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What better way to ace the AP exam than to learn from someone who aced it himself? Professor John Zhu brings together education and teaching experience to Educator's AP Calculus AB course.  John explains complicated calculus ideas in easy, understandable terms so that any student can succeed on the exam. In addition, all the topics on the test are covered with many extra examples, as well as a full length practice test at the end of the course. Topics include an Overview of Functions, Derivatives, Integrals, Area between Curves, Revolving Solids, and Differential Equations. Professor Zhu received his B.S. in Electrical Engineering from Michigan State, his MBA from Webster University, and has been teaching AP Calculus for over eight years.

## Section 1: Functions

Definitions & Properties of Functions 11:26
Intro 0:00
Definition 0:28
Properties: Vertical Line Test 1:32
Domain 1:38
Range 1:59
Vertical Line test 2:19
Example 1 2:33
Example 2 3:10
Properties: Roots or Zeros 4:04
Finding the Root 4:16
Properties: Forms 5:12
Graphically 5:20
List 5:46
Equation 6:11
Function 6:38
Properties: Odd & Even 7:12
Even Function 7:14
Odd Function 8:25
Properties: Increasing & Decreasing 9:17
Increasing Function 9:22
Decreasing Function 10:21
Graphing 13:58
Intro 0:00
Manipulating 0:10
A in the Equation 0:39
B in the Equation 0:44
C & D in the Equation 0:49
Negative values 0:59
Example 1 1:17
Example 2 1:51
Example 3: Absolute Value Functions 3:43
Example 4 4:57
Example 5 6:17
Example 6 8:02
Example 7 9:10
Example 8 11:02
Example 9 11:47
Inverse Functions 6:47
Intro 0:00
Inverse 0:08
Definition 0:18
Example: Finding the Inverse 1:03
Example 2 2:29
Example 3 3:12
Example 4 4:41
Polynomial Functions 5:04
Intro 0:00
Types of Functions: Polynomials 0:07
No Domain Restrictions 0:12
No Discontinuities 0:19
Degree Test 0:31
Types of Functions: Polynomials 1:17
Leading Coefficient Positive, Even Degree 1:54
Leading Coefficient Positive, Odd Degree 2:13
Leading Coefficient Negative Even Degree 2:34
Leading Coefficient Positive, Odd Degree 2:46
Examples: Types of Functions: Polynomials 3:03
Examples: Types of Functions: Polynomials 4:18
Trigonometric Functions 6:45
Intro 0:00
Types of Functions: Trigonometric 0:05
6 Functions To Be Familiar With 0:14
Example 1: SIN 1:38
Example 2: COS 3:22
Example 3: TAN 4:38
Inverse Trigonometric Functions 5:58
Intro 0:00
Types of Functions: Trigonometric- Inverse Trig Functions 0:07
Example: Inverse SIN of X 0:45
Example: Inverse Function 2:30
Example: Inverse TAN of X 4:42
Trigonometric Identities 17:42
Intro 0:00
Types of Functions: Trigonometric- Trig Identities 0:07
4 Identities 0:24
Pythagorean 0:28
Double Angle 1:10
Power Reducing 1:28
Sum or Difference 1:42
Couple More Identities 1:59
Negative Angle 2:04
Product to Sum 2:39
Example 1: Prove 3:00
Example 2: Simplify Expression 5:02
Example 3: Prove 5:56
Example 4: Prove 8:02
Example 5: Prove With TAN 12:43
Exponential Functions 5:53
Intro 0:00
Types of Functions: Exponentials 0:07
General Form 0:10
Special Exponential Function 0:17
Example 1: Using Exponential Properties 0:46
Example 2: Using Exponential Properties 1:58
Example 3: Using Trig Identities & Exponential Properties 3:16
Example 4: Using Exponential Properties 4:37
Logarithmic Functions 7:08
Intro 0:00
Types of Functions: Logarithmic 0:06
General Form 0:10
2 Special Logarithmic Func. 0:19
Euler's # / Natural Log 0:27
Logarithmic & Exponential Relationship 0:45
Log form 1:56
Properties 2:09
Example 1: Apply Basic Principle of Log Func. 3:05
Example 2: Use Properties 3:40
Example 3: Regular Log 5:16
Rational Functions 15:36
Intro 0:00
Types of Functions: Rational - Definition 0:06
Example 1: Graph Rational Func. 0:36
Example 2: Find Asymptotes of Func. 7:02
Example 3: Find Asymptotes of Func. 8:59
Example 4: Graph Rational Func. 11:08
Conic Sections 14:58
Intro 0:00
Types of Conic Sections 0:06
Parabolas 0:19
Circles 1:36
Ellipses 2:40
Hyperbolas 4:42
Complete the Square 6:40
Example: Conic Sections 9:08
Example 2: Conic Sections 10:59
Example 3: Graph Conic Sections 12:21

