GRE,
GRE
GRE Math includes:
age and weight problems; consecutive integer problems; profit, cost, and loss problems; fraction word problems; and problems involving money, digits, and length.
simplifying exponents and exponent expressions, solving algebra and exponents, solving addition and subtraction with exponents, simplifying radicals, and algebra with radicals.
quadratic equations, applied algebra, and advanced equation setup and solving inequalities and absolutes (other topics are included within inequalities and quantitative comparison questions).
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: 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.
It also includes:
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.
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.
circles, triangles, squares, hexagons, squares inscribed in triangles, triangles inscribed in squares, as well as other shaded region questions.
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.
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.
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
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
Overlapping Sets-- including sets with fractions, decimals, and percents and algebra within sets. Students are also taught to solve three-circle Venn diagrams.
geometric sequences and arithmetic sequences
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.