MCV4U Calculus and Vectors
©2011 Iulia & Teodoru Gugoiu
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Course Notes Worksheets with Solutions and Practice Tests
Chapter 1 Introduction to Calculus: Limits

Radical Expressions: Rationalizing Denominators
Notes 2010 | Handout | PowerPointShow

 

The Slope of Tangent Line
Notes 2009 | Notes 2010 | Handout | PowerPointShow

 

Rate of Change
Notes 2009 | Notes 2010 | Handout | PowerPointShow

Limits 10 Limits 11

Mid-Chapter Review

Quiz 1 Limits with Solutions

The Limit of a Function
Notes 2009 | Notes 2010 | Handout | PowerPointShow

Limits 06 Limits 08

Properties of Limits
Notes 2009 | Notes 2010 | Handout | PowerPointShow

Limits 01 Limits 02 Limits 03
Limits 04 Limits 05 Limits 06 Limits 08

Continuity
Notes 2009 | Notes 2010 | Handout | PowerPointShow

Limits 07 Limits 09

Chapter 1 Review

Winter 2009 T1 V1
Winter 2009 T1 V2
Summer 2009 T1
Winter 2010 T1 V1
Winter 2010 T1 V2
Summer 2010 T1 V1
Summer 2010 T1 V2

Chapter 2 Derivative Rules

Derivative Function. First Principle
Notes 2009 | Notes 2010 | Handout | PowerPointShow

First Principle

Power Rule. Derivative of Polynomial Functions
Notes 2009 | Notes 2010 | Handout | PowerPointShow

Power Rule
Power, Sum/Difference Rules
Derivatives of Polynomial Functions
Piecewise Defined Functions
Power Functions
Functions Defined by a Graph
Power Functions (II)

Product Rule
Notes 2009 | Notes 2010 | Handout | PowerPointShow

Product Rule

Mid-Chapter Review

Quiz 2 Derivative Rules with Solutions

Quotient Rule
Notes 2009 | Notes 2010 | Handout | PowerPointShow

Quotient Rule

Chain Rule
Notes 2009 | Notes 2010 | Handout | PowerPointShow

Chain Rule (I)
Chain Rule (II)
Chain Rule (III)
Chain Rule (IV)
Chain Rule (V)
Chain Rule (VI)

Tangent and Normal Line

Tangent Line (I)
Tangent Line (II)
Tangent Line (III)
Tangent Line (IV)
Tangent Line (V)
Tangent Line (VI)
Tangent Line (VII)
Normal Line

Chapter 2 Review

Winter 2009 T2 V1
Winter 2009 T2 V2
Fall 2009 T2
Winter 2010 T2 V1
Summer 2010 T2 V1
Summer 2010 T2 V2

Chapter 3 Applications of Derivatives

Higher Order Derivatives. Velocity and Acceleration
Notes 2009 | Notes 2010 | Handout | PowerPointShow

Higher Derivatives (I)
Higher Derivatives (II)
Higher Derivatives (III)
Velocity and Acceleration (I)
Velocity and Acceleration (II)
Velocity and Acceleration (III)

Minimum and Maximum on an Interval. Global Extrema
Notes 2009 | Notes 2010 | Handout | PowerPointShow


Optimization
Notes 2009 | Notes 2010 | Handout | PowerPointShow


Chapter 4 Applications of Derivatives

Increasing and Decreasing Functions
Notes 2009 | Notes 2010 | Handout | PowerPointShow


Critical Points. Local Extrema
Notes 2009 | Notes 2010 | Handout | PowerPointShow


Asymptotes
Notes 2009 | [Notes 2010 | Handout | PowerPointShow


Mid Chapter Review


Concavity and Points of Inflection
Notes 2009 | [Notes 2010 | Handout | PowerPointShow


Curve Sketching
Notes 2009 | [Notes 2010 | Handout | PowerPointShow

Curve Sketching (I)
Curve Sketching (II)

Curve Sketching (III)
Curve Sketching (IV)
Curve Sketching (V)

Chapter 4 Review

Winter 2009 T3 V1
Winter 2009 T3 V2
Fall 2009 T3
Winter 2010 T3 V1
Winter 2010 T3 V2
Summer 2010 T3

Chapter 5 Transcedental Functions and Optimization

Exponential Functions
Notes 2010 | Handout | PowerPointShow

Basic Rules
Sum/Difference Rule
Product Rule
Quotient Rule
Chain Rule (I)
Chain Rule (II)
Chain Rule (III)
Chain Rule (IV)
Higher Derivatives
Velocity and Acceleration
Tangent Lines

Logarithmic Functions
Notes 2010 | Handout | PowerPointShow

Trigonometric Functions
Notes 2010 | Handout | PowerPointShow

Mid-Unit Review

[Quiz 4 v1 Winter 2009] [Solutions]
[Quiz 4 v2 Winter 2009] [Solutions ]

