G12 Calculus and Vectors
Course Description
The Calculus and Vectors course is designed to prepare students for university programs, such as science, engineering, and economics that include a calculus or linear algebra course in the first year. 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.
Calculus is introduced in the Rate of Change strand by extending the numeric and graphical representation of rates of change introduced in the Advanced Functions course to include more abstract algebraic representations. The Derivatives and Their Applications strand provides students with the opportunity to develop the algebraic and problem-solving skills needed to solve problems associated with rates of change. Prior knowledge of geometry and trigonometry is used in the Geometry and Algebra of Vectors strand to develop vector concepts that can be used to solve interesting problems, including those arising from real-world applications.
Overall Curriculum Expectations
By the end of this course, students will:
A. Rate of Change
| A1 | 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; |
| A2 | 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; |
| A3 | 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. |
B. Derivatives and Applications
| B1 | 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; |
| B2 | 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
| C1 | demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications; |
| C2 | 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; |
| C3 | 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; |
| C4 | represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections. |
Course Content
| Unit | Title | Hours |
|---|---|---|
| Unit1 | Rates of Change • Radical Expressions • The slope of the Tangent • Rates of change • The limit of a function • Properties of limits • ContinuityDerivatives of Sinusoidal Functions • The Derivative function • The derivatives of Polynomial function • The product rule • The quotient rule • The derivatives of composite functionsExponential and Logarithmic Functions • Higher-order derivatives • Maximum and minimum on an interval • Optimization problems |
39 hours |
| Unit2 | Derivatives
Curve Sketching
|
28 hours |
| Unit3 | Geometric Vectors
Cartesian Vectors
Lines and Planes
|
43 hours |
| Total | 110 hrs |
Strategies actually used in the classroom are indicated in the chart above and reflected in classroom instruction
- Assessment for learning (AFL) is diagnostic and formative for the purposes of greater learning achievement and is used at the beginning of a unit to help determine a starting point for instruction.
- Assessment as learning (AAL) is assessment as a process of developing and supporting students’ active participation in their own learning.
- Assessment of learning (AOL) is assessment for purposes of providing evidence of achievement for reporting. It is conducted at the end of each learning unit/work section and provides students with the opportunity to synthesize/apply/demonstrate their learning and their achievement of the stated expectations.
There are four levels of achievement for students who are passing the course:
- Level 1 (50-59%)
- Level 2 (60-69%)
- Level 3 (70-79%)
- Level 4 (80-100%)
Level 3 is the provincial standard for student achievement.
The final grade will include the following weighting:
| Knowledge | Thinking/Inquiry | Communication | Application |
|---|---|---|---|
| 12.5 | 25 | 25 | 25 |
| Understanding | |||
| 12.5 |
Seventy percent (70%) of the grade will be based on evaluation conducted throughout the course. Final evaluation will take into account the student’s most recent and most consistent performance.
Thirty percent (30%) of the grade will be based on a final evaluation consisting of the final examination and the independent study unit, which will take into account the entire course, including the student’s most recent and most consistent performance.
Proctoring
- The tests are typically a paper-pen evaluation written at a mutually agreed time, date, and location. The tests will be proctored, meaning a suitable adult with a dedicated identifiable and authentic email address will supervise you writing the tests. This process ensures the security and integrity of the test. Any person related or affiliated to the student in a personal way cannot serve as a test supervisor.
Resources required by the student
- A non-programmable, non-graphing, scientific calculator
- A scanner, smart phone camera, or similar device to upload handwritten or hand-drawn work
- A front-facing camera on a desktop, laptop, or mobile device to allow for proctoring over the internet
- Internet access and a modern standards-compliant web browser
The tuition for this course is $800 for Canadian students and $2000 for international students.
Refunds
Maple Leaf School does not issue refunds. When a student enrolls in our course, MLS administration team undertakes many tasks including establishing electronic/physical files, assigning teachers and tracking the enrolment for Ministry purposes, etc. The work is completed by our school the moment you register online.
Course Curriculum
| Resources | |||
| Course Outline | 00:00:00 | ||
| Hour Breakdown | 00:00:00 | ||
| Mark Breakdown | 00:00:00 | ||
| Unit 1 | |||
| U1L1 | 00:00:00 | ||
| U1L2 | 00:00:00 | ||
| U1L3 | 00:00:00 | ||
| U1L4 | 00:00:00 | ||
| U1L5 | 00:00:00 | ||
| Unit 2 | |||
| U2L1 | 00:00:00 | ||
| U2L2 | 00:00:00 | ||
| U2L3 | 00:00:00 | ||
| Unit 3 | |||
| U3L1 | 00:00:00 | ||
| U3L2 | 00:00:00 | ||
| U3L3 | 00:00:00 | ||
| Unit 4 | |||
| U4L1 | 00:00:00 | ||
| U4L2 | 00:00:00 | ||
| U4L3 | 00:00:00 | ||
| Unit 5 | |||
| U5L1 | 00:00:00 | ||
| U5L2 | 00:00:00 | ||
| U5L3 | 00:00:00 | ||
| U5L4 | 00:00:00 | ||
| U5L5 | 00:00:00 | ||
| U5L6 | 00:00:00 | ||
| Unit 6 | |||
| U6L1 | 00:00:00 | ||
| U6L2 | 00:00:00 | ||
| Final Exam | |||
| How to request | 00:00:00 | ||
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MCV4U
This course gave me an in-depth understanding of the knowledge and application of calculus