Grade 12 Calculus
Canada High School
Course Overview
Lessons & Practice
I. Welcome
1. Review
46min2. Rate of Change
3hr2.1.1. The Slope of Tangent Lines2.1.2. Example: Drawing Tangent Lines2.1.3. Example: Calculating Slopes of Tangents2.1.4. Practice: Calculating Slopes of Tangents2.1.5. Example: Equation of the Tangent Line2.1.6. Practice: Equation of the Tangent Lines2.1.7. Example: Slope of Tangent Line *(Tricky)2.1.8. Practice: Slope of Tangent Line
2.3.1. Definition of Limits2.3.2. Example: Limits From Graphs2.3.3. Limits Properties & Direct Substitution2.3.4. Example: Evaluating Limits2.3.5. Practice: Evaluating Limits2.3.6. Practice: Evaluating Limits2.3.7. Example: Evaluating Limits (*Tricky*)2.3.8. Practice: Evaluating Limits2.3.9. Infinite Limits2.3.10. Limits at Infinity
3. Derivatives of Polynomials
3hr3.1.1. Intro to Derivatives3.1.2. Example: Differentiability3.1.3. Example: Derivative of a Function at a Point3.1.4. Practice: Derivative of a Function of a Point3.1.5. Example: Derivative of a Function3.1.6. Practice: Equation of Tangent Line3.1.7. Example: Derivatives & Their Graphs3.1.8. Practice: Derivatives & Their Graphs3.1.9. Practice: Definition of Derivatives
3.2.1. Derivative Rules for Polynomials3.2.2. Example: Derivative Rules (Level 1)3.2.3. Practice: Derivative Rules (Level 1)3.2.4. Example: Derivative Rules (Level 2)3.2.5. Practice: Derivative Rules (Level 2)3.2.6. Example: Derivative Rules (Level 3)3.2.7. Practice: Derivative Rule (Level 3)3.2.8. Practice: Derivatives3.2.9. Example: Horizontal Tangents3.2.10. Practice: Normal Line3.2.11. Practice: Tangent Lines3.2.12. Example: Derivative of Piecewise Functions
3.3.1. Product Rule & Power of a Function Rule3.3.2. Practice: Product Rule3.3.3. Practice: Power of a Function Rule3.3.4. Example: Product & Power of a Function Rule3.3.5. Practice: Product & Power of a Function Rule3.3.6. Example: Product & Power of a Function Rule Application3.3.7. Practice: Product & Power of a Function Rule Application3.3.8. Example: Product Rule & Rational Functions3.3.9. Practice: Product Rule & Rational Functions3.3.10. Example: Product Rule for 3 Functions3.3.11. Practice: Product Rule for 3 Functions3.3.12. Practice: Product Rule (*Tricky)
3.5.1. Chain Rule3.5.2. Example: Chain Rule & Product Rule3.5.3. Practice: Chain Rule & Quotient Rule3.5.4. Example: Chain Rule & Leibniz Notation3.5.5. Practice: Chain Rule & Leibniz Notation3.5.6. Example: Multiple Chain Rules3.5.7. Practice: Multiple Chain Rules3.5.8. Example: Chain Rule (*Tricky)3.5.9. Practice: Chain Rule* (*Tricky)
4. Derivative Applications
1.8hr4.3.1. Optimization Problems4.3.2. Example: Optimization (Rectangular Field)4.3.3. Practice: Optimization (Open-topped box)4.3.4. Example: Optimization (Numbers)4.3.5. Practice: Optimization (Parabola)4.3.6. Practice: Optimization (Distance)4.3.7. Example: Optimization (Revenue)4.3.8. Practice: Optimization (Cylinder)
5. Curve Sketching
4hr5.3.1. Vertical Asymptotes5.3.2. Example: Vertical Asymptotes5.3.3. Practice: Vertical Asymptotes5.3.4. Horizontal Asymptotes5.3.5. Example: Horizontal Asymptotes5.3.6. Practice: Horizontal Asymptotes5.3.7. Practice: Vertical & Horizontal Asymptotes5.3.8. Oblique (Slant) Asymptote5.3.9. Practice: Asymptotes5.3.10. Example: Asymptotes
6. Derivatives of Exponential (& Logarithmic) Functions
