Welcome to Grade 12 Calculus & Vectors! This on-demand course was put together especially for Grade 12 Calculus & Vectors at Ontario High School. Use the video lessons and notes to understand your lecture topics better, and the practice questions to cement your knowledge. And don't hesitate to leave a question in the Q&A box under each lesson if you need additional help with anything. Happy studying!
Grade 12 Calculus & Vectors
Ontario High School
Course Overview
Lessons & Practice
I. Welcome
2 min1. Review
46min2. Rate of Change & Limits
3hr- 2.I. Chapter Expectations
2.1.1. The Slope of Tangent Lines13 min2.1.2. Example: Drawing Tangent Lines8 min2.1.3. Example: Calculating Slopes of Tangents9 min2.1.4. Practice: Calculating Slopes of Tangents8 min2.1.5. Example: Equation of the Tangent Line5 min2.1.6. Practice: Equation of the Tangent Lines5 min2.1.7. Example: Slope of Tangent Line *(Tricky)7 min2.1.8. Practice: Slope of Tangent Line5 min
2.3.1. Definition of Limits7 min2.3.2. Example: Limits From Graphs9 min2.3.3. Limits Properties & Direct Substitution4 min2.3.4. Example: Evaluating Limits5 min2.3.5. Practice: Evaluating Limits42 sec2.3.6. Practice: Evaluating Limits3 min2.3.7. Example: Evaluating Limits (*Tricky*)3 min2.3.8. Practice: Evaluating Limits2 min2.3.9. Infinite Limits5 min2.3.10. Limits at Infinity3 min
2.9.1. Continuity6 min2.9.2. Example: Discontinuity8 min2.9.3. Practice: Discontinuity From Graphs2 min2.9.4. Example: Continuity of Piecewise Functions4 min2.9.5. Example: Continuity of Piecewise Functions3 min2.9.6. Practice: Continuity of Piecewise Functions3 min2.9.7. Practice: Continuous Functions4 min
3. Derivatives of Polynomials
3hr- 3.I. Chapter Expectations
3.1.1. Intro to Derivatives10 min3.1.2. Example: Differentiability4 min3.1.3. Example: Derivative of a Function at a Point5 min3.1.4. Practice: Derivative of a Function of a Point2 min3.1.5. Example: Derivative of a Function4 min3.1.6. Practice: Equation of Tangent Line3 min3.1.7. Example: Derivatives & Their Graphs4 min3.1.8. Practice: Derivatives & Their Graphs2 min3.1.9. Practice: Definition of Derivatives2 min
3.2.1. Derivative Rules for Polynomials4 min3.2.2. Example: Derivative Rules (Level 1)5 min3.2.3. Practice: Derivative Rules (Level 1)2 min3.2.4. Example: Derivative Rules (Level 2)5 min3.2.5. Practice: Derivative Rules (Level 2)5 min3.2.6. Example: Derivative Rules (Level 3)5 min3.2.7. Practice: Derivative Rule (Level 3)4 min3.2.8. Practice: Derivatives3 min3.2.9. Example: Horizontal Tangents2 min3.2.10. Practice: Normal Line5 min3.2.11. Practice: Tangent Lines6 min3.2.12. Example: Derivative of Piecewise Functions4 min
3.3.1. Product Rule & Power of a Function Rule6 min3.3.2. Practice: Product Rule3 min3.3.3. Practice: Power of a Function Rule2 min3.3.4. Example: Product & Power of a Function Rule3 min3.3.5. Practice: Product & Power of a Function Rule3 min3.3.6. Example: Product & Power of a Function Rule Application7 min3.3.7. Practice: Product & Power of a Function Rule Application4 min3.3.8. Example: Product Rule & Rational Functions2 min3.3.9. Practice: Product Rule & Rational Functions4 min3.3.10. Example: Product Rule for 3 Functions5 min3.3.11. Practice: Product Rule for 3 Functions3 min3.3.12. Practice: Product Rule (*Tricky)6 min
