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Calculus and Vectors

MCV4U-GRADE 12

Course Code:

MCV4U

Subject:

Calculus and Vectors

Course type:

open

Prerequiste:

None

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The course combines the study of rate of

The course combines the study of rate of change, derivatives, and curve sketching with an in-depth look at vectors and their geometric applications

  • Students learn to apply calculus to motion
  • Optimization
  • Modeling problems
  • While exploring vectors in two
  • Three dimensions
The course emphasizes both conceptual understanding and analytical problem-solving

Unit 1: Rates of Change and Limits

Students explore foundational concepts in differential calculus.
Lessons include:

  • Limits and Continuity

  • Average and Instantaneous Rates of Change

  • The Slope of the Tangent

  • Introduction to Derivatives and Notation

Unit 2: Derivatives and Applications

This unit introduces differentiation rules and real-world applications.
Lessons include:

  • · Chain Rule and Product/Quotient Rules

  • Derivatives of Trigonometric and Exponential Functions

  • Higher-Order Derivatives

  • Derivatives in Motion and Business Contexts

Unit 3: Curve Sketching and Optimization

Students apply calculus to graphing and problem-solving
Lessons include:

  • Finding Extrema and Points of Inflection

  • Optimization Problems

  • Analyzing Concavity

  • Complete Curve Sketching Using Calculus

Unit 4: Vectors in Geometry and Algebra

This unit focuses on organizational planning and strategic tools for decision-making.
Lessons include:

  • Geometric and Algebraic Vectors

  • Vector Operations and Equations

  •  The Dot and Cross Product

  •  Equations of Lines and Planes

  • Applications of Vectors in Physics and Geometry

Unit 5: Final Evaluation

Students demonstrate mastery through comprehensive assessments.
Lessons include:

  • Culminating Project (e.g., Real-World Optimization or 3D Vector Model)

  • Final Exam

  • 70% of the final grade is based on coursework, including:

    • Calculus and vector problem sets

    • Application tasks and optimization models

    •  Curve sketching projects and unit quizzes

    • Discussions on motion, rates of change, and 3D space

  • 30% of the final grade is based on final evaluations:

    • 10% Culminating strategic leadership project

    • 20% Final exam on management theory, planning, and leadership practices

All assessments follow Ontario curriculum standards and are designed to build essential analytical, modeling, and theoretical skills required for success in STEM-related postsecondary programs

Industry-Standard Tools

Access to the latest software and hardware used in the technology industry

Expert Faculty

Learn from experienced professionals with industry background

Project-Based Learning

Develop practical skills through hands-on projects and assignments.

Career Support

Guidance for future education and career opportunities

Where Flexibility Meets Academic Excellence

Your Future Starts with the Right High School:
Get the OSSD Advantage for Top University Admissions

At Futures Canadian School, students earn the Ontario Secondary School Diploma (OSSD) through a fully online, Ministry-inspected program designed for success—anywhere in the world. Our flexible format, expert support, and university-prep focus empower students to reach their academic goals on their terms, while meeting the highest standards of Ontario education. Whether you're aiming for top universities in Canada or abroad, we provide a pathway that fits your pace and ambition.

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Frequently Asked Questions

Q) Is the school accredited by the Ministry of Education?
Ans) Yes, Futures Canadian School is fully inspected and accredited by the Ontario Ministry of Education to ensure that we meet the highest standards of academic quality.
Ans) You can reach us by email, phone or through our website to begin your application or speak directly with an admissions counselor.
Ans) We offer over 80 college and college preparatory courses covering fields such as health sciences, business, engineering, design and more.
Ans) Students receive personalized academic advising, tutoring, and regular progress monitoring to help them succeed.
Ans) Yes! We offer comprehensive college application support, including program selection, personal statement writing, and meeting deadlines.

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