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Recently retired from a major pharmaceutical company as a PhD in biochemistry, my qualifications include: mentoring junior scientists, adjunct professor of biology at SCCC, tutoring in … Read more

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The ACT is similar to the SAT so my approach to preparation for the ACT is basically the same as I describe for the SAT. The ACT has a stronger emphasis on intermediate algebra, coordinate geometry, and elementary trigonometry, so these topics are reviewed in more detail with the student taking the ACT.

An important goal of any mathematics program is to develop a student's ability to solve problems. I first assure the student has the required arithmetic skills (i.e. manipulation of real and rational numbers, fractions, exponents, radicals) and then I focus heavily on solving word problems, which are at the core of Algebra 1. Success in any mathematics course requires solid problem solving skills whether it's algebra, trigonometry, geometry, calculus. The ability to solve word problems is also essential in order to do well on standardized tests such as the ACT and the SAT. By weaving problem solving into each lesson of Algebra 1, I begin to help the student build a self-confident, "I can do this" attitude towards math which is a useful trait that extends beyond the math classroom.

Math is a powerful tool with far-reaching application throughout your life. In Algebra 2, I continue to emphasize the same tenets I focus on in Algebra 1 - development of mathematical skills and effective problem solving techniques. Furthermore, Algebra 2 builds upon the skills learned in Algebra 1 expanding those skills to enhance an understanding of mathematical principles and developing mathematical reasoning. I help the student of Algebra 2 grasp the theorems of algebra as it extends beyond arithmetic. Topics covered in this course include mathematical properties, use of the variable, equivalence, solving equations and inequalities, proportionality, function, and data modeling. In addition, basic concepts of statistics and probability will be studied along with an introduction to geometry. Finally, and depending on the scope of the course, I will help the student with foundational principles of trigonometry and the introduction to precalculus.

The study of Geometry is typically contained within Algebra 2, at least at the high school level, but it can also exist as a stand-alone course. I will introduce students to concepts of geometry within Algebra 2 where visualization and transformation of geometric figures are studied. Also covered are measurements of area and volume of geometric figures. Introduction to the coordinate plane exposes the student to beginning concepts of planar geometry. Finally, geometry is a necessary prerequisite to begin a study of trigonometry and precalculus.

To do well in algebra the student needs to feel comfortable with most topics of basic arithmetic. With this in mind, I provide a thorough review of these topics; fractions and decimals, percents, ratios and proportions, and averages. In addition to mastering arithmetic basics the student needs to acquire problem solving abilities to be successful in algebra. I review with the student several tactical approaches to word problem solving, help them visualize the problem through diagram creation, ensure they can clearly define what is being asked for in the question, help them to identify those equations that can be used as tools to solve the problem, and finally confirm they can apply those equations to develop the solution.

Precalculus is often referred to as Algebra 3 as it is a logical extension of the concepts and principles learned in Algebra 2. In some schools, precalculus is divided into two subjects: Algebra and Trigonometry and thus it follows that some exposure to precalculus occurs at the end of any course of Algebra 2. While prealgebra prepares the student for algebra, precalculus does not involve calculus. Instead, precalculus explores topics that will be applied in calculus - thus, precalculus introduces the student to the mathematic tools that will be used to solve problems using calculus. Many of these tools are integral parts of algebra 1 and algebra 2 and are covered in my tutorials of these courses, including; sets, real numbers, complex numbers, solving equations and inequalities, properties of functions, composite functions, polynomial and rational functions, exponential and logarithmic functions, matrices, and basic trigonometry. A course in precalculus extends these topics to also include vectors, conic sections, and polar coordinates. My approach to tutoring precalculus is to confirm the student fully understands the underlying concepts of basic trigonometry, the unit circle, special right triangles, and manipulation of trigonometric functions. Once mastered, these tools can then be used to start developing skills in calculus that describe mathematical functions beyond the confines of the Cartesian coordinate plane.

The mathematics portion of the SAT is divided approximately among three areas: arithmetic, elementary algebra, and fundamentals of geometry. The math needed to do well on the SAT does not require advanced skills, so why do so many students find the SAT questions so difficult? The answer lies in the fact that the SAT is designed to assess mathematical reasoning ability that requires relatively simple mathematical tools to solve. While it is true the student needs to be proficient in basic mathematics, it is equally important that the student also understands how to take the SAT. In my approach to coaching for the SAT, I not only provide a thorough review of 18 topics covering basic concepts of arithmetic, algebra, and geometry, but I also provide the student with a series of 17 tactics and strategies that can be applied to SAT problems that enhance the student's probability of selecting the correct answer. Finally, I have many SAT-like tests, in the format of the SAT, that can be used as additional learning tools and competency assessments to further help the student identify not only strengths, but more importantly, areas of weakness that require additional study.

Fundamentals of trigonometry are often covered at the end of the Algebra 2 course. In keeping with this assumption, I review with the student the concepts of periodic data, angles and the unit circle, radian measure, the sine, cosine and tangent functions, translation of sine and cosine functions, and reciprocal trigonometric functions. Then, as defined by the scope of the course, I am prepared to review with the student definitions and use of trigonometric identities, solving trigonometric equations, right triangles and trigonometric ratios, and the Laws of Sine and Cosine. Completion of the above constitutes the basic tenets of precalculus.

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