**AP Calculus Tutoring**

# AP Calculus Tutoring

## Ace the exam with the help of personalized AP Calculus Expert Tutors

**AP Calculus tutor**online especially when you hope to pursue math in college. The course, offered by the American College Board consists of two different parts namely AP Calculus AB and AP Calculus BC. The former will introduce you to derivatives, integers and limits while the latter will cover a range of additional topics in addition. Both courses are similar to college calculus course taught in first year at American Colleges and Universities. It is impossible to take both exams simultaneously as the dates usually clash. However, you can opt for one or the other according to your comfort level. You will be pleased to learn that you qualify for receiving a sub score based on your performance in AB Calculus if you choose to take Calculus BC after AB.

## Online AP Calculus tutoring

You can breeze through the course if you have an aptitude for math. Getting the help of a seasoned **AP Calculus tutor** will set you on the right path as well. The subject matter tutor will guide you perfectly as you learn how to determine the values and express the solutions using proven mathematical tactics**. AP Calculus Course **will help you to understand how to use the correct terms and notations for communicating the results once you find the solution.

The entire course for AP Calculus AB & BC is divided into 10 units for easy understanding. The **Calculus Tutor and Tutoring** resources are free to streamline the process further in accordance with your needs. You may check out the percentage of questions expected from each unit by looking at the chart below.

AP Calculus (AB) | Percentage of Qs Expected | Multiple Choice Questions | Free Response Questions | Approx number of Sessions |
---|---|---|---|---|

Unit 1: Limits & Continuity | 10%-12% | 45 | 3 | 12 |

Unit 2: Differentiation: Definition and Fundamental Properties | 10%-12% | 30 | 3 | 13 |

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions | 9%-13% | 15 | 3 | 10 |

Unit 4: Contextual Applications of Differentiation | 10%-15% | 15 | 3 | 12 |

Unit 5: Analytical Applications of Differentiation | 15%-18% | 35 | 3 | 12 |

Unit 6: Integration and Accumulation of Change | 17%-20% | 25 | 3 | 18 |

Unit 7: Differential Equations | 6%-12% | 15 | 3 | 10 |

Unit 8: Applications of Integration | 10%-15% | 30 | 3 | 13 |

AP Calculus (BC) | Percentage of Qs Expected | Multiple Choice Questions | Free Response Questions | Approx number of Sessions |
---|---|---|---|---|

Unit 1: Limits & Continuity | 4%-7% | 45 | 3 | 10 |

Unit 2: Differentiation: Definition and Fundamental Properties | 4%-7% | 30 | 3 | 9 |

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions | 4%-7% | 15 | 3 | 9 |

Unit 4: Contextual Applications of Differentiation | 6%-9% | 15 | 3 | 7 |

Unit 5: Analytical Applications of Differentiation | 8%-11% | 35 | 3 | 8 |

Unit 6: Integration and Accumulation of Change | 17%-20% | 35 | 3 | 15 |

Unit 7: Differential Equations | 6%-9% | 20 | 3 | 8 |

Unit 8: Applications of Integration | 6%-9% | 30 | 3 | 12 |

Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions | 11%-12% | 25 | 3 | 8 |

Unit 10: Infinite Sequences and Series | 17%-18% | 45 | 3 | 14 |

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#### Our experienced tutor will guide you towards fulfillment of your objectives by helping you closely with the following.

**Unit 1: Limits and Continuity (Multiple-Choice: ~ 45 questions Free-Response: 3 questions- partial)**

1.1 Introducing Calculus: Can Change Occur at an Instant?

1.2 Defining Limits and Using Limit Notation

1.3 Estimating Limit Values from Graphs

1.4 Estimating Limit Values from Tables

1.5 Determining Limits Using Algebraic Properties of Limits

1.6 Determining Limits Using Algebraic Manipulation

1.7 Selecting Procedures for Determining Limits

1.8 Determining Limits Using the Squeeze Theorem

1.9 Connecting Multiple Representations of Limits

1.10 Exploring Types of Discontinuities

1.11 Defining Continuity at a Point

1.12 Confirming Continuity 1 over an Interval

1.13 Removing Discontinuities

1.14 Connecting Infinite Limits and Vertical Asymptotes

1.15 Connecting Limits at Infinity and Horizontal Asymptotes

1.16 Working with the Intermediate Value Theorem (IVT)

**Unit 2: Differentiation: Definition and Basic Derivative Rules (Multiple-Choice : ~ 30 questions Free – Response: 3 questions- partial)**

2.1 Defining Average and Instantaneous Rates of Change at a Point

2.2 Defining the Derivative of a Function and Using Derivative Notation

2.3 Estimating Derivatives of a Function at a Point

2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist

2.5 Applying the Power Rule

2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple

2.7 Derivatives of cos x, sin x, and ln x

2.8 The Product Rule

2.9 The Quotient Rule

2.10 Finding the Derivatives of Tangent, Cotangent, 1Secant, and/or Cosecant Functions

**Unit 3: Differentiation: Composite, Implicit, and Inverse Functions (Multiple-Choice: ~15 questions Free-Response: 3 questions- partial/full)**

