Calculus and Vectors MCV4U-H — Grade 12 Math Lessons | PrepBox

Calculus and Vectors MCV4U-H — Grade 12

Explore Calculus and Vectors MCV4U-H for Grade 12. Follow the chapter and section outline to find available interactive lessons and video explanations. These are independent PrepBox learning resources; PrepBox is not affiliated with the textbook publisher.

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633 topic entries in the outline · 3 interactive entries · 441 video entries. Topics may appear in more than one section.

Chapter 1 Rates of Change

1.1 Rates of Change and the Slope of a Curve

1.2 Rates of Change Using Equations

1.3 Limits

  • Find Limit of a Sequence · Not yet available
  • Evaluate One-Sided Limit by Substitution · Video available
  • Sketch Graph from Limit Conditions · Video available
  • Solve Piecewise Function Word Problems · Not yet available
  • Limits at Infinity · Not yet available
  • Evaluate Specific Term From General Formula · Video available
  • Prove Statement Using Mathematical Induction · Video available
  • Find One-Sided Limit from Continuity Graph · Video available
  • Evaluate One-Sided Limit Numerically · Video available
  • Determine Limit Existence from Both Sides · Video available
  • Evaluate Limit at Infinity (Numerator = Denominator) · Video available
  • Analyze Polynomial Graph Properties · Not yet available
  • One-Sided Limit: Continuity Analysis · Not yet available
  • Prove or Explain Continuity Concepts · Not yet available

1.4 Limits and Continuity

1.5 Introduction to Derivatives

Chapter Limits Review

Rates of Change, Limits and Continuity Chapter Test

Chapter 2 Derivatives

Prerequisite Skills

2.1 Derivative of Polynomial Function

2.2 The Product Rule

2.3 Velocity, Acceleration, and Second Derivatives

2.4 The Chain Rule

2.5 Derivatives of Quotients

2.6 Rate of Change Problems

Derivatives Chapter Review

Derivate Chapter Test

Chapter 3 Curve Sketching

3.1 Increasing and Decreasing Functions

  • Critical Numbers · Not yet available
  • Find Critical Points of Quadratic · Not yet available
  • Find Critical Points of Polynomial · Video available
  • Determine True/False Power Rule Concepts · Not yet available

3.2 Maxima and Minima

  • Sketch Polynomial Curve Fully · Video available
  • Solve Polynomial Modelling Word Problems · Video available
  • Find Critical Points of Quadratic · Not yet available
  • Find Critical Points of Polynomial · Video available
  • Optimize Maximum Area or Perimeter · Not yet available
  • Find Critical Numbers of Algebraic Functions · Video available
  • Optimize Volume/Surface Area Problems · Not yet available

3.3 Concavity and the Second Derivative Test

3.4 Simple Rational Functions

3.5 Putting It All Together

3.6 Optimization Problems

Chapter Review Graphing and Optimization

Chapter Test Max and Min

Chapter 4 Derivatives of Sinusodial Functions

4.1 Instantaneous Rates of Change of Sinusodal Functions

4.2 Derivatives of the Sine and Cosine Functions

  • Evaluate Determinate Trig Limit · Video available
  • Differentiate Primary Trig Functions · Video available
  • Find Tangent Line of Trig Function · Not yet available
  • Find Trig Derivative by Limit Definition · Not yet available
  • Trig Limit: Tangent Line · Not yet available
  • Trig Limit: Behavior Analysis · Not yet available
  • Find nth Derivative of a Trigonometric Function · Video available

4.3 Differentiation Rules for Sinusodal Functions

  • Differentiate Primary Trig Functions · Video available
  • Differentiate Trig Power Using Chain Rule · Not yet available
  • Differentiate Trig Product Using Product Rule · Video available
  • Differentiate Power of Trig Function · Video available
  • Differentiate Reciprocal Trig Functions · Not yet available
  • Find Trig Derivative by Limit Definition · Not yet available
  • Differentiate sin(ax+b) and cos(ax+b) · Not yet available
  • Differentiate sin^n(x) and cos^n(x) · Not yet available
  • Trig Limit: Behavior Analysis · Not yet available
  • Trig Limit: Basic Evaluation · Not yet available

