Hakim’s current tutoring subjects are listed at the left. You
can read more about
Hakim’s qualifications in specific subjects below.
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.
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.
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, left/right/center/trapezoidal area approximations, integration rules and techniques (u-substitution, partial fractions, integration by parts, etc), average value of a function, improper integrals, arc length, surfaces of revolution, cross-sectional areas, L'hopital's Rule, Taylor and Maclaurin series, tests for convergence/divergence, graphing calculator usage, and prep for the AB and BC Calc exam
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 high school students for on-campus college-prep summer programs. While at MIT, I've also traveled to college admissions conferences at other universities, including Yale and Princeton, where I learned and interacted with college counselors at both the high school and university level.
However, my college counseling experience extends beyond my time at MIT. In the summer of 2006, I taught SAT Math to a class of 24 high school students for a program called Legal Outreach Inc, which prepares inner-city high school students for college. While I was an undergraduate, I worked in the admissions office at Boston University as a student representative and coordinator of minority recruitment efforts. In the summer of 2009, I tutored and mentored a group of 5 students through the Upward Bound program at BU. From 2009-2010, I worked as a Corps member at the MATCH Charter High School, whose sole mission is to ensure that students succeed in college and beyond. And after working at MATCH and joining MIT, I continued to support MATCH by conducting college essay writing workshops. Finally, I complemented my MIT position by working part-time as an SAT Math teacher for Upward Bound at Wheelock College, and by tutoring MATCH alumni in their college courses.
Based on all of my experience, I am very proficient in all aspects of the college counseling process, including standardized test preparation, college essay writing, interviewing tips, school selection, financial aid and scholarships, and transitioning into college life.
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, fields, and other related topics.
As a current PhD student in Mathematics, I am very proficient in these topics and more, as I use them very frequently in my advanced math courses.
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.
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, and other related topics.
Particularly, I have been familiar with matrices and matrix operations since my junior year of high school. In my experience, many students are uncomfortable using matrices, and are therefore uncomfortable with Linear Algebra. My long experience with linear algebra concepts will ensure that you have the proper background to succeed in the subject.
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, I took a Mathematical Logic course with a well-known logician, and earned a B+. In this class, I learned about advanced topics in Logic, such as logical axioms, languages and structures, basic model theory, first-order logic used in philosophical arguments and mathematical proofs ("for all", "there exists", etc.), tautologies and logical implication, the definition of truth, the conjunctive and disjunctive normal formula, consistency, deduction, proofs, meta theorems, the Soundness and Completeness Theorem, and the Incompleteness Theorem. As a current PhD student in Math, my intended research area is in Logic, and so I am currently taking a graduate course in Logic.
As a long-time mathematics student, I am extremely familiar with using logical concepts in writing proofs and explaining them to others. However, I am also very familiar with applying logic to other subjects as well. For example, last year one of my coworkers at MIT was studying for the LSAT, and I tutored her in the logical reasoning section of the test. So I can also help with logic as it applies to LSAT preparation.
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 last year as an SAT Math teacher for Upward Bound. As a PhD student in Mathematics, I am especially well-versed in helping students prepare for the mathematics portion of the Praxis exams.
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
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
Basic probability formula, probabilities with/without replacement, probabilities of multiple events, basic probability distributions (Bernoulli, binomial, normal, etc), permutations/combinations, basic statistics
All areas of mathematics covered on the math section of the SAT, test-taking strategy and timing
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.