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Lesson 1: Definition of limits and Using Limit Notation

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Lesson 2: One sided vs Two sided limits

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Lesson 3: Estimating limit values from graphs

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Lesson 4A: Estimating limit values from tables

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Lesson 4B: Using the direct substitution method to find the limit of a function

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Lesson 5: Properties of limits

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Lesson 6: Determining limits using algebraic properties of limits

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Lesson 7: Determining limits using algebraic manipulation

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Lesson 8: Limits of Absolute Functions

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Lesson 9: Limits of Trigonometric Functions

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Lesson 10: Determining Limits Using the Squeeze Theorem

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Game Time! True or false

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Lesson 11: Key features of the graphs of functions created by adding, subtracting, multiplying, or dividing functions

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Game Time! Find the right graphs and tables

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Lesson 12 & 13: Continuity

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Lesson 14: Types of discontinuities

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Lesson 15: Removing discontinuities

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Game Time! Identify the discontinuities

Game Time! Remove the discontinuity

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Lesson 16: Vertical asymptotes

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Lesson 17: Infinite limits and horizontal asymptotes

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Lesson 18: Given the equation of a rational function, locate removable discontinuities and determine the equations of the vertical asymptotes

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Lesson 19: The Intermediate Value Theorem

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Game Time! Crossword

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Lesson 1: Review of Average rate of change, Instantaneous rate of change at a point, slope of secant and tangent lines

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Lesson 2: Review of Estimating the slope of the tangents using secants

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Lesson 3: History and definition of derivatives

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Lesson 4: Derivative Notation

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Game Time! Find the right value

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Lesson 5: Estimating Derivatives of a Function at a Point

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Lesson 6: Using the first principle definition to find the derivative of a function

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Game Time! Find f'(x)

Game Time! Find f'(x)

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Lesson 7: Connecting Differentiability and Continuity: Determining when derivatives do and do not exist

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Lesson 8: Make connections between the graphs of f(x) and f ’(x) or y and dy/dx

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Lesson 9: Derivative Rules: Constant, Sum, Difference, and Constant Multiple

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Lesson 10: Verify the power rule for functions of the form f(x) = x , where n is a natural number

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Lesson 11: Verify that the power rule applies to functions of the form f(x) = xn , where n is a rational number

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Lesson 12: The Product Rule

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Lesson 13: The Quotient Rule

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Lesson 14: Notation for composite functions & Understand how to represent composite functions as composites of simpler functions

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Lesson 15: The Chain Rule

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Lesson 16: Solve problems using multiple derivative rules like product, quotient, and chain rules, involving the derivatives of polynomial functions, rational, and radical functions & Calculate the slope of the tangent to the tangent to the function at a

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Lesson 17: Exploring e^x and its derivative

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Lesson 18: The Natural Logarithm

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Lesson 19: Derivative of exponential functions

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Lesson 20: Use understanding of derivatives to solve real-world problems involving exponential functions

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Lesson 21: Derivatives of cosine, sine

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Lesson 22: Derivative of tangent

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Lesson 23: Use understanding of derivatives to solve real-world problems involving trigonometric functions

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Lesson 1: Implicit Differentiation

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Lesson 2: Differentiating Inverse Functions

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Lesson 3: Differentiating Inverse Trigonometric Functions: Finding the derivatives of arctan, arcsin, and/or arccos functions

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Lesson 4: Selecting Procedures for Calculating Derivatives

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Lesson 6: Calculating higher-order derivatives

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Lesson 7: Recognize the second derivative as the rate of change of the slope of the tangent, and sketch the graphs of the first and second derivatives, given the graph of a smooth function

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Lesson 8: Determine algebraically the equation of the second derivative

Quiz: Lesson 8

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Game Time! Find the right graph

Mini Challenge: Lesson 8

Lesson 9: Locate stationary points and determine their nature, and use information about stationary points in sketching graphs

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Mini Challenge: Lesson 9

Lesson 10: Describe key features of a polynomial function when given information about its first and/or second derivatives

