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- Calculus AB

#### Calculus AB

- Rates of Change
- The Limit of a Function and One Sided Limits
- Finding limits by tables and graphs
- Properties and methods used to evaluate limits
- Limits and Asymptotes
- Calculating Limits Using the Limit Laws
- Behavior and characteristics of vertical and horizontal asymptotes
- Finding infinite limits and limits approaching infinity
- Definition of continuity and determining if a function is continuous
- Properties of Continuity and Intermediate Value Theorem

- Definition of Derivatives and the Power Rule
- Defining the derivative using the difference quotient
- The Product and Quotient Rules and Higher Derivatives
- Explanation of when derivatives do not exist
- Simple differentiation rules
- The Chain Rule and the Composite Functions
- Using derivatives in velocity and acceleration problems
- Derivatives of Trigonometric Functions
- Derivatives of Exponential and Logarithmic Functions
- The Tangent Lines and the Normal Lines
- Implicit Differentiation
- Related rate problems
- Derivatives of an Inverse Function
- Derivatives of Inverse Trigonometric Functions
- Approximating a Derivative

- Define extremas, critical points and maximum/minimum problems
- Rolles theorem and mean value theorem
- Using the 1st and 2nd derivative tests
- Position, Velocity, and Acceleration
- Curves of f , f ′ , f ′′ and Curve Sketching
- Discussion of the optimization problems
- Optimization Problems
- Tangent Line Approximation and Differentials
- Linearization and differentials including business application

- General anti-derivatives using simple integration formulas
- Solving simple differentiation equations

- Antiderivatives and Indefinite Integrals
- Riemann Sum and Area Approximation
- Definite Integral, Area Under a Curve, and Application
- Properties of Definite Integral
- Trapezoidal Rule
- The Fundamental Theorem of Calculus Part 1
- The Fundamental Theorem of Calculus Part 2
- Integration by Substitution
- Integration of Exponential and Logarithmic Function
- Accumulation of a rate of change
- Rectangular approximation methods

- Area of a Region between Two Curves
- Volumes by Disk and Washers
- Volumes of Solids with Known Cross Sections
- The Total Change Theorem (Application of FTC)
- Motion of a Particle, Distance, and Displacement
- Average Value of a Function
- Finding volume by cross-sectional areas
- Arc length

- Review of logarithms and inverse functions
- Derivative and integral of natural logs
- Derivative and integral of exponential functions
- Finding derivative and integral of bases other than e
- Growth and decay applications including logistic curves
- Inverse trig functions
- Derivatives and integrals of inverse trig function
- Logistic Growth
- Slope fields and Euler’s method

At Refresh Kid tutoring sessions, we offer a comprehensive Calculus AB course curriculum designed to provide students with a strong understanding of fundamental calculus concepts and develop their problem-solving skills. Our goal is to help students succeed in the AP Calculus AB exam and build a solid foundation for future math and science courses. Here is an overview of our Calculus AB course curriculum:

- Limits and Continuity:

- Understanding the concept of a limit and evaluating limits algebraically and graphically.
- Exploring the properties of limits, including the limit laws and the squeeze theorem.
- Investigating continuity and identifying discontinuities in functions.

- Differentiation:

- Introducing the derivative as the rate of change and its interpretation.
- Applying differentiation rules, including the power rule, product rule, quotient rule, and chain rule.
- Analyzing the behavior of functions using the first and second derivative tests.
- Investigating optimization problems and related rates.

- Applications of Differentiation:

- Solving related rates problems involving geometric and physical situations.
- Finding local and global extrema using critical points and the first and second derivative tests.
- Understanding the Mean Value Theorem and its applications.
- Exploring curve sketching and the behavior of functions using derivatives.

- Integration and Accumulation:

- Introducing the concept of integration as the accumulation of quantities.
- Applying the definite integral to find area, displacement, and total change.
- Understanding antiderivatives and indefinite integrals.
- Investigating the Fundamental Theorem of Calculus and its applications.

- Applications of Integration:

- Solving problems involving area between curves, volume of solids, and length of curves.
- Applying integration to solve physics and engineering-related problems.
- Exploring the concept of differential equations and their solutions.

Throughout the course, students will engage in practice problems, conceptual discussions, and real-world applications to reinforce their understanding of the concepts covered. Our tutors provide individualized attention, clear explanations, and step-by-step guidance to help students master each topic.

We are dedicated to supporting students' progress and offer additional resources, practice materials, and ongoing support to ensure their success in Calculus AB and the AP exam.

At Refresh Kid, we believe that a solid foundation in Calculus AB is crucial for students' future success in advanced mathematics and STEM-related fields. Enroll in our tutoring program today and empower your child with the skills and knowledge needed to excel in Calculus AB and beyond.