Algebra is the generalization of arithmetic. Where before a student learns 2+3 and 3*5, algebra allows for circumstances when a number is not known -- and often to solve such situations.
Lines are thoroughly reviewed in algebra 1. I show students how linear equations occur in their lives, and how to understand both their graphs and their equations. The course also covers polynomial basics and a detailed review of the parabola.
Algebra 2, sometimes called precalculus, is a more complex review of algebra. Polynomials are studied in detail, specifically finding its "zeroes". I show students what the problems really ask, and the techniques to solve them.
This class usually introduces trigonometry, a detailed study of circles. This course also goes into the relationship between parabolas and circles, and the equations and graphs of all conic sections.
Whereas algebra is the study of variables, numbers that change, calculus is a study of how variables change -- their rate of change, to be specific. As an analogy, algebra can tell you the average speed of a rocket ship, but Calculus can tell you its exact speed at any time, just like an odometer. I show my students how Calculus is found nearly everywhere, including in business, medicine, and nature.
Differential equations was a basic requirement for me as a mathematics major at college. I enjoy the challenge of tutoring this course. Differential equations is the subject of discovering solution functions to the given rules of how equations behave. I find this subject to be fascinating, and I work to covey the meaning of the equations to my students, as well as understanding how to obtain the solutions.
I have taught this material for years to students across the entire spectrum of competence -- and confidence. While seeming to be easy for many, this is a critical area of study for those seeking to get their GED. I show my students how they do this math everyday, and I reveal how they can adopt the practices for real life. I cover arithmetic and then the basics of algebra, along with a sense of how the number system behaves.
Geometry is based on points, lines, and angles, but mostly logic. A question like "Why do the angles of a triangle add to 180°?" can be answered very early in a geometry class using the basic concepts of a straight angle. Other concepts build upon this, such as: "The sum of the exterior angles of a polygon is 360°." I explain how these concepts are viewed and how viewing them in right order shines light onto the entire course.
If necessary, I cover the format of the GMAT and the question types of the Integrated Reasoning and Quantitative Sections. Then I explain specific strategies for the different question types, which we return to as we cover both the math fundamentals and specific questions. In particular, several question types are reviewed in depth, since many are likely to occur once.
To do well on the quantitative sections of the GRE, you must know more than just the mathematics of algebra and geometry. The newly revamped test has four types of questions on the Quantitative sections. These questions will require out-of-the-box thinking, beyond the skills taught in high school. I have been reviewing these question types, and have found strategies for them. Along with the math, I will teach you the format and how to successfully navigate the questions you that will confront you.
Arguably the single most important software ever developed, the spreadsheet is indespensible in any business endeavor. Its applications are extraordinary, and powerfully revealing information can be gleaned from data by even a moderately experienced user.
I explain the very basics of MS Excel, including proper keyboard use so students learn quickly and efficiently. Then I teach "cut, copy, paste" along with basic functions, and how to quickly fill a column or row with data. Other functions are taught to collect and alter data, and formats are explained to show information in nearly any way imaginable.
I help students understand prealgebra by reviewing the basics of arithmetic and introducing concepts of generalization. For example, imagine you travel 4 mph faster on your bike than I do on mine. What speed are you going if I am going 12 mph? What's my speed if you're going 9 mph? These sorts of questions introduce concepts to students, concepts that build to the idea of a variable, a letter that is used for any unknown number.
Precalculus is Algebra 2 or Algebra 3, because it includes the final study algebra prior to Calculus. Polynomials are studied in detail, including finding real and complex "zeroes" from Descartes' Rule of Signs.
Also studied is trigonometry, the study of circles. I teach this in very clear terms, using circular props so students can visualize the sine and cosine waves. This course often ends with limits and an intro to the rate of change of a function, such as speed.
I have taught the Mathematics portion of the SAT numerous times in the past, to groups and individuals. (I have created a workbook to assist students, which I am currently updating.) If needed, I first focus first on the format of the exam, and how to take advantage of the question types. Then I go over the content and the math needed to understand. Throughout, I discuss solving strategies with the student, so that they understand what to expect and how to approach the questions.
Trigonometry is a detailed study of circles. Imagine a point on a circle, as the circle slowly turns. How does the point move as the circle moves? What is its height from the center, and left-right distance from the center? The study of trigonometry often involves graphing trig functions, the study and graphs of inverse trig functions, and trig identities. I explain these concepts and others in a straightforward manner, so students can see the basic functions and why they are studied.