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Mini Challenge: Lesson 10

Lesson 11: Sketch the graph of a polynomial function, given its equation, by using a variety of strategies to determine its key features

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Game Time! Find the right graph

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Lesson 1: Interpreting the Meaning of the Derivative in Context

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Lesson 2: Straight-Line Motion: Connecting Position, Velocity, and Acceleration

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Lesson 3: Rates of Change in Applied Contexts Other Than Motion

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Lesson 6: Solving Related Rates Problems

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Game Time! Solve the Related Rates Problem

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Lesson 7: Approximating Values of a Function Using Local Linearity and Linearization

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Lesson 8: Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms

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Game Time! Memory Game

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Lesson 1: Using the Mean Value Theorem

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Lesson 2: Extreme Value Theorem, Global Versus Local Extrema, and Critical Points

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Lesson 3: Determining Intervals on Which a Function Is Increasing or Decreasing

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Lesson 4: Using the First Derivative Test to Determine Relative (Local) Extrema

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Lesson 6: Determining Concavity (increasing/decreasing) of Functions over Their 2 Domains

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Lesson 8: Sketching Graphs of Functions and their derivatives

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Lesson 9: Connecting a Function to its features, its First Derivative, and its Second Derivative

Quiz: Lesson 9

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Lesson 11: Introduction to Optimization –what is it?

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Quiz: Lesson 12

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Lesson 14: Exploring Behaviors of Implicit Relations

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Lesson 15: Newton’s method

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Game Time! Put the images in the proper sequence

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No Mini Challenge: Lesson 16

Lesson 1: Exploring Accumulations of Change

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Lesson 2: Rectangle Approximation method

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Lesson 3: Approximating Areas with Riemann Sums

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Lesson 4: Trapezoidal method

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Lesson 5: Riemann Sums, Summation Notation, and Definite Integral Notation

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Lesson 6: The Fundamental Theorem of Calculus and Accumulation Functions

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Lesson 7: Interpreting the Behavior of Accumulation Functions Involving Area

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Lesson 8: Definite vs indefinite integrals

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Lesson 9: Properties of definite integrals

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Lesson 10: Finding Antiderivatives and Indefinite Integrals: Introduction, Basic Rules, and Notation

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Lesson 11: Applying Properties of definite Integrals to solve problems

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Lesson 12: Evaluate definite integrals

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Game Time! Find the correct integral

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Lesson 13: The Fundamental Theorem of Calculus with the GDC

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Lesson 14: Make the connection between definite integrals and area under a curve

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Lesson 15: Find area under a curve and area enclosed by the function and the x-axis

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Lesson 16: Use definite integration to find the area between two curves or between a curve and a line parallel to one of the axes

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Lesson 17: Use definite integration to find – the area of a region bounded by a curve and lines parallel to the axes

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Lesson 18: Use definite integration to find the area between two curves or between a curve and a line

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Game Time! Find the right graphs

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Lesson 19 & 20 : Integration by substitution

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Lesson 21: Find indefinite integrals using inspection or substitution

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Lesson 22: Use a given substitution to simplify and evaluate either a definite or an indefinite integral.

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Lesson 23: Use trigonometric relationships in carrying out integration

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Game Time! Find the antiderivative

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Lesson 24: Find antiderivatives of composite functions in the form y = f (ax +b)

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Lesson 25: Recognize an integrand of the form kf ’(x) / f(x) and integrate such functions

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Lesson 26: Recognize when an integrand can usefully be regarded as a product, and use integration by parts

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Lesson 27: Integrating Functions Using Long Division and Completing the Square

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Lesson 28: Using Linear Partial Fractions

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Lesson 29: Integrate rational functions by means of decomposition into partial fractions

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Lesson 30: Evaluating Improper Integrals

Quiz: Lesson 30

Game Time! Find the convergent integrals

Mini Challenge: Lesson 30

Lesson 31: Selecting Techniques for Antidifferentiation ( Part 1 ) - substitution, IBP, Trig substitution