1.9hr6.4.1. Derivative of Exponential Functions 6.4.2. Practice: Derivative of Exponential Functions 6.4.3. Example: Derivative of Exponential Functions 6.4.4. Practice: Derivative of Exponential Functions 6.4.5. Example: Derivative of Exponential Functions Application6.4.6. Example: Derivative of Exponential Functions & Differential Equations
7. Derivative of Trigonometric Functions
1.1hr7.2.1. Derivative of Trigonometric Functions7.2.2. Practice: Derivative of Trigonometric Functions7.2.3. Example: Equation of Tangent Line7.2.4. Practice: Equation of Tangent Line7.2.5. Example: Higher Order Derivative7.2.6. Practice: Higher Order Derivative7.2.7. Practice: Derivative of Trig Functions
8. Vectors
2hr- 8.I. Chapter Expectations
8.3.1. Vector Scalar Multiplication8.3.2. Vector Addition in Cartesian Form8.3.3. Vector Subtraction in Cartesian Form8.3.4. Practice: Vector Operations8.3.5. Practice: Position Vectors8.3.6. Parallelogram Rule8.3.7. Example: Finding Magnitude & Direction8.3.8. Practice: Finding Magnitudes8.3.9. Vector Properties
9. Vector Products
1.3hr10. Equations of Lines & Planes
2hr- 10.I. Chapter Expectations
10.1.1. Intro to Equations of Lines10.1.2. Vector, Parametric & Symmetric Equations in & 10.1.3. Example: Equations of Lines in 10.1.4. Practice: Equation of Lines in 10.1.5. Example: Converting Equations of Lines in 10.1.6. Practice: Converting Equations of Lines in & 10.1.7. Example: Points on Lines in 10.1.8. Cartesian (Scalar) & Normal Equations in 10.1.9. Example: Equations of Lines in 10.1.10. Practice: Equations of Lines in 10.1.11. Practice: Converting Equations of Lines in 10.1.12. Angle Between Lines
10.2.1. Intro to Equations of Planes in 10.2.2. Vector & Parametric Equations of Planes in 10.2.3. Example: Equations of Planes in 10.2.4. Practice: Equations of Planes in 10.2.5. Example: Equations of Planes in 10.2.6. Cartesian (Scalar) & Normal Equations of Planes in 10.2.7. Example: Equations of Planes in 10.2.8. Example: Equations of Planes in 10.2.9. Practice: Equations of Planes in 10.2.10. Practice: Converting Equations of Planes in 10.2.11. Angle Between Two Planes
11. Intersections of Lines & Planes
2.5hr11.1.1. Intersection of 2 Lines in & 11.1.2. Example: Intersection of Lines11.1.3. Practice: Intersection of Lines11.1.4. Example: Intersection of Identical Lines11.1.5. Example: Intersection of Parallel Lines11.1.6. Example: Intersection of Skewed Lines11.1.7. Practice: Intersection of lines11.1.8. Practice: Intersection of lines
11.3.1. Intersection of 2 Planes11.3.2. Example: Intersection of 2 Parallel Planes11.3.3. Practice: Intersection of 2 Parallel Planes11.3.4. Example: Intersection of 2 Coincident Planes11.3.5. Practice: Intersection of 2 Coincient Planes11.3.6. Example: Intersection of 2 Planes (free choice for parameter)11.3.7. Example: Intersection of 2 Planes (no choice for parameter)11.3.8. Practice: Intersection of 2 Planes11.3.9. Practice: Intersection of 2 Planes
11.4.1. Intersection of 3 Planes11.4.2. Example: Intersection of 3 Planes (p.o.i. = point)11.4.3. Example: Intersection of 3 Planes (p.o.i. = line)11.4.4. Example: Intersection of 3 Planes (p.o.i. = line)11.4.5. Example: Intersection of 3 Planes (p.o.i. = plane)11.4.6. Practice: Intersection of 3 Planes11.4.7. Example: Intersection of 3 Planes (no p.o.i.)11.4.8. Example: Intersection of 3 Planes (no p.o.i.)11.4.9. Example: Intersection of 3 Planes (no p.o.i.)11.4.10. Practice: Intersection of 3 Planes
12. Distance Between Lines & Planes
49minI Welcome
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Welcome to Calculus & Vectors!
