Calculus and Vectors (MCV4U1)

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 modeling 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:

A student’s final report card grade will be based on the evidence provided of these overall curriculum expectations:

Process Expectations

• Students will be actively engaged in the following seven processes which are integrated into all areas of the course: problem solving, reasoning and proving, reflecting, connecting, representing, selecting tools and computational strategies, and communicating.

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, which 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.

YOUR REPORT CARD GRADE WILL BE DETERMINED AS FOLLOWS:

ACADEMIC STANDARDS:

It is your responsibility to provide evidence of your learning within established timelines. Due dates for assignments and the scheduling of tests will be communicated well in advance to allow you to schedule your time. If you aren’t going to be able to follow an agreed upon timeline, you should demonstrate your responsibility and organizational skills by discussing with your teacher the challenges you’re facing as far in advance of the deadline as possible.

It is your responsibility to be academically honest in all aspects of your schoolwork so that the marks you receive are a true reflection of your achievement. Plagiarism is using the words, ideas or work of someone else without giving appropriate credit to the original creator. This is a form of cheating.

Consequences for not meeting these academic standards may include:

· Reporting the issue to your parents;

· Requiring you to complete the original or alternative work after school or during your lunch hour;

· Requiring you to complete an alternative assignment;

· Suspension;

· Assigning a “zero” for an assignment not completed prior to an agreed upon closure date;

· Mark deduction of 5% / day.

NOTE: The complete HDSB policies and administrative procedures for Lates and Missed Assignments and Cheating and

Plagiarism policies may be found at www.hdsb.ca

LEARNING SKILLS & WORK HABITS:

These learning skills and work habits will be taught, assessed and evaluated throughout the course.

UNITS OF STUDY:

REQUIRED MATERIALS:

Students will require the following materials and should bring them to class everyday.

· Scientific Calculator

· 3 Ring Binder

· Lined Paper

· Graph Paper

· Pencil

· Ruler

· Highlighter

NOTE: You are encouraged to use a non-graphing scientific calculator during class and while doing homework, as you are not

permitted to use a graphing calculator, cell phone, MP3 player, or tablet during Quizzes, Tests, the Summative, or the Final

Exam.

ATTENDANCE:

All absences should be accompanied by a note from you parent/guardian on the day you return to school. You must notify your teacher in advance of any planned absences. You are responsible for any work missed during your absence.

It is the expectation of the Halton District School Board that students will attend school on scheduled school days and take holidays according to the school year calendar. In the event that parents choose to take their child(ren) out of school at times other than school holidays, the onus lies with them to provide program. Teachers cannot provide detailed daily homework assignments that replicate the missed school work.