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MCV4U - Grade 12 Calculus and Vectors
1.1 - Rationalizing Radical Expressions
Rationalizing One Term Radicals Overview (video)
Rationalizing One Term Radicals Example (video)
Rationalizing Two Term Radicals Overview (video)
Rationalizing Two Term Radicals Example (video)
Extra Rationalizing Expressions Examples (video)
1.2 - Slope of a Tangent
Slope of Tangent Overview (video)
Slope of Tangent Example 1 (video)
Slope of Tangent Example 2 (video)
Slope of Tangent Example 3 (video)
Slope of Tangent Example 4 (video)
Slope of Tangent Example 5 (video)
Slope of Tangent Example 6 (video)
Slope of Tangent Example 7 (video)
Slope of Tangent Example 8 (video)
Slope of Tangent Example 9 (video)
Where is Tangent Parallel to Secant Line? (video)
Slope of Tangent with Third Root Function (video)
Find Equation of Tangent Using Diff Quotient - Rational (video)
Find Equation of Tangent Using Diff Quotient - Radical (video)
1.3 - Rates of Change
Rate of Change Overview (video)
Rate of Change Example 1 (video)
Rate of Change Example 2 (video)
Rate of Change Example 3 (video)
Rate of Change Example 4 (video)
Rate of Change Example 5 (video)
Rate of Change Example 6 (video)
Rate of Change Example 7 (video)
1.4 - The Limit Of A Function
Limit of a Function Overview (video)
Limit of a Function Example 1 (video)
Limit of a Function Example 2 (video)
Limit of a Function Example 3 (video)
Limit of a Function Example 4 (video)
Drawing a Function given Limits 1 (video)
Drawing a Function given Limits 2 (video)
1.5 - Properties Of Limits
Properties of Limits Overview (video)
Properties of Limits Example 1 (video)
Properties of Limits Example 2 (video)
Solving Limits - Direct Substitution (video)
Solving Limits - Factoring (video)
Solving Limits - Factoring Example 1 (video)
Solving Limits - Factoring Example 2 (video)
Solving Limits - Factoring Example 3 (video)
Solving Limits - Factoring Example 4 (video)
Solving Limits - Factoring Example 5 (video)
Solving Limits - Rationalization Example 1 (video)
Solving Limits - Rationalization Example 2 (video)
Solving Limits - Rationalization Example 3 (video)
Solving Limits - Algebraic Manipulation Example 1 (video)
Solving Limits - Algebraic Manipulation Example 2 (video)
Solving Limits - Change of Variable Overview (video)
Solving Limits - Change of Variable Example 1 (video)
Solving Limits - Change of Variable Example 2 (video)
Solving Limits - Change of Variable Example 3 (video)
Solving Limits - Change of Variable Example 4 (video)
Solving Limits - Change of Variable Example 5 (video) (4:31)
Solving Limits - Change of Variable Example 6 (video)
Solving Limits - Change of Variable Example 7 (video)
Solving Limits - One Sided Limits Overview (video)
Solving Limits - One Sided Limits Example 1 (video)
Solving Limits - One Sided Limits Example 2 (video)
Solving Limits - One Sided Limits Example 3 (video)
Solving Limits - One Sided Limits Example 4 (video)
Solving Limits - One Sided Limits Example 5 (video)
Solving Limits - One Sided Limits Example 6 (video)
Rationalization + Factoring Limit Example 1 (video)
Rationalization + Factoring Limit Example 2 (video)
Rationalization vs Change of Variable (video)
Limit with Factoring and Trig Identities (video)
Student Sent Unique Limit Questions (written)
Limit with Absolute Value + Diff of Cubes (video)
Limit with an Absolute Value Function (video)
Different Methods for the Same Limit (video)
Find Constants so Limit Exists (video)
Double Rationalization Limit 1 (video)
Double Rationalization Limit 2 (video)
