GMAT Math Curriculum
Our students come to us with varied skills and unique goals. Because each of those students brings a unique set of strengths and weaknesses, our private GMAT tutoring is highly personalized; we alter the specifics of our approach to cover the issues you need to learn. The following 19 GMAT math lessons can represent a menu of choices for those needing to brush up on definite topics or a full lesson plan for those needing a more comprehensive review. Our private tutoring emphasizes the mastery of GMAT-specific content and the development of intelligent strategies and effective analytical skills.
Lesson 1: Number Properties
A complete understanding of number properties is critical for success on the GMAT since properties of numbers are frequently tested. For most students, it has been some time since they've considered things such as the least common multiple, the greatest common factor, remainder theory, prime numbers, divisibility, factors and multiples, powers of ten, absolute values, factorials, perfect squares, terminating decimals, number patterns, consecutive integers, or any of the numerous other number properties that are common on the GMAT. Students will leave this lesson with a comprehensive set of note cards covering the most important number properties that the GMAT tests. In this lesson, a strong emphasis is placed on data sufficiency problems.
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Lesson 2: Algebra Foundation I
Students are first taught the conventional algebra that will be used on almost all GMAT questions, such as solving basic linear equations for one, two, and three variables; solving equations with fractions; solving an equation for one variable in terms of other variables; maintaining the order of operations; solving basic equations involving exponents; and solving basic quadratic equations. Second, students are taught the basic algebra that is unique to the GMAT. This includes solving for the addition or subtraction of multiple variables, handling simultaneous equation traps, and learning how to group equations with multiple variables. In this lesson, a strong emphasis is placed on data sufficiency problems.
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Lesson 3: GMAT-Specific Word Problems
Word problems are also at the heart of the GMAT. In this lesson, students learn intelligent strategies for recognizing, developing, and solving numerous common GMAT word problems. Some of these word problems include age and weight problems; consecutive integer problems; profit, cost, and loss problems; fraction word problems; and problems involving money, digits, and length. The skills gained in this lesson will continuously be reinforced throughout the lessons that follow.
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Lesson 4: Rate-Time-Distance Problems
Rate-time-distance word problems are important enough to warrant their own lesson. Students begin this lesson by learning how to convert units (measurement problems) since many rate-time-distance problems require some change of units. Then students learn to solve average rate questions, converging and diverting rates questions, catch up rates questions, round trip rate questions, relative rate questions, relative motion rate questions, hypothetical rate questions, and a mix of other prominent question types. Students learn a mechanical, yet flexible, approach to solving these question types while concurrently building the concepts that are critical in solving rate data sufficiency questions. In the later part of this lesson, students apply their new knowledge to data sufficiency questions involving rates.
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Lesson 5: Work Problems
The material taught in this lesson piggy-backs on the material taught in the lesson on rate-time-distance problems. Work problem are a specific, but unique, type of rate problem. In this lesson, students learn to solve single worker problems and the many variants of multiple worker problems such as problems in which workers work together and against one another, problems in which one worker leaves prior to job completion, problems in which the rate or time of a worker or workers is unknown, relative work problems, and many other classic GMAT work question types. Students are shown how to apply their new skills to work data sufficiency questions.
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Lesson 6: Exponents and Radicals
This lesson covers all of the necessary rules of exponents and radicals. Students leave this lesson with a formal set of note cards and problem case studies. Most importantly, this lesson teaches students to recognize and solve the unique problems that the GMAT typically presents. Some of these include simplifying exponents and exponent expressions, solving algebra and exponents, solving addition and subtraction with exponents, simplifying radicals,and algebra with radicals.
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Lesson 7: Percents
This lesson teaches students to work confidently with percents and percent word problems. Students are taught how to convert percents and decimals, solve specific percents word problems such as "percent of," "what percent," "percent less than,""percent greater than," and "percent change" problems. In addition, students are taught to comfortably work with percents in variable form.
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Lesson 8: Ratios
Ratios are also common on the GMAT, and students must have a strong knowledge of ratios to solve many geometry problems, as well as many word problems and probability problems. Students learn all of the important details of ratios, including what information a ratio does and does not convey, the ratio multiplier, multipart ratios, adding and subtracting to achieve a desired ratio, and applying ratio skills to a range of other problem types such as rates, work, and geometry. We also apply these skills to specific data sufficiency problems, showing the various traps that can occur in ratio problems. Finally, students learn to solve proportion problems as well as direct and inverse variation problems.
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Lesson 9: Algebra Foundation II
In this lesson, students are taught more complex skills and strategies for working with algebra on the GMAT, including quadratic equations, applied algebra, and advanced equation setup and solving. Students will learn which classic quadratic equations to memorize and how to apply them in specific situations.