Optimization
Notes 2009 | Notes 2010 | Handout | PowerPointShow


Chapter 5 Review

Test 4 Winter 2009 Version 1
Test 4 Winter 2009 Version 2
Test 4 Fall 2009
Test 4 Winter 2010

Chapter 6 Vectors

An Introduction to Vectors
Notes 2010 | Handout | PowerPointShow


Vector Addition and Subtraction
Notes 2010 | Handout | PowerPointShow


Multiplication of a Vector by a Scalar
Notes 2010 | Handout | PowerPointShow


Properties of Vectors
Notes 2010 | Handout | PowerPointShow


Vectors in R2 and R3
Notes 2010 | Handout | PowerPointShow


Operations with Vectors in R2
Notes 2010 | Handout | PowerPointShow


Operations with Vectors in R3
Notes 2010 | Handout | PowerPointShow


Chapter 6 Review

Test 5 Part 1 Version 1 Winter 2010
Test 5 Part 1 Version 2 Winter 2010
Test 5 Part 1 Fall 2009
Test 5 Winter 2009 Version 1
Test 5 Winter 2009 Version 2
Test 5 Summer 2010

Chapter 7 Applications of Vectors

Vectors as Forces
Notes 2010 | Handout | PowerPointShow



Velocity
Notes 2010 | Handout | PowerPointShow



Dot Product of two Geometric Vectors
Notes 2010 | Handout | PowerPointShow



Dot Product of Algebraic Vectors
Notes 2010 | Handout | PowerPointShow



Scalar and Vector Projections
Notes 2010 | Handout | PowerPointShow



Cross Product of two Vectors
Notes 2010 | Handout | PowerPointShow



Applications of the Dot and Cross Products
Notes 2010 | Handout | PowerPointShow



Chapter 7 Review

Test 5 Part 2 Version 1 Winter 2010
Test 5 Part 2 Version 2 Winter 2010
Test 5 Part 2 Fall 2009
Test 5 Winter 2009 Version 1
Test 5 Winter 2009 Version 2
Test 5 Summer 2010

Chapter 8 Equations of Lines and Planes

Vector and Parametric Equations of a line in R2
Notes 2010 | Handout | PowerPointShow



Cartesian Equation of a Line
Notes 2010 | Handout | PowerPointShow



Vector, Parametric, and Symmetric Equations of a Line in R3
Notes 2010 | Handout | PowerPointShow



Vector and Parametric Equations of a Plane
Notes 2010 | Handout | PowerPointShow


Cartesian Equation of a Plane
Notes 2010 | Handout | PowerPointShow


Review: Lines

Test 6 Lines Winter 2009 Version 1
Test 6 Lines Winter 2009 Version 2
Test 6 Lines Fall Fall 2009
Test 6 Lines Winter 2010
Test 6 Summer 2010

Chapter 9 Relationships betwenn Points, Lines, and Planes

Intersection of two Lines
Notes 2010 | Handout | PowerPointShow



Intersection of a Line with a Plane
Notes 2010 | Handout | PowerPointShow


Intersection of two Planes
Notes 2010 | Handout | PowerPointShow


Intersection of three Planes
Notes 2010 | Handout | PowerPointShow


Distance from a Point to a Line
Notes 2010 | Handout | PowerPointShow



Distance from a Point to a Plane
Notes 2010 | Handout | PowerPointShow


Review: Planes

Test 6 Planes Winter 2009 Version 1
Test 6 Planes Winter 2009 Version 2
Test 6 Planes Fal 2009
Test 6 Planes Winter 2010
Test 6 Summer 2010

Course Evaluation (December 6, 2010)

Final Exam Review

Final Exam Review [pdf]

Answers:
p01 p02 p03 p04 p05_1 p05_2 p06 p07 p08 p09 p10 p11 p12

Resourses Online

1. Paul's Online Math Notes [Algebra] [Calculus I Online] [Calculus I PDF] [Cheat Sheets]
2. Math with MR. LECKIE [PreCalculus] [Calculus]
3. Calculus I [Worksheets]
4. HMC Mathematics Online Tutorial [PreCalculus] [Single Variable Calculus]
5. The Calculus Lifesaver [Video Page]
6. S.O.S. Mathematics [Algebra] [Calculus]
7. Wolfram MathWorld [Online Mathematics Dictionary] [Calculus Dictionary]
8. Calc101.com Automatic Calculus and Algebra Help [Step-by-Step Derivatives]
9. Ask Dr. Math® [Calculus]
10. Purplemath [Algebra]
11. The Math Forum @Drexel [PreCalculus] [Calculus] [Ask Dr. Math] [Math Topics for Calculus]
12. Math Department at Dartmouth [Calculus RealPlayer Movies]
13. Calculus Applets [Go]
14. The UBC Calculus Online [Course Notes]
15. Math Applets for Calculus at SLU [Go]
16. MathCentre [Go]

La Citadelle [From Rate of Change to Derivative]

Graphing Calculators
1. Draw Function Graphs [Online]
2. Winplot [Download] [Video Tutorials]

Other Resources
1. INTUTE [Go]
2. MERLOT [Go]