3.1 The Chain Rule

3.2 Implicit Differentiation

3.3 Differentiating Inverse Functions

3.4 Differentiating Inverse Trigonometric Functions

3.5 Selecting Procedures for Calculating Derivatives

3.6 Calculating Higher Order Derivatives

**Unit 4: Contextual Applications of Differentiation (Multiple-Choice: ~15 questions Free-Response: 3 questions)**

4.1 Interpreting the Meaning of the Derivative in Context

4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration

4.3 Rates of Change in Applied Contexts Other Than Motion

4.4 Introduction to Related Rates

4.5 Solving Related Rates Problems

4.6 Approximating Values of a Function Using Local Linearity and Linearization

4.7 Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms

**Unit 5: Analytical Applications of Differentiation (Multiple-Choice: ~35 questions Free-Response: 3 questions)**

5.1 Using the Mean Value Theorem

5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points

5.3 Determining Intervals on Which a Function Is Increasing or Decreasing

5.4 Using the First Derivative Test to Determine Relative (Local) Extrema

5.5 Using the Candidates Test to Determine Absolute (Global) Extrema

5.6 Determining Concavity of Functions over Their Domains

5.7 Using the Second Derivative Test Determine Extrema

5.8 Sketching Graphs of Functions and Their Derivatives

5.9 Connecting a Function, Its First Derivative, and Its Second Derivative

5.10 Introduction to Optimization Problems

5.11 Solving Optimization Problems

5.12 Exploring Behaviors of Implicit Relations

**Unit 6: Integration and Accumulation of Change (Multiple-Choice: ~25 questions(AB) 35 questions (BC) Free-Response: 3 questions)**

6.1 Exploring Accumulations of Change

6.2 Approximating Areas with Riemann Sums

6.3 Riemann Sums, Summation Notation, and Definite Integral Notation

6.4 The Fundamental Theorem of Calculus and Accumulation Functions

6.5 Interpreting the Behavior of Accumulation Functions Involving Area

6.6 Applying Properties of Definite Integrals

6.7 The Fundamental Theorem of Calculus and Definite Integrals

6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation

6.9 Integrating Using 1 Substitution

6.10 Integrating Functions Using Long Division Integrating Functions Using Long Division and Completing the Square

6.11 Integrating Using Integration by Parts BC only

6.12 Using Linear Partial Fractions BC only

6.13 Evaluating Improper Integrals BC only

6.14 Selecting Techniques for Anti-differentiation

**Unit 7: Differential Equations (Multiple-Choice: ~15 questions(AB) 20 questions (BC) Free-Response: 3 questions)**

7.1 Modeling Situations with Differential Equations

7.2 Verifying Solutions for Differential Equations

7.3 Sketching Slope Fields

7.4 Reasoning Using Slope Fields

7.5 Approximating Solutions Using Euler’s Method BC only

7.6 Finding General Solutions Using Separation of Variables

7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables

7.8 Exponential Models with Differential Equations

7.9 Logistic Models with Differential Equations BC only

**Unit 8: Applications of Integration (Multiple-Choice: ~30 questions Free-Response: 3 questions)**

8.1 Finding the Average Value of a Function on an Interval

8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals

8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts

8.4 Finding the Area Between Curves Expressed as Functions of x

8.5 Finding the Area Between Curves Expressed as Functions of y

8.6 Finding the Area Between Curves That Intersect at More Than Two Points

8.7 Volumes with Cross Sections: Squares and Rectangles

8.8 Volumes with Cross Sections: Triangles and Semicircles

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

8.10 Volume with Disc Method: Revolving Around Other Axes

8.11 Volume with Washer Method: Revolving Around the x- or y-Axis

8.12 Volume with Washer Method: Revolving Around Other Axes

8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled BC only

**Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions for BC only (Multiple-Choice: ~25 questions Free-Response: 3 questions)**

9.1 Defining and Differentiating Parametric Equations

9.2 Second Derivatives of Parametric Equations

9.3 Finding Arc Lengths of Curves Given by Parametric Equations

9.4 Defining and Differentiating Vector Valued Functions

9.5 Integrating Vector1 Valued Functions

9.6 Solving Motion Problems Using Parametric and Vector Valued Functions

9.7 Defining Polar Coordinates and Differentiating in Polar Form

9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve

9.9 Finding the Area of the Region Bounded by Two Polar Curves

**Unit 10: Infinite Sequences and Series for BC only (Multiple-Choice: ~45 questions Free-Response: 3 questions)**

10.1 Defining Convergent and Divergent Infinite Series

10.2 Working with Geometric Series

10.3 The nth Term Test for Divergence

10.4 Integral Test for Convergence

10.5 Harmonic Series and p-Series

10.6 Comparison Tests for Convergence

10.7 Alternating Series Test for Convergence

10.8 Ratio Test for Convergence

10.9 Determining Absolute or Conditional Convergence

10.10 Alternating Series Error Bound

10.11 Finding Taylor Polynomial Approximations of Functions

10.12 Lagrange Error Bound

10.13 Radius and Interval of Convergence of Power Series

10.14 Finding Taylor or Maclaurin Series for a Function

10.15 Representing Functions as Power Series

## eTutorWorld Advantage – AB Calculus Tutoring & BC Calculus Tutoring

**Stay Ahead-**Remain a step ahead of your peers by preparing for the AP Calculus exam in fall. You can manage your time perfectly by choosing to study at your convenience**Master Math**– It is necessary to understand the concepts of Math before beginning on the AP Calculus course. You will be able to practice with a subject matter expert as you dive into Algebra, Trigonometry and analytical geometry.**Math tutoring**from eTutorWorld is known for its high quality and high success rates**Get College Credit**– Almost all schools award students who perform well in AP Calculus exams. You stand a chance of obtaining a better GPA score that will help you earn admission to the college of your choice. AP Calculus course is extensive and requires long hours of study every day. Our tutors are adept at drawing a systematic plan formulated specially for you.**Excel In College**– College level Calculus will be easy for you to tackle when you go through extensive and personalized tutoring sessions with eTutorWorld. You will not only get to perform well in college tests but will also find it easy to obtain scholarships in future.

## Frequently Asked Questions (FAQs)

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