I taught Algebra 1 as an intensive summer course at a private education facility. I am intimately familiar with the curriculum. I tutored several students privately as well and I would love to help your child to establish a good foundation for future math courses.
I master all the Algebra 2 concepts, such as:
- Linear equations/functions and inequalities
- Systems of equations and inequalities
- Quadratic equations/functions and graphs
- Matrices and determinants
- Polynomials and polynomial functions
- Exponential and logarithmic functions
- Conic sections
- Rational equations/inequalities and functions
- Probability and statistics (combinations and permutations)
- Trigonometry ratios and functions
- Trigonometry identities
I tutored on a daily basis AP Calculus AB/BC students dealing with the following topics:
- Limits and Continuity (including L`Hopitale Rule)
- Rates of Change
- Explicit Differentiation Rules: (sum/difference, product/quotient, power, chain rule)
- Implicit Differentiation
- Applications of Differentiation
- Basic Antiderivatives
- Riemann Sums
- Trapezoidal, Rectangular Rule
- Fundamental Theorem of Calculus
- Average Function Value
- Substitution Method
- Trigonometric Integrals
- Partial Fractions
- Integration by Parts
- Differential Equations and Slope Fields
- Applications of Integrals: areas, volume, arc length, curvature, - Series, limits and convergence criteria
I took two undergraduate courses pertaining to differential equations: Ordinary Differential Equations, and Partial Differential Equations.
The former course is the one I could offer my expertise on. The course started with the classification of differential equations (first/second order, linear/non-linear, constant/variable coefficients) and continued with solution methodologies for different types of ODEs and for systems of ODEs.
Solution strategies were presented for several types of ODE configurations. For first degree ODEs I learned the following strategies: separation of variable, substitutions of variable, Bernoulli DE, Exact DE
For second order DE I learned the following methods: fundamental sets of solution,complementary solutions for constant, homogeneous DEs, method of undetermined coefficients and of annihilators for constant, non-homogeneous DEs, method of variation of parameters and Euler's Method
I also learned how to combine the DE general solution with the given initial conditions in order to obtain specific solution. Application problems were from the areas of mechanical vibrations, flow, heat transfer, concentration, etc.
At the end of the course, I learned Laplace's transforms as an alternative for solving ODEs.
I master the following subjects in Geometry, and I teach them on a regular basis:
- Coordinate geometry: cartesian system, line equations
- Distance, length, and midpoint formula
- Angles, Lines and Points: definitions, parallel lines, angle relations in triangles and polygons
- Special Triangles: isosceles, equilateral
- Right Triangles: properties, Pythagora's theorem, introduction to SOHCAHTOA
- Solving Triangles: Sine and Cosine Law
- Congruency and Similitude proofs in Triangles
- Polygons: Parallelograms, Rectangles, Squares, Hexagons, regular polygons
- Circles: properties, formulas, equation
- 3D bodies: classification, properties, surface areas and volume formulas
I completed a Bachelor of Science in Mechanical Engineering within a co-op program, which means that I got to apply a lot of the concepts that I learned at school in real-world problems.
I am qualified to tutor in any Mechanical Engineering subjects because I completed numerous projects for each course, some on an individual basis and some on a collective basis. I received excellent marks and I am convinced that I can help any ME student to do the same. I also participated in numerous tutorial sessions, as each course had its assigned course tutorial taught by a PhD student.
I still have most of the textbooks and I passed from the first attempt the NCEES Fundamentals of Engineering examination - an 8 hr exam which is mandatory for professional engineering licensing and which coverd every single major topic in Mechanical Engineering.
I graduated mechanical engineering so I successfully completed the following courses:
- Physics I: Newton's Laws, Energy, Momentum, etc. for linear and rotation systems
- Physics II: Oscillatory Motion, Sound & Optics
- Dynamics: Newton's Laws applied to kinematics and kinetics for single particles and for rigid bodies. That includes linear and circular motion systems, linear and circular momentum and impulse, energy analysis
- Thermodynamics I/II: Conservation of mass, Conservation of Energy, 2nd Law of Thermodynamics, analysis of thermodynamics systems (plants, engines).
I have plenty of experience in tutoring precalculus, gained both from private tutoring and from my current employment. I master all the precalculus topics, such as:
- line equations and inequalities (including the ones with absolute values)
- cartesian system of coordinates
- functions: notation, domain, range, composition, transformations, inverse functions
- Polynomial functions and their simplification and graphing (quadratic, square root)
- Rational functions: evaluation and graphing
- Trigonometry: SOHCAHTOA, unit circle and CAST rule, trig identities and formulas, trig equations, parent graphs and transformations, data modelling
- Logs and exponent: notation and evaluation, simplification formulas, equations, applications (growth and decay)
I grew up in Romania for 15 years and I studied Romanian language, grammar and literature up to 8th grade. I am proud of my Romanian heritage and I would love to share my language with anyone interested.
I recently taught SAT I math at Academic Education Center. In my teaching and in my private sessions I use Barron's SAT I textbook, which includes all the topics on the SAT I test, including but not limited to: Arithmetic concepts such as fractions and decimals, ratios and proportions, averages; Algebra I concepts such as equations and inequalities, polynomials, word problems; Planar geometry concepts such as lines and angles, triangles, quadrilaterals and polygons, circles; Solid geometry concepts such as volumes, surface areas of common solids; Coordinate geometry concepts such as coordinate system, point coordinates, distance; Functions and their graphs concepts such as line equation, slope, functional notation, function graphs and manipulations; and Counting and probability concepts, including arithmetic/geometric sequences, permutations and combinations.
In addition, I also tutor SAT II Math to individual students, where I cover more advanced concepts and their applications, such as Algebra II, Matrices and Determinants, Trigonometry, Pre-calculus, etc.
- Angle ratios (sin, cos, tan), their variations (csc, sec, cot) and their inverses
- Applications in right triangles and scalene triangles (sine and cosine law)
- CAST rule, reference and co-terminal angles, radians
- Pythagorean identity and its variations; simplification of trig expressions
- (Systems of) trig equations
- Double angle formula and its variations
- Graph of trig ratios and inverses; graph transformations of trig ratios (amplitude, period, translation)