Andrew’s current tutoring subjects are listed at the left. You
can read more about
Andrew’s qualifications in specific subjects below.
This is a truncated description, which will be updated soon. I tutor all areas of Algebra I, including the following:
Principles of Algebra; Number Theory; Set Theory; Order of Operations; Solving one and two step equations; Graphs of Linear Equations; Inequalities, Graphing Inequalities; Solving Systems of Two Equations in Two Variables, using Substitution and Elimination; Rules of Exponents; Polynomials; Quadratic Equations and Graphing them; Factoring Simple Quadratics; Factoring Difficult Quadratics; Completing the Square; the Quadratic Formula; Use of the Discriminant; Practical Applications; Word Problems, including work problems, two vehicle problems, and mixture problems; Basic Statistics; Ratio and Proportion.
I tutor all areas of Algebra II, including: use of the graphing calculator; number systems, properties of numbers; algebraic expressions, functions, and their transformations; linear equations and inequalities; systems of linear equations in two and three variables; linear programming; matrices, Cramer's rule, augmented matrices, and row and column operations; quadratic functions and complex numbers with roots, graphs, modeling and curve fitting; higher order polynomials and factoring with roots, graphs and curve fitting; exponential, inverse, and logarithmic functions with modeling; direct variation, rational functions and radical functions; representations of functions, piecewise functions and inverse functions with modeling; conic sections (circle, ellipse, parabola, hyperbola) and solutions of non-linear systems; permutations, combinations, probability, statistics and binomial distributions; arithmetic, geometric and infinite sequences and series with recursive formulas; trigonometric and inverse trigonometric functions; the laws of sines and cosines and Heron's formula; graphing trigonometric functions; trigonometric identities, sum and difference angle formulas, half-angle and double angle formulas.
I tutor all areas of high school mathematics: Algebra Readiness, Algebra I, Geometry, Algebra II, Pre-Calculus, Calculus, and Statistics. Primary focus is on proper application of principles, sound basic math skills, logical reasoning, appropriate use of a calculator, graphing skills, and algebraic principles. I also address test taking strategies such as eliminating incorrect answers, substituting possible answers, and statistical analysis of answered versus unanswered questions.
Functions, modeling, and use of graphing calculators; Exponential Functions, Inverse Functions, and Logarithms; Limits, Calculating Limits, Limit Laws, Precise Definition of a Limit; Limits at Infinity; Tangents, Velocity, and Rate of Change; Definition of the Derivative; Derivative as a Function; Derivatives of Polyn9omial and Exponential Functions; Product Rule, Quotient Rule; Rate of Change; Chain Rule; Derivatives of Trigonometric Functions; Implicit Differentiation; Higher Derivatives; Derivatives of Logarithmic Functions; Related Rates; Linear Approximations and Differentials; Maxima and Minima; Rolle's Theorem, the Intermediate Value Theorem, the Mean Value Theorem; Using Derivatives to Determine the Shape of a Graph; Indeterminate Forms, l'Hopital's Rule; Curve sketching Graphing using Calculus with the Calculator; Optimization; Business and Ecmnomics Applications; Newton's Method; Antiderivatives; Areas and Distances; Riemann Sums; Indefinite Integrals and The Definite Integral; The Fundamental Theorem of Calculus; Trapezoidal Approximations; Simpson's Rule; The Substitution Rule; The Logarithm as an Integral; Areas between Curves; Volumes of Rotation and Cylindrical Shells; Work as an Integral; Average Value of a Function; Techniques of Integration, including Integration by Parts, Trigono9metric Integrals, Trigonometric Substitution, Partial Fractions, Strategies for Integration, Using Tables of Integrals, Approximation by Numerical Methods, Improper Integrals; Arc Length; Area of a Surface of Revolution; Application to Physics, Engineering, Economics, and Biology; Probability; Introduction to Differential Equations; Direction Fields; Euler's Method; Separable Equations; Exponential Growth and decay; Parametric Equations; Polar Coordinates, and Area and Length in polar Coordinates; Conic Sections; Infinite Sequences and series; The Integral Test; Comparison Tests; Alternating Series; Absolute Convergence; Ratio and Root Tests; STrategy for Testing Series for Convergence; Power Series and Function Representation; Taylor and MacLaurin Series; The Binomial Series; Multivariable Calculus; Partial Derivatives; Gradients, Multiple Derivatives, Hessians; The Spherical Integral; Double and Triple Integrals.
