Calculus and Vectors MCV4U — Grade 12 Math Lessons | PrepBox

Calculus and Vectors MCV4U — Grade 12

Explore Calculus and Vectors MCV4U 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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900 topic entries in the outline · 1 interactive entries · 608 video entries. Topics may appear in more than one section.

Chapter 1 Introduction to Calculus

1.1 Rationalizing Denominators

1.2 The Slope of a Tangent

1.3 Rates of Change

Mid Chapter Review for Rates of Change

1.4 Limit of a Function

1.5 Limits Properties and Laws

1.6 Continuity

Chapter Review Limits and Continuity

Chapter Test

Chapter 2 Derivatives

2.1 The Derivative Function

2.2 The Derivatives of Polynomial Functions

2.3 The Product rule

  • Solve Derivative Conditions (Product) · Not yet available
  • Find Tangent Using Product Rule · Video available
  • Differentiate Product of Chain Powers · Video available
  • Differentiate Absolute Value (Chain Rule) · Not yet available
  • Differentiate deg1/deg1 Using Quotient Rule · Not yet available
  • Differentiate poly*poly Using Product Rule · Video available
  • Differentiate linear*linear Using Product Rule · Video available
  • Differentiate Product with Power (Chain) · Video available
  • Determine Differentiability of Absolute Value · Video available
  • Differentiate Product in Function Notation · Video available
  • Motion: Applied Rates (Volume, Area) · Not yet available
  • Differentiate Product of Three Functions · Not yet available
  • Analyze Derivative Properties · Not yet available

Mid Chapter Review upto Product Rule

2.4 The Quotient Rule

2.5 Chain Rule

Chapter Review Derivative Rules

Chapter Test - Derivatives(Nel)

Chapter 3 Derivatives and their Applications

3.1 High Order Derivatives, Velocities, and Acceleration

3.2 Max and Min on a Interval

Mid Chapter Review Derivative Application

3.3 Optimization Problems

3.4 Optimization in Economics and Science

  • Solve Revenue and Profit Problems · Video available
  • Optimize Maximum Box Volume · Video available
  • Optimize Cost and Revenue · Video available
  • Optimize Volume/Surface Area Problems · Not yet available
  • Optimize Cost/Profit/Business Problems · Not yet available
  • Find General Extrema · Not yet available

Chapter Review Optimization

Chapter Test on Optimization

Chapter 4 Curve Sketching

4.1 Increasing and Decreasing Functions

4.2 Critical Points, Local Maxima, Local Minima

4.3 Vertical and Horizontal Asymptotes

Graphing Mid Chapter Review

4.4 Concavity and Points of Inflection

4.5 An Algorithm for Curve Sketching

Chapter Review Curve Sketching

Chapter Test Graphing

Chapter 5 Derivatives of Exponential and Trigonometric Functions

5.1 Derivatives of Exponential Functions, y=e^x

5.2 Derivative of y =b^x

  • Graph and Interpret Exponential Model · 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
  • Differentiate Quotient with a^x · Not yet available
  • Find Tangent Line to a^x Curve · Not yet available

5.3 Optimization Problems Involving Exponential Functions

  • Simplify Exponent and Log Expressions · Video available
  • Simplify Log Expressions (Exponent Rules and Exponential Form Conversion) · Video available
  • Optimize Maximum Revenue or Profit (Exponential) · Not yet available
  • Find General Extrema · Not yet available

Mid Chapter Review Derivatives of Exponential Functions

5.4 The Derivatives of sinx and cosx

  • Optimize Minimum Distance to Curve · Video available
  • Differentiate Trig Using Chain Rule (Double) · Not yet available
  • Optimize Maximum Area or Perimeter · Not yet available
  • Optimize Area Inside Area · Video available
  • Find Critical Numbers of Trig Functions · Video available
  • Differentiate Primary Trig Functions · Video available
  • Differentiate Trig Power Using Chain Rule · Not yet available
  • Differentiate Trig Product Using Product Rule · Video available
  • Differentiate Trig/Trig Using Quotient Rule · Video available
  • Differentiate Power of Trig Function · Video available
  • Model with Trig Derivatives · Not yet available
  • Differentiate Reciprocal Trig Functions · Not yet available
  • Find Tangent Line of Trig Function · Not yet available
  • Find Trig Derivative by Limit Definition · 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: Basic Evaluation · Not yet available

5.5 Derivative of tan(x)

  • Differentiate Trig Power Using Chain Rule · Not yet available
  • Differentiate Trig Product Using Product Rule · Video available
  • Differentiate Trig/Trig Using Quotient Rule · Video available
  • Find Higher Order Derivatives of Trig · Not yet available
  • Differentiate Reciprocal Trig Functions · Not yet available
  • Find Tangent Line of Trig Function · 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
  • Differentiate Nested Trig Functions · Not yet available
  • Differentiate Trig with Polynomial · Not yet available
  • Find Tangent of Trig Composite · Not yet available
  • Trig Limit: Tangent Line · Not yet available
  • Trig Limit: Basic Evaluation · Not yet available

