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MATHEMATICS Notre Dame Catholic Secondary School Course Code: MCV4U1 Course Name: Calculus and Vectors Level: Grade 12, University Prerequisite: Grade 12 Advanced Functions, MHF4U1, University must be taken prior to or concurrently with Calculus and Vectors. The Ontario Curriculum Grades 11 and 12, 2007 3.0 y 2.0 1.0 -p -p/2 -1.0 -2.0 -3.0 x p/2 p 3p/2 Course Overview: 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. Note: The new Advanced Functions course (MHF4U) must be taken prior to or concurrently with THE OVERALL SPECIFIC EXPECTATIONS INCLUDE: Calculus and VectorsAND (MCV4U). A. RATE OF CHANGE 1. Demonstrate an understanding of rate of change. 2. Graph the derivatives of polynomial, sinusoidal, and exponential functions. 3. Verify graphically and algebraically the rules for determining derivatives. B. DERIVATIVES AND THEIR APPLICATIONS 1. 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; 2. 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. C. GEOMETRY AND ALGEBRA OF VECTORS 1. Demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications; 2. 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; 3. Distinguish between the geometric representations of a single linear equation or a system of two linear equations in two-space and three-space. 4. Represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections. Resources: Course Breakdown Chapter Chapter Chapter Chapter Chapter 1 2 3 4 5 Chapter Chapter Chapter Chapter 6 7 8 9 - Introduction to Calculus Derivatives Derivatives and their Applications Curve Sketching Derivatives of Exponential and Trigonometric Functions - An Introduction to Vectors – Applications on Vectors – Equations of Lines and Planes - Relationships between Points, Lines and Planes The course will use a variety of resources including video, CD-ROM, Internet Applications and a variety of print sources. The Nelson’s textbook, Calculus and Vectors will be distributed to students during the first week of the course. The text and all other resources assigned to students are the responsibility of the student. Any damage incurred will result in payment for replacement. Replacement cost for the text is $100. Evaluation Structure: Knowledge/Understanding 30 % Thinking 20 % Communication 20 % Application 30 % The above is reflected both in the term work (worth 70% of the final mark) and the summative work (worth 30% of the final mark). Summative work consists of a Final Exam (30%) Evaluation Policy Students will be assessed & evaluated according to the work produced & skills displayed. Methods of providing feedback will include assessing work in process & evaluating completed assignments, tests, co-operative learning activities, simulations and presentations. Peer & self-evaluations will also be utilized. Student marks will be determined by evaluating process & product according to 4 categories & 4 levels. Please see the chart below for specific skills and key words used to determine student competency in the different categories. Level Category Knowledge/Understanding Knowledge of facts & terms Understanding of concepts & relationships • • Thinking/Inquiry Critical thinking skills Creative thinking skills Inquiry Skills • • • Communication Communication of ideas and information Use of symbols & visuals Oral & written communication • • • Level 1: 50-59% Level 2: 60-69% Level 3: 70-79% Level 4: 80-100% -Limited display of knowledge, skills and ability to apply concepts -Some success in displaying knowledge, skills and application of concepts -Considerable display of knowledge skills and ability to apply concepts -Thorough understanding of concepts and ability to communicate, think creatively and apply concepts Application Applications in familiar contexts Transfer of concepts to new contexts Making logical conclusions and predictions Use of technology Making connections • • • • • Feedback will also be provided for student learning skills. Skills like working independently, team work, organization, work habits and homework, and initiative are assessed independently student achievement and will be conducted through the use of a rubric indicating specific criteria to be achieved to receive each of the following letter grades: E –Excellent G – Good S – Satisfactory N - Needs Improvement Other Evaluation Issues § § § § LATE ASSIGNMENTS. Assignments submitted after the Primary Due Date established by the teacher will be accepted with a penalty of 5% off for the first day late and 2% for subsequent days to a maximum of 10%. This four day Penalty Zone is the maximum time allowed for submissions. The fourth day after the assignment is due is considered the Closure Date upon which no further assignments will be accepted. If the teacher returns the marked assignments within the four day penalty zone, the date of return is considered the closure date. Repeated lateness in submissions indicates poor organization skills and will result in parental contact and will be reflected in the learning skills section of the report card. INCOMPLETE ASSSIGNMENTS Assignments will be graded according to the extent with which they meet the criteria established in the rubric or evaluation structure. MISSED TESTS Tests missed with a legitimate reason will be written within a few days of the student returning from the absence. Student eligibility to write the test and the date of writing will be at the discretion of the teacher in consultation with the department head. Plagiarism in any form reflects academic dishonesty and will result in a mark of zero for the assignment in question.