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Course curriculum

  • 01

    Registration

    • Registration Information

    • Required Student Information

  • 03

    Limits and Discontinuities

    • Lesson 1: Definition of limits and Using Limit Notation

    • Quiz: Lesson 1

    • Mini Challenge: Lesson 1

    • Worksheet: Lesson 1

    • Lesson 2: One sided vs Two sided limits

    • Quiz: Lesson 2

    • Mini Challenge: Lesson 2

    • Worksheet: Lesson 2

    • Lesson 3: Estimating limit values from graphs

    • Worked Out Example: Lesson 3

    • Quiz: Lesson 3

    • Game Time! Question set

    • Mini Challenge: Lesson 3

    • Worksheet: Lesson 3

    • Lesson 4A: Estimating limit values from tables

    • Worked Out Example: Lesson 4

    • Quiz: Lesson 4A

    • Mini Challenge: Lesson 4A

    • Worksheet: Lesson 4A

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

    • Quiz: Lesson 4B

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 4B

    • Worksheet: Lesson 4B

    • Lesson 5: Properties of limits

    • Worked Out Example: Lesson 5

    • Quiz: Lesson 5

    • Mini Challenge: Lesson 5

    • Worksheet: Lesson 5

    • Lesson 6: Determining limits using algebraic properties of limits

    • Worked Out Example: Lesson 6

    • Quiz: Lesson 6

    • Game Time! Question set

    • Mini Challenge: Lesson 6

    • Worksheet: Lesson 6

    • Lesson 7: Determining limits using algebraic manipulation

    • Worked Out Example: Lesson 7

    • Quiz: Lesson 7

    • Mini Challenge: Lesson 7

    • Worksheet: Lesson 7

    • Lesson 8: Limits of Absolute Functions

    • Quiz: Lesson 8

    • Worked Out Example: Lesson 8

    • Mini Challenge: Lesson 8

    • Worksheet: Lesson 8

    • Lesson 9: Limits of Trigonometric Functions

    • Worked Out Example: Lesson 9

    • Quiz: Lesson 9

    • Game Time! Flip and learn

    • Mini Challenge: Lesson 9

    • Worksheet: Lesson 9

    • Lesson 10: Determining Limits Using the Squeeze Theorem

    • Worked Out Example: Lesson 10

    • Quiz: Lesson 10

    • Game Time! True or false

    • Mini Challenge: Lesson 10

    • Worksheet: Lesson 10

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

    • Quiz: Lesson 11

    • Game Time! Find the right graphs and tables

    • Mini Challenge: Lesson 11

    • Worksheet: Lesson 11

    • Lesson 12 & 13: Continuity

    • Worked Out Example: Lesson 12

    • Quiz: Lesson 12&13

    • Mini Challenge: Lesson 12&13

    • Worksheet: Lesson 12&13

    • Lesson 14: Types of discontinuities

    • Quiz: Lesson 14

    • Mini Challenge: Lesson 14

    • Worksheet: Lesson 14

    • Lesson 15: Removing discontinuities

    • Worked Out Example: Lesson 15

    • Quiz: Lesson 15

    • Game Time! Identify the discontinuities

    • Game Time! Remove the discontinuity

    • Mini Challenge: Lesson 15

    • Worksheet: Lesson 15

    • Lesson 16: Vertical asymptotes

    • Quiz: Lesson 16

    • Mini Challenge: Lesson 16

    • Worksheet: Lesson 16

