Calculus Vectors (MCV4U)

This unit immerses students in problems centered around rates of change and the principle of limits. It includes an exploration of the relationship between secant and tangent lines to a curve, deepening the understanding of limits. Previously, students focused on calculating the slope of a tangent at a specific point; this unit expands their skills to finding functions for tangent slopes, paralleling the concept with secant slopes. A key part of the unit is learning to sketch the graph of a derivative function.

This unit guides students through diverse problem-solving scenarios using derivatives. They will tackle individual problem types, encompassing scenarios like Pythagorean Theorem applications, including classic ladder and intersection problems. The unit also covers Volume Problems, where students explore scenarios involving the filling or emptying of three-dimensional shapes. Additionally, Through Problems, Shadow Problems, and a variety of General Rate Problems are integral parts of this unit's curriculum.

This foundational unit of the course addresses four major topics. It begins with an introductory overview of vectors and scalars, laying the groundwork for further study. Following this, the unit progresses to a detailed exploration of vector properties. Next, students will engage with various vector operations, gaining practical skills in their application. The unit culminates with an in-depth look into the properties of plane figures, integrating vector concepts into geometric contexts.

This unit begins by guiding students in formulating vector, parametric, and symmetric equations for lines in both two and three dimensions (R2 and R3). It then progresses to the study of vector, parametric, symmetric, and scalar equations for planes in three-dimensional space. A key part of the curriculum involves understanding how lines intersect in three-dimensional space and how a line intersects with a plane in the same space.

Students will also develop proficiency in solving intersections of two or three planes by setting up and solving linear equations systems with three variables. The unit further delves into matrix-related concepts, including matrix operations like addition, subtraction, and multiplication. Students will learn to solve linear equation systems with up to three variables using row reduction methods, both manually and with technological tools. The unit concludes by interpreting row reductions as the formulation of new linear systems equivalent to the original ones, encapsulating the final topics of this comprehensive unit.

Final Exam (30%): 3 hours

This proctored assessment, lasting three hours, marks the conclusion of the course. It is a comprehensive evaluation, covering a wide array of course topics and significantly influencing the student's final grade.

• Scanner or smartphone camera for uploads.
• Laptop/PC (Chrome or Firefox recommended).
• Video recording and scanning device (e.g., phone, tablet, webcam).
• Stable internet.
• Non-programmable scientific calculator.

• Google Suites or Microsoft Education for word processing and presentations (student accounts provided).
• Supplemental Reading materials.
• Tutorial and Solution Videos via Screencast.
• Access to educational platforms: Gizmos, Labster, Mathletics, GeoGebra, Padlet (student accounts provided).