Mathematics — Grade 12 University Preparation

∫ MCV4U: Calculus and Vectors

Derivatives, curve sketching, optimization, vectors in 2D/3D, lines and planes

110 hours · 72 video lessons · 9 units · Prerequisite: MHF4U Advanced Functions (concurrent)

Unit 1: Introduction to Calcul Unit 2: Derivatives Unit 3: Derivative Application Unit 4: Curve Sketching Unit 5: Exp. & Trig. Derivativ Unit 6: Introduction to Vector Unit 7: Vector Applications Unit 8: Lines and Planes Unit 9: Intersections

Unit 1: Introduction to Calculus

Limits, slopes of tangents, rates of change, continuity

📚 Strand A: Rate of Change 📹 6 lessons
📹 Video Lessons
📊 Unit 1 Assessments
📖 Calculus 1.1 Rationalizing denominators of radical expressions 9:00 ▶
📖 Calculus 1.2 The slope of a tangent to a curve 22:42 ▶
📖 Calculus 1.3 Rates of Change 12:39 ▶
📖 Calculus 1.4 The Limit of a Function 17:10 ▶
📖 Calculus 1.5 Properties of Limits and 0/0 including u substitution 24:37 ▶
📖 Calculus 1.6 Continuity 13:47 ▶

Unit 2: Derivatives

Derivative rules: power, product, quotient, chain rule

📚 Strand A: Rate of Change 📹 6 lessons
📹 Video Lessons
📊 Unit 2 Assessments
📖 Calculus 2.1 Sketching Derivative Functions 12:35 ▶
📖 Calculus 2.1 The Derivative Function - Derivatives from First Principles 12:34 ▶
📖 Calculus 2.2 Derivatives of Polynomials 24:21 ▶
📖 Calculus 2.3 The product rule 16:02 ▶
📖 Calculus and Vectors 2.4 The Quotient Rule (THE EASIEST WAY TO REMEMBER IT!) 13:49 ▶
📖 Calculus and Vectors 2.5 The Derivatives of Composite Functions 16:40 ▶
📖 Implicit Differentiation Explained — Product Rule, Quotient & Chain Rule — The Organic Chemistry Tutor 18:15 ▶
📖 Higher Order Derivatives — The Organic Chemistry Tutor 8:03 ▶

Unit 3: Derivative Applications

Velocity, acceleration, optimization problems

📚 Strand B: Derivatives & Applications 📹 10 lessons
📹 Video Lessons
📊 Unit 3 Assessments
📖 Calculus 3.1 Velocity and Acceleration Part 1 17:53 ▶
📖 Calculus 3.1 Velocity and Acceleration Part 2 10:26 ▶
📖 Calculus 3.2 Maximum and Minimum on an Interval 8:00 ▶
📖 Calculus 3.3 Optimization Problems Part 1 25:28 ▶
📖 Calculus 3.3 Optimization Problems Part 2 24:58 ▶
📖 Calculus 3.3 Optimization Part 3 24:33 ▶
📖 Calculus 3.3 Optimization problem 13 page 146 12:57 ▶
📖 Calculus and Vectors 3.4 Economics and Science Optimization Problems 28:15 ▶
📋 Calculus Chapter 3 Optimization practice test Part 1 18:20 ▶
📋 Calculus Chapter 3 Optimization Practice Test Part 3 11:58 ▶
📖 Introduction to Related Rates — The Organic Chemistry Tutor 12:08 ▶

Unit 4: Curve Sketching

Increasing/decreasing, critical points, concavity, asymptotes

📚 Strand B: Derivatives & Applications 📹 10 lessons
📹 Video Lessons
📊 Unit 4 Assessments
📖 Calculus 4.1 Increasing and Decreasing Functions 28:49 ▶
📖 Calculus 4.1 Continued 16:36 ▶
📝 Calculus 4.1 Homework questions p 171 # 10 and # 12 9:51 ▶
📋 Calculus 4.2 Critical Points, First Derivative Test 34:00 ▶
📖 Calculus 4.3 Vertical and Horizontal Asymptotes (Obliques too!) 27:55 ▶
📖 Calculus 4.3 Sketching a Rational Function with an Oblique or Slant Asymptote 18:38 ▶
📋 Calculus 4.4 Concavity, Points of Inflection and the 2nd Derivative Test 36:42 ▶
📝 Calculus 4.4 Concavity and Points of Inflection homework questions 35:07 ▶
📖 Calculus 4.5 An Algorithm for Curve Sketching 18:57 ▶
📋 Calculus Chapter 4 Practice Test 41:52 ▶