## Section 2: Limits and Continuity

Limit Definition & Properties 7:15
Intro 0:00
Definition 0:06
Example: Limit 0:17
Properties 1:13
1st Property 1:21
2nd Property 1:34
Special Property 1:51
Limits 2:36
Explain Example 2:49
Limits Example 4:39
Limits Example 5:21
Solving Limits with Algebra 8:01
Intro 0:00
Solving Limits with Algebra 0:07
Example 1: Solve Algebraically 0:30
Solving Limits with Algebra, Example 2 2:28
Solving Limits with Algebra, Example 3 3:18
Solving Limits with Algebra, Example 4 4:56
Solving Limits with Algebra, Example 5 6:26
Rational Limit Rules 3:16
Intro 0:00
Rational Limit Rules 0:07
Review of Solving Problem Algebraically 0:08
Limit Rules 0:28
Rule 1 0:35
Rule 2 0:40
Rule 3 0:45
Rational Limit Rules 1:02
Applying 1st Rule 1:22
Rational Limit Rules 1:50
Applying 2nd Rule 2:09
Rational Limit Rules 2:26
Applying 3rd Rule 2:40
One Sided Limits 9:57
Intro 0:00
Types of Limits: One-Sided Limit Rules 0:06
Example 0:19
Applying Same Rule 0:34
Rule to Keep In Mind 0:52
Types of Limits: One-Sided Limit Example 1 1:12
Limit of x² From Negative Side 2:11
Types of Limits: One-Sided Limit, Example 2 2:27
Types of Limits: One-Sided Limit, Example 3 4:26
Types of Limits: One-Sided Limit, Example 4 5:47
One-Sided Limit Example: X with Even Degree Polynomial 7:00
One-Sided Limit Example: Entire Denominator Squared 8:09
Special Trigonometric Limits 8:28
Intro 0:00
Types of Limits: Special Trig Limits 0:07
Pre-set Rules 0:35
Special Trig Limits, Example 1 0:58
Special Trig Limits, Example 2 2:50
Special Trig Limits, Example 3 3:55
Special Trig Limits, Example 4: With More Degrees 4:57
Special Trig Limits, Example 5 6:21
Limits & Continuity 10:14
Intro 0:00
Definition 0:06
3 Rules: f(x) Is Continuous… 0:21
Example 1: Finding Continuity 1:06
Types of Discontinuity 2:44
Jump 2:52
Point 3:24
Essential (Asymptote) 3:47
Removable 4:17
Example 2: Continuity Examples 4:41
Example 3: Continuity Examples 6:13
Example 4: Locate & Identify Type of Discontinuities 8:00
Limits: Multiple Choice Practice 6:16
Intro 0:00
Problem 1 0:08
Problem 2 1:51
Problem 3 2:54
Problem 4 4:31

