Algebra 1
Algebra 1 covers topics such as linear equations, systems of linear equations, polynomials, factoring, quadratic equations, exponential functions, radical expressions, and rational functions.
A student of Algebra 1 must adjust his/her thinking from static arithmetic computations to manipulating expressions and equations to solve for variables. A student must also begin to develop a physical interpretation of his/her work by graphing equations and solutions. Both of these endeavors can...
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Algebra 2
Algebra 2 covers topics such as linear equations, systems of linear equations and inequalities, matrices, quadratic functions and inequalities, polynomial functions, radical equations and inequalities, rational expressions and equations, exponential and logarithmic relations, and conic sections.
A student of Algebra 2 must expand upon his/her understanding of Algebra 1 to develop a robust understanding of more advanced algebraic concepts. This can be challenging, because advanced concepts...
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Calculus
Calculus is an expansive part of mathematics that requires two years to learn in high school, college, and university.
Calculus AB covers topics such as functions, graphs, and limits; differentiation and its applications; and integration and its applications.
Calculus BC covers topics such as functions, graphs, and limits; differentiation and its applications; integration and its applications; and polynomial approximations and series.
A university Calculus 1 course...
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Vocabulary
Vocabulary is an essential part of a well-rounded education. Broad vocabulary allows students to increase their proficiencies with English. This includes speaking, listening, reading comprehension (context usage), and writing (sentence variation, style).
Additionally, students who have a well-defined vocabulary have decisive advantages over their peers at school (independent/select secondary schools and undergraduate/graduate programs).
Typically, students choose to increase...
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Grammar
Grammar is a crucial skill for students to develop but difficult to master.
Grammar is important for refining communication skills, adhering to national standards, scoring well on standardized examinations, preparing for college and/or university admissions, and showing promise to prospective employers.
I have supported students with the English and Writing sections of the ACT and the Writing and Essay portions of the SAT for over a decade. I have also supported graduate...
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Geometry
Geometry covers topics such as reasoning and proofs (deductive, inductive, diagrams), parallel and perpendicular lines, congruent triangles (SSS, SSA, SAS, ASA, AAS, HL, isosceles, equilateral, transformations), relationships within triangles (Midsegment Theorem, perpendicular bisectors, angle bisectors, medians, altitudes, inequalities), similarities (ratio, proportions, geometric mean, similar figures), right triangles and trigonometry (Pythagorean Theorem, sine and cosine ratios), quadrilaterals,...
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Physics
Physics is an attempt to describe and explain the physical world, at an extremely fundamental level, through the use of mathematics.
AP Physics B primarily uses algebra and trigonometry to cover topics such as Newtonian mechanics, fluid mechanics and thermal physics, electricity and magnetism, waves and optics, and atomic and nuclear physics.
AP Physics C is divided into two sections: Mechanics and Electricity & Magnetism. Both sections use a combination of algebra, trigonometry,...
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Prealgebra
Prealgebra covers topics such as number properties and operations, solving equations using addition, subtraction, multiplication, and division, multiple step equations and inequalities, polynomials, factors, fractions, exponents, scientific notation, rational numbers and equations, ratios, proportions, percents, non-linear factors, basic geometry, and basic probability.
A student of Prealgebra must adjust his/her thinking from static arithmetic computations to manipulating expressions...
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Precalculus
Precalculus, otherwise known as Algebra 3, covers topics such as sets, real numbers, complex numbers, solving inequalities and equations, properties of functions, composite functions, polynomial functions, rational functions, trigonometric functions, inverses, identities, conic sections, exponential functions, logarithmic functions, sequences and series, binomial theorem, vectors, parametric equations, polar coordinates, matrices and determinants, mathematical induction, and limits.
A...
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Reading
Reading comprehension is a crucial skill for students to develop but difficult to master. Students must be able to understand the context of the words in individual sentences and also understand multiple concepts when reading longer passages.
There are two types of reading comprehension: concrete and abstract. Concrete comprehension skills are the easier of the two. They include the ability to answer questions when the information is explicitly stated in the passage. Concrete skills...