    • Lesson 17: Infinite limits and horizontal asymptotes

    • Quiz: Lesson 17

    • Mini Challenge: Lesson 17

    • Worksheet: Lesson 17

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

    • Worked Out Example: Lesson 18

    • Quiz: Lesson 18

    • Game Time! Question set

    • Game Time! Find the right graphs

    • Mini Challenge: Lesson 18

    • Worksheet: Lesson 18

    • Lesson 19: The Intermediate Value Theorem

    • Quiz: Lesson 19

    • Mini Challenge: Lesson 19

    • Game Time! Crossword

    • Worksheet: Lesson 19

  • 04

    Differentiation, Derivative Rules, and Rate of Change

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

    • Worked Out Example: Lesson 1

    • Quiz: Lesson 1

    • Mini Challenge: Lesson 1

    • Worksheet: Lesson 1

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

    • Quiz: Lesson 2

    • Mini Challenge: Lesson 2

    • Worksheet: Lesson 2

    • Lesson 3: History and definition of derivatives

    • Quiz: Lesson 3

    • Game Time! Drag and drop

    • Mini Challenge: Lesson 3

    • Worksheet: Lesson 3

    • Lesson 4: Derivative Notation

    • Quiz: Lesson 4

    • Game Time! Find the right value

    • Mini Challenge: Lesson 4

    • Worksheet: Lesson 4

    • Lesson 5: Estimating Derivatives of a Function at a Point

    • Quiz: Lesson 5

    • Mini Challenge: Lesson 5

    • Worksheet: Lesson 5

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

    • Quiz: Lesson 6

    • Game Time! Find f'(x)

    • Game Time! Find f'(x)

    • Mini Challenge: Lesson 6

    • Worksheet: Lesson 6

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

    • Quiz: Lesson 7

    • Game Time! Find the right graphs

    • Mini Challenge: Lesson 7

    • Worksheet: Lesson 7

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

    • Quiz: Lesson 8

    • Mini Challenge: Lesson 8

    • Worksheet: Lesson 8

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

    • Quiz: Lesson 9

    • Mini Challenge: Lesson 9

    • Worksheet: Lesson 9

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

    • Quiz: Lesson 10 (question 3 incorrect?)

    • Mini Challenge: Lesson 10

    • Worksheet: Lesson 10

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

    • Worked Out Example: Lesson 11

    • Quiz: Lesson 11

    • Game Time! Drag and drop

    • Mini Challenge: Lesson 11

    • Worksheet: Lesson 11

    • Lesson 12: The Product Rule

    • Worked Out Example: Lesson 12

    • Quiz: Lesson 12

    • Mini Challenge: Lesson 12

    • Worksheet: Lesson 12

    • Lesson 13: The Quotient Rule

    • Worked Out Example: Lesson 13

    • Quiz: Lesson 13

    • Game Time! Question set

    • Mini Challenge: Lesson 13

    • Worksheet: Lesson 13

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

    • Worked Out Example: Lesson 14

    • Quiz: Lesson 14

    • Mini Challenge: Lesson 14

    • Worksheet: Lesson 14

    • Lesson 15: The Chain Rule

    • Worked Out Example: Lesson 15

    • Quiz: Lesson 15 (question 4 incomplete)