Unit 5: Exp. & Trig. Derivatives

Derivatives of exponential, sine, cosine, tangent functions

📚 Strand A: Rate of Change 📹 7 lessons
📹 Video Lessons
📊 Unit 5 Assessments
📖 Calculus 5.1 Derivatives of Exponential Functions y = e^x 25:59 ▶
📖 Calculus 5.2 The Derivative of y = b^x 20:27 ▶
📖 Logarithmic Functions Differentiation — Derivative of ln x and log_b x — Khan Academy 8:39 ▶
📖 Calculus 5.3 Optimization Problems using exponential functions 32:58 ▶
📖 Calculus 5.4 Derivatives of Sine and Cosine Functions 24:00 ▶
📖 Calculus 5.4 Extreme Values on an Interval P 257 # 6 a, b, c 19:20 ▶
📖 Calculus 5.5 Derivatives of Tangent and Cotangent Functions 12:50 ▶
📋 Calculus chapter 5 Practice Test 41:38 ▶
📖 Logarithmic Differentiation Formula — The Organic Chemistry Tutor 11:21 ▶
📖 Logarithmic Differentiation of Exponential Functions — The Organic Chemistry Tutor 40:13 ▶
📖 Sinusoidal Models — Daily Temperature Word Problem — Khan Academy 5:42 ▶
📖 Sinusoidal Word Problems — Tides & Periodic Functions — Khan Academy 7:55 ▶

Unit 6: Introduction to Vectors

Vector representation, operations, R2 and R3, spanning sets

📚 Strand C: Vectors 📹 9 lessons
📹 Video Lessons
📊 Unit 6 Assessments
📖 Vectors 6.1 Introduction to Vectors 14:15 ▶
📖 Vectors 6.2 Adding and Subtracting Vectors 36:13 ▶
📖 Vectors 6.3 Multiplication of a vector by a scalar 23:28 ▶
📖 Vectors 6.4 Properties of Vectors 10:00 ▶
📖 Vectors 6.5 Vectors in R3 21:00 ▶
📖 Vectors 6.6 Cartesian Vectors in R2 15:04 ▶
📖 Vectors 6.7 Operations with vectors in R3 20:54 ▶
📖 Vectors 6.8 Linear Combinations and Spanning Sets 26:01 ▶
📋 Vectors Chapter 6 & 7 Unit test on vectors in R3 24:52 ▶

Unit 7: Vector Applications

Forces, dot product, cross product, projections

📚 Strand C: Vectors 📹 8 lessons
📹 Video Lessons
📊 Unit 7 Assessments
📖 Vectors 7.1 Vectors as Forces 22:12 ▶
📖 Vectors 7.1 7.2 Rope tension and velocity 20:40 ▶
📖 Vectors 7.2 Take me to the River 13:22 ▶
📖 Vectors 7.3/7.4 The Dot Product (R2) 24:19 ▶
📖 Vectors 7.4 Dot Product in R3 20:44 ▶
📖 Vectors 7.5 Scalar and Vector Projections 20:17 ▶
📖 Cross Product of Two Vectors — Definition & Calculation — The Organic Chemistry Tutor 12:53 ▶
📖 Vectors 7.7 Applications of Cross Product and The Triple Scalar Product 26:22 ▶
📋 Vectors Chapter6/7 Test Vectors in R2 28:44 ▶

Unit 8: Lines and Planes

Equations of lines in 2D/3D, equations of planes

📚 Strand C: Vectors 📹 7 lessons
📹 Video Lessons
📊 Unit 8 Assessments
📖 Vectors 8.1 Equations of lines in 2 space 18:44 ▶
📖 Vectors 8.2 Cartesian Equation of a line (R2) 24:17 ▶
📖 Vectors 8.1/8.2 Necessary skills with equations of lines 16:20 ▶
📖 Vectors 8.3 Vector, Parametric and Symmetric equations of lines in R3 26:03 ▶
📖 Vectors 8.4 Vector Equation of a Plane 21:12 ▶
📖 Vectors 8.5 The Cartesian Equation of a Plane 14:13 ▶
📖 Equation of a Plane Given a Point and Perpendicular Normal Vector — Scalar/Normal Form — The Organic Chemistry Tutor 10:58 ▶
📋 Vectors Chapter 8 Practice Test Equations of Lines and Planes 28:39 ▶

Unit 9: Intersections

Intersection of lines, planes, distances, matrices

📚 Strand C: Vectors 📹 9 lessons
📹 Video Lessons
📊 Unit 9 Assessments
📖 Vectors 9.1 Intersection of lines with planes 14:32 ▶
📖 Vectors 9.1 Intersection of lines in R2 and R3 Part 2 23:44 ▶
📖 Vectors 9.2 Systems of Equations - Matrices 23:45 ▶
📖 Vectors 9.3 Intersection of 2 planes 25:24 ▶
📖 Vectors 9.4 Intersection of 3 Planes (Part 1) 28:28 ▶
📖 Vectors 9.4 Intersection of 3 planes part 2 16:20 ▶
📖 Vectors 9.5 Distance between a point and a line in R2 and R3 20:32 ▶
📖 Vectors 9.6 The Distance from a point to a Plane 9:35 ▶
📋 Vectors Chapter 9 Practice Test Intersections of Lines and Planes 37:00 ▶
📘 Final Evaluation — 30% of Final Grade

MCV4U Final Exam (Cumulative)

3 hours · 100 marks · K/U 25 / T 25 / C 25 / A 25 · Covers all 9 units. Includes a complete answer key.

📝 Open Final Exam 📋 Curriculum Document