Worked Out Example: Lesson 31

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Mini Challenge: Lesson 31

Lesson 32: Selecting Techniques for Antidifferentiation ( Part 2 ) - Long division, Completing the square, Partial Fractions

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Lesson 33: Use definite integration to find a volume of revolution about one of the axes

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Worksheet: lesson 33

Lesson 1A: Find by integration a general form of solution for a first order differential equation in which the variables are separable

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Lesson 1B: Formulate a simple statement involving a rate of change as a differential equation

Worked Out Example: Lesson 1

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Lesson 2: Verifying Solutions for Differential Equations

Quiz: Lesson 2

Game Time! Solve the Differential Equation

Game Time! True or false

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Worksheet: lesson 2

Lesson 3: Sketching Slope Fields

Quiz: Lesson 3

Mini Challenge: Lesson 3

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Lesson 4: Reasoning Using Slope Fields

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Game Time! Find the correct slope field

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Lesson 5: Approximating Solutions Using Euler’s Method

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Lesson 6A: Solving a Separable First Order Differential Equation by Integration

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Game Time! Solve the Differential Equation

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Lesson 6B: Finding General Solutions Using Separation of Variables

Lesson 7: Exponential Models with Differential Equations

Worked Out Example: Lesson 7

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Lesson 8: Logistic Models with Differential Equations

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Quiz: Lesson 8

Game Time! Find the correct function

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Game Time! Find the correct function

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Worksheet: lesson 8

Lesson 9: Given particular values, solve differential equations by determining the value of the constant term; relate to motion problems

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Lesson 1: Finding the Average Value of a Function on an Interval

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Lesson 2: Connecting Position, Velocity, and Acceleration of Functions Using Integrals

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Lesson 3: Using Accumulation Functions and Definite Integrals in Applied Contexts

Quiz: Lesson 3

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Lesson 4: Finding the Area Between Curves Expressed as Functions of x

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Lesson 5: Finding the Area Between Curves Expressed as Functions of y

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Lesson 6: Finding the Area Between Curves That Intersect at More Than Two Points

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Lesson 7: Volumes with Cross Sections: Squares and Rectangles

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Lesson 8: Volumes with Cross Sections: Triangles and Semicircles

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Lesson 10: Volume with Disc Method: Revolving Around the x- or y-Axis

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Lesson 11: Volume with disc method: revolving around other axes

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Lesson 12: Volume with Washer Method: Revolving 4 Around the x- or y-Axis

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Lesson 13: Volume with washer method: revolving around other axes

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Lesson 14: The Arc Length of a Smooth, Planar Curve and Distance Traveled bc only

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Lesson 16: Connect distance travelled to area under a curve

Quiz: Lesson 16

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Worksheet: lesson 16

Lesson 17: Connect displacement to a single definite integral

Quiz: Lesson 17

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Lesson 19: Initial value problems and anti-derivatives

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Lesson 1: Defining and Differentiating Parametric Equations

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Lesson 3: Finding Arc Lengths of Curves Given by Parametric Equations

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Lesson 4: Defining and Differentiating Vector Valued Functions

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Lesson 6: Solving Motion Problems Using Parametric and Vector-Valued Functions

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Lesson 7: Defining Polar Coordinates and differentiating in polar form

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Lesson 8: Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve

Quiz: Lesson 8

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Worked Out Example: Lesson 9

Lesson 1: Defining convergent and divergent infinite series

Quiz: Lesson 1

Mini Challenge: Lesson 1

Worksheet: lesson 1-4

Lesson 2: Working with Geometric Series

Quiz: Lesson 2

Mini Challenge: Lesson 2

Lesson 3: The nth term test for divergence

Quiz: Lesson 3

Mini Challenge: Lesson 3

Lesson 4: Integral test for convergence

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Lesson 5: P Series

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Worksheet: lesson 5-8

Lesson 6: Harmonic Series

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Mini Challenge: Lesson 6

Lesson 7: Comparison tests for convergence

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Lesson 8: Alternating series test for convergence