    • Mini Challenge: Lesson 15

    • Worksheet: Lesson 15

    • 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

    • Worked Out Example: Lesson 16

    • Quiz: Lesson 16

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 16

    • Worksheet: Lesson 16

    • Lesson 17: Exploring e^x and its derivative

    • Quiz: Lesson 17

    • Mini Challenge: Lesson 17

    • Worksheet: Lesson 17

    • Lesson 18: The Natural Logarithm

    • Quiz: Lesson 18

    • Mini Challenge: Lesson 18

    • Worksheet: Lesson 18

    • Lesson 19: Derivative of exponential functions

    • Worked Out Example: Lesson 19

    • Quiz: Lesson 19

    • Game Time! Question set

    • Mini Challenge: Lesson 19

    • Worksheet: Lesson 19

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

    • Worked Out Example: Lesson 20

    • Quiz: Lesson 20

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 20

    • Worksheet: Lesson 20

    • Lesson 21: Derivatives of cosine, sine

    • Worked Out Example: Lesson 21

    • Quiz: Lesson 21

    • Mini Challenge: Lesson 21

    • Worksheet: Lesson 21

    • Lesson 22: Derivative of tangent

    • Worked Out Example: Lesson 22

    • Quiz: Lesson 22

    • Game Time! Drag and drop

    • Mini Challenge: Lesson 22

    • Worksheet: Lesson 22

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

    • Worked Out Example: Lesson 23

    • Quiz: Lesson 23

    • Mini Challenge: Lesson 23

    • Game Time! Drag and Drop

    • Worksheet: Lesson 23

  • 05

    Implicit & Inverse Functions

    • Lesson 1: Implicit Differentiation

    • Worked Out Example: Lesson 1

    • Quiz: Lesson 1

    • Game Time! Question set

    • Mini Challenge: Lesson 1

    • Worksheet: Lesson 1

    • Lesson 2: Differentiating Inverse Functions

    • Quiz: Lesson 2

    • Mini Challenge: Lesson 2

    • Worksheet: Lesson 2

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

    • Worked Out Example: Lesson 3

    • Quiz: Lesson 3

    • Game Time! Question set

    • Mini Challenge: Lesson 3

    • Worksheet: Lesson 3

    • Lesson 4: Selecting Procedures for Calculating Derivatives

    • Worked Out Example: Lesson 4

    • Quiz: Lesson 4

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 4

    • Lesson 6: Calculating higher-order derivatives

    • Worked Out Example: Lesson 6

    • Quiz: Lesson 6

    • Mini Challenge: Lesson 6

    • 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

    • Quiz: Lesson 7

    • Mini Challenge: Lesson 7

    • Lesson 8: Determine algebraically the equation of the second derivative

    • Quiz: Lesson 8

    • Game Time! Question set

    • 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

    • Quiz: Lesson 9

    • Mini Challenge: Lesson 9

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

    • Quiz: Lesson 10

    • 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

    • Worked Out Example: Lesson 11

    • Quiz: Lesson 11

    • Game Time! Question set

    • Game Time! Find the right graph

    • Mini Challenge: Lesson 11

    • Game Time! Drag and Drop

  • 06

    Contextual Applications of Differentiation

    • Lesson 1: Interpreting the Meaning of the Derivative in Context

    • Quiz: Lesson 1

    • Mini Challenge: Lesson 1

    • Worksheet: Lesson 1

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

    • Worked Out Example: Lesson 2

    • Quiz: Lesson 2

    • Mini Challenge: Lesson 2

    • Worksheet: lesson 2

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

    • Worked Out Example: Lesson 3

    • Quiz: Lesson 3

    • Game Time! Drag and drop

    • Mini Challenge: Lesson 3

    • Worksheet: lesson 3

    • Lesson 6: Solving Related Rates Problems

    • Worked Out Example: Lesson 6

    • Quiz: Lesson 6

    • Game Time! Solve the Related Rates Problem

    • Mini Challenge: Lesson 6

    • Worksheet: Lesson 6

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

    • Quiz: Lesson 7

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 7

    • Worksheet: lesson 7

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

    • Worked Out Example: Lesson 8

    • Quiz: Lesson 8

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 8

    • Game Time! Memory Game

    • Worksheet: lesson 8

  • 07

    Analytical Applications of Differentiation

    • Lesson 1: Using the Mean Value Theorem

    • Worked Out Example: Lesson 1

    • Quiz: Lesson 1

    • Game Time! Find the right graphs

    • Mini Challenge: Lesson 1

    • Worksheet: Lesson 1

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

    • Worked Out Example: Lesson 2

    • Quiz: Lesson 2

    • Mini Challenge: Lesson 2

    • Worksheet: lesson 2

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

    • Worked Out Example: Lesson 3

    • Quiz: Lesson 3

    • Mini Challenge: Lesson 3

    • Worksheet; Lesson 3

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

    • Worked Out Example: Lesson 4

    • Quiz: Lesson 4

    • Game Time! Question set

    • Mini Challenge: Lesson 4

    • Worksheet: Lesson 4

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

    • Worked Out Example: Lesson 6

    • Quiz: Lesson 6

    • Mini Challenge: Lesson 6

    • Worksheet: Lesson 6 and 7

    • Lesson 8: Sketching Graphs of Functions and their derivatives

    • Quiz: Lesson 8

    • Mini Challenge: Lesson 8

    • Worksheet; lesson 8

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

    • Quiz: Lesson 9

    • Game Time! Question set

    • Game Time! Find the right graph

    • Mini Challenge: Lesson 9

    • Worksheet; Lesson 9

    • Lesson 11: Introduction to Optimization –what is it?