## Section 3: Derivatives

Derivative Definition & Properties 4:11
Intro 0:00
Definition 0:09
Formal Definition 0:45
Difference Quotient 1:12
Basic Derivatives 1:16
Differentiability 2:54
Basic Rules of Differentiation 7:07
Intro 0:00
Basic Rules of Differentiation 0:09
Constant Rule 0:14
Constant Multiple Rule 1:10
Example 1: Constant Rule 2:25
Example 2: Constant Multiple Rule 3:01
Example 3: Constant Multiple Rule 3:35
Example 4: Constant Rule 4:34
Example 5: Constant Multiple Rule 5:03
Example 6 5:33
Power Rule 7:14
Intro 0:00
Power Rule 0:07
Power Rule Definition 0:30
Example 1 1:11
Example 2 2:25
Example 3 3:05
Example 4 4:18
Example 5 5:13
Trigonometric Rules 7:53
Intro 0:00
Trigonometric Rules 0:07
COS X 0:38
Find Derivative 1:02
Example 1 2:46
Example 2: COS Function 3:09
Example 3: Composite Expression 3:54
Example 4: Sec Function 5:02
Example 5: CSC 5:33
Example 6L COT 6:42
Product Rule 11:11
Intro 0:00
Product Rule 0:07
Definition 0:20
Example 1 0:43
Example 2 2:11
Example 3 4:24
Example 4 5:24
Example 5 6:42
Example 6 7:51
Quotient Rule 16:50
Intro 0:00
Quotient Rule 0:07
Definition 0:30
Example 1 1:17
Example 2: With No X In Numerator 2:49
Example 3 4:30
Example 4: With Decimals 6:46
Example 5 8:53
Example 6: With Trig Functions 12:55
Chain Rule 19:48
Intro 0:00
Chain Rule 0:07
Definition 0:17
Example 1: Applying the Chain Rule 1:33
Example 2 4:25
Example 3 6:02
Example 4 9:25
Example 5 12:47
Example 6 15:27
Higher Order Derivatives 15:00
Intro 0:00
Types of Derivatives: Higher Order Derivatives 0:07
1st Derivative / F Prime 0:19
2nd Derivative 0:25
3rd Derivative 0:32
Example 1 1:48
Example 2: Find 3rd Derivative 3:13
Example 3: Acceleration 4:25
Example 4 10:20
Example 5: 2nd Derivative 12:11
Derivatives of Exponential Functions 13:14
Intro 0:00
Types of Derivatives: Exponential Functions 0:08
Derivatives: Definition/ Formula 0:28
Example 1 1:25
Example 2 2:47
Example 3 4:13
Example 4 7:11
Example 5 9:23
Example 6 11:06
Derivatives of Logarithmic Functions 11:30
Intro 0:00
Types of Derivatives: Logarithmic Functions 0:06
Rule for Logarithmic Functions 0:28
Example 1 0:58
Example 2 3:10
Example 3 4:38
Example 4 7:18
Example 5 8:48
Example 6 9:38
Derivatives of Inverse Trigonometric Functions 16:54
Intro 0:00
Types of Derivatives: Inverse Trigonometric Functions 0:06
6 Fundamental Properties of Inverse Trigonometric Functions 0:38
Example 1 2:17
Example 2 3:41
Example 3 5:37
Example 4 7:24
Example 5 10:08
Implicit Differentiation 16:53
Intro 0:00
Implicit Differentiation: First Order 0:07
Example 1: Setting Up 0:45
Example 1: Solving 1:41
Implicit Differentiation: Second Order (Ex. 2) 4:55
Example 3: Implicit Differentiation 9:11
Example 4: Implicit Differentiation 9:56
Example 5: Implicit Differentiation With Double Derivative 12:46
Multiple Choice Practice: Derivatives 11:07
Intro 0:00
Practice Problem 1 0:09
Practice Problem 2 3:36
Practice Problem 3 6:42
Practice Problem 4 8:43
Practice Problem 5 9:41

