Calculus and Vectors (MCV 4U)

Course Overview

Course Title: Calculus and Vectors, Grade 12
Course Code: MCV 4U
Grade: 12
Course Type: University
Credit Value: 1.0
Prerequisite: Any Grade 11 University Math course. Please note that: Grade 12 Advanced Functions must be taken prior to or concurrently with Calculus and Vectors. br>Department: Mathematics
Tuition Fee (CAD): $639

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.

Overall Curriculum Expectations

By the end of the course, students will gain proficiency in the following areas:

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.

Unit Overview

Unit 1: Review of Concepts10 hours
Unit 2: Rates of Change15 hours
Unit 3: Derivatives 15 hours
Unit 4: Curve Sketching and Optimization 15 hours
Unit 5: Trigonometric and Exponential Functions20 hours
Unit 6: Geometric and Cartesian Vectors20 hours
Unit 7: Lines and Planes20 hours
Total Hours115 hours
Teaching and Learning Strategies

Enthusiastic teachers and instructors bring unique teaching and assessment methods to the classroom because students learn best when they are engaged in a range of different learning techniques. The activities allow students to apply learned concepts to current world social, economic, and environmental issues which impact daily life. Opportunities to relate knowledge and skills to these wider contexts will motivate students to learn in a meaningful way and to become life-long learners. Instructors also inspire students to become successful problem solvers by investigating, providing alternative reasoning and solutions to problems as well as dedicating time and energy to the tasks at hand.

Effective instructional techniques utilize students’ existing knowledge and by capturing their interest and engaging in meaningful participation. Students will be engaged when they are able to see the correlation between the learned concepts and their ability to apply them to the world around them and in real-life situations. Students will have the chance to learn using a wide range of methods which include self-learning, cooperative learning as well as learning through teacher guidance as well has hands-on experiences. The methods and strategies teachers implement will be tailored to the learning requirements and the individual needs of the students. Teachers will achieve effective instruction in an online environment by using videos, interactive animations and virtual labs and discussion forums and video conferencing/live chat.

Individualized Accommodations for Students

Our methodology for student assessment follows the Growing Success Assessment, Evaluation and Reporting in Ontario Schools First Edition, Covering Grades 1 to 12 (2010) manual published by the Ontario Ministry of Education. Assessment is the process of gathering information that accurately reflects how well a student is achieving the curriculum expectations in a subject or course. Assessment tools are designed to improve student learning which includes descriptive feedback, coaching, observations and self-assessments. In addition, student can be independent and set individual goals, monitor progress against these goals, determine next steps and reflect on their thinking and learning.

For a student with special education needs who requires modified or alternative expectations, assessment and evaluation of his or her achievement will be based on the modified curriculum expectations or alternative expectations outlined in the student’s Individual Education Plan (IEP). Accommodations required to facilitate the student’s learning may be identified by the teacher, however recommendations from a School Board generated in the form of an Individual Education Plan (IEP) should be used, if available. 


For a student with special education needs who requires “accommodations only”, as described in his or her IEP, assessment and evaluation of achievement will be based on the appropriate subject/ grade/course curriculum expectations and the achievement levels outlined in the curriculum documents.

A student’s Individual Education Plan (IEP) describes his or her educational program and any accommodations that may be required. The IEP specifies whether the student requires:
accommodations only; or
modified learning expectations, with the possibility of accommodations;

Assessment accommodations are changes in procedures that enable the student to demonstrate his
or her learning. These may include:
visual supports to clarify verbal instructions, assistive devices, or some form of human support;
alternative methods for the student to demonstrate his or her achievement of expectations (e.g., allowing the student to take tests orally) or the allowance of extra time to complete the assessment;
alternative settings that may be more suitable for the student to demonstrate his or her learning.

If accommodations are required to assess and evaluate student learning, the strategies to be used are outlined in the student’s IEP.
For further details about the different types of accommodations, modified learning expectation and alternative programs please refer to Growing Success Assessment, Evaluation and Reporting in Ontario Schools First Edition, Covering Grades 1 to 12 (2010)

Materials Required

Standard Computer Requirements for all courses:
-Processor speed of 2 GHz or faster
-Memory of 4 GB RAM or greater
-A high speed internet connection with a connection speed of 10 MB/s or better.
-Monitor and video card with 1024×768 or greater resolution
-Keyboard and Mouse is recommended
-Speakers/Headphones