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


We follow the US curriculum, especially as per your School State Standards. Our goals are to 

  1. Make sure Students understand the concept clearly, 
  2. Get enough practice to Master the topics.
  3. Talk to the Math Teacher during the sessions for any Homework/ Assignment Help. 

All our Sessions are 1: 1 and Online Only. 

Parents usually pick one of these goals:

  1. Catch up to the grade level and give them enough practice so they can perform well in the class. 
  2. Just align to the class and go a little ahead in the class curriculum 
  3. Exceeding expectations of the grade level and preparing well for Math Competitions like Math Olympiad, Math League, Noetic Math, AMC8, Math Kangaroo, Math Counts. 

Each child at Refresh Kid is set a personalized lesson plan as per his / her standards

We have Monthly Competition within Refresh Kid students (6 to 8 students) in the same level as your child. 

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