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Lesson 10: Absolute Values and Inequalities
Inequalities are common on the GMAT, especially in data sufficiency problems. Students often stumble over these problems or fall into classic answer traps. Here, we teach students all of the inequality rules necessary for the GMAT, and, most importantly, we teach student how to handle the unique ways in which the GMAT tests inequality knowledge. Absolute value problems present similar difficulties for students. We ensure that students know the rules of absolute values and provide the students with powerful strategies for handling the unique ways that the GMAT tests these problem types. Once both these concepts are learned, we provide various data sufficiency problems that include both inequalities and absolutes. This lesson also provides a sound review of data sufficiency in general as many other topics are included within inequalities and data sufficiency.
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Lesson 11: Overlapping Sets
In this lesson, we demystify set problems and provide students with a mechanical, yet flexible and adaptable, approach to solving overlapping set problems. We cover a wide-range of these problems, including sets with fractions, decimals, and percents and algebra within sets. Students are also taught to solve three-circle Venn diagrams.
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Lesson 12: Statistics
Statistics problems are becoming more frequent on the GMAT. In this lesson, students learn to handle averages (arithmetic mean), weighted averages, median, mean, mode, range, and standard deviation. Students also learn how to solve mixture problems, which are similar to weighted average problems.
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Lesson 13: Combinatorics
Combinations and permutations are used to count the number of ways that certain tasks could be accomplished. As these problem types have become more commonly tested on the GMAT, it has become more necessary to fully understand them. Students learn how to solve all of the necessary combinations and permutations that are tested on the GMAT, includlng basic combinations, combinations with restrictions, basic permutations, permutations with restrictions, mutually exclusive events, and the fundamental counting principle.
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Lesson 14: Probability
In this lesson, students will master basic and advanced probability concepts, including independent events, dependent events, the complement rule, sample spaces, blending probability with overlapping sets, blending probability with combinations and permutations, and many others.
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Lesson 15: Functions and Sequences
In this lesson, students learn the inner-working of functions and sequences. We cover geometric sequences and arithmetic sequences, and we examine numerous problems to which these skills can be applied. Functions are shown from an algebraic and well as a graphical point of view.
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Lesson 16: Coordinate Geometry
The coordinate plane, points, lines, graphing lines, slope of a line, the point-slope formula, the slope-intercept equation, properties of vertical and horizontal lines, properties of parallel and perpendicular lines, geometrical shapes on the coordinate plane, the distance formula, the midpoint formula, and graphing inequalities are taught in this lesson. In addition, students will reinforce and reapply their knowledge of functions.
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Lesson 17: Lines, Angles, and Triangles
In this lesson, students master skills on one of the GMAT's favorite shapes – the triangle. Students begin by learning the properties of lines and angles, which include parallel lines, perpendicular lines, lines cut by a transversal, and the sum of angles. Then, these skills are applied to the study of triangles: isosceles triangles, equilateral triangles, and the special right triangles, including the 3-4-5 right triangle, 5-12-13 right triangle, 8-15-17 right triangle. Students will also learn all the important triangle computations: the Pythagorean theorem, triangle inequality theorem, exterior angle theorem, similar triangles, area of a triangle, perimeter of a triangle, and simplifying angles within a triangle. These concepts are also applied to various data sufficiency problems. After this lesson students will have a list of formulas and concepts to be memorized and mastered.
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Lesson 18: Polygons, Quadrilaterals, and Solid Geometry
Properties of the square, rectangle, parallelogram, rhombus, and trapezoid are covered in detail. These properties include area, perimeter, sum of interior angles, and sum of exterior angles. Next students are taught about the three main three dimensional shapes: the cylinder, cube, and rectangular solid. We cover the formulas for surface area, volume, and diagonal for the cube and rectangular solid and the formulas for surface area and for volume of a cube. Finally students are taught how to attack these types of shapes when used in a data sufficiency format.
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Lesson 19: Circles and Multiple Figures
In this lesson students are first taught the basics of circles, including area, circumference, arcs, sectors, inscribed and central angles. Since circles are one of the most common shapes in multiple figure problems, students are then taught how to relate different shapes when they are inscribed in circles, such as triangles, squares, hexagons, etc. Finally students are shown other types of multiple figure problems including squares inscribed in triangles and triangles inscribed in squares. This lesson serves as an excellent review of the geometry learned.
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GMAT Verbal Curriculum
Because each of our students brings a unique set of strengths and weaknesses, our private GMAT tutoring is highly personalized; we alter the specifics of our approach to cover the issues you need to learn. The following GMAT lessons can represent a menu of choices for those needing to brush up on definite topics or a full lesson plan for those needing a more comprehensive review. Our private tutoring emphasizes the mastery of GMAT-specific content and the development of intelligent strategies, effective analytical skills, and the ability to recognize what issues are being treated in any specific question. In addition to this sequence of topics, students are expected to practice extensively, thus providing constant feedback to the tutor. The tutor and student will review any errors in detail.