    • Worked Out Example: Lesson 11

    • Game Time! Fill in the blanks

    • No Quiz: Lesson 11

    • Quiz: Lesson 12

    • Mini Challenge: Lesson 12

    • Worksheet: Lesson 12

    • Lesson 14: Exploring Behaviors of Implicit Relations

    • Quiz: Lesson 14

    • Mini Challenge: Lesson 14

    • Worksheet: Lesson 14

    • Lesson 15: Newton’s method

    • Quiz: Lesson 15

    • Mini Challenge: Lesson 15

    • Game Time! Put the images in the proper sequence

    • Worksheet: lesson 15

    • No Mini Challenge: Lesson 16

  • 08

    Integration and Accumulation of Change

    • Lesson 1: Exploring Accumulations of Change

    • Worked Out Example: Lesson 1

    • Quiz: Lesson 1

    • Mini Challenge: Lesson 1

    • Worksheet: Lesson 1

    • Lesson 2: Rectangle Approximation method

    • Quiz: Lesson 2

    • Mini Challenge: Lesson 2

    • Worksheet: lesson 2

    • Lesson 3: Approximating Areas with Riemann Sums

    • Quiz: Lesson 3

    • Mini Challenge: Lesson 3

    • Worksheet: lesson 3

    • Lesson 4: Trapezoidal method

    • Quiz: Lesson 4

    • Mini Challenge: Lesson 4

    • Worksheet; Lesson 4

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

    • Quiz: Lesson 5

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 5

    • Worksheet: Lesson 5

    • Lesson 6: The Fundamental Theorem of Calculus and Accumulation Functions

    • Quiz: Lesson 6

    • Mini Challenge: Lesson 6

    • Worksheet: Lesson 6

    • Lesson 7: Interpreting the Behavior of Accumulation Functions Involving Area

    • Quiz: Lesson 7

    • Mini Challenge: Lesson 7

    • Worksheet: Lesson 7

    • Lesson 8: Definite vs indefinite integrals

    • Quiz: Lesson 8

    • Mini Challenge: Lesson 8

    • Worksheet: Lesson 8

    • Lesson 9: Properties of definite integrals

    • Quiz: Lesson 9

    • Mini Challenge: Lesson 9

    • Worksheet: Lesson 9

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

    • Worked Out Example: Lesson 10

    • Quiz: Lesson 10

    • Game Time! Question set

    • Mini Challenge: Lesson 10

    • Lesson 11: Applying Properties of definite Integrals to solve problems

    • Quiz: Lesson 11

    • Mini Challenge: Lesson 11

    • Lesson 12: Evaluate definite integrals

    • Worked Out Example: Lesson 12

    • Quiz: Lesson 12

    • Game Time! Find the correct integral

    • Game Time! Question set

    • Mini Challenge: Lesson 12

    • Lesson 13: The Fundamental Theorem of Calculus with the GDC

    • Quiz: Lesson 13

    • Mini Challenge: Lesson 13

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

    • Quiz: Lesson 14

    • Mini Challenge: Lesson 14

    • Worksheet: Lesson 14

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

    • Worked Out Example: Lesson 15

    • Quiz: Lesson 15

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 15

    • Worksheet: lesson 15

    • 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

    • Quiz: Lesson 16

    • Mini Challenge: Lesson 16

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

    • Quiz: Lesson 17

    • Mini Challenge: Lesson 17

    • Worksheet: lesson 17

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

    • Worked Out Example: Lesson 18

    • Quiz: Lesson 18

    • Game Time! Find the right graphs

    • Mini Challenge: Lesson 18

    • Worksheet: lesson 18

    • Lesson 19 & 20 : Integration by substitution

    • Worked Out Example: Lesson 20

    • Quiz: Lesson 19 & 20

    • Mini Challenge: Lesson 19 & 20

    • Lesson 21: Find indefinite integrals using inspection or substitution

    • Worked Out Example: Lesson 21

    • Quiz: Lesson 21

    • Mini Challenge: Lesson 21

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

    • Worked Out Example: Lesson 22

    • Quiz: Lesson 22

    • Game Time! Question set

    • Mini Challenge: Lesson 22

    • Worksheet: lesson 22

    • Lesson 23: Use trigonometric relationships in carrying out integration

    • Worked Out Example: Lesson 23

