Algebra I Generally Covers These Topics:
Number Properties, Operations, and Linear Equations
Graphing and Systems of Linear Equations
Quadratics and Polynomials
Functions and Rational Expressions
Often, solutions to word problem, knowledge of definitions and proofs are required. It is important for the student to work homework assignments and ask questions if concepts are not clear as new subjects build on mastering the previous subjects.
I am experienced with all of the general material of Algebra 2, such as concepts of Number and Operations including: properties of logarithms and functions to simplify expressions or solve equations; operations of matrices and complex numbers using various methods; teaching numerical computations and how to check their results; solve problems involving proportions.
I excel in Algebraic Relationships including: generalized patterns using explicitly or recursively defined functions and various forms of representations of patterns; properties of linear, absolute value, quadratic, exponential, logarithmic, polynomial, and rational functions; teaching the effects of parameter changes on exponential, logarithmic and polynomial functions; the use symbolic algebra to represent and solve problems that involve exponential and logarithmic relationships; the use of algebraic manipulations involving the rules of exponents and functions; the solution of equivalent forms of equations and inequalities and systems of linear and quadratic equations or inequalities with two variables. Story problems are a specialty of mine and I can assist students to identify quantitative relationships and determine the type(s) of functions that might model the situation to solve the problem. Regarding graphing, I have expertise in the definition of exponential, logarithmic, polynomial and rational functions and can teach students about rates of change, intercepts, and asymptotes. Often the application of Geometric and Spatial Relationships is a difficult concept in Algebra 2. I have experience in teaching simple transformations and their compositions on linear, quadratic, logarithmic and exponential functions including comparing and contrasting basic conics, demonstrate and accurately present circles and parabolas and their graphs. Finally, I help students with the concepts of Measurement including: successive approximation and unit analysis to solve problems involving rates, such as speed, density, or population density.
Many problems require data analysis and probabilities to reach a solution including: the conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data, the use of approximate lines of fit and the determination of the type of function that models the data.
I have a PhD and MS degree in laser physics engineering. As part of that I had almost every mathematics course possible, including college Algebra, Advanced Algebra, Differential Equations, Calculus I & II,Applied Engineering Mathematics, Mathematical Methods of Physics, Statistics, Probability Theory, Stochastic Processes and Fourier Series & Boundary Value Problems. I have tutored 10 Junior and Senor High students in Algebra I, II and Advanced Algebra with Honors.
I have a PhD in Physics. Currently I have 10 tutoring students with many in Algebra. Last year many of my students started with low grades and finished much improved. Two got A finals. I've tutored physics students at FIT.
I have successfully taught over 8 students how to prepare and study for the Math SAT and ACT. I have a 4-step process that involves (1) Understanding the SAT (or ACT), (2) Review sheets that contain all the Key Math Concepts on the tests, (3) test strategy (when to guess, techniques to quickly get the right answer, etc.) and (4) plenty of free practice tests for the student to work with my answers.
I have a PhD and MS degree in laser physics engineering. As part of that I have developed superior study skills. I have tutored 10 Junior and Senor High students in Algebra I, II and Advanced Algebra with Honors. As part of tutoring, I have developed a 4 point method to study and succeed to pass a mid-chapter, chapter & final test. These methods have improved 3 recent students previously getting C's to 2 getting A finals and 2 getting a B+ at the end of the 2013-14 school year.