## Section 4: Applications of Derivatives

Tangent & Normal Lines 22:36
Intro 0:00
Tangent and Normal Lines 0:10
Definition 0:22
Example 1 0:55
Tangent and Normal Lines: Example 2 2:43
Tangent and Normal Lines 5:21
Example 3 5:35
Tangent and Normal Lines: Example 4 9:14
Tangent and Normal Lines: Example 5 12:27
Tangent and Normal Lines: Example 6 15:54
Tangent and Normal Lines: Example 7 19:05
Position Velocity & Acceleration 18:42
Intro 0:00
Position, Velocity, and Acceleration 0:10
Position Function 0:14
Velocity Function 0:34
Acceleration Function 1:01
Example 1 1:20
Example 2 6:31
Example Continue: Velocity When Acceleration is Zero 6:32
Example 3: Where Is Particle Changing Directions? 8:16
Example 4: Total Distance Traveled From 0 to 2 Second 11:09
Example 5: Ball Drop Problem 16:40
Related Rates 26:22
Intro 0:00
Related Rates 0:06
Finding Rate of Change: Organization & Big Picture 0:23
Example 2: Area of a Circle 1:17
Example 3: Spherical Volume Expanding 4:19
Example 4: Traveling Problem 7:57
Example 5: Square Increase 12:37
Example 6: Standard Related Rates Problem 16:59
Example 7: Standard Related Rates Problem 19:49
Minimum & Maximum 12:22
Intro 0:00
Extrema: First Derivative Test 0:09
Example 1 0:46
Example 2: Real World Application/ Cost Function 4:05
Example 3: Minimums & Maximums 7:10
Example 4: Find Critical Points 10:52
Concavity 11:43
Intro 0:00
Concavity: Second Derivative Test 0:06
Definition 0:34
Example 1 0:54
Example 2 2:51
Example 3 4:08
Example 4 5:52
Rolles Theorem 8:28
Intro 0:00
Rolle's Theorem 0:07
Conditions 0:11
Summary 0:41
Example 1 1:09
Example 2 3:08
Example 3 4:48
Mean Value Theorem 9:39
Intro 0:00
Mean Value Theorem 0:06
Rolle's Theorem 0:07
Mean Value Theorem Conditions 0:24
Mean Value Theorem Definition 0:36
Example 1 0:56
Example 2 2:44
Example 3 5:28
Example 4 7:15
Differentials 12:25
Intro 0:00
Differentials 0:08
1st Differential Formula 0:29
2nd Differential Formula 0:57
Example 1 1:06
Example 2 3:21
Example 3 5:49
Example 4 7:19
Example 5 9:06
Applications of Derivatives: Multiple Choice Practice 13:21
Intro 0:00
Practice Problem 1 0:10
Practice Problem 2 2:08
Practice Problem 3 5:45
Practice Problem 4 10:12
Practice Problem 5 11:52
Applications of Derivatives: Free Response Practice 10:22
Intro 0:00
Practice Problem 1 0:10
Slope 1:30
Tangent Line Equation 2:17
Absolute Minimum 2:24
2 Possible X Points With Minimums 3:15
One Interest Point 4:14
Concavity 4:33
Positive Value = Positive Concavity 4:10
Minimum Point 5:34
Absolute Minimum 6:18
Point(s) of Inflection 6:31
Definition 6:49
2 Points Of Inflection 9:59

## Section 5: Integrals

Definition of Integrals 1:08
Intro 0:00
Definition 0:09
Definition 0:16
Example 0:20
Integrals of Power Rule 8:50
Intro 0:00
Power Rule 0:06
Example 1 0:25
Example 2 2:02
Example 3 2:54
Example 4 3:45
Example 5 4:49
Example 6 6:47
Integrals Basic Rules of Integration 9:43
Intro 0:00
Basic Rules of Integration 0:09
Constant Rule 0:22
Example 1 0:40
Example 2 1:58
Example 3: Subtraction/ Difference Rule 2:47
Example 4 3:55
Example 5 5:19
Example 6 7:37
Trigonometric Rules of Integrals 8:58
Intro 0:00
Trigonometric Rules 0:09
Integral of SIN 0:38
Example 1: Integral of SIN 1:46
Example 2: Integral of COS 2:38
Example 3: With 2 terms of X 3:06
Example 4: Integral of SEC 4:15
Example 5: Integral of CSC 5:06
Example 6 6:18
Chain Rule 13:59
Intro 0:00
Chain Rule 0:07
Example 1 0:37
Example 2 3:17
Example 3 5:09
Example 4 7:53
Example 5 9:40
Example 6 11:39
Integrals of Exponential Functions 12:52
Intro 0:00
Types of Integrals: Exponential Functions 0:09
Rule 1 0:30
Rule 2 0:49
Example 1 1:11
Example 2 2:54
Example 3 4:19
Example 4 5:19
Example 5 7:37
Example 6 9:04
Integrals of Natural Logarithmic Functions 13:00
Intro 0:00
Types of Integrals: Natural Log Functions 0:09
Example 1 0:49
Example 2 2:06
Example 3 4:01
Example 4 5:37
Example 5 7:30
Example 6 9:05
Integrals of Inverse Trigonometric Functions 8:29
Intro 0:00
Types of Integrals: Inverse Trig Functions 0:09
One Property 0:40
Example 1 1:19
Example 2 3:44
Example 3 4:53
Example 4 5:53
Integrals: Multiple Choice Practice 15:37
Intro 0:00
Problem 1 0:09
Problem 2 4:33
Problem 3 5:59
Problem 4 8:06
Problem 5 10:43

