Pre-Calculus

  • Modeling and Equation Solving - Algebraic Models and Geometric Models
  • Zero Factor Property, Grapher Failure and Hidden Behaviour
  • Function Definition and Notation
  • Domain and Range of a Function
  • Continuity
  • Increasing and Decreasing Functions
  • Boundedness, Local and Absolute Extrema, Symmetry, Asymptotes, End Behaviour
  • Twelve Basic Functions
  • Combining Functions Algebraically and Composition of Functions
  • Relations and Implicitly Defined Functions
  • Relations Defined Parametrically
  • Inverse Relations and Inverse Functions
  • Vertical and Horizontal Translations, Reflections Across Axes, Vertical and Horizontal Stretches and Shrinks, Combining Transformations
  • Forming Functions from Formulas
  • Functions from Graphs, Functions from Verbal Descriptions, Functions from Data
  • Polynomial Functions
  • Linear Functions and Their Graphs
  • Average Rate of Change
  • Association, Correlation, and Linear Modeling
  • Quadratic Functions and Their Graphs
  • Applications of Quadratic Functions
  • Power Functions and Variation, Graphs of Power Functions, Modeling with Power Functions
  • Monomial Functions and Their Graphs
  • End Behavior of Polynomial Functions
  • Zeros of Polynomial Functions
  • Intermediate Value Theorem
  • Modeling
  • Polynomial Division - Long Division and the Division Algorithm
  • Remainder and Factor Theorems, Synthetic Division
  • Rational Zeros Theorem
  • Upper and Lower Bounds
  • Fundamental Theorem of Algebra, Linear Factorization Theorem
  • Complex Conjugate Zeros
  • Factoring with Real Number Coefficients
  • Rational Functions and Domain of Rational Functions
  • Transformations of the Reciprocal Function
  • Limits and Asymptotes
  • Analyzing Graphs of Rational Functions
  • Exploring Relative Humidity
  • Solving Rational Equations - Extraneous Solutions
  • Exponential Functions and Their Graphs
  • Transforming Exponential Functions
  • Natural Base e
  • Logistic Functions and Their Graphs
  • Graphing Logistic Growth Functions
  • Constant Percentage Rate and Exponential Functions
  • Exponential Growth and Decay Models
  • Using Regression to Model Population
  • Inverses of Exponential Functions
  • Changing Between Logarithmic and Exponential Form
  • Evaluating Logarithmic and Exponential Expressions
  • Common Logarithms—Base 10
  • Basic Properties of Common Logarithms
  • Natural Logarithms—Base e
  • Graphs of Logarithmic Functions
  • Transforming Logarithmic Graphs
  • Measuring Sound Using Decibels
  • Properties of Logarithms
  • Exploring the Arithmetic of Logarithms - Expanding the Logarithm of a Product, Expanding the Logarithm of a Quotient.
  • Change of Base
  • Graphs of Logarithmic Functions with Base b
  • Solving Exponential Equations
  • Solving Logarithmic Equations
  • Orders of Magnitude and Logarithmic Models
  • Newton’s Law of Cooling
  • Logarithmic Re-expression
  • Degrees and Radians
  • Circular Arc Length
  • Angular and Linear Motion
  • Right Triangle Trigonometry
  • Evaluating Trigonometric Functions of 45° & Evaluating Trigonometric Functions of 30°
  • Applications of Right Triangle Trigonometry
  • Trigonometric Functions of Any Angle
  • Evaluating Trig Functions of Quadrantal Angles
  • Trigonometric Functions of Real Numbers
  • Periodic Functions
  • The 16-Point Unit Circle
  • Sine and Cosine Functions
  • Sinusoids and Transformations
  • Modeling Periodic Behavior with Sinusoids
  • Tangent and Cotangent Function
  • Secant and Cosecant Function
  • Inverse Sine, Cosine and Tangent Functions
  • Composing Trigonometric and Inverse Trigonometric Functions
  • Applications of Inverse Trigonometric Functions
  • Simple Harmonic Motion
  • Basic Trigonometric Identities
  • Pythagorean Identities
  • Cofunction Identities
  • Odd-Even Identities
  • Simplifying Trigonometric Expressions
  • Solving Trigonometric Equations
  • Proving Identities and Disproving Non-Identities
  • Identities in Calculus
  • Cosine of a Difference and Cosine of a sum
  • Sine of a Difference or Sum
  • Tangent of a Difference or Sum
  • Verifying a Sinusoid Algebraically
  • Double-Angle Identities
  • Power-Reducing Identities
  • Half-Angle Identities
  • Deriving the Law of Sines
  • Solving Triangles (AAS, ASA) and The Ambiguous Case (SSA)
  • Deriving the Law of Cosines
  • Triangle Area and Heron’s Formula


  • Two-Dimensional Vectors, Head Minus Tail (HMT) Rule for Vectors, Vector Operations
  • Unit Vector, Direction Angles
  • Applications of Vectors
  • Dot Product of Vectors, Properties of Dot Product
  • Angle Between Vectors
  • Orthogonal Vectors
  • Projecting One Vector onto Another
  • Parametric Equations and Parametric Curves
  • Eliminating the Parameter
  • Lines and Line Segments
  • Simulating Motion with a Grapher
  • Polar Coordinate System
  • Coordinate Conversion and Equation Conversion
  • Finding Distance Using Polar Coordinates
  • Polar Curves and Parametric Curves, Symmetry
  • Analyzing Polar Graphs, Rose Curves, Limaçon Curves
  • De Moivre’s Theorem and nth Roots



  • Solving system of equations - The Method of Substitution
  • Solving Systems Graphically
  • The Method of Elimination
  • Multivariate Linear Systems and Row Operations
  • Matrix Algebra
  • Systems of Inequalities in Two Variables
  • Conic Sections and Geometry of a Parabola
  • Translations of Parabolas
  • Reflective Property of a Parabola
  • Geometry of an Ellipse
  • Translations of Ellipses, Orbits and Eccentricity
  • Reflective Property of an Ellipse
  • Geometry of a Hyperbola
  • Translations of Hyperbolas
  • Eccentricity and Orbits
  • Reflective Property of a Hyperbola
  • Long-Range Navigation

  • Sequences and Series
  • Arithmetic Sequences and Partial Sums
  • Geometric Sequences and Series
  • Pascal’s Triangle
  • Binomial Theorem
  • Factorial Identities
  • Average Velocity, Instantaneous Velocity
  • The Connection to Tangent Lines
  • The Derivative
  • Distance from a Constant Velocity
  • Distance from a Changing Velocity
  • Limits at Infinity
  • The Connection to Areas
  • The Definite Integral
  • Properties of Limits
  • Limits of Continuous Functions
  • One-Sided and Two-Sided Limits
  • Limits Involving Infinity
  • Computing a Derivative from Data
  • Computing a Definite Integral from Data

Mathematics: 

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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