4.4 Applications of Sinusoidal Functions and Their Derivatives

  • Set Up and Solve Sinusoidal Word Problem · Video available
  • Differential Equations Overview · Not yet available
  • Model with Trig Derivatives · Not yet available
  • Find Trig Derivative by Limit Definition · Not yet available
  • Trig Limit: Basic Evaluation · Not yet available
  • Model Spring/Pendulum Oscillation (Degrees) · Not yet available

4.5 Chapter Review

  • Differentiate Trig Using Chain Rule (Double) · Not yet available
  • Differentiate Primary Trig Functions · Video available
  • Differentiate Trig Power Using Chain Rule · Not yet available
  • Combine Polynomial and Trig Functions · Not yet available
  • Differentiate Trig Product Using Product Rule · Video available
  • Differentiate Power of Trig Function · Video available
  • Model with Trig Derivatives · Not yet available
  • Find Tangent Line of Trig Function · Not yet available
  • Differentiate sin(ax+b) and cos(ax+b) · Not yet available
  • Differentiate Nested Trig Functions · Not yet available
  • Find General Extrema · Not yet available
  • Trig Limit: Tangent Line · Not yet available
  • Trig Limit: Behavior Analysis · Not yet available

4.6 Chapter Test

  • Differentiate Primary Trig Functions · Video available
  • Differentiate Trig Power Using Chain Rule · Not yet available
  • Combine Polynomial and Trig Functions · Not yet available
  • Differentiate Trig Product Using Product Rule · Video available
  • Model with Trig Derivatives · Not yet available
  • Find Trig Derivative by Limit Definition · Not yet available
  • Trig Limit: Tangent Line · Not yet available
  • Trig Limit: Behavior Analysis · Not yet available

Chapter 5 Exponential and Logarithmic Functions

5.1 Rates of Change and the Number e

5.2 The Natural Logarithm

5.3 Derivatives of Exponential Functions

  • Differentiate e^x Functions · Video available
  • Differentiate a^x Exponential Functions · Video available
  • Model with e^x · Video available
  • Differentiate Product of Polynomial and a^x · Not yet available
  • Find Tangent Line to a^x Curve · Not yet available
  • Conceptual Questions about a^x Derivatives · Not yet available

5.4 Differentiation Rules for Exponential Functions

5.5 Making Connections Exponential Models

No named lesson topics are currently listed for this section.

5.6 Chapter Review

5.7 Chapter Test

Chapter 6 Geometric Vectors

6.1 Introduction to Vectors

6.2 Tutorials of Addition and Subtraction of Vectors

6.3 Tutorials of Multiplying a Vector by a Scalar

6.4 Applications of Vector Addition

6.5 Resolution of Vectors Into Rectangular Components

6.6 Chapter Review

Practice Test Sum of Vectors

Chapter 7 Cartesian Vectors

7.1 Cartesian Vectors

7.2 Dot Product

7.3 Applications of the Dot Product

7.4 Vectors in Three-Space

7.5 Cross Product and Its Properties

7.6 Applications of the Dot Product and Cross Product

7.7 Chapter Review

7.8 Chapter Test

Chapter 8 Lines and Planes

8.1 Equations of Lines in Two-Space

8.2 Equation of Planes

8.3 Properties of Planes

8.4 Intersections of Lines in Two-Space and Three-Space

  • Vector Lines Overview · Not yet available
  • Vector Planes Overview · Not yet available
  • Lines and Planes Overview · Not yet available
  • Solve System in Terms of Variable Coefficients · Video available
  • Determine No Solution or Infinite Solutions · Video available
  • Find Properties of a 3D Line in Vector Form · Video available
  • Identify and Name Polygons · Not yet available

8.5 Intersection of Lines and Planes

8.6 Intersections of Planes

  • Find Intersection Line of Two Planes · Video available
  • Three Planes Overview · Not yet available
  • Find Point of Intersection of Three Planes · Video available
  • Determine Relative Orientation of Planes · Not yet available
  • Three Parallel Planes · Not yet available

8.7 Chapter Review

8.8 Chapter Test

8.10 Course Review

No named lesson topics are currently listed for this section.