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AP Calculus AB is roughly equivalent to a first semester college calculus course devoted to topics in differential and integral calculus. The AP course covers topics in these areas, including concepts and skills of limits, derivatives, definite integrals, and the Fundamental Theorem of Calculus. The course teaches students to approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections amongst these representations. Students learn how to use technology to help solve problems, experiment, interpret results, and support conclusions.

1.1 Introduction: Solving Limit of a Function

1.2 Different Techniques on Solving Limits

1.3 Evaluating Limit Given the Graph of the Function

2.2 Derivative Rules: Power Rule and Constant Rule

* 2.5 Computing for the Tangent Line Given a Point

2.7 Using Derivative Rules in Evaluating Functions

2.8 Application of Derivatives on Rectilinear Motions

2.9 Movement of a particle: Backward, Forward, Speeding Up, Slowing Down

3.1 Derivatives of Trigonometric Functions

3.2 Derivatives of the Inverse of a Trigonometric Function

3.3 Derivatives – Exponential Functions (e and constant)

3.4 Derivatives of Logarithmic and Ln Functions.

3.5 Derivatives of Transcendental Functions

3.6 Solving for the Tangent Lines Given Transcendental Functions

4.1 Application of Derivative Rules Given a Table

4.3 Higher Order Derivatives Using Implicit Differentiation

4.4 Related Rates – Balloon and Ripple Problems

4.5 Solving Related Rates on Ladder and Cone Problem

4.6 Finding the Critical Numbers Using Derivatives

4.7 Absolute and Relative (Local) Extrema

4.8 1st Derivative Test for Local Maximum and Local Minimum

4.9 2nd Derivative Test for Concavity and Point of Inflection

4.10 Analyzing the f function given the f' graph

5.2 Antiderivatives of Transcendental Functions

5.3 Riemann Sums – Area Under the Curve

5.4 Area Under the Curve: Reimann Sums Using a Calculator ti84

5.5 Riemann Sums – Estimating Distance Traveled by a Moving Object

5.6 Solving Definite Integrals

5.7 Evaluating Integrals Using its Properties and Common Geometric Figures

5.8 Integral of Absolute Value Functions

5.9 Using the Fundamental Theorem of Calculus in Integrals

5.10 Using U-Substitution or Substitution Method in Integration.

6.1 Applications of Definite Integrals – On Rectilinear Motion

6.2 How to compute for the area under the curve using integrals

6.3 Solving Areas Between Curves Using Ti-84

6.4 Solving Areas Between Curves: Using Subregions

6.6 Integrals – Volumes of a Solid Figure