    • Quiz: Lesson 23

    • Game Time! Find the antiderivative

    • Mini Challenge: Lesson 23

    • Worksheet: lesson 23

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

    • Quiz: Lesson 24

    • Mini Challenge: Lesson 24

    • Worksheet: lesson 24

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

    • Quiz: Lesson 25

    • Mini Challenge: Lesson 25

    • Worksheet: lesson 25

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

    • Worked Out Example: Lesson 26

    • Quiz: Lesson 26

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 26

    • Worksheet: lesson 26

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

    • Worked Out Example: Lesson 27

    • Quiz: Lesson 27

    • Mini Challenge: Lesson 27

    • Worksheet: lesson 27

    • Lesson 28: Using Linear Partial Fractions

    • Quiz: Lesson 28

    • Mini Challenge: Lesson 28

    • Worksheet: lesson 28

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

    • Worked Out Example: Lesson 29

    • Quiz: Lesson 29

    • Game Time! Drag and drop

    • Mini Challenge: Lesson 29

    • Worksheet: lesson 29

    • 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

    • Quiz: Lesson 31

    • Mini Challenge: Lesson 31

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

    • Worked Out Example: Lesson 32

    • Quiz: Lesson 32

    • Game Time! Drag and Drop

    • Mini Challenge: Lesson 32

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

    • Quiz: Lesson 33

    • Mini Challenge: Lesson 33

    • Worksheet: lesson 33

  • 09

    Differential Equations

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

    • Quiz: Lesson 1A

    • Mini Challenge: Lesson 1A

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

    • Worked Out Example: Lesson 1

    • Quiz: Lesson 1B

    • Mini Challenge: Lesson 1B

    • Lesson 2: Verifying Solutions for Differential Equations

    • Quiz: Lesson 2

    • Game Time! Solve the Differential Equation

    • Game Time! True or false

    • Mini Challenge: Lesson 2

    • Worksheet: lesson 2

    • Lesson 3: Sketching Slope Fields

    • Quiz: Lesson 3

    • Mini Challenge: Lesson 3

    • Worksheet: lesson 3

    • Lesson 4: Reasoning Using Slope Fields

    • Quiz: Lesson 4

    • Game Time! Find the correct slope field

    • Mini Challenge: Lesson 4

    • Worksheet: lesson 4

    • Lesson 5: Approximating Solutions Using Euler’s Method

    • Quiz: Lesson 5

    • Mini Challenge: Lesson 5

    • Worksheet: lesson 5

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

    • Worked Out Example: Lesson 6

    • Quiz: Lesson 6

    • Game Time! Solve the Differential Equation

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 6

    • Worksheet: lesson 6

    • Lesson 6B: Finding General Solutions Using Separation of Variables

    • Lesson 7: Exponential Models with Differential Equations

    • Worked Out Example: Lesson 7

    • Quiz: Lesson 7

    • Mini Challenge: Lesson 7

    • Worksheet: lesson 7

    • Lesson 8: Logistic Models with Differential Equations

    • Worked Out Example: Lesson 8

    • Quiz: Lesson 8

    • Game Time! Find the correct function

    • Game Time! Fill in the blank

    • Game Time! Find the correct function

    • Game Time! Fill in the blank

    • Mini Challenge: Lesson 8

    • Worksheet: lesson 8

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

    • Worked Out Example: Lesson 9

    • Quiz: Lesson 9

    • Mini Challenge: Lesson 9

    • Game Time! Flip and Learn

    • Worksheet: lesson 9

  • 10

    Applications of Integration

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

    • Worked Out Example: Lesson 1

    • Quiz: Lesson 1

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 1

    • Worksheet: lesson 1

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

    • Quiz: Lesson 2

    • Mini Challenge: Lesson 2

    • Worksheet: lesson 2

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

    • Quiz: Lesson 3