My name is Jess and I'm the instructor for this course.
Feel free to go through this course at your own pace
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Recommended Study Schedule (Each day is ~40-60 minutes)
Chapter 1 - Review
- Day 1 - Allow yourself about a day to complete this review chapter
Chapter 2 - Rate of Change & Limits
- Day 2 - 2.1 The Slope of Tangent Lines
- Day 2 - 2.1 The Slope of Tangent Lines
- Day 4 - 2.2 Rates of Change
- Day 5 - 2.3 Limits
- Day 6 - 2.4 to 2.6 (Evaluating limits of the form by factoring and simplifying radicals)
- Day 7 - 2.7 to 2.8 (Evaluating limits of the form by simplifying absolute values and substitution)
- Day 8 - Continuity
Chapter 3 - Derivatives of Polynomials
- Day 9 - 3.1 Intro to Derivatives & Differentiability
- Day 10 - 3.2 Derivative Rules
- Day 11 - 3.2 Derivative Rules
- Day 12 - 3.3 Product Rule
- Day 13 - 3.3 Product Rule
- Day 14 - 3.4 Quotient Rule
- Day 15 - 3.5 Chain Rule
- Day 16 - 3.5 Chain Rule
Chapter 4 - Derivative Application
- Day 17 - 4.1 HIgher Order Derivative
- Day 18 - 4.2 Max & Min on a Closed Interval
- Day 19 - 4.3 Optimization Problems
- Day 20 - 4.3 Optimization Problems
Chapter 5 - Curve Sketching
- Day 21 - 5.1 Increasing & Decreasing Intervals
- Day 22 - 5.2 Critical Points & Local Max/Min
- Day 23 - 5.3 Inflection Points & Concavity
- Day 24 - 5.4 Asymptotes
- Day 25 - 5.5 Curve Sketching
Chapter 6 - Derivative of Exponential & Logarithmic Functions
- Day 26 - 6.1 & 6.2 Review and Derivative of Exponential Functions
- Day 27 - 6.3 & 6.4 Review and Derivative of Exponential Functions
- Day 28 - 6.5 Optimization Problems
Chapter 7: Derivative of Trig Functions
- Day 29 - 7.1 & 7.2 Review and Derivative of Trig Functions
- Day 30 - 7.3 Optimization Problems
Chapter 8: Vectors
- Day 31 - 8.1 Introduction to Vectors
- Day 32 - 8.2 Magnitude of a Vector + 8.3 Vector Operations
- Day 33 - 8.4 Vector Application
Chapter 9: Vector Products
- Day 34 - 9.1 & 9.2 Dot Product and Applications
- Day 35 - 9.3 & 9.4 Cross Product and Applications
Chapter 10 - Equations of Lines & Planes
- Day 36 - 10.1 Equations of a Line in R2 & R3 (10.1.1 - 10.1.7)
- Day 37 - 10.1 Equations of a Line in R2 & R3 (10.1.8 - 10.1.12)
- Day 38 - 10.2 Equations of Planes in R3 (10.2.1 - 10.2.5)
- Day 39 - 10.2 Equations of Planes in R3 (10.2.6 - 10.2.11)
Chapter 11 - Intersection of Lines & Planes
- Day 40 - 11.1 Intersection of 2 Lines
- Day 41 - 11.2 Intersection of a Line & Plane
- Day 42 - 11.3 Intersection of 2 Planes
- Day 43 - 11.4 Intersection of 3 Planes
Chapter 12 - Distance Between Lines & Planes
- Day 44 - 12.1 Distance from a Point to a Line in and 12.2 Distance from a Point to a Plane in
- Day 45 - 12.3 Distance from a Point to a Line in