What MCV4U focuses on

MCV4U builds on students’ previous experience with functions and rates of change. Students study limits, derivatives, applications of derivatives, vectors, and equations of lines and planes in three-dimensional space.

How students apply learning

Students solve problems using algebraic, graphical, geometric, and technological representations while modelling real-world relationships connected to science, engineering, economics, business, and university-level mathematics.

Rates of change and limits

• Connect average rate of change over an interval with instantaneous rate of change at a point.
• Use slopes of secants and tangents to understand the meaning of a derivative.
• Explore limits numerically, graphically, and algebraically.
• Develop the foundation needed for derivative rules and applications.
• Time: 15 Hours

Derivative rules, curve sketching, and optimization

• Graph derivatives and connect functions with their first and second derivatives.
• Apply rules for differentiating polynomial, sinusoidal, exponential, rational, and radical functions.
• Use derivative concepts to identify increasing/decreasing intervals, extrema, concavity, and points of inflection.
• Solve related rates, optimization, modelling, and real-world application problems.
• Time: 35 Hours

Vector representations and operations

• Represent vectors algebraically and geometrically in two-space and three-space.
• Perform vector operations including addition, subtraction, scalar multiplication, and linear combinations.
• Use vector properties to solve problems from geometric and real-world contexts.
• Interpret magnitude, direction, displacement, force, and other vector-based quantities.
• Time: 20 Hours

Three-dimensional vector applications

• Extend vector concepts to three-dimensional coordinate systems.
• Apply dot product and cross product to solve geometric and physical problems.
• Determine angles, projections, areas, and relationships between vectors.
• Use three-dimensional vectors to describe movement, position, direction, and spatial relationships.
• Time: 20 Hours

Lines, planes, intersections, and distances

• Represent lines and planes using vector, parametric, and scalar equations.
• Distinguish between geometric configurations of lines and planes in three-space.
• Solve systems involving lines and planes to determine intersections or parallel relationships.
• Apply equations of lines and planes to distance and spatial reasoning problems.
• Time: 20 Hours

How marks are calculated

• 70% — Course work, tests, quizzes, worksheets, projects, and other evaluations.
• 30% — Final evaluation, culminating task, and examination.
• Achievement Categories: Knowledge & Understanding (20%), Thinking & Inquiry (20%), Application (40%), Communication (20%).

Main course resources

• Advanced Functions 12 – McGraw-Hill Ryerson, 2008
• Advanced Functions – Nelson Education Ltd., 2008
• Teacher-prepared notes, worksheets, solved examples, and assessment materials.
• Selected online mathematics resources and technology-supported learning tools.