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Lesson 9: Determining absolute or conditional convergence

Quiz: Lesson 9

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Worksheet: lesson 9-12

Lesson 10: Ratio Test for Convergence

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Mini Challenge: Lesson 10

Lesson 11: Alternating series Error Bound

Quiz: Lesson 11

Mini Challenge: Lesson 11

Lesson 12: Finding Taylor Polynomial Approximations of Functions

Worked Out Example: Lesson 12

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Lesson 13: Lagrange error bound

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Worksheet: lesson 13-16

Lesson 14: Radius and Interval of Convergence of Power Series

Worked Out Example: Lesson 14

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Lesson 15: Representing Functions as Power Series

Worked Out Example: Lesson 15

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Lesson 16: Finding Taylor or Maclaurin Series for a Function

Worked Out Example: Lesson 16

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Lesson 1: What are vectors? (Definition, idea, purpose)

Quiz: Lesson 1

Mini Challenge: Lesson 1

Worksheet: lesson 1

Lesson 2: Use of notations

Quiz: Lesson 2

Mini Challenge: Lesson 2

Lesson 3: Magnitude and direction of a vector

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Lesson 4: Represent a vector, in two-space, geometrically as a directed line segment

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Lesson 5: Scalar vs. vector quantities

Quiz: Lesson 5

Mini Challenge: Lesson 5

Lesson 6: Determine using trigonometric relationships, the Cartesian representation of a vector in two-space

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Lesson 7: Multiplication of vector by a scalar

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Lesson 8: Adding and subtracting vectors in two dimensions, algebraic properties of addition and salar multplication

Worked Out Example: Lesson 8

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Lesson 9B: Adding position vectors by components

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Lesson 9C: Adding position vectors with the cosine law

Quiz: Lesson 9C

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Lesson 9A: Real-world applications of vectors

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Lesson 10: Recognize that points and vectors in three-space can both be represented using Cartesian coordinates

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Lesson 11: Translation by a vector

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Lesson 12: Use of sum and difference of two vectors to express given vectors in terms of two coplanar vectors

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Lesson 13: Solve problems involving the addition, subtraction, and scalar multiplication of vectors

Quiz: Lesson 13

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Lesson 14A: The dot product of two vectors

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Lesson 14B: The geometric form of the dot product and its equivalence to the component form

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Mini Challenge: Lesson 14B

Worksheet: lesson 14B

Lesson 15: Using the dot product to calculate angles between vectors

Worked Out Example: Lesson 15

Quiz: Lesson 15

Mini Challenge: Lesson 15

Worksheet: lesson 15

Lesson 16: Unit vectors and the i, j, k basis vectors

Quiz: Lesson 16

Mini Challenge: Lesson 16

Lesson 17: Using the dot product to find projections

Worked Out Example: Lesson 17

Quiz: Lesson 17

Mini Challenge: Lesson 17

Lesson 18: Using the dot product to find the closest distance between a line and a point

Worked Out Example: Lesson 18

Quiz: Lesson 18

Mini Challenge: Lesson 18

Worksheet: lesson 18

Lesson 19: Perform the operation of cross product on two vectors represented in Cartesian form

