Strategies
Students will explore mathematical concepts through theoretical frameworks and follow specific examples. They will practice abstract math questions and solve complex problems that require the use of these concepts or apply the theory to a real-world application. They will complete exercises and review against correct solutions. They will do assignments, quizzes, and tests.
Textbooks and other required resources
- Nelson Calculus and Vectors ISBN: 9780176374440 (provided by COS)
- Graphing paper and a non-programmable scientific calculator
- An Internet connection and a device with basic web browsing capabilities (see System Requirements in Course Calendar) and scanning function to upload handwritten work (or a high resolution camera with good lighting)
Assessment & Evaluation
Assessment & evaluation is based on the Ministry of Education’s Growing Success (click to access) guidelines. Students are evaluated on:
|Four Achievement Categories
· Knowledge & Understanding (KU)
· Thinking & Inquiry (TI)
· Communication (C)
· Application (A)
These are incorporated in every assessment as part of each curriculum strand.
| Curriculum Strands
· Rate of Change
· Derivatives and their Applications
· Geometry and Algebra of Vectors
These are the areas of learning that students will be evaluated against Ontario curriculum standards.
|Six Learning Skills/Work Habits
· Independent Work
These are assessed and reported separately from curriculum expectations.
Strands and Overall Expectations
Rate of Change
- 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.
Derivatives and their Applications
- 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.
Geometry and Algebra of Vectors
- 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.
Special Program Planning Considerations
COS develops its programs with consideration for Ontario Ministry of Education policies and initiatives. Many areas of special consideration are embedded naturally within course content. These include but are not limited to the following:
- Students with special education needs: Our courses and teachers will strive to equitably accommodate exceptional students with support and/or modified expectations they may need as per their Individual Education Plan (IEP). The modified expectations or support may take the form of altered assignments, differently formatted tests/exams, the use of special technological tools, etc. Special education accommodations are only implemented to provide fair treatment to students who have a demonstrated and documented need.
- English language learners: COS has strategies in place to support students who are learning English as a second language. Teachers are made aware which students are in or were in ESL programs and will make appropriate accommodations or provide resources to help them gain more proficiency.
- Environmental protection: Whenever possible, issues in environmental protection are highlighted, provided as extra interest topics, or used as examples during courses.
- Healthy Relationships: Every student is entitled to a safe environment based on mutual respect. Our courses use online discussions, case studies, role play, etc, to encourage cooperation and constructive comments. Students also learn about building healthy relationships through course content that highlights inclusive values.
- Equity and inclusive education: Diversity is valued at COS and we encourage students to share their unique life experiences and perspective while respecting others’ different values or viewpoints. Learning activities and the curriculum reflect the multicultural nature of Canada and the importance of equitable and inclusive treatment of all others.
- Financial literacy: Students must learn to make informed financial decisions and understand economic forces to be effective members of society. COS and the Ministry are working to embed financial literacy skills and knowledge in courses as appropriate.
- Critical thinking, literacy, numeracy and inquiry: Literacy is more than reading and writing. Its definition is constantly evolving and by today’s standard increasingly needs more sophisticated skills. It is the entire set of skills that allow a person to critically comprehend, analyze, generate and process information in all its forms, and then communicate it meaningfully to others. Every subject is responsible for enhancing students’ literacy, including mathematical literacy (numeracy). Students learn to inquiry deeply and think critically at all times, use relevant terminology, and conduct their own research. They will form opinions backed by logical evidence, detect bias, uncover implied meanings, and take big picture perspectives. With numeracy, students learn to not only perform mathematical operations but also understand their significance, application, and hidden biases.
- School library: A library provides access to resources and also allows students to develop skills in research. COS does not have a library in the conventional sense but we do provide information to students on how to access information they need, find useful texts or other media, and use electronic tools of research. In general, this information is made publicly available through our website.
- Information and communications technology (ICT): By use the COS online learning platform, students will naturally develop transferable skills relating to ICT. Students will learn to use various electronic tools to communicate, cooperate, and conduct research. Students will also be made aware of pitfalls and potential abuse in using the Internet or other electronic tools.
- The Ontario Skills Passport: This is a free bilingual web-based resource to help students understand what are Essential Skills needed for success in school, work, and life. We encourage students to review their learning and see how they develop such skills. For more information, visit http://www.skills.edu.gov.on.ca.
- Education and career/life planning: As students progress through their courses, they will be provided opportunities to learn about future opportunities and how to make career choices. Teachers are available to guide students through their planning and COS provides resources for students to research these opportunities on their own, using the Individual Pathways Plan process.
- Cooperative education and experiential learning: COS does not have a co-op program but we recognize the value of experiential learning and will direct students to information regarding Ministry programs and opportunities when needed.
- Ethics: As part of the process of forming opinions and thinking critically, students will learn to develop their sense of ethics as it relates to both society and private decision making. As an academic institution, COS also requires students to understand ethical conduct in their academic work. Students learn about the consequences of plagiarism both dishonest and negligent, as well as the accepted conventions for citing the work of others properly.