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 3

    • Worksheet: lesson 3

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

    • Worked Out Example: Lesson 4

    • Quiz: Lesson 4

    • Mini Challenge: Lesson 4

    • Worksheet: lesson 4

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

    • Worked Out Example: Lesson 5

    • Quiz: Lesson 5

    • Mini Challenge: Lesson 5

    • Worksheet: lesson 5

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

    • Worked Out Example: Lesson 6

    • Quiz: Lesson 6

    • Game Time! Question set

    • Mini Challenge: Lesson 6

    • Worksheet: lesson 6

    • Lesson 7: Volumes with Cross Sections: Squares and Rectangles

    • Quiz: Lesson 7

    • Mini Challenge: Lesson 7

    • Worksheet: lesson 7

    • Lesson 8: Volumes with Cross Sections: Triangles and Semicircles

    • Quiz: Lesson 8

    • Mini Challenge: Lesson 8

    • Worksheet: lesson 8

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

    • Quiz: Lesson 10

    • Mini Challenge: Lesson 10

    • Worksheet: lesson 10

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

    • Quiz: Lesson 11

    • Game Time! Drag and drop

    • Mini Challenge: Lesson 11

    • Worksheet: lesson 11

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

    • Quiz: Lesson 12

    • Mini Challenge: Lesson 12

    • Worksheet: lesson 12

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

    • Quiz: Lesson 13

    • Game Time! Drag and drop

    • Mini Challenge: Lesson 13

    • Worksheet: lesson 13

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

    • Quiz: Lesson 14

    • Mini Challenge: Lesson 14

    • Lesson 16: Connect distance travelled to area under a curve

    • Quiz: Lesson 16

    • Mini Challenge: Lesson 16

    • Worksheet: lesson 16

    • Lesson 17: Connect displacement to a single definite integral

    • Quiz: Lesson 17

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 17

    • Worksheet: lesson 17

    • Lesson 19: Initial value problems and anti-derivatives

    • Worked Out Example: Lesson 19

    • Quiz: Lesson 19

    • Game Time! Find the correct function

    • Mini Challenge: Lesson 19

    • Game Time! Drag and Drop

    • Worksheet: lesson 19

  • 11

    Parametric Equations, Polar Coordinates, and Vector-Valued Functions

    • Lesson 1: Defining and Differentiating Parametric Equations

    • Worked Out Example: Lesson 1

    • Quiz: Lesson 1

    • Mini Challenge: Lesson 1

    • Worksheet: lesson 1

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

    • Quiz: Lesson 3

    • Mini Challenge: Lesson 3

    • Worksheet: lesson 3

    • Lesson 4: Defining and Differentiating Vector Valued Functions

    • Worked Out Example: Lesson 4

    • Quiz: Lesson 4

    • Mini Challenge: Lesson 4

    • Worksheet: lesson 4

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

    • Worked Out Example: Lesson 6

    • Quiz: Lesson 6

    • Mini Challenge: Lesson 6

    • Worksheet: lesson 6

    • Lesson 7: Defining Polar Coordinates and differentiating in polar form

    • Quiz: Lesson 7

    • Mini Challenge: Lesson 7

    • Worksheet: lesson 7

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

    • Quiz: Lesson 8

    • Game Time! Flip and Learn

    • Mini Challenge: Lesson 8

    • Worksheet: lesson 8

    • Worked Out Example: Lesson 9

  • 12

    Infinite Sequences and Series

    • 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

    • Worked Out Example: Lesson 4

    • Quiz: Lesson 4

    • Mini Challenge: Lesson 4

    • Lesson 5: P Series

    • Quiz: Lesson 5

    • Mini Challenge: Lesson 5

    • Worksheet: lesson 5-8

    • Lesson 6: Harmonic Series

    • Quiz: Lesson 6

    • Mini Challenge: Lesson 6

    • Lesson 7: Comparison tests for convergence

    • Worked Out Example: Lesson 7

    • Quiz: Lesson 7

    • Mini Challenge: Lesson 7

    • Lesson 8: Alternating series test for convergence

    • Worked Out Example: Lesson 8