3.5.1. Chain Rule6 min3.5.2. Example: Chain Rule & Product Rule5 min3.5.3. Practice: Chain Rule & Quotient Rule4 min3.5.4. Example: Chain Rule & Leibniz Notation3 min3.5.5. Practice: Chain Rule & Leibniz Notation3 min3.5.6. Example: Multiple Chain Rules9 min3.5.7. Practice: Multiple Chain Rules5 min3.5.8. Example: Chain Rule (*Tricky)2 min3.5.9. Practice: Chain Rule* (*Tricky)6 min
4. Derivative Applications
1.8hr- 4.I. Chapter Expectations
4.1.1. Higher Order Derivatives6 min4.1.2. Practice: Second Derivative6 min4.1.3. Displacement, Velocity, & Acceleration9 min4.1.4. Example: Displacement, Velocity, & Acceleration8 min4.1.5. Example: Displacement, Velocity, & Acceleration Graphs7 min4.1.6. Practice: Displacement, Velocity, & Acceleration9 min
4.3.1. Optimization Problems3 min4.3.2. Example: Optimization (Rectangular Field)6 min4.3.3. Practice: Optimization (Open-topped box)7 min4.3.4. Example: Optimization (Numbers)4.3.5. Practice: Optimization (Parabola)5 min4.3.6. Practice: Optimization (Distance)4 min4.3.7. Example: Optimization (Revenue)8 min4.3.8. Practice: Optimization (Cylinder)5 min
5. Curve Sketching
4hr- 5.I. Chapter Expectations
5.3.1. Vertical Asymptotes4 min5.3.2. Example: Vertical Asymptotes11 min5.3.3. Practice: Vertical Asymptotes2 min5.3.4. Horizontal Asymptotes5 min5.3.5. Example: Horizontal Asymptotes11 min5.3.6. Practice: Horizontal Asymptotes2 min5.3.7. Practice: Vertical & Horizontal Asymptotes5 min5.3.8. Oblique (Slant) Asymptote9 min5.3.9. Practice: Asymptotes6 min5.3.10. Example: Asymptotes2 min
6. Derivatives of Exponential (& Logarithmic) Functions
1.9hr- 6.I. Chapter Expectations
6.2.1. Derivative of Exponential Functions 6 min6.2.2. Practice: Derivative of Exponential Functions 4 min6.2.3. Practice: Derivative of Exponential Functions 3 min6.2.4. Example: Derivative of Exponential Functions Application9 min6.2.5. Practice: Derivative of Exponential Functions Application4 min
6.4.1. Derivative of Exponential Functions 4 min6.4.2. Practice: Derivative of Exponential Functions 3 min6.4.3. Example: Derivative of Exponential Functions 2 min6.4.4. Practice: Derivative of Exponential Functions 5 min6.4.5. Example: Derivative of Exponential Functions Application5 min6.4.6. Example: Derivative of Exponential Functions & Differential Equations5 min
7. Derivative of Trig Functions
1.1hr7.2.1. Derivative of Trigonometric Functions8 min7.2.2. Practice: Derivative of Trigonometric Functions5 min7.2.3. Example: Equation of Tangent Line5 min7.2.4. Practice: Equation of Tangent Line5 min7.2.5. Example: Higher Order Derivative3 min7.2.6. Practice: Higher Order Derivative6 min7.2.7. Practice: Derivative of Trig Functions6 min
8. Vectors
2hr- 8.I. Chapter Expectations2 min
8.1.1. What are Points, Scalars, & Vectors?2 min8.1.2. Practice: Scalar VS Vector?2 min8.1.3. 2D Vectors9 min8.1.4. Practice: 2D Vectors5 min8.1.5. Converting Between Vector Forms7 min8.1.6. Example: Converting Between Vector Forms4 min8.1.7. Practice: Cartesian Polar3 min8.1.8. Practice: Polar Cartesian3 min8.1.9. 3D Vectors3 min