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Trigonometry
Trigonometry covers topics such as angles, degrees, special triangles, trigonometric functions, identities, right triangle trigonometry, radians (measure, conversion, arc length, area, velocities), graphing, inverse trigonometric functions, identities and formulas (sum and difference, double-angle, half-angle), solving trigonometric equations, parametric equations, complex numbers, and polar coordinates.
A student of Trigonometry must adjust his/her thinking from algebraic manipulations...
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Writing
Writing is an essential part of a well-rounded education. Proficiency with writing allows students to increase their command of the English language. This includes building confidence through a sense of one's own voice, creating and strengthening identities, fostering emotional growth and coping skills, developing critical thinking skills, and understanding and communicating complicated ideas. Most importantly, writing leads to guaranteed improvement in academic achievement.
Additionally,...
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Statistics
Statistics is the study of the collection, organization, analysis, interpretation and presentation of data.
Students are usually first introduced to statistics at the college or university level. Many formulations of statistics rely on algebra. However, statistics can use calculus to create more useful and meaningful results.
Statistics may also be combined with probability, and covered in a dedicated course, to provide a student with a more robust understanding of the subject...
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English
English is an essential language to know for many reasons: English is the language of science (mathematics is the quantitative language, and English is the qualitative language), English speakers earn more money than non-English speakers, English is the most commonly used language among foreign language speakers, English is based on an alphabet making it much easier to learn, and English is the language of the film industry making it easier for English speakers to assimilate new information and...
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SAT Math
The SAT Mathematics section consists of three sections: two 25 minute sections and one 20 minute section. Students are expected to answer 44 multiple-choice questions and 10 "grid-ins". This section tests concepts from Arithmetic, Algebra 1, Geometry, and Algebra 2.
Students must not only be aware of the structure and content of the Mathematics section of the SAT, but they must also learn the approaches and tactics necessary to achieve exceptional performance. This can be difficult...
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GRE
The revised GRE General Test measures verbal and quantitative reasoning, critical thinking, and analytical writing skills. These skills have evolved over a long period of time and bare no relation to specific fields of study. Therefore, the main purpose of this examination is to verify that a student is prepared for graduate studies.
The three sections of the GRE are Verbal Reasoning, Quantitative Reasoning, and Analytical Writing.
The Verbal Reasoning section measures the...
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Proofreading
Proofreading is a crucial step to the writing process. Before an academic research paper, essay, email, memo, or any other written document can be submitted or published, one must ensure that it is adequately proofread.
There are essentially two phases to the proofreading process. The first phase is called "overview editing". During this phase, the work is read for consistencies in message, structure, and organization. This is necessary to ensure the writing is adequately serving its...
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SAT Reading
Students are given 70 minutes to complete 67 multiple-choice questions on the Critical Reading section of the SAT. This section tests the ability to read passages, to answer comprehension questions, and to complete sentences.
Students must not only be aware of the structure and content of the Critical Reading section of the SAT, but they must also learn the approaches and tactics necessary to achieve exceptional performance. This can be difficult when a student has limited experience...
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SAT Writing
The SAT Writing section consists of three sections: one 25 minute section, one 10 minute section, and one 25 minute essay. Students are expected to answer 49 multiple-choice questions and 1 essay prompt. This section tests the ability to identify sentence errors and to improve sentences and paragraphs.
Students must not only be aware of the structure and content of the Writing section of the SAT, but they must also learn the approaches and tactics necessary to achieve exceptional performance...
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GMAT
The GMAT (Graduate Management Admission Test) is a computer adaptive test (CAT) which evaluates an individual's analytical, writing, quantitative, verbal, and reading skills in preparation for admission to graduate management programs, such as an MBA, Master of Accountancy, and Master of Finance. More than 5,900 programs offered by more than 2,100 universities and institutions use the GMAT exam as part of their selection criteria.
An integrated reasoning section was recently introduced...
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Probability
Probability is the measure of how likely something will happen or the likelihood that a statement is true.
Students are usually first introduced to probability at the end of an algebra course. However, probability can use calculus to expand upon its algebraic formulations.
