Lesson 1: Algebra Foundation I
Students are first taught the conventional algebra that will be used on almost all GRE 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 GRE. 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 quantitative comparison problems.
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Lesson 2: GRE-Specific Word Problems
Word problems are also at the heart of the GRE. In this lesson, students learn intelligent strategies for recognizing, developing, and solving numerous common GRE 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 3: 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 GRE 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 4: Algebra Foundation II
In this lesson, students are taught more complex skills and strategies for working with algebra on the GRE, 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 5: Absolute Values and Inequalities
Inequalities are common on the GRE, especially in quantitative comparison questions. Students often stumble over these problems or fall into classic answer traps. Here, we teach students all of the inequality rules necessary for the GRE, and, most importantly, we teach student how to handle the unique ways in which the GRE 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 GRE tests these problem types. Once both these concepts are learned, we provide various comparison questions problems that include both inequalities and absolutes. This lesson also provides a sound review of quantitative comparison questions in general as many other topics are included within inequalities and quantitative comparison questions.
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Lesson 6: Lines, Angles, and Triangles
In this lesson, students master skills on one of the GRE’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 quantitative comparison questions. After this lesson students will have a list of formulas and concepts to be memorized and mastered.
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Lesson 7: Polygons, Quadrilaterals, and Solid Geometry
Properties of the square, rectangle, parallelogram, rhombus, trapezoid and all other polygons 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 cylinder. Finally students are taught how to attack these types of shapes when used in a quantitative comparison format.
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Lesson 8: 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, triangles inscribed in squares, as well as other shaded region questions. This lesson serves as an excellent review of the geometry learned in previous lessons.
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Lesson 9: 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 begin to build their knowledge of functions.
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Lesson 10: Ratios
Ratios are also common on the GRE, 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 quantitative comparison questions, 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 11: 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 12: Statistics
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: Data Interpretation
In this lesson, students will get comfortable with the various ways in which graphing questions are presented, i.e. Bar graphs, line graphs, scatter graphs, and pie charts. Skills learned in previous sections, such as statistics, percents, ratios, and fraction questions, will be used to solve these graphing questions. Finally, students are shown various types of logic questions and how to apply a strategy that eliminates incorrect answer choices.
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Lesson 14: Number Properties
A complete understanding of number properties is critical for success on the GRE 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 GRE. Students will leave this lesson with a comprehensive set of note cards covering the most important number properties that the GRE tests. In this lesson, a strong emphasis is placed on quantitative comparison questions.
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Lesson 15: Rate Problems and Measurement 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.
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Lesson 16: 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 GRE work question types.
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Lesson 17: 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 18: 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 GRE, 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 GRE, including basic combinations, combinations with restrictions, basic permutations, permutations with restrictions, mutually exclusive events, and the fundamental counting principle.
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Lesson 19: 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 20: 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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