Lesson 1: Sentence Structure
The primary skill necessary for success in the Sentence Correction portion of the verbal test is the ability to recognize an English sentence. This lesson will provide a precise description of simple, compound, and complex sentences. In addition, students will learn to recognize the different types of clauses out of which sentences are built: independent clauses, subordinate clauses, and relative clauses. Students will also learn to distinguish between adverb clauses, adjective clauses, and noun clauses. Students will learn how to avoid fragments and run-ons, two major errors that are a pervasive problem throughout the Sentence Correction section.
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Lesson 2: Noun Modifiers
A significant subset of Sentence Correction problems involves the recognition and accurate manipulation of the different linguistic structures that are capable of modifying nouns. Students will acquire a precise understanding of relative clauses, participial phrases, appositives, prepositional phrases, and infinitive phrases. Students will also learn principles that will help them choose which structures to use in differing contexts. Importantly, they will also learn the common mistakes in modifier usage that the test attempts to exploit.
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Lesson 3: Syntax – Subject-Verb Agreement -- Punctuation
Students will learn the importance of recognizing the proper contexts for using commas and semi-colons, the two punctuation marks the GMAT continually tests. They will learn how syntax, the natural order of the English sentence, conveys meaning and dictates punctuation usage. Students will also gain practice in recognizing situations where subject and verb agreement problems are likely to appear.
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Lesson 4: Parallelism
Parallelism is a major sentence correction issue on the GMAT. Students must be able to recognize contexts that require parallel grammatical structures: idioms of comparison and idioms of contrast, elements in a series, and elements joined by coordinating conjunctions. Students will get in-depth practice in identifying clues that trigger parallelism.
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Lesson 5: Verbs
All verb related issues that the GMAT tests will be highlighted in this lesson. Students will learn when to use the past perfect and present perfect tenses, the passive and active voices, and the subjunctive mood. Students will also learn how to recognize and properly form the command subjunctive. The importance of finding the finite verb and correctly identifying subject verb agreement errors, both covered in earlier lessons, will be reinforced here.
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Lesson 6: Diction and Idioms
This lesson covers idioms characteristically tested on the GMAT, including idioms of comparison and contrast, verb plus preposition formations, and noun plus preposition formations. In addition, students will learn proper adverb and adjective usage. The discussion will also cover stylistic conventions such as conciseness, converting abstract nouns into active verbs, and avoiding redundancy.
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Lesson 7: Introduction to Concepts in Logic
This introduction to the Critical Reasoning portion of the GMAT will cover the conventions of accurate argumentation. Students will learn to distinguish between deductive and inductive modes of reasoning and learn to recognize the language appropriate to each. The lesson will also cover the proper relationship between premises, assumptions, and conclusions.
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Lesson 8: Weakening – Strengthening – Resolve the Paradox
This lesson will begin the discussion of specific Critical Reasoning question types. It will cover those questions that require the evaluation of new information. The discussion will also cover how new information affects arguments.
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Lesson 9: Assumption and Inference
In this lesson, students learn how to differentiate between deductive and inductive assumption questions and what strategies are appropriate to each type. Similarly, the lesson will cover the difference between drawing proper inferences in both deductive and inductive inference questions. Discussion will cover how to recognize valid, warranted conclusions and how to avoid over-inferring.
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Lesson 10: Useful to Know – Function – Strategy Questions
A third tier of Critical Reasoning questions will be covered in this lesson, questions that consistently, though less frequently, appear on the GMAT. These questions require the student to analyze a given argument, recognize gaps in arguments, and identify the parts of arguments.
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Lesson 11: Miscellaneous Questions
In this lesson, we cover the miscellaneous set of questions that occasionally appear on the GMAT, including flaw questions, complete the sentence questions, restate the conclusion questions, and "except" questions.
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Lesson 12: Introduction to Reading Comprehension
This lesson will show the student the similarities between the Critical Reasoning and Reading Comprehension portions of the test. Discussion will revolve around applying principles of logic to longer passages and accurately identifying and understanding extended arguments.
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Lesson 13: Dividing and Conquering the Text
Students will learn to identify the logical backbone of each passage, taking note of major divisions and using transition words to break the arguments down into manageable portions. Students will be taught to distinguish between what is being asserted in a given argument and what serves as support for those assertions. We will discuss "mapping" techniques that help the student find important elements of the argument when responding to questions.
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Lesson 14: Reading Comprehension Questions
As in Critical Reasoning, it is important to develop a consistent approach to each of the different question types (many of them the same as in Critical Reasoning). Students will learn to identify questions by type, for instance, main point, author's attitude, according to the passage, and the passage suggests questions. Students will then learn how to find good evidence for their responses in the passage.
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