Ontario Grade 12 Calculus and Vectors (MCV4U) curriculum and lessons

The course map includes Rate of Change, Derivatives and Their Applications, Geometry and Algebra of Vectors. Follow the complete section list above for the full study path.

درس حسابان و بردارها پایه دوازدهم انتاریو (MCV4U) چه مباحثی دارد؟ از جمله مباحث این درس نرخ تغییر، مشتق و کاربردهای آن، هندسه و جبر بردارها است. فهرست کامل بخش‌ها در بالای صفحه قرار دارد.

The 51-topic course map is available now. Written lessons appear here only after they have been reviewed and published. Check the official Ontario curriculum for exact requirements.

درس‌ها و برنامهٔ درسی حسابان و بردارها پایه دوازدهم انتاریو را از کجا پیدا کنم؟ نقشهٔ 51 موضوع این درس در دسترس است. درس‌های نوشتاری پس از بررسی و انتشار در همین صفحه نمایش داده می‌شوند. برای شرایط دقیق به برنامهٔ درسی رسمی انتاریو مراجعه کنید.

Limits, derivatives, rules, and rates of change.

• A1.1 · Interpret rate-of-change applications and representations (written lesson not published)
• A1.2 · Connect secant and tangent slopes with rates (written lesson not published)
• A1.3 · Approximate instantaneous rate with approaching secants (written lesson not published)
• A1.4 · Interpret limits graphically and numerically (written lesson not published)
• A1.5 · Use the difference quotient for rates of change (written lesson not published)
• A1.6 · Compare simplified and unsimplified first-principles derivatives (written lesson not published)
• A2.1 · Use derivative signs to describe intervals (written lesson not published)
• A2.2 · Generate derivative values and graphs (written lesson not published)
• A2.3 · Differentiate polynomial functions from first principles (written lesson not published)
• A2.4 · Relate sine and cosine functions to their derivatives (written lesson not published)
• A2.5 · Investigate derivatives of exponential functions (written lesson not published)
• A2.6 · Identify the special derivative property of e to the x (written lesson not published)
• A2.7 · Connect natural logarithms with the inverse of e to the x (written lesson not published)
• A2.8 · Differentiate exponential functions with any base (written lesson not published)
• A3.1 · Verify the power rule for natural-number exponents (written lesson not published)
• A3.2 · Apply constant, multiple, sum, and difference rules (written lesson not published)
• A3.3 · Differentiate polynomials and solve rate problems (written lesson not published)
• A3.4 · Extend the power rule to rational exponents (written lesson not published)
• A3.5 · Apply product and chain rules to composite functions (written lesson not published)

Curve sketching, motion, modelling, and optimization.

• B1.1 · Sketch a derivative graph from a function graph (written lesson not published)
• B1.2 · Interpret the second derivative as slope change (written lesson not published)
• B1.3 · Connect features of a function and its first two derivatives (written lesson not published)
• B1.4 · Infer possible functions from derivative information (written lesson not published)
• B1.5 · Sketch polynomial curves using derivatives (written lesson not published)
• B2.1 · Model displacement, velocity, and acceleration (written lesson not published)
• B2.2 · Solve applications using derivatives (written lesson not published)
• B2.3 · Solve instantaneous-rate problems (written lesson not published)
• B2.4 · Solve optimization problems (written lesson not published)
• B2.5 · Apply and interpret calculus models (written lesson not published)

Vector operations and equations of lines and planes.

• C1.1 · Interpret vector magnitude, direction, and applications (written lesson not published)
• C1.2 · Represent two-dimensional vectors in Cartesian and polar form (written lesson not published)
• C1.3 · Convert two-dimensional vector representations (written lesson not published)
• C1.4 · Represent points and vectors in three dimensions (written lesson not published)
• C2.1 · Add, subtract, and multiply vectors by scalars (written lesson not published)
• C2.2 · Verify properties of vector operations (written lesson not published)
• C2.3 · Solve applications with vector operations (written lesson not published)
• C2.4 · Calculate and interpret the dot product (written lesson not published)
• C2.5 · Apply properties of the dot product (written lesson not published)
• C2.6 · Calculate and interpret the cross product (written lesson not published)
• C2.7 · Apply properties of the cross product (written lesson not published)
• C2.8 · Solve applications with dot and cross products (written lesson not published)
• C3.1 · Interpret intersections of lines and systems in two dimensions (written lesson not published)
• C3.2 · Interpret intersections of planes and systems in three dimensions (written lesson not published)
• C3.3 · Analyze geometric configurations of lines and planes (written lesson not published)
• C4.1 · Write scalar, vector, and parametric equations of lines in two dimensions (written lesson not published)
• C4.2 · Write vector and parametric equations of lines in three dimensions (written lesson not published)
• C4.3 · Use normal vectors to describe planes (written lesson not published)
• C4.4 · Solve systems representing three planes (written lesson not published)
• C4.5 · Derive scalar, vector, and parametric equations of planes (written lesson not published)
• C4.6 · Convert among equations of lines and planes (written lesson not published)
• C4.7 · Solve line-plane intersection and distance problems (written lesson not published)

Differentiate f(x) = 3x⁴ − 2x² + 5.

Worked method: Apply the power rule term by term: f′(x) = 12x³ − 4x.

For a = (1, 2) and b = (3, 0), find a · b.

Worked method: Multiply corresponding components and add: a · b = 1(3) + 2(0) = 3.

Differentiate y = (2x − 1)³.

Find the magnitude of v = (2, −3, 6).