Tough Thinking Problem Involving Limits (video)
Limits Worksheet 1
Questions (pdf)
Written Solutions (pdf)
Limits Worksheet 2
Questions and Solutions (jpg)
1.6 - Continuity
Continuity Conditions and Overview (video)
Continuity Example 1 (video)
Continuity Example 2 (video)
Types of Discontinuity (video)
Find Constant so Piecewise Function Limit Exists (video)
Find Where Function is Discontinuous from Graph (video)
Explain in Detail Why Function is Continuous (video)
Explain in Detail Why Function is Discontinuous (video)
Continuity Definition Example Part 1 (video)
Continuity Definition Example Part 2 (video)
Continuity Definition Example Part 3 (video)
Properties of Limits and Continuity Example 1 (video)
Properties of Limits and Continuity Example 2 (video)
Find Two Constants to Make Function Continuous (video)
When is a Function is Discontinuous?? (video)
How to make a function continuous??? (video)
Find Relationship Between Constants for Continuity (video)
Some Tough Questions
Tough Limit Example 1 (video) (4:51)
Tough Limit Example 2 (video) (10:35)
One Sided Limit within Continuity Question (video) (7:45)
Unit 1 (Introduction to Calculus) - Mock Test 1
Test 1 Questions (pdf)
Test 1 Solutions (pdf)
Knowledge Section Video Solutions
Application Section Video Solutions
Communication Section Video Solutions (9:59)
Thinking Section Video Solutions
Unit 1 (Introduction to Calculus) - Mock Test 2
Questions (pdf)
Solutions (pdf)
Knowledge Section Video Solutions
Application Section Video Solutions
Communication Section Video Solutions
Thinking Section Video Solutions
Unit 1 (Introduction to Calculus) - Mock Test 3
Mock Test 3 Questions - MCV4U Chapter 1 (pdf)
Mock Test 3 Solutions - MCV4U Chapter 1 (pdf)
Unit 1 (Introduction to Calculus) - Mock Test 4
Mock Test 4 Questions - MCV4U Chapter 1 (pdf)
Mock Test 4 Solutions - MCV4U Chapter 1 (pdf)
Unit 1 (Introduction to Calculus) - Mock Test 5
Mock Test 5 Questions - MCV4U Chapter 1 (pdf)
Mock Test 5 Solutions - MCV4U Chapter 1 (pdf)
2.1 - The Derivative Function
The Definition of a Derivative Overview (video)
The Derivative of a Rational Function (video)
Equation of a Tangent on a Radical Function (video)
Equation of a Normal on a Polynomial Function (video)
Finding a Limit using the Derivative Definition (video)
Derivative Definition of Complex Function 1 (video)
Alternative Derivative Definition of Complex Function 1 (video)
Derivative Definition of Complex Function 2 (video)
Alternative Derivative Definition of Complex Function 2 (video)
Derivative Definition of Complex Function 3 (video)
Alternative Derivative Definition of Complex Function 3 (video)
State Function given Derivative Limit Part 1 (video)
State Function given Derivative Limit Part 2 (video)
State Function given Derivative Limit Part 3 (video)
Differentiability - When does a Limit Exist? (video)
Non-Differentiability Case 1 (Corner)
Non-Differentiability Case 2 (Cusp)
Non-Differentiability Case 3 (Vertical Tangent)
Non-Differentiability Case 4 (Asymptote)
Non-Differentiability Case 5 (Point Discontinuity Part 1)
Non-Differentiability Case 6 (Point Discontinuity Part 2)
Non-Differentiability Case 7 (Jump Discontinuity)
Non-Differentiability Case 8 (Continuous Piecewise Function)
Show a Function is Differentiable at a Point (video)
Show a Function is Not Differentiable at a Point (video)
2.2 - The Derivatives Of Polynomial Functions
The Power Rule for Derivatives Overview (video)
The Power Rule for Derivatives Example 1 (video)
The Power Rule for Derivatives Example 2 (video)
Proving Tangents are Perpendicular (video)
Equation of Tangent using Power Rule (video)