## Section 6: Applications of Integrals

Fundamental Theorem of Calculus 15:55
Intro 0:00
Fundamental Theorem of Calculus: Properties 0:10
Definition of Integral 0:49
Example 1 1:14
Fundamental Theorem of Calculus: Properties 2:40
Rule 1 2:50
Rule 2 3:14
Rule 3 3:33
Rule 4 3:52
Example 2 4:07
Example 3 6:17
Example 4 9:31
Example 5 10:52
Example 6 13:34
Area Under A Curve 18:34
Intro 0:00
Area Under Curve 0:07
Definition of Integral 0:09
Left Endpoint 1:17
Right Endpoint 1:47
Midpoints 2:09
Example 1 2:40
Example 2 4:59
Example 3 8:48
Example 4 10:23
Example 5 12:30
Example 6 15:32
Reimann Sums 10:35
Intro 0:00
Reimann Sums 0:08
Definition 1:07
Example 1 2:48
Example 2 5:38
Example 3 7:21
Example 4 9:14
Trapezoid Rule 12:46
Intro 0:00
The Trapezoid Rule 0:09
Definition: Area Of A Trapezoid 0:26
Terms of Formula 1:35
Example 1 2:11
Example 2 4:29
Example 3 7:22
Example 4 10:01
Mean Value Theorem 11:22
Intro 0:00
Mean Value Theorem of Integration 0:06
Example 1 0:53
Example 2 2:29
Example 3 3:48
Example 4 6:02
Second Fundamental Theorem of Calculus 4:44
Intro 0:00
Second Fundamental Theorem of Calculus 0:07
Definition 0:39
Example 1 1:08
Example 2 2:07
Example 3 2:48
Example 4 3:23
Area Between Curves 16:39
Intro 0:00
Example 1 0:10
Example 2 3:00
Example 3 4:46
Example 4 8:22
Example 5 11:04
Example 6 13:09
Revolving Solids Washer Disk Methods 21:09
Intro 0:00
Revolving Solids Washer Disk Methods 0:11
Explanation 0:33
Formula 3:12
Example 1 3:42
Example 2 6:54
Example 3 9:29
Example 4 12:16
Example 5 15:35
Revolving Solids Cylindrical Shells Method 26:46
Intro 0:00
Revolving Solids: Cylindrical Shells Method 0:09
Volume Of A Solid 0:25
Formula 2:51
Example 1 2:56
Example 2 7:28
Example 3 11:39
Example 4 17:36
Example 5 21:45
Revolving Solids Known Cross Sections 27:41
Intro 0:00
Revolving Solids Known Cross Sections 0:08
Example 1 0:35
Example 2 6:01
Example 3 11:03
Example 4 17:29
Example 5 22:19
Differential Equations Eulers Method 17:54
Intro 0:00
Differential Equations 0:08
Example 1 0:30
Differential Equations: Euler's Method 2:33
Rules 2:39
Example 2 3:00
Example 3 5:42
Example 4 9:44
Example 5 14:14
Differential Equations Slope Fields 16:30
Intro 0:00
Slope Fields 0:08
What Are Slope Fields 0:21
Example 1 0:42
Example 2 6:30
Example 3 11:17
Application of Integrals: Multiple Choice Practice 14:19
Intro 0:00
Practice Problem 1 0:10
Practice Problem 2 3:49
Practice Problem 3 6:26
Practice Problem 4 8:07
Practice Problem 5 11:05
Application of Integrals: Free Response Practice 9:14
Intro 0:00
Problem 1 0:10
Part A 0:24
Part A: Solution 2:04
Part B 2:10
Problem 1, Part B Continue 2:23
Part B: Solution 6:15
Problem 1, Part C 6:58
Part C: Solution 12:40
Problem 2 12:52
Part A 13:02
Part A: Solution 15:34
Part B 16:03
Part B: Solution 18:48

