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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 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 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 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 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

Students who intend to take both AB and BC Calculus are expected to go through the course material for all 10 units diligently. eTutor World tutors will assist you in preparing for Calculus AB only if you are not interested in taking Calculus BC. The tutors will then make sure to cover Units 1 through 8 well before the test date. You will also find it beneficial to practice with a subject matter expert Math tutor before enrolling for the coveted AP Calculus course. Here are certain skills that you need to imbibe to think like a mathematician.

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