Where is a Tangent parallel to a Line? (video)
Equation of a Tangent through Coordinate (video)
Solve for Constants given Tangent Information (video)
2.3 - The Product Rule
Product Rule of Derivatives Overview (video)
Finding the Equation of a Tangent using Product Rule (video)
Finding Horizontal Tangents using Product Rule (video)
Product Rule of Derivatives Example (video)
Power of a Function Rule for Derivatives Overview (video)
Combining the Product and Power of a Function Rule (video)
Rate of Change using Derivatives of Water Leak Example (video)
Finding Constants given Tangent and Coordinate (video)
Product Rule of Derivatives using Constants (video)
Proving Line is Tangent to a Function (video)
2.4 - The Quotient Rule
The Quotient Rule for Derivatives (video)
Finding Tangent that is Horizontal and Parallel to Line (video)
Proving Tangent is always Positive using Quotient Rule (video)
Find Constants given Horizontal Tangent using Quotient Rule (video)
Conditions on Constants for Tangent to be Positive (video)
Find Location of Horizontal Asymptote (video)
Find Tangent Perpendicular to Line with Quotient Rule (video)
2.5 - The Derivatives of Composite Functions
Chain Rule for Derivatives Overview (including Leibniz notation) - (video)
Using Quotient Rule within Chain Rule to find Derivative (video)
Using Chain Rule within Product Rule to find Derivative (video)
Where Two Functions Have same Slope of Tangent (video)
Tricky Question finding Derivative using Chain Rule (video)
Finding Derivative using Leibniz Notation Chain Rule (video)
Student Sent Chain Rule Example (written)
Chain Rule for Complex Function 1 (video)
Chain Rule with Complex Function 2 (video)
Chain Rule with Complex Function 3 (video)
Chain Rule Thinking Problem 1 (video)
Chain Rule Thinking Problem 2 (video)
Chain Rule Thinking Problem 3 (video)
Chain Rule Thinking Problem 4 (video)
Chain Rule Thinking Problem 5 (video)
Chain Rule Thinking Problem 6 (video)
Chain Rule Thinking Problem 7 (video)
Chain Rule Thinking Problem 8 (video)
Show Same Tangent at Two Different Points (video)
Chain Rule with 3 Variables (video)
Chain Rule of Composite Function (video)
Unit 2 (Derivatives) - Mock Test 1
Questions (pdf)
Solutions (pdf)
Knowledge Section Video Solutions
Application Section Video Solutions
Communication Section Video Solutions (2:05)
Thinking Section Video Solutions
Unit 2 (Derivatives) - Mock Test 2
Questions (pdf)
Solutions (pdf)
Knowledge Section Video Solutions
Application Section Video Solutions
Communication Section Video Solutions
Thinking Section Video Solutions
Unit 2 (Derivatives) - Mock Test 3
Mock Test 3 Questions - MCV4U Chapter 2 (pdf)
Mock Test 3 Solutions - MCV4U Chapter 2 (pdf)
Unit 2 (Derivatives) - Mock Test 4
Mock Test 4 Questions - MCV4U Chapter 2 (pdf)
Mock Test 4 Solutions - MCV4U Chapter 2 (pdf)
Unit 2 (Derivatives) - Mock Test 5
Mock Test 5 Questions - MCV4U Chapter 2 (pdf)
Mock Test 5 Solutions - MCV4U Chapter 2 (pdf)
Chapter 3 - Applications of Derivatives ($40)
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Chapter 4 - Curve Sketching ($40)
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Chapter 5 - Exponential and Trigonometric Derivatives ($40)
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6.1 - Introduction to Vectors
Definition of a Vector (video)
Scalar vs Vector (video)
Opposite Vectors (video)
Equal Vectors (video)
Example 1 (video)
Example 2 (video)
6.2 - Vector Addition
Overview - Triangle and Parallelogram Law of Addition (video)
Example 1 (video)
Example 2 (video)
Example 3 (video)
6.3 - Multiplication of a Vector by a Scalar