5.6 Chapter Review Log and Trig Functions

  • Differentiate e^x Functions · Video available
  • Differentiate Trig Using Chain Rule (Double) · Not yet available
  • Optimize Maximum Area or Perimeter · Not yet available
  • Differentiate Simple Power or Constant · Video available
  • Differentiate Primary Trig Functions · Video available
  • Differentiate Trig Power Using Chain Rule · Not yet available
  • Differentiate a^x Exponential Functions · Video available
  • Differentiate Trig Product Using Product Rule · Video available
  • Differentiate Trig/Trig Using Quotient Rule · Video available
  • Differentiate e^f(x) Using Chain Rule · Video available
  • Find Higher Order Derivatives of Trig · Not yet available
  • Differentiate Power of Trig Function · Video available
  • Differentiate Product of Polynomial and e^x · Video available
  • Optimize Maximum Revenue or Profit (Exponential) · Not yet available
  • Second-Order Linear Differential Equations · Video available
  • Optimize Maximum Length (Hallway Problem) · Not yet available
  • Find Tangent Line of Trig Function · Not yet available
  • Differentiate Quotient of e^x · Video available
  • Optimize Area/Perimeter Problems · Not yet available
  • Optimize Volume/Surface Area Problems · Not yet available
  • Find General Extrema · Not yet available
  • Trig Limit: Tangent Line · Not yet available
  • Differentiate a^{f(x)} with Nonlinear Chain Rule · Not yet available
  • Differentiate Quotient with a^x · Not yet available

Chapter Test on Logs and Trig Derivatives

  • Differentiate e^x Functions · Video available
  • Differentiate Trig Using Chain Rule (Double) · Not yet available
  • Differentiate Trig Power Using Chain Rule · Not yet available
  • Differentiate a^x Exponential Functions · Video available
  • Find Higher Order Derivatives of Trig · Not yet available
  • Differentiate Product of Polynomial and e^x · Video available
  • Find AROC of Exponential Functions · Video available
  • Trig Limit: Tangent Line · Not yet available
  • Differentiate a^{f(x)} with Nonlinear Chain Rule · Not yet available
  • Find Tangent Line to a^x Curve · Not yet available

Cumulative Calculus Review

Chapter 6 Introduction to Vectors

6.0 Chapter Pre Req. Review of Trig

6.1 An Introduction to Vectors

6.2 Vector Addition

6.3 Multiplication of a Vector by a Scalar

6.4 Properties of Vectors

Mid Chapter Review

6.5 Vectors in 2D and 3D

6.6 Operations with Algebraic Vectors in 2D

6.7 Operation with Vectors in 3D

6.8 Linear Combination and Spanning Sets

  • Linear Combination and Span · Not yet available

Vectors Chapter Review

Chapter 6 Test

No named lesson topics are currently listed for this section.

Chapter 7 Applications of Vectors

7.1 Vectors as Forces

7.2 Vectors as Velocity

7.3 The Dot Product of Two Geometric Vectors

7.4 The Dot Product of Algebraic Vectors

Mid Chapter Review

7.5 Scalar and Vector Projections

7.6 The Cross Product of Two Vectors

7.7 Applications of Dot and Cross Product

Applications of Vectors Chapter Review

Chapter 8 Equations of Lines and Planes

8.1 Vector and Parametric Equations of a Line in 2D

8.2 Cartesian equation of a Line

8.3 Vector, Parametric and Symmetric Equations of a line in 3D

8.7 Mid Chapter Review

8.4 Vector and Parametric Equations as Plane

8.5 The Cartesian Equation of a Plane

  • Vector Lines Overview · Not yet available
  • Vector Planes Overview · Not yet available
  • Find k for Perpendicular Planes · Not yet available
  • Line in Symmetric Form · Video available
  • Angle Between Two Planes · Video available
  • Plane From Point and Normal Vector · Video available
  • Scalar Equation of Plane From Three Points · Video available
  • Normal Vector From Scalar Plane Equation · Not yet available

8.6 Sketching Planes in 3D

Chapter Review

Chapter Test

No named lesson topics are currently listed for this section.

Chapter 9 Relations between Points, Lines and Planes

9.1 The intersection of a Line with a Plane and the Intersection of Two Lines

9.2 System of Equations

9.3 The Intersection of Two Planes

  • Find Intersection Line of Two Planes · Video available
  • Find Plane Given Two Lines (Advanced) · Not yet available
  • Find Parameter k for Two Planes · Not yet available
  • Find Line Through Point on Two Planes · Not yet available
  • Show Intersection Line Lies in a Third Plane · Not yet available
  • Determine if Two Planes Are Coincident or Parallel · Not yet available
  • Find k for Perpendicular Planes · Not yet available

9.4 The Intersection of Three Planes

  • Find Point of Intersection of Three Planes · Video available
  • Determine Relative Orientation of Planes · Not yet available
  • Three Planes Intersecting in a Line · Video available
  • Find Parameter k for Three Planes · Not yet available
  • Three Parallel Planes · Not yet available
  • Solve Three Planes in Reduced Form · Not yet available
  • Solve Three-Variable Linear System (Reduce to Standard Form) · Not yet available

9.5 The Distance from a Point to a Line in R2

9.6 The Distance from a Point to a Plane

Relations between Points, Lines and Planes Chapter Review

  • Vector Lines Overview · Not yet available
  • Vector Planes Overview · Not yet available
  • Lines and Planes Overview · Not yet available
  • Three Planes Overview · Not yet available
  • Find Intersection of Three or More Equations · Not yet available
  • Solve Three Equations With Three Unknowns · Video available
  • Find Partial Fraction Decomposition (Advanced) · Not yet available
  • Solve Three-Variable Linear System (Reduce to Standard Form) · Not yet available

Relations between Points, Lines and Planes Test

Vectors Cumulative Review

Chapter 10 Appendix

10.1 Implicit Differentiation

10.2 Related Rates

  • Related Rates · Not yet available
  • Solve Related Rates with Similar Triangles · Video available
  • Solve Related Rates with Moving Triangles · Video available
  • Solve Related Rates from Equation · Not yet available
  • Solve Related Rates with Volume/Surface Area · Video available
  • Solve Related Rates with Circular Motion · Video available
  • Related Rates: Distance Between Objects · Not yet available
  • Related Rates: Rectangle/Square Area · Not yet available

10.3 Derivative of Natural Logs

10.4 Derivative of Log Functions

10.5 Derivative of Log or Exponent that Requires Implicit