Worked Out Example: Lesson 19

Quiz: Lesson 19

Mini Challenge: Lesson 19

Worksheet: lesson 19

Lesson 20: Determine properties of the cross product

Quiz: Lesson 20

Mini Challenge: Lesson 20

Worksheet: lesson 20

Lesson 21: Solve problems involving dot product and cross product

Worked Out Example: Lesson 21

Game Time! Drag and Drop

Quiz: Lesson 21

Mini Challenge: Lesson 21

Worksheet: lesson 21

Lesson 23: Perform algebraic operations on vector equations

Quiz: Lesson 23

Mini Challenge: Lesson 23

Worksheet: lesson 23

Lesson 24&25: Connecting parallelism to scalar multiplication

Quiz: Lesson 24&25

Game Time! Flip and Learn

Mini Challenge: Lesson 24&25

Worksheet: lesson 25

Lesson 1: Understanding the solutions to a system of two linear equations

Quiz: Lesson 1

Mini Challenge: Lesson 1

Worksheet: lesson 1-3

Lesson 2: Connect ideas of direction vector and slope

Quiz: Lesson 2

Mini Challenge: Lesson 2

Lesson 3: Represent lines in Cartesian form as well as vector & parametric form

Worked Out Example: Lesson 3

Quiz: Lesson 3

Mini Challenge: Lesson 3

Lesson 4: Use the vector form of a line to find out which points are on it

Worked Out Example: Lesson 4

Quiz: Lesson 4

Mini Challenge: Lesson 4

Worksheet: lesson 4-6

Lesson 5: Understand the significance of all the symbols used when the equation of a straight line is expressed in the form r = a + tb

Worked Out Example: Lesson 5

Quiz: Lesson 5

Mini Challenge: Lesson 5

Lesson 6: Solve problems involving motion in a straight line with constant velocity

Worked Out Example: Lesson 6

Quiz: Lesson 6

Mini Challenge: Lesson 6

Lesson 7: Geometric applications of r=a+tb: solve more complex constant-velocity motion problems

Quiz: Lesson 7

Mini Challenge: Lesson 7

Worksheet: lesson 7

Lesson 9: Find the angle between lines connections and between a scalar equation, a vector equation, and parametric equations of a line in two-space

Worked Out Example: Lesson 9

Quiz: Lesson 9

Mini Challenge: Lesson 9

Worksheet: lesson 9

Lesson 10: Recognize that a line in three-space cannot be represented by a scalar equation

Quiz: Lesson 10

Mini Challenge: Lesson 10

Worksheet: Lesson 10

Game Time! Memory Game

Lesson 11: Recognize a normal to a plane geometrically, and determine some geometric properties of the plane

Quiz: Lesson 11

Mini Challenge: Lesson 11

Worksheet; lesson 11

Lesson 12: Investigation: The solution points (x, y, z) in three-space of a single linear equation in three variables form a plane and the solution points (x, y, z)

Quiz: Lesson 12

Mini Challenge: Lesson 12

Worksheet; lesson 12

Lesson 13: Determine different geometric configurations of combination of up to three lines and/or planes in three-space

Quiz: Lesson 13

Mini Challenge: Lesson 13

Lesson 14: Determine the intersection of three planes represented using scalar equations

Worked Out Example: Lesson 14

Quiz: Lesson 14

Mini Challenge: Lesson 14

Lesson 15: The scalar, vector, and parametric equations of a plane

Quiz: Lesson 15

Mini Challenge: Lesson 15

Lesson 16: Solve problems relating to lines and planes in three-space that are represented in a variety of ways

Worked Out Example: Lesson 16

Quiz: Lesson 16

Game Time! Select the correct answer

Mini Challenge: Lesson 16

Lesson 1A: Geometric Constructions: angles, triangles, triangle centres, quadrilaterals

Quiz: Lesson 1A

Mini Challenge: Lesson 1A

Worksheet; lesson 1

Lesson 1B: Triangle constructions

Quiz: Lesson 1B

Mini Challenge: Lesson 1B

Lesson 2: Parallel and Perpendicular: Angle bisector

Quiz: Lesson 2

Mini Challenge: Lesson 2

Lesson 3: Using circles as tools: constructing equal segments, midpoints

Quiz: Lesson 3

Mini Challenge: Lesson 3

Lesson 4: Perpendicular bisector

Quiz: Lesson 4

Game Time! Crossword

Mini Challenge: Lesson 4

Lesson 1: Interpreting and using y = mx + b to solve problems

Worked Out Example: Lesson 1

Quiz: Lesson 1

Mini Challenge: Lesson 1

Lesson 2: Interpreting and using y – y1 = m(x – x1) to solve problems

Worked Out Example: Lesson 2

Quiz: Lesson 2

Mini Challenge: Lesson 2

Lesson 3: Interpreting and using ax + by + c = 0 to solve problems

Worked Out Example: Lesson 3

Quiz: Lesson 3

Mini Challenge: Lesson 3

Lesson 4: Understanding (x – a) + (y – b) 2 = r 2 represents the circle with centre (a, b) and radius r

