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Algebra 1

Working with basic algebraic terms (constants, coefficients, variables, exponents), solving linear equations and systems of linear equations (both algebraically and graphically), solving quadratic equations (factoring, the quadratic formula, completing the square), FOIL, word problems involving all of the above, etc.

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Algebra 2

Translations of graphs (reflections, shifts, rotations, expand/shrink), solving inequalities (algebraically and graphically), solving and graphing absolute value equations, solving systems of equations with 3 equations, cubic polynomials and higher, working with radicals/roots and fractional exponents, logarithms, word problems involving all of the above, etc.

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Calculus

Limits, continuity, definition of a derivative, derivative rules/techniques, trigonometric derivatives, implicit differentiation, linear approximation, local and absolute max/min of a function, increasing/decreasing intervals for a function, critical points, inflection points, concavity, Intermediate Value Theorem, Rolle's Theorem, Mean Value Theorem, related rates, optimization, applications to physics (velocity, acceleration, etc), antiderivatives, Fundamental Theorem of Calculus, Riemann integral,...
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Geometry

All Coordinate Geometry, points, lines and line segments, parallel/perpendicular/intersecting lines, angles, triangles and basic trigonometry, similar and congruent triangles, geometry proofs, regular polygons, area/perimeter problems, circle geometry (arc measure, central angles, etc.), inscribed and circumscribed figures, 3-dimensional shapes, volume/surface area problems, etc.

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Prealgebra

All mathematics covered before Algebra I, fractions, percents, decimals, basic operations, PEMDAS, basic probability and statistics, reading and interpreting charts and graphs (pie graphs, bar graphs, histograms, etc), basic calculator use, the coordinate plane, all word problems, etc

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Precalculus

Functions of a variable, analyzing polynomial equations and their behavior, trigonometric functions and their behavior, conic sections (parabolas, ellipses, hyperbolas, circles), asymptotes, advanced coordinate geometry, matrices and their operations

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Trigonometry

Basic geometry of triangles (acute/obtuse/right, similar/congruent, angle/side measure, area/perimeter, etc), trigonometric functions (sine, cosine, tangent), SOHCAHTOA, inverse and reciprocal trig functions, trig identities, using double-angle/half-angle/sum formulas, the unit circle, degrees vs. radian measure of angles, inscribed/circumscribed triangles, using triangles to find area/perimeter/angles of other polygons, etc.

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SAT Math

All areas of mathematics covered on the math section of the SAT, test-taking strategy and timing

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Probability

Basic probability formula, probabilities with/without replacement, probabilities of multiple events, basic probability distributions (Bernoulli, binomial, normal, etc), permutations/combinations, basic statistics

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Discrete Math

In my junior year of college, I simultaneously took both courses of a Discrete Mathematics sequence, earning a B+ in the first course, and an A in the second. These courses covered the following topics: basic set theory, set-theoretic operations (unions, intersections, difference, symmetric difference, complement, etc), combinatorics (counting problems), proofs by induction, the pigeon-hole principle, basic number theory (prime numbers, the Euclidean algorithm), Latin squares, group theory, rings,...
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College Counseling

The majority of my college counseling experience comes from my former position as an Admissions Counselor in the Admissions Office at the Massachusetts Institute of Technology (MIT). From January 2011 until August 2012, I was responsible for traveling to high schools to inform prospective students about MIT, conducting information sessions on and off campus for visitors, representing MIT at local college fairs, reading undergraduate applications, participating in selection committees, and counseling/mentoring...
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Linear Algebra

I am a current PhD student in Mathematics In my sophomore year at Boston University, I took a college course in Linear Algebra, and received an A in the class. The course covered material such as: solving systems of linear equations, matrices and matrix operations, Gauss-Jordan elimination, row-echelon form, determinants of square matrices, dimension/rank/kernel, vector and scalar operations, bases for a vector space, eigenvalues and eigenvectors, characteristic polynomials, Cayley-Hamilton Theorem,...
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Logic

I have been exposed to logical concepts my entire life, beginning with logic puzzles that I would work on for fun outside of school. However, my first formal exposure to logic was in my 8th grade Algebra I class, where I first learned about propositional logic, including truth tables, Boolean algebra (negation/and/or/if-then/if-and-only-if), and logical laws (contradiction, contrapositive, modus ponens, modus tollens, syllogism, De Morgan's laws, etc.).

In my senior year of college,...
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Praxis

Last year, a friend of mine who was struggling in Math needed to take the Praxis II exam in order to earn her certification to teach music in Philadelphia. After helping her study for the Math section of the Praxis exam, she passed the test and earned her certification.

In general, I have had plenty of experience teaching and tutoring standardized test material and strategies to students, from my first college summer job as an SAT Math teacher for Legal Outreach Inc, to my position...
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