8.3.1. Vector Scalar Multiplication3 min8.3.2. Vector Addition in Cartesian Form4 min8.3.3. Vector Subtraction in Cartesian Form3 min8.3.4. Practice: Vector Operations2 min8.3.5. Practice: Position Vectors3 min8.3.6. Parallelogram Rule3 min8.3.7. Example: Finding Magnitude & Direction5 min8.3.8. Practice: Finding Magnitudes4 min8.3.9. Vector Properties7 min
9. Vector Products
1.3hr10. Equations of Lines & Planes
2hr- 10.I. Chapter Expectations1 min
10.1.1. Intro to Equations of Lines2 min10.1.2. Vector, Parametric & Symmetric Equations in & 8 min10.1.3. Example: Equations of Lines in 10 min10.1.4. Practice: Equation of Lines in 6 min10.1.5. Example: Converting Equations of Lines in 5 min10.1.6. Practice: Converting Equations of Lines in & 5 min10.1.7. Example: Points on Lines in 4 min10.1.8. Cartesian (Scalar) & Normal Equations in 3 min10.1.9. Example: Equations of Lines in 9 min10.1.10. Practice: Equations of Lines in 5 min10.1.11. Practice: Converting Equations of Lines in 6 min10.1.12. Angle Between Lines7 min
10.2.1. Intro to Equations of Planes in 3 min10.2.2. Vector & Parametric Equations of Planes in 2 min10.2.3. Example: Equations of Planes in 8 min10.2.4. Practice: Equations of Planes in 3 min10.2.5. Example: Equations of Planes in 6 min10.2.6. Cartesian (Scalar) & Normal Equations of Planes in 2 min10.2.7. Example: Equations of Planes in 11 min10.2.8. Example: Equations of Planes in 4 min10.2.9. Practice: Equations of Planes in 2 min10.2.10. Practice: Converting Equations of Planes in 7 min10.2.11. Angle Between Two Planes4 min
11. Intersections of Lines & Planes
2.5hr11.1.1. Intersection of 2 Lines in & 7 min11.1.2. Example: Intersection of Lines5 min11.1.3. Practice: Intersection of Lines6 min11.1.4. Example: Intersection of Identical Lines3 min11.1.5. Example: Intersection of Parallel Lines3 min11.1.6. Example: Intersection of Skewed Lines5 min11.1.7. Practice: Intersection of lines3 min11.1.8. Practice: Intersection of lines8 min
11.3.1. Intersection of 2 Planes5 min11.3.2. Example: Intersection of 2 Parallel Planes3 min11.3.3. Practice: Intersection of 2 Parallel Planes2 min11.3.4. Example: Intersection of 2 Coincident Planes2 min11.3.5. Practice: Intersection of 2 Coincient Planes3 min11.3.6. Example: Intersection of 2 Planes (free choice for parameter)5 min11.3.7. Example: Intersection of 2 Planes (no choice for parameter)5 min11.3.8. Practice: Intersection of 2 Planes4 min11.3.9. Practice: Intersection of 2 Planes5 min
11.4.1. Intersection of 3 Planes7 min11.4.2. Example: Intersection of 3 Planes (p.o.i. = point)5 min11.4.3. Example: Intersection of 3 Planes (p.o.i. = line)5 min11.4.4. Example: Intersection of 3 Planes (p.o.i. = line)7 min11.4.5. Example: Intersection of 3 Planes (p.o.i. = plane)4 min11.4.6. Practice: Intersection of 3 Planes12 min11.4.7. Example: Intersection of 3 Planes (no p.o.i.)3 min11.4.8. Example: Intersection of 3 Planes (no p.o.i.)2 min11.4.9. Example: Intersection of 3 Planes (no p.o.i.)4 min11.4.10. Practice: Intersection of 3 Planes7 min
12. Distance Between Lines & Planes
49minGrade 12 Calculus & Vectors Overview
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Course Notes
Wizeprep's course notes with hundreds of easy-to-understand explanations, diagrams, and practice problems.
Course Notes
Wizeprep's course notes with hundreds of easy-to-understand explanations, diagrams, and practice problems.