Students who need a refresher in topics from pre-calculus will be assisted, especially with regard to Graphical Techniques, Inverse Functions, and all aspects of Trigonometry.
I tutor all areas of high school chemistry, including honors chemistry, as well as lower division college general and honors chemistry. I cover the following topics:
Alchemy; matter, properties of elements, physical changes in chemistry; periodic table and element names; scientific method; measurements and conversion units, calculations, graphing, scientific notation, significant figures; atomic theory, atomic mass, isotopes, moles, simple compounds; quantum theory, electron shells and orbitals, Pauli exclusion principle, Heisenberg uncertainty principle, emission spectra; periodicity, groups of elements, chemical properties of elements, electron affinity, ionization energy; covalent bonding, ionic bonding, metallic bonding, hydrogen bonding; resonance structures, Lewis electron dot structures,molecular geometry; chemical names, formulas, ionization and oxication states; chemical reactions and chemical equations; mole ratios, molar masses, conversions, limiting reactants, and percent yield; gases, gas theory; Boyle's Law, Charles' Law, Dalton's Law, Ideal Gas Law; mixtures of gases, gases in chemical reactions; properties of solids and liquids, changes of state, crystalline structure; chemical solutions, solubility, effects of temperature and pressure; electrolytes, dissociation, ionization, precipitation, and colligative properties; theories of acids and bases, Arrhenius acids and bases, Bronsted-Lowry acids and bases, Lewis acids and bases; neutralization reactions, pH, titrations; heats of reaction, enthalpy, entropy, reaction rates, reaction mechanisms; chemical equilibrium, ionization constants, calculations involving buffers and solubility; oxidation-reduction reactions, electrochemistry; carbon-based compounds, carbon allotropes (graphite and diamond); classification and functional groups of organic compounds; nuclear reactions, radioactive decay, radiation, fission, and fusion.
I tutor all areas of elementary school math, which includes the following:
Counting, addition, subtraction, multiplication, division; geometric shape recognition, pattern recognition; elementary fractions; measurement; number systems; special properties of numbers and basic number theory; graphing; using tables to sort data; elementary statistics (finding range, mean, median, and mode); adding and subtracting fractions using lowest common denominator.
I tutor all areas of high school and college geometry, including the following: points, lines, planes, and angles; measure, congruency, angle pairs; formulas; inductive and deductive reasoning; conditional and biconditional statements; logic, algebraic proof, geometric proof; parallel, perpendicular, intersecting and coinciding lines; angle congruency postulates and theorems; equations of lines, slope-intercept form, point-slope form, two-point form*; triangle types, congruency, SSS, SAS, ASA, AAS, HL, HA, special triangles; perpendicular and angle bisectors, medians, and altitudes of triangles; circumcenter, incenter, centroid, and orthocenter; midsegment theorem; indirect proof (proof by contradiction); triangle inequality theorem; right triangles, Pythagorean theorem, special cases; properties of polygons; parallelograms, rhombii, rectangles, squares; kites and trapezoids, midsegment theorem; ratio and proportion; ratio in similar polygons and triangles (scale factor); porperties of similar triangles, porportionality, similarity in the coordinate plane; similarity in right triangles, basic definitions in trigonometry, solving right triangles; angles of elevation and depression; law of sines, law of cosines, Heron's law*; vectors; area and perimeter formulas; composite figures; perimeter and area in the coordinate plane; effects of changing dimension; geometric probability; solid geometry, isometric, orthographic, and perspective drawings; formulas in three dimensions; surface area and volume of solids; tangents, chords, secants, arcs, and sectors of circles; inscribed angles, angle and segment relationships in circles; circles in the coordinate plane; rigid transformations (translations, rotations, reflections), compositions of transformations; symmetry; tesselations; dilations; introduction to trigonometry*.
