 ## Calculus and Vectors Strands and Subgroups in the Grade 12 Course

• A. RATE OF CHANG
- Investigating Instantaneous Rate of Change at a Point
- Investigating the Concept of the Derivative Function
- Investigating the Properties of Derivatives
• B. DERIVATIVES AND THEIR APPLICATIONS
- Connecting Graphs and Equations of Functions and Their Derivatives
- Solving Problems Using Mathematical Models and Derivatives
• C. GEOMETRY AND ALGEBRA OF VECTORS
- Representing Vectors Geometrically and Algebraically
- Operating With Vectors
- Describing Lines and Planes Using Linear Equations
- Describing Lines and Planes Using Scalar, Vector, and Parametric Equations

### Chapter 1: Rates of Change

1.1: Rates of Change and the Slope of a Curve
1.2: Rates of Change Using Equations
1.3: Limits
1.4: Limits and Continuity
1.5: Introduction to Derivatives

### CHAPTER 2: Derivatives

2.1: Derivative of a Polynomial Function
2.2: The Product Rule
2.3: Velocity, Acceleration, and Second Derivatives
2.4: The Chain Rule
2.5: Derivatives of Quotients
2.6: Rate of Change Problems

### CHAPTER 3: Curve Sketching

3.1: Increasing and Decreasing Functions
3.2: Maxima and Minima
3.3: Concavity and the Second Derivative Test
3.4: Simple Rational Functions
3.5: Putting It All Together
3.6: Optimization Problems

### CHAPTER 4: Derivatives of Sinusoidal Functions

4.1: Instantaneous Rates of Change of Sinusoidal Functions
4.2: Derivatives of the Sine and Cosine Functions
4.3: Differentiation Rules for Sinusoidal Functions
4.4: Applications of Sinusoidal Functions and Their Derivatives

### CHAPTER 5: Exponential and Logarithmic Functions

5.1: Rates of Change and the Numbere
5.2: The Natural Logarithm
5.3: Derivatives of Exponential Functions
5.4: Differentiation Rules for Exponential Functions
5.5: Making Connections: Exponential Models

### CHAPTER 6: Geometric Vectors

6.1: Introduction to Vectors
6.2: Addition and Subtraction of Vectors
6.3: Multiplying a Vector by a Scalar
6.5: Resolution of Vectors Into Rectangular Components

### CHAPTER 7: Cartesian Vectors

7.1: Cartesian Vectors
7.2: Dot Product
7.3: Applications of the Dot Product
7.4: Vectors in Three-Space
7.5: The Cross Product and Its Properties
7.6: Applications of the Dot Product and Cross Product

### CHAPTER 8: Lines and Planes

8.1: Equations of Lines in Two-Space and Three-Space
8.2: Equations of Planes
8.3: Properties of Planes
8.4: Intersections of Lines in Two-Space and Three-Space
8.5: Intersections of Lines and Planes
8.6: Intersections of Planes

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### Chapter 1: Introduction to Calculus

1.2: The Slope of a Tangent
1.3: Rates of Change
1.4: Limit of a Function
1.5: Properties of Limits
1.6: Continuity

### CHAPTER 2: Derivatives

2.1: The Derivative Function
2.2: The Derivatives of Polynomial Functions
2.3: The Product Rule
2.4: The Quotient Rule
2.5: The Derivatives of Composite Functions

### CHAPTER 3: Derivatives and their Applications

3.1: Higher Order Derivaties, Velocity and Accerleration
3.2: Minimum and Maximum on an Interval (Extreme Values)
3.3: Optimization Problems
3.4: Optimization Problems in Economics and Science

### CHAPTER 4: Curve Sketching

4.1: Increasing and Decreasing Functions
4.2: Critical Points, Local Maxima, and Local Minima
4.3: Vertical and Horizontal Asymptotes
4.4: Concavity and Points of Inflection
4.5: An Algorithm for Curve Sketching

### CHAPTER 5: Derivatives of Exponential and Trigonometric Functions

5.1: Derivaties of Exponential Functions, y= ex
5.2: The Derivatie of the General Exponential Function, y= bx
5.3: Optimization Problems Involving Exponential Functions
5.4: The Derivatives of y = sin x and y = cos x
5.5: The Derivative of y = tan x

### CHAPTER 6: An Introduction to Vectors

6.1: An Introduction to Vectors
6.3: Multiplication of a Vector by a Scalar
6.4: Properties of Vectors
6.5: Vectors in R2 and R3
6.6: Operations with Algebraic Vectors R2
6.7: Operations with Vectors R3
6.8: Linear Combinations and Spanning Sets

### CHAPTER 7: Applications of Vectors

7.1: Vectors as Forces
7.2: Velocity
7.3: The Dot Product of Two Geometric Vectors
7.4: The Dot Product of Algebraic Vectors
7.5: Scalar and Vector Projections
7.6: The Cross Product of Two Vectors
7.7: Applications of the Dot Product and Cross Product

### CHAPTER 8: Equations of Lines and Planes

8.1: Vector and Parametric Equations of a Line in R2
8.2: Cartesian Equation of a Line
8.3: Vector, Parametric and Synmetric Equations of a Line in R3
8.4: Vector and Parametric Equations of a Plane
8.5: The Cartesian Equation of a Plane
8.6: Sketching Planes in R3

### CHAPTER 9: Relationships between Points, Lines and Planes

9.1: The Intersection of a Line with a Plane and the Intersection of Two Lines
9.2: Systems of Equations
9.3: The Intersection of Two Planes
9.4: The Intersection of Three Planes
9.5: The Distance from a Point to a Line in R2 and R3
9.6: The Distance from a Point to a Plane # Strictly Ontario Curriculum

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