MCV4U: Calculus and Vectors (University Preparation)
PREREQUISITE: Advanced Functions course (MHF4U) must be taken prior to or concurrently with Calculus and Vectors (MCV4U)
GRADE: 12 (University)
AVAILABILITY: Spark Asher Academy Online
THE ONTARIO CURRICULUM: Mathematics
Course Overview
MCV4U online is an advanced mathematics course designed to prepare students for university studies in mathematics, physics, engineering, economics, and some areas of business. It builds on students’ previous knowledge of functions and introduces new concepts related to vectors, lines and planes, rates of change, derivatives, and the applications of these concepts in real-world scenarios. This course is essential for students planning to pursue any field that requires a strong foundation in algebra, calculus, or physics. The curriculum, set by the Ministry of Education in Ontario, ensures that the course’s rigor and learning outcomes are consistent, regardless of the mode of delivery.
Course Content and Structure
MCV4U will challenge students to refine their mathematical processes and deepen their understanding through a structured curriculum that covers:
- Vectors
- Lines and Planes
- Rates of Change
- Derivatives
- Curve Sketching
- Derivatives of Exponential and Sinusoidal Functions
UNIT ONE: Vectors
Essential Question: How can mathematics be used to explain orientation in space?
- Students will explore vector quantities and their applications in various fields, particularly physics. They will solve problems involving vector operations both geometrically and algebraically.
UNIT TWO: Lines and Planes
Essential Question: How can two and three-dimensional models be used to imagine solutions to complex problems?
- The study extends to three-dimensional space, where students learn about the representation and intersection of lines and planes, enhancing their spatial reasoning and analytical skills.
UNIT THREE: Rates of Change
Essential Question: How can rates of change found in the real world be modeled using mathematics?
- This unit transitions into calculus, focusing on the concept of rate of change as a fundamental aspect of understanding how variables interact over time.
UNIT FOUR: Derivatives
Essential Question: How can mathematical concepts be used to make sense of real-world problems?
- Students will learn about derivatives, which are crucial for modeling and solving problems involving rates of change. This includes understanding the rules of differentiation and their applications.
UNIT FIVE: Curve Sketching
Essential Question: How can problem-solving tools be used to represent functions visually?
- This unit focuses on graphing functions based on their derivatives to understand behavior, trends, and key characteristics of various functions.
UNIT SIX: Derivatives of Exponential and Sinusoidal Functions
Essential Question: How can derivatives be used to analyze specific functions?
- Students apply their knowledge of derivatives to more complex functions such as exponential and sinusoidal functions, crucial for advanced studies in science and engineering.
Assessment
- 70% Course Work: Ongoing evaluations such as assignments, quizzes, and projects that reflect a student’s consistent performance and understanding throughout the course.
- 30% Final Exam: A comprehensive exam at the end of the course to assess a broad understanding of all topics covered, accounting for 30% of the final grade.
MCV4U prepares students not just for advanced mathematical studies but also equips them with critical analytical skills applicable in various future academic and professional endeavors.
For more details on final exams and the exam fee, please consult to us directly via contact page. Additional information can be found in our download section in courses page.
Ready to get started? Register today!