Worked Out Example: Lesson 4

Quiz: Lesson 4

Mini Challenge: Lesson 4

Lesson 5: Using algebraic methods to solve problems involving lines and circles

Worked Out Example: Lesson 5

Quiz: Lesson 5

Game Time! Select the correct answer

Mini Challenge: Lesson 5

Lesson 1: Determining whether two triangles are congruent or similar

Worked Out Example: Lesson 1

Quiz: Lesson 1

Mini Challenge: Lesson 1

Lesson 2: Ratio of areas of similar plane figures

Worked Out Example: Lesson 2

Quiz: Lesson 2

Mini Challenge: Lesson 2

Lesson 3: Ratio of volumes of similar solids

Worked Out Example: Lesson 3

Quiz: Lesson 3

Game Time ! Flip the Card

Mini Challenge: Lesson 3

Lesson 1: Understanding the definition of a radian

Quiz: Lesson 1

Mini Challenge: Lesson 1

Lesson 2: Using the formula s= r theta in solving problems concerning the arc length and sector area of a circle

Worked Out Example: Lesson 2

Quiz: Lesson 2

Mini Challenge: Lesson 2

Lesson 3: Using the formula A= ½ r2θ in solving problems concerning the arc length and sector area of a circle

Worked Out Example: Lesson 3

Quiz: Lesson 3

Mini Challenge: Lesson 3

Lesson 4: Properties of chords, angles, and tangents

Quiz: Lesson 4

Game Time ! Crossword

Mini Challenge: Lesson 4

Lesson 1: Isometries: transformations that maintain congruence

Quiz: Lesson 1

Mini Challenge: Lesson 1

Lesson 2: Composition of isometries

Quiz: Lesson 2

Mini Challenge: Lesson 2

Lesson 3: Isometries in tessellations

Quiz: Lesson 3

Mini Challenge: Lesson 3

Lesson 4: Non-isometric transformations: dilations and shear

Quiz: Lesson 4

Mini Challenge: Lesson 4

Lesson 5: Non-isometric transformations: topology

Quiz: Lesson 5

Game Time ! Crossword

Mini Challenge: Lesson 5

Lesson 1: Non-euclidean geometries

Quiz: Lesson 1

Mini Challenge: Lesson 1

Lesson 2: Perspective geometry

Quiz: Lesson 2

Mini Challenge: Lesson 2

Lesson 3: Taxicab distance and other notions of distance

Quiz: Lesson 3

Mini Challenge: Lesson 3

Lesson 4: Tesselations with non-euclidean geometries

Quiz: Lesson 4

Game Time ! Question Set

Mini Challenge: Lesson 4

Lesson 1: Review: What is a complex number?

Quiz: Lesson 1

Mini Challenge: Lesson 1

Lesson 2: Addition, subtraction, and multiplication, and division of two complex numbers expressed in Cartesian form x+iy

Worked Out Example: Lesson 2

Quiz: Lesson 2

Lesson 3: Solve cubic or quartic equations where one complex root is given

Worked Out Example: Lesson 3

Quiz: Lesson 3

Lesson 4: Multiplication and division of two complex numbers expressed in polar form

Worked Out Example: Lesson 4

Quiz: Lesson 4

Mini Challenge: Lesson 4

Lesson 5: Find two square roots of a complex number in exact cartesian form

Worked Out Example: Lesson 5

Quiz: Lesson 5

Mini Challenge: Lesson 5

Lesson 6: Conjugating a complex number

Quiz: Lesson 6

Mini Challenge: Lesson 6

Lesson 7: Illustrate simple equations and inequalities involving complex numbers by means of loci on Argand diagram

Quiz: Lesson 7

Mini Challenge: Lesson 7

Lesson 8: Conjugating a complex number

Game Time ! Question Set

Worked Out Example: Lesson 8