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• ### Easy to understand

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• ### Engaging Discussions

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• ### Real World Applications

Build confidence in your new skills with a variety of hands-on activities, quizzes, projects and real life simulations.

## Course curriculum

• 01

### Registration

• Registration Information

• Required Student Information

• 02

• 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

## Reviews

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## Enroll Now

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• What grade is this level for?

This level is designed for kids ages 11-12 in Grades 6 and 7.

• How is this course taught?

These (virtual) programs are designed to be completely self learnt. Students progress through the curriculum using a variety of real world applications that simulate experience, utilize creative thinking, and allow the students to test their knowledge.