    • Quiz: Lesson 8

    • Mini Challenge: Lesson 8

    • Lesson 9: Determining absolute or conditional convergence

    • Quiz: Lesson 9

    • Mini Challenge: Lesson 9

    • Worksheet: lesson 9-12

    • Lesson 10: Ratio Test for Convergence

    • Quiz: Lesson 10

    • 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

    • Quiz: Lesson 12

    • Mini Challenge: Lesson 12

    • Lesson 13: Lagrange error bound

    • Worked Out Example: Lesson 13

    • Quiz: Lesson 13

    • Mini Challenge: Lesson 13

    • Worksheet: lesson 13-16

    • Lesson 14: Radius and Interval of Convergence of Power Series

    • Worked Out Example: Lesson 14

    • Quiz: Lesson 14

    • Mini Challenge: Lesson 14

    • Lesson 15: Representing Functions as Power Series

    • Worked Out Example: Lesson 15

    • Quiz: Lesson 15

    • Mini Challenge: Lesson 15

    • Lesson 16: Finding Taylor or Maclaurin Series for a Function

    • Worked Out Example: Lesson 16

    • Quiz: Lesson 16

    • Game Time! Flip and Learn

    • Mini Challenge: Lesson 16

  • 13

    Vectors

    • 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

    • Worked Out Example: Lesson 3

    • Quiz: Lesson 3

    • Mini Challenge: Lesson 3

    • Worksheet: lesson 3

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

    • Quiz: Lesson 4

    • Mini Challenge: Lesson 4

    • Worksheet: lesson 4

    • 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

    • Quiz: Lesson 6

    • Mini Challenge: Lesson 6

    • Worksheet: lesson 6

    • Lesson 7: Multiplication of vector by a scalar

    • Quiz: Lesson 7

    • Mini Challenge: Lesson 7

    • Worksheet: lesson 7

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

    • Worked Out Example: Lesson 8

    • Quiz: Lesson 8

    • Mini Challenge: Lesson 8

    • Worksheet: lesson 8

    • Lesson 9B: Adding position vectors by components

    • Quiz: Lesson 9B

    • Mini Challenge: Lesson 9B

    • Worksheet: lesson 9B

    • Lesson 9C: Adding position vectors with the cosine law

    • Quiz: Lesson 9C

    • Mini Challenge: Lesson 9C

    • Worksheet: lesson 9C

    • Lesson 9A: Real-world applications of vectors

    • Quiz: Lesson 9A

    • Mini Challenge: Lesson 9A

    • Worksheet: lesson 9A

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

    • Worked Out Example: Lesson 10

    • Quiz: Lesson 10

    • Mini Challenge: Lesson 10

    • Worksheet: lesson 10

    • Lesson 11: Translation by a vector

    • Worked Out Example: Lesson 11

    • Quiz: Lesson 11

    • Mini Challenge: Lesson 11

    • Worksheet: lesson 11

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

    • Quiz: Lesson 12

    • Mini Challenge: Lesson 12

    • Worksheet: lesson 12

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

    • Quiz: Lesson 13

    • Mini Challenge: Lesson 13

    • Worksheet: lesson 13

    • Lesson 14A: The dot product of two vectors

    • Worked Out Example: Lesson 14A

    • Quiz: Lesson 14A

    • Mini Challenge: Lesson 14A

    • Worksheet: lesson 14A

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

    • Quiz: Lesson 14B

    • 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

  • 14

    Lines in the Plane and in Space

    • 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

  • 15

    Geometry

    • 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

  • 16

    Coordinate Geometry

    • 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

  • 17

    Congruence and Similarity

    • 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

  • 18

    Circles

    • 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

  • 19

    Transformations of 2D Shapes

    • 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

  • 20

    Non-Euclidean Geometries

    • 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

  • 21

    Complex Numbers

    • 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

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