Effects of Scalar on Vector (video)
Collinear Vectors (video)
Unit Vectors (video)
Resultant Vector Example (video)
Scalar Multiplication Example (video)
6.4 - Properties of Vectors
Associative Property of Vector Addition and Proof (video)
Distributive Property of Vector Addition and Proof (video)
Commutative Law of Vector Addition (video)
Distributive and Associative Law for Scalars and Proof (video)
Simplifying Expressions with Vector Addition Laws (video)
Vector Laws of Addition (video)
Vector Algebra (video)
Tough Vector Proof Example (video)
6.5 - Drawing Vectors
Drawing Vectors in r^3 (video)
Vector Component Algebra Example (video)
6.8 - Span of Vectors
Span of Vectors Part 1 (video)
Span of Vectors Part 2 - Coplanar Vectors (video)
Span of Vectors Part 3 - Coplanar Points (video)
Finding Constants with Coplanar Points (video)
Finding Constants with Coplanar Vectors (video)
Unit 6 Mock Test 1
Questions (pdf)
Solutions (pdf)
Knowledge Section Video Solutions
Application Section Video Solutions
Thinking Section Video Solutions
Communication Section Video Solutions (7:04)
7.1 - Force
Force Overview Part 1 (video)
Force Overview Part 2 (video)
Horizontal and Vertical Components of Force (video)
Force of Hanging Object given Angles (video)
Force of Hanging Object given Sides (video)
Force of Object Sliding Down a Ramp (video)
7.2 - Velocity
Finding Resultant Velocity Given Plane and Wind Velocity (video)
Find Resultant Velocity and Distance Travelled (video)
Find the Direction of a Plane's Velocity (video)
Find Wind Velocity given Plane and Ground Velocity (video)
Find Airspeed and Direction Example (video)
Swimming and Current Velocity Example 1 (video)
Swimming and Current Velocity Example 2 (video)
Swimming and Current Velocity Example 3 (video)
7.3 and 7.4 - The Dot Product
Find the Dot Product (video)
Find Angle with Dot Product (video)
Find Dot Product of Two Vectors in Tricky Scenarios (video)
Dot Product Proof 1 (video)
Dot Product Proof 2 (video)
Dot Product Proof 3 (video)
Dot Product Proof 4 (video)
Dot Product Proof 5 (video)
Dot Product and Collinear Vectors (video)
Constants with Collinear vs Perpendicular Vectors (video)
Unit 7 (Application of Vectors) - Mock Test 1
Application of Vectors Test 1 Questions (pdf)
Application of Vectors Test 1 Solutions (pdf)
Knowledge Question 1 Solution (video)
Knowledge Question 2 Solution (video)
Knowledge Question 3 Solution (video)
Knowledge Question 4 Solution (video)
Application Question 1 Solution (video)
Application Question 2 Solution (video)
Application Question 3 Solution (video)
Application Question 4 Solution (video)
Thinking Question 2 Solution (video)
Thinking Question 3 Solution (video)
Unit 7 (Application of Vectors) - Mock Test 2
Application of Vectors Test 2 Questions (pdf)
Application of Vectors Test 2 Solutions (pdf)
Knowledge Question 3 Solution (video) (3:35)
Knowledge Question 4 Solution (video) (3:34)
Knowledge Question 5 Solution (video) (3:34)
Application Question 1 Solution (video)
Application Question 2 Solution (video)
Application Question 3 Solution (video)
Application Question 4 Solution (video) (4:54)
Application Question 6 Solution (video)
Thinking Question 2 Solution (video)
Thinking Question 3 Solution (video) (1:16)
Thinking Question 4 Solution (video)
Communication Question 3 Solution (video) (3:07)
Lines, Planes and Their Intersections ($40 or FREE with purchase of 3 packages before)
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Non-Differentiability Case 3 (Vertical Tangent)
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