All of
Ashwin’s current tutoring subjects are listed at the left. You
can read more about
Ashwin’s qualifications in specific subjects below.
ACT Math
Pre-Algebra: Factors, Square roots and approximations, Absolute value and ordering numbers by value , Exponents, Scientific notation
Elementary Algebra: Exponents and square roots, Evaluation of algebraic expressions through substitution, Using variables to express functional relationships, Algebraic operations, Factoring and quadratic equations
Intermediate Algebra: Quadratic formula, Rational and radical expressions, Absolute value equations and inequalities, Sequences and patterns, Polynomials, Complex numbers
Coordinate Geometry: Graphing and the relations between equations and graphs, including points, lines, polynomials, circles, and other curves, Graphing inequalities, Slope, Parallel and perpendicular lines, Distance; midpoints; and conics
Plane Geometry: Angles and relations among perpendicular and parallel lines, Properties of circles, triangles, rectangles, parallelograms, and trapezoids, Transformations, Proof and proof techniques, Volume, Three-dimensional Geometry
Trigonometry:Trigonometric relations in right triangles, Values and properties of trigonometric functions, Graphing trigonometric functions, Modeling using trigonometric functions, Solving trigonometric equations
Algebra 1
Order of Operations, Distribution and Factoring, Exponents
Fractional Exponents, Radicals, One-Variable expressions
Factoring, Fractions, and Radicals with Variables
Linear Equations and Word Problems
Algebra with Multiple Variables
Systems of Two-Variable Linear Equations
Ratio and Percent
Proportion
Graphing Lines
More Lines and Introduction to Inequalities
Inequality Problem-Solving and Graphing
Quadratic Equations
Special Factorizations
Complex Numbers
Deriving the Quadratic Formula
Algebra 2
Functions and Relations
Quadratic Functions
Rational Expressions/Equations
Radicals/Absolute Value Equations/Inequalities
Exponential and Logarithmic Functions
Trigonometry
Trig Applications
Calculus
1 LIMITS AND CONTINUITY
Limits (An Intuitive Approach)
Computing Limits
Limits at Infinity: End Behavior of a Function
Limits (More Rigorously)
Continuity
2 THE DERIVATIVE
Tangent Lines and Rates of Change
The Derivative Function
Introduction to Techniques of Differentiation
The Product and Quotient Rules
Derivatives of Trigonometric Functions
The Chain Rule
3 TOPICS IN DIFFERENTIATION
Implicit Differentiation
Derivatives of Logarithmic Functions
Derivatives of Exponential and Inverse Trigonometric Functions
Related Rates
Local Linear Approximation; Differentials
L’Hôpital’s Rule: Indeterminate Forms
4 THE DERIVATIVE IN GRAPHING AND APPLICATIONS
Analysis of Functions I: Increase, Decrease, and Concavity
Analysis of Functions II: Relative Extrema; Graphing Polynomials
Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents
Absolute Maxima and Minima
Geometry
Parallel and Perpendicular Lines
Congruent Triangles
Quadrilaterals
Area
Similarity
Right Triangles
Surface Area and Volume
Circles
Transformations
Prealgebra
Properties of Arithmetic 1
Properties of Arithmetic 2
Squares, Cubes, and Higher Exponents
More Exponents
Multiples and Divisibility Tests
Primes and Prime Factorization
Least Common Multiple, Greatest Common Divisor
Fractions
Expressions and Basic Equations
Advanced Equations and Word Problems
Inequalities
Arithmetic with Decimals
Decimals and Fractions
Ratio and Proportion
Units, Speed, and Rates
Percent
Percent Increase and Decrease
Squares and Square Roots
Arithmetic with Square Roots
Angles and Parallel Lines
Angles and Polygons
Perimeter and Area
Circles
Pythagorean Theorem
Special Triangles
Quadrilaterals
Basic Statistics
Tables, Graphs, and Charts
Counting as Arithmetic
More Counting and Probability
Problem-Solving Strategies
Precalculus
POLYNOMIAL AND RATIONAL FUNCTIONS.
Quadratic Functions.
Polynomial Functions of Higher Degree.
Dividing Polynomials: Long Division and Synthetic Division.
The Real Zeros of a Polynomial Function.
Complex Zeros: The Fundamental Theorem of Algebra.
Rational Functions.
EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions and Their Graphs.
Logarithmic Functions and Their Graphs.
Properties of Logarithms.
Exponential and Logarithmic Equations.
Exponential and Logarithmic Models.
Trigonometric Functions OF ANGLES.
Angle Measure.
Right Triangle Trigonometry.
The Law of Sines.
The Law of Cosines.
TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS.
Trigonometric Functions of Real Numbers: The Unit Circle Approach.
Graphs of Sine and Cosine Functions.
Graphs of Other Trigonometric Functions.
ANALYTIC TRIGONOMETRY.
Verifying Trigonometric Identities.
Sum and Difference Identities.
Double-Angle and Half-Angle Identities.
Product-to-Sum and Sum-to-Product Identities.
Inverse Trigonometric Functions.
Trigonometric Equations.
POLAR COORDINATES AND VECTORS.
Vectors.
The Dot Product.
Polar (Trigonometric) Form of Complex Numbers.
Products, Quotients, Powers, and Roots of Complex Numbers.
Polar Coordinates and Graphs of Polar Equations.
SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES.
Systems of Linear Equations in Two Variables.
Systems of Linear Equations in Three Variables.
Matrix Algebra.
The Determinant of a Square Matrix and Cramer’s Rule.
Partial Fractions.
Systems of Linear Inequalities in Two Variables.
CONICS, SYSTEMS OF NONLINEAR EQUATIONS AND INEQUALITIES, AND PARAMETRIC EQUATIONS.
Conic Basics.
The Parabola.
The Ellipse.
The Hyperbola.
Systems of Nonlinear Equations.
Systems of Nonlinear Inequalities.
Rotation of Axes.
Polar Equations of Conics.
Parametric Equations and Graphs.
SEQUENCES AND SERIES.
Sequences and Series.
Arithmetic Sequences and Series.
Geometric Sequences and Series.
Mathematical Induction.
The Binomial Theorem.
SAT Math
Arithmetic Skills & Concepts
1. Numbers, Symbols, and Variables
2. Powers and Roots
3. Divisibility and Factors
4. Number Lines and Signed Numbers
5. Fractions and Decimals
6. Operations with Fractions
7. Fraction Word Problems
8. Percent
Algebraic Methods
9. Solving Equations
10. Equations with More Than One
Variable
11. Polynomials and Algebraic Fractions
12. Factoring
13. Quadratic Equations
14. Systems of Equations
15. Algebraic Inequalities
Geometric Concepts & Reasoning
16. Angle Relationships
17. Special Triangles
18. Triangle Inequality Relationships
19. Polygons and Parallelograms
20. Perimeter and Area
21. Circles
22. Solid Figures
23. Coordinate Geometry
Word Problems
24. Translating from English to Algebra
25. Percent Problems
26. Some Special Types of Word Problems
27. Ratio and Variation
28. Rate Problems
Special Problem Types
29. Average Problems
30. Counting Problems
31. Probability Problems
32. Graphs and Tables
33. Miscellaneous Problem Types
Algebra II Methods
34. Integer and Rational Exponents
35. Solving Special Types of Equations and Inequalities
36. Working with Functions
37. Some Special Functions
38. Simple Transformations of Functions