Course Description
The small group class is designed to re-enforce students’ understanding of the school
curriculum. The classes will include homework, quizzes/tests to prep for the school
quizzes/tests. The topics covered are listed below. We’ll be happy to open additional small
group classes focusing on your school specific topics upon request.
Unit 1 – Functions and Their Properties
Domain and range
Polynomial, absolute value, logarithmic, exponential, rational, and
radical functions and families of their equations
Linear equations, lines
Unit 2 – Function Analysis (Continuity and Infinity)
Discuss the continuity and end behavior of a function.
Extrema of a function and determine whether a function is increasing
or decreasing
Piecewise functions
Limits from the graph
Unit 3 – Polynomial & Rational Functions
Determine the roots, both positive and negative, of a polynomial
equation through algebraic techniques and using the discriminant of
quadratic equations
Find factors of polynomials using various theorems
Unit 4 – Exponential and Logarithmic Functions
Exponential Functions and graphs
Inverse of a functions and graphs
Logarithmic Functions and graphs
Exponential and Logarithmic Equations
Unit 5 – Trigonometric Functions
The six trigonometric functions using trigonometric ratios and the unit
circle
Graphs of Trigonometric Functions
Equations of sine and cosine functions – amplitude, period, phase shift,
and vertical translation
Applications
Unit 6 – Trigonometric Equations and Identities
Solve trigonometric equations using various identities
Use the basic trigonometric identities to verify other identities
Inverse Trigonometric Functions
Unit 7 – Additional Trigonometry Topics/Applications
Complex numbers arithmetic
Polar representation of complex numbers (De’Moivre’s Formula)
Vectors
Law of Sines and Cosines
Unit 8 – Analytic Geometry
Conics
Polar Coordinates
Parametric Equations
Unit 8 – Various Topics from Precalculus (if time permits)

Mr. Koutsothodoros (Kouts

Mathematics, Physics, and Computer Science Teacher

Mr. Koutsothodoros is a professional teacher of Mathematics with a Master’s
degree and a Bachelor’s degree in Mathematics. He has over 15 years of teaching
experience on Math, Physics, and Computer Science, including SAT/ACT Math,
AP Calculus AB, AP Calculus BC, AP Statistics, Precalculus, Algebra I, Algebra
II, Geometry, Honor Physics, and AP Physics C (Mechanics and E&M), AP
Physics I & II, and AP Computer Science A. He emphasizes on teaching the
fundamentals so that students can build a solid foundation on both the subject
and problem-solving skills required to excel on exams and applications of
concepts in the real world. Being extremely familiar with the structure and style
of questions, Mr. Koutsothodoros has helped hundreds of students achieve high
and perfect scores.