## Section 7: Sample AP Test

AP Calculus AB Practice test: Section 1: Multiple Choice Part 1 17:50
Intro 0:00
Problem 1 0:20
Problem 2 1:24
Problem 3 2:53
Problem 4 3:56
Problem 5 8:18
Problem 6 9:06
Problem 7 10:14
Problem 8 12:16
Problem 9 14:13
AP Calculus AB Practice test: Section 1: Multiple Choice Part 2 17:32
Intro 0:00
Problem 10 0:18
Problem 11 2:26
Problem 12 6:11
Problem 13 7:04
Problem 14 8:06
Problem 15 10:32
Problem 16 11:40
Problem 17 13:00
Problem 18 14:43
AP Calculus AB Practice test: Section 1: Multiple Choice Part 3 22:14
Intro 0:00
Problem 19 0:21
Problem 20 2:33
Problem 21 7:23
Problem 22 10:24
Problem 23 12:18
Problem 24 13:13
Problem 25 15:52
Problem 26 17:03
Problem 27 19:44
AP Calculus AB Practice test: Section 1: Multiple Choice Part 4 19:35
Intro 0:00
Problem 28 0:23
Problem 29 3:50
Problem 30 5:31
Problem 31 9:02
Problem 32 10:07
Problem 33 11:27
Problem 34 13:47
Problem 35 15:21
Problem 36 16:53
AP Calculus AB Practice test: Section 1: Multiple Choice Part 5 25:43
Intro 0:00
Problem 37 0:22
Problem 38 2:27
Problem 39 5:36
Problem 40 7:21
Problem 41 10:08
Problem 42 11:29
Problem 43 13:07
Problem 44 18:18
Problem 45 21:08
AP Calculus AB Practice Test: Section 2: Free Response Part 1 16:50
Intro 0:00
Problem 1, Part A 0:20
Problem 1, Part B 3:03
Problem 1, Part C 4:11
Problem 1, Part D 5:36
Problem 2, Part A 7:37
Problem 2, Part B 9:02
Problem 2, Part C 12:31
AP Calculus AB Practice Test: Section 2: Free Response Part 2 21:36
Intro 0:00
Problem 3, Part A 0:18
Problem 3, Part B 5:57
Problem 4, Part A 11:26
Problem 4, Part B 12:28
Problem 4, Part C 15:35
Problem 4, Part D 18:56
AP Calculus AB Practice Test: Section 2: Free Response Part 3 13:39
Intro 0:00
Problem 5, Part A 0:21
Problem 5, Part B 3:07
Problem 5, Part C 6:43
Problem 6 8:24

Duration: minutes

Number of Lessons:

#### Student Feedback

4.1

15 Reviews

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By Mohamed Al MohannadiFebruary 1, 2017
Thank you yes thats what i thought
By Bilbo BagginsSeptember 4, 2015
don't take calculus if you don't understand, don't slow down the entire class because you are whining and think you are some genius who can understand calculus right away and then go on to create something generations ahead of you will remember.
By Nolan ZhangApril 10, 2015
that explanation of Chain rule really helped me a lot!
By Nolan ZhangApril 7, 2015
Good evening, so by what is the definition of 'reflect something over X/Y axis as in example 3'. It seems to me that you simply draw out what G(x) looks like using the given info. So does 'reflect' simply means 'draw something out?'
By Debora MroczekMarch 3, 2015
You're a great teacher! =)

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