*These three topics (two-point form of a line, Heron's law, and trigonometry) are not covered in all geometry texts or courses. I offer them to aid students in various aspects of solving problems.
I cover all areas of prealgebra, including the following: Basic principles, Commutative Law, Associative Law, Distributive Law; Integers and Basic Operations, Addition, Subtraction, Multiplication, Division; Use of Exponents, Laws of Exponents; Order of Operations; Rational Numbers; Irrational Numbers; Collecting, displaying and Analyzing Data; Elements of Plane Geometry, Perimeter, Area, and Volume; Ratios, Proportions, and Similarity; Percentage, using Percentage as a Proportion; Probability; Equations, Inequalities, and Graphing; Sequences; Functions; Polynomials; Set Theory; Discrete Math.
real numbers, relations, and functions, mathematical patterns, arithmetic sequences; lines, linear models, geometric sequences, infinite geometric series; solving equations graphically, solving quadratic equations algebraically; applications of equations, other types of equations; inequalities; functions, graphs of functions, quadratic functions; graphs and transformations, operations on functions, inverse functions, rates of change; polynomial functions, real zeros, graphs of polynomial functions; rational functions; complex numbers; the Fundamental Theorem of Algebra; radicals and rational exponents, exponential functions with applications; common and natural logarithmic functions, properties and laws of logarithms, solving exponential and logarithmic equations; exponential, logarithmic, and other models; right-triangle trigonometry, trigonometric applications, angles and radian measure trigonometric functions, basic trigonometric identities; graphs of the sine, cosine, tangent, cosecant, secant, and cotangent functions, periodic graphs, amplitude and phase shifts; graphical solutions to trigonometric equations, inverse trigonometric functions, algebraic solutions of trigonometric equations, simple harmonic motion and modeling;
identities and proofs, addition and subtraction identities, other identities, using trigonometric identities; the laws of cosines and sines; the complex plane and polar form for complex numbers, DeMoivre’s theorem and nth roots of complex numbers; vectors in the plane with applications; ellipses, hyperbolas, translations and rotations of conics; polar coordinates, polar equations of conics, plane curves and parametric equations; solving systems of equations, matrices, matrix operations; matrix methods for square systems, nonlinear systems; basic statistics, measures of center and spread; basic probability, determining probabilities, normal distributions; limits of functions, properties of limits, the formal definition of limit, continuity, limits involving infinity; preview of calculus, basic ideas of the derivative and the integral.
Interpretation and presentation of data in graphs and tables; mean, median, mode, quartiles, variance, standard deviation; Normal distribution, density curves, empirical rule; Scatter plots and correlation; regression; Marginal distributions, conditional distributions, Simpson's paradox; Sampling, creating experiments, interpreting experiments; Probability, randomness, probability rules, probability models, random variables; combinatorics; Sampling distributions, x-bar, the central limit theorem; Rules of probability, independence and multiplication, conditional probability; Binomial distribution, binomial probability, binomial mean and standard deviation; confidence intervals; testing significance and p-values, tests for a population mean; inference, z-tests; one and two sample t-tests; population proportions, significance tests for proportions; two-variable statistics, chi-square test, z test, good ness of fit; the regression model and inference.
I tutor all aspects of plane trigonometry, including the following: review of coordinate geometry; polar coordinate system and radian measure; standard position of an angle; basic trigonometric definitions (sine, cosine, tangent, cotangent, secant, cosecant); relationships and signs of trig. functions; quadrantal angles; functions of negative angles; the right triangle and solutions thereof; values of trig. functions; fundamental identities; graphs of trig. functions; sum and difference formulas, double angle and half angle formulas; exponential and logarithmic functions; oblique tirangles; law of sines, law of cosines, Heron's law; inverse trig. functions; trig. equations; vectors; complex numbers and the complex plane; DeMoivre's theorem.
This subject matter is often tutored within the larger scope of a high school pre-calculus course. I am fully capable of tutoring all aspects of pre-calculus, but it is beyond the scope of this description to be included.