Probability may also be combined with statistics, and covered in a dedicated course, to provide a student with a more robust understanding of the subject matter.
Scientists must apply probabilities...
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PSAT
The PSAT/NMSQT is a standardized test designed to provide firsthand practice for the SAT. Additionally, it gives students the opportunity to enter NMSC programs (university and career planning tools are included).
The test focuses on three major areas of a student's education: critical reading skills, math problem-solving skills, and writing skills.
The test is approximately two and one half hours in duration, composed of two twenty-five minute critical reading sections,...
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SSAT
The SSAT is designed for students who are seeking entrance to independent schools worldwide. The purpose of the SSAT is to measure the basic verbal, quantitative, and reading skills students develop over time—skills that are needed for successful performance in independent schools. The SSAT provides independent school admission professionals with meaningful information about the possible academic success of potential students at their institutions, regardless of students’ background or experience...
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ACT Reading
Students have 35 minutes to complete 40 multiple choice questions on the Reading section of the ACT.
The ACT covers four types of reading passages:
Prose Fiction (25%)
Social Studies (25%)
Humanities (25%)
Natural Sciences (25%)
The prose fiction and humanities passages require students to have a well-developed understanding of figurative writing. Students must infer what is being conveyed by interpreting figurative language.
The social...
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ACT English
Students have 45 minutes to complete 75 multiple choice questions on the English section of the ACT. This section tests usage and mechanics (punctuation, grammar, usage, sentence structure) and rhetorical skills (strategy, organization, style).
Students must not only be aware of the structure and content of the English section of the ACT, but they must also learn the approaches and tactics necessary to achieve exceptional performance. This can be difficult when a student has limited...
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ACT Math
Students have 60 minutes to complete 60 multiple choice questions on the Mathematics section of the ACT.
The ACT covers several areas of mathematics including:
Pre-Algebra (23%)/Elementary Algebra (17%)
Intermediate Algebra (15%)
Coordinate Geometry (15%)/Plane Geometry (23%)
Trigonometry (7%)
Students must not only be aware of the structure and content of the Mathematics section of the ACT, but they must also learn the approaches and tactics necessary...
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ACT Science
Students have 35 minutes to complete 40 multiple choice questions on the Science section of the ACT.
The ACT covers three areas of science:
Data Representation (38%)
Research Summaries (45%)
Conflicting Viewpoints (17%)
Students must not only be aware of the structure and content of the Science section of the ACT, but they must also learn the approaches and tactics necessary to achieve exceptional performance. This can be difficult when a student has...
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Study Skills
Study skills are crucial to finding success with academics. Many times, it is not the intelligence or disposition of a student that causes difficulties. Instead, it is the approach of the student that needs "fine tuning". This is where effective study skills can make the difference.
Throughout my educational pursuits, both as a student and instructor, I have developed organized, logical, and structured approaches to academics. Not only am I able to provide outstanding support for most...
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Differential Equations
Differential Equations covers topics such as solving first-order differential equations (separable, exact, linear, non-linear, Bernoulli, etc.), solving higher order differential equations (linear, homogeneous, non-homogenous, Cauchy-Euler, etc.), and various methods to transform differential equations into forms that can be more easily solved (substitution, reduction of order, superposition, annihilation, variation of parameters, etc.).
A student of Differential Equations must adjust...
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MCAT
As an undergraduate, at the University of Michigan, I was initially enrolled as a pre-med student. I fulfilled nearly all requirements for this designation (microbiology, organic chemistry, biochemistry, etc.).
Towards the end of my tenure, I chose to take the GRE instead of the MCAT, because I wanted to pursue physics and mathematics instead of medicine.
However, during my graduate tenure, I assisted countless students with preparation for the MCAT (all sections). I created...
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ISEE
The ISEE is an admissions exam to independent and select schools. The Upper Level is for students in grades 8 through 11 who are candidates for grades 9 through 12.
The ISEE consists of three parts: (a) carefully constructed and standardized verbal and quantitative reasoning tests that measure a student's capability for learning; (b) reading comprehension and mathematics achievement tests that provide specific information about a student's strengths and weakness in those areas; and...
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